U.S. patent application number 13/295795 was filed with the patent office on 2012-05-24 for conductive nitride semiconductor substrate and method for producing the same.
This patent application is currently assigned to SUMITOMO ELECTRIC INDUSTRIES, LTD.. Invention is credited to Makoto Kiyama, Seiji Nakahata, Fumitaka Sato.
Application Number | 20120126371 13/295795 |
Document ID | / |
Family ID | 45532228 |
Filed Date | 2012-05-24 |
United States Patent
Application |
20120126371 |
Kind Code |
A1 |
Sato; Fumitaka ; et
al. |
May 24, 2012 |
CONDUCTIVE NITRIDE SEMICONDUCTOR SUBSTRATE AND METHOD FOR PRODUCING
THE SAME
Abstract
A method for producing a conductive nitride semiconductor
substrate circuit includes the steps of forming, on an underlying
substrate, a mask including dot or stripe masking portions having a
width or diameter of 10 to 100 .mu.m and arranged at a spacing of
250 to 10,000 .mu.m; growing a nitride semiconductor crystal on the
underlying substrate by hydride vapor phase epitaxy (HVPE) at a
growth temperature of 1,040.degree. C. to 1,150.degree. C. by
supplying a group III source gas, a group V source gas, and a
silicon-containing gas in a V/III ratio of 1 to 10; and removing
the underlying substrate, thus forming a free-standing conductive
nitride semiconductor crystal substrate having a resistivity r of
0.0015 .OMEGA.cm.ltoreq.r.ltoreq.0.01 .OMEGA.cm, a thickness of 100
.mu.m or more, and a radius of bow curvature U of 3.5
m.ltoreq.U.ltoreq.8 m.
Inventors: |
Sato; Fumitaka; (Itami-shi,
JP) ; Nakahata; Seiji; (Itami-shi, JP) ;
Kiyama; Makoto; (Itami-shi, JP) |
Assignee: |
SUMITOMO ELECTRIC INDUSTRIES,
LTD.
|
Family ID: |
45532228 |
Appl. No.: |
13/295795 |
Filed: |
November 14, 2011 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
12950686 |
Nov 19, 2010 |
8110484 |
|
|
13295795 |
|
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|
Current U.S.
Class: |
257/615 ;
257/E29.089; 257/E29.107 |
Current CPC
Class: |
H01L 21/02576 20130101;
H01L 21/02664 20130101; H01L 21/02639 20130101; C30B 25/04
20130101; H01L 21/02573 20130101; H01L 21/02395 20130101; H01L
21/02433 20130101; C30B 29/403 20130101; H01L 21/0254 20130101;
H01L 21/0262 20130101 |
Class at
Publication: |
257/615 ;
257/E29.107; 257/E29.089 |
International
Class: |
H01L 29/32 20060101
H01L029/32; H01L 29/20 20060101 H01L029/20 |
Claims
1-17. (canceled)
18. A conductive nitride semiconductor substrate comprising a
bottom portion, an inner portion, and a surface portion in order in
a crystal growth direction, the bottom portion and the inner
portion including crystal defect cluster regions H,
low-dislocation-density single-crystal regions Z, and a c-plane
growth region Y periodically arranged in the order of the crystal
defect cluster regions H, the low-dislocation-density
single-crystal regions Z, the c-plane growth region Y, and the
low-dislocation-density single-crystal regions Z in a direction
perpendicular to the growth direction, thereby forming an HZYZHZYZ
. . . structure, the crystal defect cluster regions H in the bottom
portion and the inner portion having a width or diameter of 10 to
100 .mu.m in a cross section perpendicular to the growth direction,
ZYZ portions defined between the adjacent crystal defect cluster
regions H having a width of 250 to 10,000 .mu.m, the surface
portion including the c-plane growth region Y and not including the
crystal defect cluster regions H or the low-dislocation-density
single-crystal regions Z, the low-dislocation-density
single-crystal regions Z and the crystal defect cluster regions H
being doped with silicon and oxygen, the c-plane growth region Y
being doped with silicon, the conductive nitride semiconductor
substrate having a thickness of 100 .mu.m or more, a diameter of 18
mm or more, a cracking ratio K of 1%.ltoreq.K.ltoreq.22%, a radius
of bow curvature U of 3.5 m.ltoreq.U.ltoreq.8 m, and a resistivity
r of 0.0015 .OMEGA.cm.ltoreq.r.ltoreq.0.01 .OMEGA.cm.
19. The conductive nitride semiconductor substrate according to
claim 18, wherein the resistivity r is 0.0018
.OMEGA.cm.ltoreq.r.ltoreq.0.01 .OMEGA.cm.
20. A conductive nitride semiconductor substrate according to claim
18 comprising a bottom portion, an inner portion, and a surface
portion in order in a crystal growth direction, the bottom portion
and the inner portion including crystal defect cluster regions H,
low-dislocation-density single-crystal regions Z, and c-plane
growth regions Y periodically arranged in the order of the crystal
defect cluster regions H, the low-dislocation-density
single-crystal regions Z, the c-plane growth regions Y, and the
low-dislocation-density single-crystal regions Z in a direction
perpendicular to the growth direction, thereby forming an HZYZHZYZ
. . . structure, the crystal defect cluster regions H in the bottom
portion and the inner portion forming a pattern of parallel stripes
having a width of 10 to 100 .mu.m in a cross section perpendicular
to the growth direction, ZYZ portions defined between the adjacent
crystal defect cluster regions H having a width of 250 to 10,000
.mu.m, the surface portion including the c-plane growth regions Y
and not including the crystal defect cluster regions H or the
low-dislocation-density single-crystal regions Z, the
low-dislocation-density single-crystal regions Z and the crystal
defect cluster regions H being doped with silicon and oxygen, the
c-plane growth regions Y being doped with silicon, the conductive
nitride semiconductor substrate having a thickness of 100 .mu.m or
more, a diameter of 18 mm or more, a cracking ratio K of
1%.ltoreq.K.ltoreq.22%, a radius of bow curvature U of 4.0
m.ltoreq.U.ltoreq.8 m, and a resistivity r of 0.0018
.OMEGA.cm.ltoreq.r.ltoreq.0.01 .OMEGA.cm.
21. A conductive nitride semiconductor substrate according to claim
18 comprising a bottom portion, an inner portion, and a surface
portion in order in a crystal growth direction, the bottom portion
and the inner portion including crystal defect cluster regions H,
low-dislocation-density single-crystal regions Z, and a c-plane
growth region Y periodically arranged in the order of the crystal
defect cluster regions H, the low-dislocation-density
single-crystal regions Z, the c-plane growth region Y, and the
low-dislocation-density single-crystal regions Z in a direction
perpendicular to the growth direction, thereby forming an HZYZHZYZ
. . . structure, the crystal defect cluster regions H in the bottom
portion and the inner portion forming a pattern of dots having a
diameter of 10 to 100 .mu.m in a cross section perpendicular to the
growth direction, ZYZ portions defined between the adjacent crystal
defect cluster regions H having a width of 250 to 10,000 .mu.m, the
surface portion including the c-plane growth region Y and not
including the crystal defect cluster regions H or the
low-dislocation-density single-crystal regions Z, the
low-dislocation-density single-crystal regions Z and the crystal
defect cluster regions H being doped with silicon and oxygen, the
c-plane growth region Y being doped with silicon, the conductive
nitride semiconductor substrate having a thickness of 100 .mu.m or
more, a diameter of 18 mm or more, a cracking ratio K of
4%.ltoreq.K.ltoreq.13%, a radius of bow curvature U of 3.5
m.ltoreq.U.ltoreq.4.8 m, and a resistivity r of 0.005
.OMEGA.cm.ltoreq.r.ltoreq.0.009 .OMEGA.cm.
22. The conductive nitride semiconductor substrate according to
claim 19, wherein if the resistivity of the conductive nitride
semiconductor substrate is denoted by r and the silicon
concentration of the conductive nitride semiconductor substrate is
denoted by [Si], the resistivity is represented by the following
equation: log r=3.55-0.311 log [Si] (where log is a common
logarithm).
23. The conductive nitride semiconductor substrate according to
claim 19, wherein if the resistivity r of the conductive nitride
semiconductor substrate is expressed as r'.times.10.sup.-3
.OMEGA.cm and the silicon concentration [Si] of the conductive
nitride semiconductor substrate is expressed as
[Si'].times.10.sup.18 cm.sup.-3, the resistivity is represented by
the following equation: log r'=-0.311 log [Si']+0.954 (where log is
a common logarithm).
24. The conductive nitride semiconductor substrate according to
claim 19, wherein if the resistivity r of the conductive nitride
semiconductor substrate is expressed as r'.times.10.sup.-3
.OMEGA.cm and the silicon concentration [Si] of the conductive
nitride semiconductor substrate is expressed as
[Si'].times.10.sup.18 cm.sup.-3, the resistivity is represented by
the following equation: 0.689.ltoreq.log r'+0.311 log
[Si'].ltoreq.1.032 (where log is a common logarithm).
25. The conductive nitride semiconductor substrate according to
claim 18, wherein the cracking ratio K is 3% 18%, the radius of bow
curvature U is 4.2 m.ltoreq.U.ltoreq.6.5 m, and the resistivity r
is 0.0015 .OMEGA.cm.ltoreq.r.ltoreq.0.008 .OMEGA.cm.
26. A conductive nitride semiconductor substrate according to claim
18 comprising crystal defect cluster regions H,
low-dislocation-density single-crystal regions Z, and c-plane
growth regions Y periodically arranged in the order of the crystal
defect cluster regions H, the low-dislocation-density
single-crystal regions Z, the c-plane growth regions Y, and the
low-dislocation-density single-crystal regions Z in a direction
perpendicular to a crystal growth direction, thereby forming an
HZYZHZYZ . . . structure, the crystal defect cluster regions H
forming a pattern of parallel stripes having a width of 10 to 100
.mu.m in a cross section perpendicular to the growth direction, ZYZ
portions defined between the adjacent crystal defect cluster
regions H having a width of 250 to 10,000 .mu.m, the
low-dislocation-density single-crystal regions Z and the crystal
defect cluster regions H being doped with silicon and oxygen, the
c-plane growth regions Y being doped with silicon, the conductive
nitride semiconductor substrate having a thickness of 100 .mu.m or
more, a diameter of 18 mm or more, a cracking ratio K of
5%.ltoreq.K.ltoreq.18%, a radius of bow curvature U of 4.8
m.ltoreq.U.ltoreq.6.5 m, and a resistivity r of 0.0015
.OMEGA.cm.ltoreq.r.ltoreq.0.008 .OMEGA.cm.
27. A conductive nitride semiconductor substrate according to claim
18 comprising crystal defect cluster regions H,
low-dislocation-density single-crystal regions Z, and a c-plane
growth region Y periodically arranged in the order of the crystal
defect cluster regions H, the low-dislocation-density
single-crystal regions Z, the c-plane growth region Y, and the
low-dislocation-density single-crystal regions Z in a direction
perpendicular to a crystal growth direction, thereby forming an
HZYZHZYZ . . . structure, the crystal defect cluster regions H
forming a pattern of dots having a diameter of 10 to 100 .mu.m in a
cross section perpendicular to the growth direction, ZYZ portions
defined between the adjacent crystal defect cluster regions H
having a width of 250 to 10,000 .mu.m, the low-dislocation-density
single-crystal regions Z and the crystal defect cluster regions H
being doped with silicon and oxygen, the c-plane growth region Y
being doped with silicon, the conductive nitride semiconductor
substrate having a thickness of 100 .mu.m or more, a diameter of 18
mm or more, a cracking ratio K of 3%.ltoreq.K.ltoreq.6%, a radius
of bow curvature U of 4.2 m.ltoreq.U.ltoreq.5 m, and a resistivity
r of 0.004 .OMEGA.cm.ltoreq.r.ltoreq.0.008 .OMEGA.cm.
28. The conductive nitride semiconductor substrate according to
claim 25, wherein if the resistivity r of the conductive nitride
semiconductor substrate is expressed as r'.times.10.sup.-3
.OMEGA.cm, the silicon concentration [Si] of the conductive nitride
semiconductor substrate is expressed as [Si'].times.10.sup.18
cm.sup.-3, and the oxygen concentration [O] of the conductive
nitride semiconductor substrate is expressed as
[O'].times.10.sup.18 cm.sup.-3, the resistivity is represented by
the following equation: log r'=-0.311 log(1.6[O']+[Si'])+1.032
29. The conductive nitride semiconductor substrate according to
claim 25, wherein if the resistivity r of the conductive nitride
semiconductor substrate is expressed as r'.times.10.sup.-3
.OMEGA.cm, the silicon concentration [Si] of the conductive nitride
semiconductor substrate is expressed as [Si'].times.10.sup.18
cm.sup.-3, and the oxygen concentration [O] of the conductive
nitride semiconductor substrate is expressed as
[O'].times.10.sup.18 cm.sup.-3, the resistivity is represented by
the following equation: log r'=-0.311 log([O']+[Si'])+0.62
30. The conductive nitride semiconductor substrate according to
claim 25, wherein if the resistivity r of the conductive nitride
semiconductor substrate is expressed as r'.times.10.sup.-3
.OMEGA.cm, the silicon concentration [Si] of the conductive nitride
semiconductor substrate is expressed as [Si'].times.10.sup.18
cm.sup.-3, and the oxygen concentration [O] of the conductive
nitride semiconductor substrate is expressed as
[O'].times.10.sup.18 cm.sup.-3, the resistivity is represented by
the following equation: log r'=-0.311 log(K[O']+[Si'])+S (where K
is 1 to 1.6 and S is 0.62 to 1.032).
31. The conductive nitride semiconductor substrate according to
claim 25, wherein if the resistivity r of the conductive nitride
semiconductor substrate is expressed as r'.times.10.sup.-3
.OMEGA.cm, the silicon concentration [Si] of the conductive nitride
semiconductor substrate is expressed as [Si'].times.10.sup.18
cm.sup.-3, and the oxygen concentration [O] of the conductive
nitride semiconductor substrate is expressed as
[O'].times.10.sup.18 cm.sup.-3, the resistivity is represented by
the following equation: log r'=1.478-log {[Si']+[O']}
32. The conductive nitride semiconductor substrate according to
claim 25, wherein if the resistivity r of the conductive nitride
semiconductor substrate is expressed as r'.times.10.sup.-3
.OMEGA.cm, the silicon concentration [Si] of the conductive nitride
semiconductor substrate is expressed as [Si'].times.10.sup.18
cm.sup.-3, and the oxygen concentration [O] of the conductive
nitride semiconductor substrate is expressed as
[O'].times.10.sup.18 cm.sup.-3, the resistivity is represented by
the following equation: r'=30/{[Si']+[O']}
33. The conductive nitride semiconductor substrate according to
claim 25, wherein if the resistivity r of the conductive nitride
semiconductor substrate is expressed as r'.times.10.sup.-3
.OMEGA.cm, the silicon concentration [Si] of the conductive nitride
semiconductor substrate is expressed as [Si'].times.10.sup.18
cm.sup.-3, and the oxygen concentration [O] of the conductive
nitride semiconductor substrate is expressed as
[O'].times.10.sup.18 cm.sup.-3, the resistivity is represented by
the following inequality: 0.9213-0.5728 log {[Si']+[O']}.ltoreq.log
r'.ltoreq.1.478-log {[Si']+[O']}
34. The conductive nitride semiconductor substrate according to
claim 25, wherein if the resistivity r of the conductive nitride
semiconductor substrate is expressed as r'.times.10.sup.-3
.OMEGA.cm, the silicon concentration [Si] of the conductive nitride
semiconductor substrate is expressed as [Si'].times.10.sup.18
cm.sup.-3, and the oxygen concentration [O] of the conductive
nitride semiconductor substrate is expressed as
[O'].times.10.sup.18 cm.sup.-3, the resistivity is represented by
the following inequality:
8.34257/{[Si']+[O']}.sup.0.5728.ltoreq.r'.ltoreq.30/{[Si']+[O']}
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to conductive nitride
semiconductor substrates and methods for producing such substrates.
Nitride semiconductors include gallium nitride (GaN), aluminum
nitride (AlN), indium nitride (InN), and mixed crystals such as
InGaN and AlInGaN. The invention is directed not to thin films
deposited on underlying substrates, but to free-standing crystal
substrates. Here, GaN will be mainly discussed. GaN, which has a
wide bandgap, is used as a material for blue light-emitting
devices.
[0003] In the related art, blue light-emitting devices such as
light-emitting diodes and semiconductor lasers are produced by
epitaxially growing a nitride semiconductor thin-film crystal such
as InGaN, GaN, or AlInGaN on a single-crystal sapphire substrate
(.alpha.-Al.sub.2O.sub.3). Sapphire has the same crystal system as
GaN, namely, a hexagonal system. A c-plane GaN thin film is grown
on a c-plane sapphire crystal.
[0004] A sapphire substrate, however, has insulation properties,
and consequently a cathode cannot be formed on the bottom surface
thereof. In addition, chips must be separated by a cutting machine
because the cleavage plane of GaN differs from that of a sapphire
substrate. This is disadvantageous because such chip separation
takes much time and effort and also results in poor yield.
[0005] In addition, GaN differs greatly from sapphire in lattice
constant. A GaN crystal grown on a sapphire substrate has high
dislocation density and large bow. Accordingly, in order to use GaN
itself as a substrate, the preparation of a substrate crystal of
GaN has been attempted. GaN, which has a wide bandgap, is thought
to be a material suitable for blue light-emitting devices. A highly
conductive substrate is desired for light-emitting devices because
such a substrate is advantageous in forming a cathode on the bottom
surface and an anode on the top surface.
[0006] In the production of nitride semiconductor substrates, the
growth of n-type nitride semiconductor crystals, which have high
free electron density, has so far been researched. Currently,
free-standing oxygen-doped n-type GaN substrates having a diameter
of two inches can be produced.
[0007] 2. Description of the Related Art
[0008] To produce light-emitting devices, metal organic chemical
vapor deposition (MOCVD) is often used to form a nitride
semiconductor thin film (such as a GaN, InGaN, or AlGaN thin film)
on a sapphire substrate. Because MOCVD is a vapor synthesis
process, the source materials are supplied in vapor phase. Nitrogen
is supplied in the form of ammonia (NH.sub.3). In MOCVD, a group
III element is supplied in the form of an organic metal. An organic
metal of a group III element, such as gallium or indium (for
example, trimethylgallium or triethylindium), and NH.sub.3 are
supplied as source materials to a heated sapphire substrate.
[0009] Hydride vapor phase epitaxy (HVPE) is also frequently used
as a vapor synthesis process for forming a GaN-based semiconductor
thin film. In this process, a gallium boat filled with molten
gallium is disposed above a susceptor, and HCl is blown therein to
synthesize GaCl for use as a gallium source material. Thus, the
source gases are GaCl and ammonia.
[0010] PCT International Publication No. WO99/23693 (PCT
International Application No. PCT/JP98/04908) (Patent Document 1)
discloses a technique for forming a thick GaN crystal by forming a
GaN buffer layer on a GaAs substrate on which a mask having a
window diameter of 1 to 5 .mu.m and a window pitch of 4 to 10 .mu.m
is formed and performing c-plane growth of GaN thereon at
820.degree. C. or 970.degree. C. by MOCVD or at 970.degree. C.,
1,000.degree. C., 1,010.degree. C., 1,020.degree. C., or
1,030.degree. C. by HVPE.
[0011] Patent Document 1 uses a mask having fine windows. FIG. 1
shows a plan view of an example of the mask. The mask is formed on
an underlying substrate U. This mask has numerous small windows W
regularly arranged in a large, continuous masking portion M. The
underlying substrate U is exposed in the windows W. The masking
portion M has a much larger area than exposed portions E (windows
W). The masking portion M is a continuous thin film having the same
dimensions as the underlying substrate U. The exposed portions E
(openings: windows W) are larger in number but are smaller in total
area.
[0012] The mechanism by which dislocations are reduced by the mask
method will be described with reference to FIGS. 2A to 2G. FIGS. 2A
to 2G are sectional views illustrating how a crystal is grown by
the mask method. Referring to FIG. 2A, a mask M is formed by
applying a mask material to the underlying substrate U and forming
small windows W (exposed portions E) in a regular pattern. As GaN
is grown in vapor phase, GaN crystals G are formed only in the
windows W (exposed portions E). In the exposed portions E, numerous
upward dislocations T occur at the boundaries between the crystals
G and the underlying substrate U (see FIG. 2B).
[0013] As the growth proceeds, a portion of the crystals G growing
on the exposed portions E (windows W) overgrow the masking portions
(mask) M and grow across the mask M (masking portions) laterally
(see FIG. 2C). As the crystals G grow laterally, the dislocations T
also propagate laterally. The lateral surfaces are low-index facets
F. Referring to FIG. 2D, the crystals G grow upward and laterally,
thus having the shape of a truncated cone. The top surface of the
truncated cone is the c-plane (C). Referring to FIG. 2E, the
crystals G growing from the adjacent windows W contact each other.
The dislocations T then propagate laterally and collide with each
other. This causes some dislocations T to cancel each other
out.
[0014] Referring to FIG. 2F, the grooves defined by the facets F
are gradually filled and narrowed. Finally, the grooves defined by
the facets F are completely filled, thus forming a flat surface C.
The flat surface C is the c-plane. Thereafter, the growth continues
at the flat c-plane surface C. The number of dislocations T is
large above the windows W (exposed portions E) and is small above
the masking portion (mask) M.
[0015] Patent Document 1 is important in the related art because it
discloses specific data such as growth temperature and source
material partial pressure. Patent Document 1 discloses that the
growth temperature is 970.degree. C., 1,000.degree. C.,
1,010.degree. C., 1,020.degree. C., or 1,030.degree. C. for HVPE
and is 820.degree. C. or 970.degree. C. for MOCVD.
[0016] For HVPE, the source materials are HCl, molten gallium, and
NH.sub.3. The group III source material is GaCl, which is produced
by reacting the molten gallium with HCl gas. The amounts of group
III and V source materials supplied are expressed as the partial
pressures P.sub.GaCl and P.sub.NH3 of GaCl and NH.sub.3,
respectively. As used herein, the unit of partial pressure is Pa,
where 0.1 MPa (100,000 Pa) is approximated to 1 atmospheric
pressure (1 atm). More frequently, kPa (1,000 Pa) is used as a
unit; in this case, 100 kPa is approximated to 1 atm. The ratio b
of the group V source material to the group III source material can
be expressed as the ratio of the NH.sub.3 partial pressure
P.sub.NH3 to the GaCl partial pressure P.sub.GaCl. The ratio of the
group V source material to the group III source material is
According to Patent Document 1, the GaN crystal formed by the mask
method has a resistivity r of 0.005 to 0.08 .OMEGA.cm.
[0017] The substrate temperature and the V/III ratio b during
growth are important conditions responsible for crystal growth.
FIG. 22 lists the growth temperatures and the V/III ratios b of all
of Patent Document 1 to 11 described below, where the horizontal
axis indicates the substrate temperature (.degree. C.) and the
vertical axis indicates the V/III ratio b. The coordinates of the
substrate temperatures and V/III ratios b of the GaN crystals shown
in the patent documents are marked with dots. The black dots
indicate GaN crystals formed by HVPE, and the circled black dots
indicate GaN crystals formed by MOCVD. The numbers beside the black
dots and the circled black dots are the number of the patent
documents. The growth conditions for MOCVD disclosed in the
examples in Patent Document 1 are as follows.
[0018] The growth temperature Tq, the NH.sub.3 partial pressure
P.sub.NH3, the trimethylgallium (TMG) partial pressure P.sub.TMG,
and the V/III ratio b are shown below in the above order:
TABLE-US-00001 970.degree. C. 20 kPa 0.2 kPa 100 times 970.degree.
C. 25 kPa 0.2 kPa 100 times 820.degree. C. 20 kPa 0.3 kPa 67 times
970.degree. C. 20 kPa 0.2 kPa 100 times 1,000.degree. C. 20 kPa 0.4
kPa 50 times 970.degree. C. 25 kPa 0.5 kPa 50 times
[0019] The substrate temperature for MOCVD in Patent Document 1 is
820.degree. C. to 1,000.degree. C., and the V/III ratio b is 50 to
100 times. These examples are indicated by the five circled black
dots in the middle left of FIG. 22. The third example, namely,
820.degree. C. and 67 times, is omitted from FIG. 22 because the
temperature is excessively low and deviates from FIG. 22.
[0020] The growth conditions for HVPE disclosed in the examples in
Patent Document 1 are as follows.
[0021] The growth temperature Tq, the NH.sub.3 partial pressure
P.sub.NH3, the HCl partial pressure P.sub.HCl, and the V/III ratio
b are shown below in the above order:
TABLE-US-00002 970.degree. C. 25 kPa 2 kPa 12.5 times 970.degree.
C. 25 kPa 2.5 kPa 10 times 970.degree. C. 25 kPa 0.5 kPa 50 times
1,000.degree. C. 20 kPa 2 kPa 10 times 950.degree. C. 25 kPa 2 kPa
12.5 times 1,020.degree. C. 25 kPa 2 kPa 12.5 times 1,000.degree.
C. 25 kPa 2 kPa 12.5 times 1,010.degree. C. 25 kPa 2 kPa 12.5 times
1,030.degree. C. 25 kPa 2 kPa 12.5 times
The substrate temperature for HVPE in Patent Document 1 is
950.degree. C. to 1,030.degree. C., and the V/III ratio b is 10 to
50 times.
[0022] Japanese Patent No. 3788037 (Japanese Patent Application No.
10-171276, Japanese Unexamined Patent Application Publication No.
2000-012900) (Patent Document 2) provides a free-standing GaN
substrate having a diameter of 20 mm or more, a thickness of 70
.mu.m or more, and a deflection (bow) of 0.55 mm or less on a 50 mm
diameter wafer basis by forming a mask having a staggered pattern
of fine windows on a GaAs substrate, growing a thick GaN film
thereon by HVPE while maintaining the c-plane, and removing the
GaAs substrate. A central deflection (bow) of 0.55 mm on a 50 mm
diameter wafer basis is equivalent to a radius of curvature R of
about 600 mm=0.6 in, meaning that the curvature is large.
[0023] In Patent Document 2, the growth temperature for HVPE is
970.degree. C., 1,020.degree. C., or 1,030.degree. C., the GaCl
partial pressure P.sub.GaCl is 1 or 2 kPa (0.01 to 0.02 atm), and
the NH.sub.3 partial pressure P.sub.NH3 is 4 or 6 kPa. Patent
Document 2 discloses that a crystal formed at a GaCl partial
pressure P.sub.GaCl of 1 kPa is impractical because it has a flat
surface but has large bow and large internal stress and cracks
easily, and it cannot be formed to a thickness of 70 .mu.m or
more.
[0024] Conversely, according to Patent Document 2, a crystal formed
at a GaCl partial pressure P.sub.GaCl of 2 kPa has a rough surface
but has small bow and small internal stress. The NH.sub.3 partial
pressure is 6, 12, or 24 kPa. The V/III ratio b is 3, 6, or 12. The
radius of curvature is about 1 m. The resistivity is 0.0035 to
0.0083 .OMEGA.cm. This crystal is n-type.
[0025] The growth conditions disclosed in the examples in Patent
Document 2 are as follows.
[0026] The growth temperature Tq, the NH.sub.3 partial pressure
P.sub.NH3, the GaCl partial pressure P.sub.GaCl, and the V/III
ratio b are shown below in the above order:
TABLE-US-00003 1,030.degree. C. 4 kPa 1 kPa 4 times 1,030.degree.
C. 6 kPa 1 kPa 6 times 970.degree. C. 6 kPa 2 kPa 3 times
970.degree. C. 6 kPa 1 kPa 6 times 970.degree. C. 6 kPa 1 kPa 6
times 1,020.degree. C. 6 kPa 2 kPa 3 times 1,020.degree. C. 6 kPa 2
kPa 3 times 1,030.degree. C. 6 kPa 1 kPa 6 times 970.degree. C. 6
kPa 2 kPa 3 times 970.degree. C. 12 kPa 2 kPa 6 times 970.degree.
C. 24 kPa 2 kPa 12 times
All examples are formed by HVPE. The substrate temperature is
970.degree. to 1,030.degree. C., and the V/III ratio b is 3 to 12
times. The growth conditions (substrate temperature and V/III ratio
b) of Patent Document 2 are indicated by the eleven black dots in
the lower left of FIG. 22.
[0027] Japanese Patent No. 3788041 (Japanese Patent Application No.
10-183446, Japanese Unexamined Patent Application Publication No.
2000-022212) (Patent Document 3) proposes a method for producing a
free-standing single-crystal GaN substrate by forming, on a GaAs
substrate, a mask having a dot pattern of windows arranged at
predetermined intervals in the [11-2] direction and shifted by half
the pitch in the [-110] direction, a mask having a stripe pattern
of windows extending in the [11-2] direction, or a mask having a
stripe pattern of windows extending in the [-110] direction;
forming a buffer layer; epitaxially growing GaN by HVPE while
maintaining the c-plane; and removing the substrate and the
mask.
[0028] The technique proposed in Patent Document 3 reduces
dislocations T by forming a mask having numerous small windows
arranged at a narrow pitch in two orthogonal directions on the
underlying substrate U, as shown in FIG. 1, and growing GaN in
vapor phase. The GaCl partial pressure P.sub.GaCl is 1 kPa (0.01
atm) or 2 kPa (0.02 atm). Patent Document 3 discloses that a GaN
cry a formed at a GaCl partial pressure P.sub.GaCl of 1 kPa has a
flat surface but has large internal stress and large bow and cracks
easily and that a GaN crystal formed at a GaCl partial pressure
P.sub.GaCl of 2 kPa has a rough surface but has small internal
stress and small bow and does not crack easily.
[0029] Patent Document 3 also discloses that a crystal formed at a
growth temperature of 1,020.degree. C. or 1,030.degree. C. has a
flat surface but has large internal stress and cracks easily.
[0030] Patent Document 3 also discloses that a thick GaN crystal
formed at a growth temperature of 970.degree. C. and a GaCl partial
pressure P.sub.GaCl of 2 kPa has a rough surface but has small
internal stress and small bow. The NH.sub.3 partial pressure
P.sub.NH3 is 6 to 12 kPa.
[0031] In summary, according to Patent Document 3, the conditions
for producing a GaN crystal that has a rough surface but has small
bow and small internal stress and does not crack easily are a
growth temperature of 970.degree. C., a GaCl partial pressure of 2
kPa, a NH.sub.3 partial pressure of 6 to 12 kPa, and a V/III ratio
b of about 3 to 6. The crystal has a resistivity of 0.01 to 0.017
.OMEGA.cm and is n-type.
[0032] The HVPE growth conditions disclosed in the examples in
Patent Document 3 are as follows.
[0033] The growth temperature Tq, the NH.sub.3 partial pressure
P.sub.H3, the GaCl partial pressure P.sub.GaCl, and the V/III ratio
b are shown below in the above order:
TABLE-US-00004 1,030.degree. C. 4 kPa 1 kPa 4 times 1,030.degree.
C. 6 kPa 1 kPa 6 times 970.degree. C. 6 kPa 2 kPa 3 times
970.degree. C. 6 kPa 1 kPa 6 times 970.degree. C. 6 kPa 1 kPa 6
times 1,020.degree. C. 6 kPa 2 kPa 3 times 1,020.degree. C. 6 kPa 2
kPa 3 times 1,030.degree. C. 6 kPa 1 kPa 6 times 970.degree. C. 6
kPa 2 kPa 3 times 970.degree. C. 12 kPa 2 kPa 6 times 970.degree.
C. 24 kPa 2 kPa 12 times
All examples are formed by HVPE. The substrate temperature is
970.degree. to 1,030.degree. C., and the V/III ratio b is 3 to 12
times. The growth conditions (substrate temperature and V/III ratio
b) of Patent Document 3 are indicated by the eleven black dots in
the lower left of FIG. 22.
[0034] In PCT International Publication No. WO98/47170 (PCT
International Application No. PCT/JP 98/01640) (Patent Document 4),
two or three epitaxial lateral overgrowth (ELO) masks are formed so
as to be alternately superimposed to reduce dislocations, and a
silicon-doped n-type GaN crystal is grown by MOCVD or HVPE while
maintaining the c-plane. According to Patent Document 4,
dislocations can be reduced by forming two or three ELO masks such
that windows are shifted from each other because the dislocation
density is higher above the windows and is lower above the masks.
Patent Document 4 discloses that a V/III ratio b of 30 to 2,000
times is appropriate for MOCVD.
[0035] In the examples in Patent Document 4, MOCVD is used, and
source gases are used in a V/III ratio b of 12,000 times, 2,222
times, 1,800 times, 1,500 times, 800 times, or times. Patent
Document 4 discloses that the preferred growth temperature is
950.degree. C. to 1,050.degree. C. The conditions for HVPE are not
disclosed. In FIG. 22, lines are drawn along the temperature range
of 950.degree. C. to 1,050.degree. C. at b=2,222 times, 1,800
times, 1,500 times, 800 times, and 30 times and are marked with
circled black dots. The n-type dopant is silicon. Silicon serves as
an n-type dopant because a silicon atom replaces a gallium atom to
release one free electron. Silane gas (SiH.sub.4) is used for
doping. First, truncated crystals are formed above the windows of
the ELO masks by MOCVD, and the process is switched to HVPE
immediately before the truncated crystals combine above the ELO
masks.
[0036] EPC Publication No. EP0942459 A1 (EPC Application No.
9891274.8) (Patent Document 5) is substantially the same as Patent
Document 4 and proposes a technique for reducing dislocations using
two or three ELO masks. The growth conditions, including the
substrate temperature, the group III source material partial
pressure, and the group V source material partial pressure, are the
same as those of Patent Document 4 and therefore will not be
described. Although not shown in FIG. 22, the growth conditions of
Patent Document 5 are equivalent to those of Patent Document 4.
[0037] Japanese Patent No. 3788104 (Japanese Unexamined Patent
Application Publication No. 2000-044400, Japanese Patent
Application No. 11-144151, priority claim based on Japanese Patent
Application No. 10-147716) (Patent Document 6) first proposed a
method for producing an n-type GaN substrate by doping GaN with
oxygen (O) as an n-type dopant. Oxygen may serve as an n-type
dopant because it can release one free electron by replacing
nitrogen. However, it is unknown what level oxygen forms in GaN,
and it is therefore uncertain whether oxygen serves as an n-type
dopant unless a doping test is carried out in practice. Patent
Document 6 does not specifically disclose substrate temperature or
source material partial pressure, and they are not shown in FIG.
22.
[0038] In Patent Documents 4 and 5, a crystal is doped with
silicon, which serves as an n-type dopant, using silane gas
(SiH.sub.4). The use of a large amount of silane gas for growth of
an n-type substrate is hazardous because it has the risk of
explosion. Patent Document 6 has found that oxygen forms a shallow
donor level in GaN. If a GaN crystal is grown by VPE on a GaAs
substrate on which an ELO mask is formed using a source gas, such
as NH.sub.3 or HCl, to which water is added, the crystal is doped
with oxygen from the source gas during c-plane growth to form a
donor level and produce n-type carriers, thus making the crystal
n-type. In addition, according to Patent Document 6, the activation
rate is 100% over a wide range of concentration. Thus, Patent
Document 6 first revealed that oxygen can serve as an n-type dopant
advantageous for a thick crystal such as a substrate. Patent
Document 6, however, only first pointed out that oxygen can serve
as an n-type dopant and does not recognize anisotropy in
doping.
[0039] Japanese Patent No. 3826825 (Japanese Unexamined Patent
Application Publication No. 2002-373864, Japanese Patent
Application No. 2002-103723, priority claim based on Japanese
Patent Application No. 2001-113872) (Patent Document 7) reveals
that oxygen doping of GaN has significant anisotropy, that is, the
selectivity that oxygen is not easily absorbed through the c-plane
((0001) plane) and is easily absorbed through planes other than the
c-plane. As shown in FIG. 17, Patent Document 7 proposes a
technique for growing a crystal in the c-axis direction as a whole
while forming numerous non-c-plane facets F in the surface thereof
so that oxygen is absorbed into the crystal through the non-c-plane
facets F, as shown in FIG. 17, or growing a crystal on a GaN
underlying substrate having a non-c-plane surface (hkmn)
(.noteq.(0001) plane) while doping it with oxygen through the
non-c-plane surface, as shown in FIG. 18. Thus, Patent Document 7
first revealed significant anisotropy in oxygen doping.
[0040] The HVPE growth conditions disclosed in an example in Patent
Document 7 are as follows.
[0041] The growth temperature Tq, the NH.sub.3 partial pressure
P.sub.NH3, the HCl partial pressure P.sub.HCl, and the V/III ratio
b are shown below in the above order:
[0042] 1,020.degree. C. 20 kPa 1 kPa 20 times
The coordinates of 1,020.degree. C. and 20 times in FIG. 22 are
indicated by the black dot marked with "7".
[0043] Japanese Unexamined Patent Application Publication No.
2001-102307 (Japanese Patent Application No. 11-273882) (Patent
Document 8) proposes a novel method for reducing dislocation
density that is quite different from ELO (see FIG. 1 and FIGS. 2A
to 2G; that is, as shown in FIG. 2G, a crystal is grown while
maintaining a flat c-plane surface). In Patent Document 8, as shown
in FIG. 3, numerous pits P of varying sizes defined by facets F are
intentionally formed under appropriately controlled growth
conditions, and the facets F are maintained to the end of the
growth without filling the pits P. This method is referred to as
facet growth since the facets F are maintained to the end without
filling the pits P. Although the pits P are six- or twelve-sided
pyramids, six-sided pyramid pits are shown here for brevity.
[0044] As shown in the perspective view of the pits P in FIG. 4 and
the plan view of the pits P in FIG. 5, as a crystal is grown while
maintaining the recesses (pits P) defined by the facets F, it grows
in a direction V normal to the facets F inside the pits P. Because
dislocations T propagate in the growth direction, they propagate in
the direction V normal to the facets F. During the facet growth,
the dislocations T cluster at boundaries B. Thus, clusters of
dislocations T are formed under the boundaries B (planar defects
PD).
[0045] As the facet growth proceeds, the dislocations T further
cluster at the bottoms of the pits P. Clusters of numerous
dislocations T (linear clusters of defects H) are formed at the
bottoms of the pits P. Even through the total number of
dislocations T remains nearly the same, the dislocation density is
lower at other portions because the dislocations T cluster into the
planar defects PD and the linear defects H. Unlike ELO (see FIG. 1
and FIGS. 2A to 2G), this method provides the effect of reducing
dislocations from the middle stage to the final stage of the
growth. Thus, this is a completely novel method for reducing
dislocation density. This method is referred to as facet growth
since it maintains facets to reduce dislocations by the effect of
the facets.
[0046] Because it is uncertain where the pits P (recesses) are
formed in the technique in Patent Document 8, this is referred to
as random facet growth to distinguish it from the later improved
versions. The resultant crystal has noticeable surface
irregularities.
[0047] The growth conditions disclosed in the examples in Patent
Document 8 (random facet growth) are as follows.
[0048] The growth temperature T, the NH.sub.3 partial pressure
P.sub.NH3, the HCl partial pressure P.sub.HCl, and the V/III ratio
b are shown below in the above order:
TABLE-US-00005 1,050.degree. C. 20 kPa 0.5 kPa 40 times
1,000.degree. C. 30 kPa 2 kPa 15 times 1,050.degree. C. 20 kPa 0.5
kPa 40 times 1,020.degree. C. 20 kPa 1 kPa 20 times 1,000.degree.
C. 30 kPa 2 kPa 15 times 1,000.degree. C. 40 kPa 3 kPa 13 times
980.degree. C. 40 kPa 4 kPa 10 times
In the growth conditions of Patent Document 8, the substrate
temperature is 980.degree. C. to 1,050.degree. C., and the V/III
ratio b is 10 to 40 times. The V/III ratio b is high. Seven black
dots having the substrate temperatures and the V/III ratios b shown
above as the coordinates thereof are distributed in the center of
the lower half of FIG. 22.
[0049] In Patent Document 8, the positions where facet pits are
formed are randomly determined because the substrate has no
anisotropy or specificity; thus, this method is referred to as
random facet growth. Because the pit positions are randomly
determined, it is difficult to fabricate devices on the substrate.
In addition, clustered dislocations can be redispersed as the
crystal grows because of the absence of local specificity. Because
devices are fabricated on the substrate, it will be more
advantageous if the positions where facet pits are formed can be
designated in advance. In addition, the dislocation density will be
further reduced if the dislocations can be confined and prevented
from being redispersed.
[0050] As shown in FIG. 6, Japanese Patent No. 3864870 (Japanese
Unexamined Patent Application Publication No. 2003-165799, Japanese
Patent Application No. 2002-230925, priority claim based on
Japanese Patent Application No. 2001-284323) (Patent Document 9)
uses a mask having an isolated dot pattern of masking portions M
regularly arranged on the underlying substrate U. Unlike the ELO
mask shown in FIG. 1 and FIGS. 2A to 2G, the region where the
underlying substrate U is exposed (exposed portion E) is much
larger than the masking portion (mask portions) M. The sum of the
spacing w and the diameter s of the masking portions M is the pitch
p. The spacing w is much larger than the diameter s, and the pitch
p of the masking portions M is much larger than that of an ELO
mask. GaN is grown in vapor phase on the masked underlying
substrate U. The growth starts from the exposed portion E, and a
thin film is formed on the exposed portion E. Because the growth is
delayed on the masking portions M, recesses (facet pits P) whose
bottoms are defined by the masking portions M are formed.
[0051] Facet growth using a dot mask will now be described with
reference to FIGS. 7, 8, and 9A to 9F. Referring to FIG. 9A, an
isolated dot pattern of masking portions M is formed on the
underlying substrate U. Referring to FIG. 9B, as GaN is grown in
vapor phase, a crystal G grows only on the exposed portion E of the
underlying substrate U; it does not grow on the masking portions M.
Referring to FIG. 9C, the crystal G grows upward above the exposed
portion E. The inclined surfaces are low-index facets F. Referring
to FIG. 9D, six- or twelve-sided pyramid facet pits P are formed
whose bottoms are defined by the masking portions M and whose
inclined surfaces are defined by the facets F. Referring to FIG.
9E, the crystal G overgrows the masking portions M. These portions
are closed defect cluster regions H where dislocations cluster at
high density. The portions below the facets F are single-crystal
low-dislocation-density concomitant regions Z. The flat surface is
the c-plane (C). The portion below the c-plane is a single-crystal
low-dislocation-density remaining region Y.
[0052] As shown in the perspective view of the crystal G in FIG. 7
and the plan view of FIG. 8, facet pits P defined by facets F
having the shape of an inverted cone like a flower petal are
arranged in the surface of the crystal G in two orthogonal
directions. The portions corresponding to the stalk are the closed
defect cluster regions H where dislocations cluster. The portions
corresponding to the root are the masking portions M. The flat
surface is the c-plane. The portion under the c-plane is a
low-dislocation-density region (Y). The portions below the facets F
are also low-dislocation-density regions (Z). This mask is referred
to as a dot mask to distinguish it from others. This method is
referred to as dot facet growth.
[0053] The facet pits P, as described above, have the effect of
causing dislocations in the facets F to cluster at the boundaries B
and further cluster at the bottoms of the pits P. The bottoms of
the pits P (above the masking portions M) are the closed defect
cluster regions H where dislocations cluster. The closed defect
cluster regions H are "closed" because the clustered dislocations
are no longer redispersed. The other portions are the
single-crystal low-dislocation-density concomitant regions Z
(formed below the facets F) having a low-dislocation-density and
the single-crystal low-dislocation-density remaining region Y
(formed below the c-plane). The regions Z and Y have low
dislocation density.
[0054] Patent Document 9 first introduced the concepts of the
closed defect cluster regions H, the single-crystal
low-dislocation-density concomitant regions Z, and the
single-crystal low-dislocation-density remaining region Y. The
closed defect cluster regions H are formed above the masking
portions M. The single-crystal low-dislocation-density concomitant
regions Z are formed above the exposed portion E, where the masking
portions M are not formed, beside (so as to be attached to) the
masking portions M. The single-crystal low-dislocation-density
remaining region Y is formed above the exposed portion E in a
region remote from the masking portions M. The single-crystal
low-dislocation-density concomitant regions Z are formed beside (so
as to be attached to) the masking portions M because they are
formed below the facets F, which are formed diagonally with respect
to the masking portions M so as to cover the exposed portion E.
[0055] The single-crystal low-dislocation-density remaining region
Y is formed in a region remote from the masking portions M because
they are surrounded by the single-crystal low-dislocation-density
concomitant regions Z. Unlike an ELO mask, the mask used for facet
growth does not have fine windows arranged at a small pitch, but
has a dot pattern (such as circles or squares) of masking portions
M (see FIG. 6) of considerable size in a large exposed portion.
[0056] For an ELO mask (see FIGS. 1 and 2A to 2G), the masking
portion M is a single continuous region larger than the exposed
portions E (windows W), and the numerous exposed portions E
(windows W) are small (1 to 2 .mu.m in diameter), are arranged at a
small pitch (2 to 6 .mu.m), and have a total area smaller than that
of the masking portion M.
[0057] Conversely, for the mask serving as the basis of the facet
pits P in Patent Document 9, as shown in FIG. 6, the exposed
portion E is larger than the masking portions M. The exposed
portion E is a single continuous region. The masking portions M are
large in number but have a total area smaller than that of the
exposed portion E. As shown in FIGS. 7, 8, and 9A to 9F, because
the facets F are formed above the exposed portion E and
low-dislocation-density high-quality regions, namely, the
single-crystal low-dislocation-density concomitant regions Z, are
formed directly below the facets F, it is essential to form a large
exposed portion E. The diameter of the masking portions M is
considerably large (20 to 100 .mu.m in diameter). The bottoms of
the facet pits P are located above the masking portions M. The
facet pits P collect and trap dislocations at the bottoms thereof
and do not release the dislocations. This mask is characterized in
that the closed defect cluster regions H are formed above the
masking portions M and the low-dislocation-density regions Z and Y
are formed therearound (see FIGS. 8 and 9A to 9F). The
low-dislocation-density regions Z and Y are formed above the
exposed portion E, where the masking portions M are not formed. The
regions Z are formed directly below the facets F, and the region Y
is formed directly below the c-plane growth portion. The regions Z
and Y are formed of a single crystal and have low dislocation
density. Thus, concentric HZY structures are formed around the dot
masking portions M. This relationship is opposite to that of an ELO
mask, in which high-dislocation-density regions (H) are formed
above the exposed portions E (windows W) and
low-dislocation-density regions (Z, Y) are formed above the masking
portion M.
[0058] The growth conditions of the examples in Patent Document 9
are as follows.
[0059] The growth temperature Tq, the NH.sub.3 partial pressure
P.sub.NH3, the HCl partial pressure P.sub.HCl, and the V/III ratio
b are shown below in the above order:
TABLE-US-00006 1,050.degree. C. 30 kPa 2 kPa 15 times 1,030.degree.
C. 30 kPa 2.5 kPa 12 times 1,010.degree. C. 20 kPa 2.5 kPa 8 times
1,030.degree. C. 25 kPa 2.5 kPa 10 times 1,050.degree. C. 30 kPa
2.5 kPa 12 times 1,030.degree. C. 25 kPa 2 kPa 12.5 times
1,030.degree. C. 25 kPa 2 kPa 12.5 times
The growth temperature is 1,010.degree. C. to 1,050.degree. C., and
the V/III ratio b is 8 to 15 times. These examples are indicated by
the seven black dots marked with the number "9" in the center of
the lower half of FIG. 22.
[0060] In Patent Document 9, because the mask has a regularly
distributed isolated dot pattern, the closed defect cluster regions
H are formed above the dots (masking portions), and the
single-crystal low-dislocation-density concomitant regions Z and
the single-crystal low-dislocation-density remaining region Y are
formed therearound above the exposed portion E. The dispersed
closed defect cluster regions H are disadvantageous in fabricating
devices such as semiconductor lasers or light-emitting diodes on
the substrate.
[0061] Accordingly, in Japanese Patent No. 3801125 (Japanese
Unexamined Patent Application Publication No. 2003-183100, Japanese
Patent Application No. 2002-269387, priority claim based on
Japanese Patent Application No. 2001-311018) (Patent Document 10),
as shown in FIG. 10, a mask having a regularly spaced parallel
stripe pattern of masking portions M is formed on the underlying
substrate U, and GaN is grown thereon by facet growth. The sum of
the width s of the masking portions M and the width w of the
exposed portions E is the pitch p (p=s+w). The widths s and w in
this method are larger than the pitch or spacing in ELO. The width
w is much larger than the width s. GaN is grown in vapor phase on
the underlying substrate U.
[0062] As shown in the plan view of FIG. 11 and the perspective
view of FIG. 12, numerous parallel ridge-and-valley crystals having
flat top faces are formed. Parallel crystal defect cluster regions
H are formed above the masking portions M, and parallel
low-dislocation-density single-crystal regions Z and c-plane growth
regions Y are formed above the exposed portions E. The regions
where dislocations cluster above the parallel masking portions M
are referred to as the crystal defect cluster regions H. The
regions continuously grown below the facets F adjacent to the
crystal defect cluster regions H are referred to as the
low-dislocation-density single-crystal regions Z. The c-plane
growth regions Y may or may not be formed between the adjacent
low-dislocation-density single-crystal regions Z.
[0063] Whereas Patent Document 9 uses the term "closed" to
emphasize that the defect regions H are closed because they are
formed above the isolated dot pattern of masking portions M, the
term "closed" is inappropriate for the regions H formed above the
stripe pattern of masking portions M because they are not closed at
the ends thereof; thus, the regions formed above the masking
portions M are referred to as the crystal defect cluster regions H.
These regions are the same as the closed defect cluster regions H
in Patent Document 9 and are therefore denoted by the same symbol
H. In addition, the term "concomitant" is inappropriate for the
regions Z because the exposed portions E spread continuously and
the regions Z are not necessarily concomitant with the regions H;
thus, the regions Z are referred to as the low-dislocation-density
single-crystal regions Z. These regions are the same as the
single-crystal low-dislocation-density concomitant regions Z in
Patent Document 9 and are therefore denoted by the same symbol Z.
For the dot mask in Patent Document 9, a remaining portion occurs
necessarily if osculating circles of equal radius are drawn about
the masking portions M. Accordingly, the single-crystal
low-dislocation-density remaining region Y occurs necessarily in
Patent Document 9. In Patent Document 10, on the other hand, the
regions Y may or may not be formed because the mask has a parallel
stripe pattern. The regions Y are formed where the c-plane appears.
Because the regions Y occur in the c-plane, they are referred to as
the c-plane growth regions Y in Patent Document 10. These regions
are the same as the single-crystal low-dislocation-density
remaining region Y and are therefore denoted by the same symbol
Y.
[0064] The c-plane growth regions Y may disappear depending on the
manner of growth. As shown in the plan view of FIG. 13 and the
perspective view of FIG. 14, ridge-and-valley crystals having sharp
ridges may be formed. The parallel crystal defect cluster regions H
are formed above the masking portions M, thus forming the valleys.
The parallel low-dislocation-density single-crystal regions Z are
formed above the exposed portions E adjacent thereto. The ridges
formed by the facets F are sharp and have no c-plane portion. The
c-plane growth regions Y are lost; that is, the . . . ZHZH . . .
structure is formed.
[0065] Stripe facet growth will now be described with reference to
FIGS. 15A to 15F.
[0066] Referring to FIG. 15A, a parallel stripe pattern of masking
portions M is formed on the underlying substrate U. The pitch p of
the masking portions M (20 to 2,000 .mu.m) is much larger than the
pitch of the mask windows w in FIGS. 1 and 2A to 2G (about 2 to 6
.mu.m). The exposed portions E are larger than the masking portions
M. Referring to FIG. 15B, as GaN is grown in vapor phase, crystals
G grow only on the exposed portions E of the underlying substrate
U; they do not grow on the masking portions M. Referring to FIG.
15C, the crystals G grow upward above the exposed portions E. The
inclined faces are low-index facets F. The crystals G are formed as
parallel stripes separated by the masking portions M. Referring to
FIG. 15D, parallel V-grooves whose bottoms are defined by the
masking portions M are formed by the parallel inclined faces
inclined in opposite directions. The opposite inclined faces are
the facets F inclined at the same angle in opposite directions. The
flat faces between the adjacent masking portions M are the c-plane
(C).
[0067] Referring to FIG. 15E, the crystals G overgrow the masking
portions M. These portions are the crystal defect cluster regions H
where dislocations cluster at high density. Referring to FIG. 15F,
the crystals G grow further. The crystal defect cluster regions H
above the masking portions M grow upward while substantially
maintaining their areas. The parallel facets F become larger. The
portions directly below the facets F are the
low-dislocation-density single-crystal regions Z. The boundaries
between the crystal defect cluster regions H and the
low-dislocation-density single-crystal regions Z are crystal
boundaries K. The crystal boundaries K confine dislocations within
the crystal defect cluster regions H.
[0068] The flat faces formed midway between the masking portions M
are the c-plane (C). The portions below the c-plane are the c-plane
growth regions Y. The c-plane becomes gradually narrower. The pitch
of the stripe pattern of crystals G is equal to the mask pitch p,
which is the sum the width s of the masking portions M and the
width w of the exposed portions E (p=s+w). As the crystal growth
proceeds, as shown in FIG. 16A, parallel crystals grow like a
mountain range, with the crystal defect cluster regions H forming
the bases of the mountains and the c-plane forming the ridges of
the mountains. The c-plane portions (C), corresponding to the
mountaintops, become narrower. The portions directly below the
facets F are the low-dislocation-density single-crystal regions Z,
and the portions directly below the c-plane are the c-plane growth
regions Y.
[0069] The crystals G may grow upward while maintaining their
shapes, or may grow further into the shape of parallel mountains
having sharp peaks, as shown in FIG. 16B. In this case, the c-plane
disappears, and the c-plane growth regions Y also disappear.
[0070] In Patent Document 10, the . . . ZHZYZHZYZH . . . structure
or the . . . ZHZHZH . . . structure is formed. The crystal defect
cluster regions H have dislocations concentrated therein, and the
low-dislocation-density single-crystal regions Z and the c-plane
growth regions Y are formed of a single crystal and have low
dislocation density.
[0071] The method of Patent Document 10 is referred to as stripe
facet growth because the parallel crystal defect cluster regions H
are formed by forming a mask having a parallel stripe pattern. In
this case, devices such as semiconductor lasers or light-emitting
diodes can be easily fabricated because the low-dislocation-density
single-crystal regions Z extend in a straight line.
[0072] Facet growth and ELO are totally different methods, and the
shapes, dimensions, and effects of the masks are also different. An
ELO mask, which has windows distributed in a staggered pattern, can
be clearly distinguished from a stripe mask because they have
different shapes and dimensions. An ELO mask has numerous small
windows having a diameter of 1 to 2 .mu.m and distributed at a
pitch of about 2 to 6 .mu.m. A stripe mask has a width s of about
10 to 300 .mu.m and a pitch p of about 20 to 2,000 .mu.m. A stripe
mask is a coarse mask, for example, having a width s of 50 .mu.m
and a pitch p of 500 .mu.m.
[0073] In dot facet growth and stripe facet growth, dislocations
are concentrated in the crystal defect cluster regions H above the
masking portions M and are no longer redispersed because they are
confined by the crystal boundaries K. The regions Z and Y adjacent
to the regions H have low dislocation density and are formed of a
single crystal. These portions may be used as portions where a
device current flows.
[0074] A GaN crystal can be used to form a cavity mirror of a laser
by natural cleavage because it cleaves in a {1-100} direction. A
cathode can be formed on the bottom surface of the crystal because
it is made n-type by oxygen doping so that a current flows
therethrough. In this respect, a GaN crystal is superior to a
sapphire substrate.
[0075] In ELO, high-dislocation-density regions are formed above
small exposed portions, and a low-dislocation-density region is
formed above a large masking portion. In stripe facet growth, on
the other hand, low-dislocation-density regions are formed above
wide exposed portions, and high-dislocation-density regions are
formed above narrow masking portions.
[0076] The growth conditions of the examples (all by HVPE) in
Patent Document 10 are as follows.
[0077] The growth temperature Tq, the NH.sub.3 partial pressure
P.sub.NH3, the HCl partial pressure P.sub.HCl, and the V/III ratio
b are shown below in the above order:
TABLE-US-00007 1,050.degree. C. 30 kPa 2 kPa 15 times 1,030.degree.
C. 30 kPa 2.5 kPa 12 times 1,050.degree. C. 30 kPa 2 kPa 15 times
1,010.degree. C. 20 kPa 2.5 kPa 8 times 1,030.degree. C. 25 kPa 2
kPa 12.5 times 1,030.degree. C. 25 kPa 2.5 kPa 10 times
In Patent Document 10, the substrate temperature is 1,010.degree.
C. to 1,050.degree. C., and the V/III ratio b is 8 to 15 times. The
growth conditions of Patent Document 10 are indicated by the six
dots marked with the number "10" in the center of the lower half of
FIG. 22.
[0078] Japanese Unexamined Patent Application Publication No.
2005-306723 (Japanese Patent Application No. 2005-075734, priority
claim based on Japanese Patent Application No. 2004-085372) (Patent
Document 11) proposes a method for producing an iron-doped GaN
substrate by growing an iron-doped GaN crystal on a sapphire (0001)
substrate by MOCVD using H.sub.2, TMG, and ammonia as source gases
and (C.sub.5H.sub.5).sub.2Fe as a dopant, or by HVPE using H.sub.2,
HCl, molten gallium, and ammonia as source materials and
(C.sub.5H.sub.5).sub.2Fe as a dopant. Patent Document 11 is
intended to produce a semi-insulating substrate by iron doping.
[0079] The growth conditions of an example (MOCVD) in Patent
Document 11 are as follows.
[0080] The growth temperature Tq, the NH.sub.3 partial pressure
P.sub.NH3, the TMG partial pressure P.sub.TMG, and the V/III ratio
b are shown below in the above order:
TABLE-US-00008 1,000.degree. C. 15 kPa 0.3 kPa 50 times
This example is indicated by the circled black dot at 1,000.degree.
C. and 50 times in the center of FIG. 22.
[0081] The growth conditions of an example (HVPE) in Patent
Document 11 are as follows.
[0082] The growth temperature Tq, the NH.sub.3 partial pressure
P.sub.NH3, the HCl partial pressure P.sub.HCl, and the V/III ratio
b are shown below in the above order:
[0083] 1,000.degree. C. 15 kPa 0.3 kPa 50 times
This example is indicated by the black dot at 1,000.degree. C. and
50 times in the center of FIG. 22.
[0084] The substrates that have so far been discussed are n-type
GaN substrates used as substrates for blue light-emitting diodes
and semiconductor lasers and semi-insulating (SI) GaN substrates
used as substrates for field-effect transistors (FET). AlInGaN
substrates containing small amounts of aluminum and indium have
also been produced for use as substrates for light-emitting
devices. These substrates allow a high-density current to flow
therethrough because they are n-type and have high conductivity.
The dopant is silicon (Si) or oxygen (O).
[0085] For light-emitting devices, dislocations may lead to
deterioration because a high-density current flows through the
substrate. Accordingly, a low dislocation density is desired in
view of inhibiting deterioration. However, there are other
problems.
[0086] A substrate having high dislocation density is undesirable
because it causes current leakage. Fewer dislocations are desirable
because GaN, InGaN, or AlGaN thin films having a regular lattice
structure are formed in layers on the substrate. In addition, a
substrate having little bow and low cracking ratio is desirable
because semiconductor devices are fabricated thereon. Accordingly,
as a conductive substrate, a substrate having high conductivity,
little bow, low dislocation density, and low cracking ratio is
strongly desired.
[0087] The GaN substrates mentioned as the related art (Patent
Documents 1 to 10) have low resistivity and are n-type.
[0088] Patent Document 1 discloses that the resistivity is 0.005 to
0.08 .OMEGA.cm. Patent Document 2 discloses that the resistivity is
0.0035 to 0.0083 .OMEGA.cm. Patent Document 3 discloses that the
resistivity of the GaN substrate is 0.01 to 0.017 .OMEGA.cm.
[0089] In Patent Documents 1 to 3, it is assumed that vacancies of
the group V element form a donor level or an n-type dopant element
contained in the source gases is introduced because they do not
disclose that an n-type dopant is introduced.
[0090] Patent Document 4 does not specify resistivity. Because this
intends to form a low-resistivity n-type GaN substrate using
silicon as a dopant, it is assumed that the resistivity is lower
than those of Patent Documents 1 to 3. From the descriptions
thereof, it is assumed that the upper limit of the GaN crystals of
the related art is about 0.08 .OMEGA.cm and the lower limit thereof
is about 0.005 .OMEGA.cm.
[0091] ELO cannot sufficiently reduce dislocations. Facet growth,
proposed in Patent Documents 8 and 9, have the effect of reducing
dislocation density. Currently known methods for forming conductive
GaN include oxygen doping and silicon doping. For oxygen doping, as
in Patent Documents 6 and 7, water or oxygen may be mixed in a
source gas. These are safe substances. For silicon doping, as in
Patent Documents 4 and 5, silane (SiH.sub.4) gas must be supplied.
Silane gas is a hazardous gas and therefore should not be used in
large quantities. In addition, it is uncertain whether or not the
absorption of SiH.sub.4 gas has plane dependence. There is no
research as to whether or not silicon doping has anisotropy for the
c-plane and the m- or a-plane, or generally a facet plane
(hereinafter abbreviated to "f-plane"). If silicon has the same
plane orientation dependence as oxygen, the dosage of the n-type
impurity cannot be made uniform. However, if silicon and oxygen
have different plane dependence, the resistivity may be
complementarily made uniform.
[0092] Facet growth is effective in reducing dislocation density.
By causing dislocations to cluster into closed defect cluster
regions above the masking portions, the dislocation density can be
reduced in other portions. In addition, the substrate has little
bow and low cracking ratio because it has a rough surface.
[0093] Nevertheless, facet growth has some disadvantages. One of
the disadvantages is anisotropy in oxygen absorption during oxygen
doping. The use of facet growth for forming an oxygen-doped n-type
crystal results in significant plane orientation dependence in
doping efficiency. Patent Document 7 discloses that the efficiency
of oxygen doping is lowest in the c-plane and that the amount of
oxygen absorbed through the facets is 50 times or more that through
the c-plane. Facet growth portions and c-plane growth portions are
mixed in the crystal formed by facet growth. The oxygen
concentration is lower in the c-plane because it absorbs little
oxygen and is higher in the facets because the amount of oxygen
absorbed through the facets is 50 times or more that through the
c-plane. A crystal formed by facet growth has uneven oxygen
concentration because it includes c-plane portions. If devices are
fabricated using such crystals as substrates, the devices have
significant variations in conductivity.
[0094] If a crystal is formed by c-plane growth, rather than by
facet growth, it has high resistivity because little oxygen is
absorbed. In addition, the crystal formed by c-plane growth, in
which the crystal is grown while maintaining a flat surface, cracks
and splits off easily, whereas a crystal formed by facet growth
does not crack easily and is robust. Thus, an n-type substrate
having low cracking ratio, little bow, and uniform resistivity is
desired.
SUMMARY OF THE INVENTION
[0095] Accordingly, it is an object of the present invention to
provide an n-type GaN substrate having low cracking ratio, little
bow, and uniform resistivity. One aspect of the present invention
relates to a method for producing a conductive nitride
semiconductor substrate, comprising the steps of: preparing an
underlying substrate having a c-plane or a plane with three-fold
symmetry; forming, on the underlying substrate, masking portions
having a width or diameter of 10 to 100 .mu.m and periodically
repeated at a spacing of 250 to 10,000 .mu.m and an exposed portion
where the substrate is exposed; growing a nitride semiconductor
crystal having facets in a surface thereof on the underlying
substrate by hydride vapor phase epitaxy (HVPE) at a crystal growth
temperature of 1,040.degree. C. to 1,150.degree. C. while doping
the nitride semiconductor crystal with silicon and oxygen by
supplying a group III source gas, a group V source gas, a silicon
compound gas, and water or oxygen in a V/III ratio of 1 to 10 so
that low-dislocation-density single-crystal regions Z following the
facets and a c-plane growth region Y following a flat face are
formed above the exposed portion and crystal defect cluster regions
H are formed above the masking portions, the nitride semiconductor
crystal being doped with oxygen and silicon through the facets and
with silicon through a c-plane and having an HZYZHZYZ . . .
structure in an inner portion thereof; removing the underlying
substrate; and polishing the surface of the nitride semiconductor
crystal to form a free-standing conductive nitride semiconductor
crystal having a cracking ratio K of 1%.ltoreq.K.ltoreq.22%.
[0096] Another aspect of the present invention relates to a
conductive nitride semiconductor substrate comprising a bottom
portion, an inner portion, and a surface portion in order in a
crystal growth direction, the bottom portion and the inner portion
including crystal defect cluster regions H, low-dislocation-density
single-crystal regions Z, and a c-plane growth region Y
periodically arranged in the order of the crystal defect cluster
regions H, the low-dislocation-density single-crystal regions Z,
the c-plane growth region Y, and the low-dislocation-density
single-crystal regions Z in a direction perpendicular to the growth
direction, thereby forming an HZYZHZYZ . . . structure, the crystal
defect cluster regions H in the bottom portion and the inner
portion having a width or diameter of 10 to 100 .mu.m in a cross
section perpendicular to the growth direction, ZYZ portions defined
between the adjacent crystal defect cluster regions H having a
width of 250 to 10,000 .mu.m, the surface portion including the
c-plane growth region Y and not including the crystal defect
cluster regions H or the low-dislocation-density single-crystal
regions Z, the low-dislocation-density single-crystal regions Z and
the crystal defect cluster regions H being doped with silicon and
oxygen, the c-plane growth region Y being doped with silicon, the
conductive nitride semiconductor substrate having a thickness of
100 .mu.m or more, a diameter of 18 mm or more, a cracking ratio K
of 1%.ltoreq.K.ltoreq.22%, a radius of bow curvature U of 3.5
m.ltoreq.U.ltoreq.8 m, and a resistivity r of 0.0015
.OMEGA.cm.ltoreq.r.ltoreq.0.01 .OMEGA.cm.
BRIEF DESCRIPTION OF THE DRAWINGS
[0097] FIG. 1 is a plan view of an ELO mask formed on an underlying
substrate and including a large masking portion and numerous small
windows (exposed portions) repeated at a narrow pitch in the
masking portion.
[0098] FIGS. 2A to 2G are diagrams illustrating a process of
growing GaN in vapor phase on an underlying substrate on which an
ELO mask is formed.
[0099] FIG. 3 is a partial perspective view of a crystal formed by
random facet growth in which numerous facet pits of different sizes
are randomly formed in a surface of the crystal.
[0100] FIG. 4 is a perspective view of a facet pit formed by facet
growth in which facet pits are maintained to the end of the growth,
illustrating that dislocations propagate in a direction normal to
facets inside the facet pit because the growth direction is
parallel to the dislocation direction, reach the boundaries between
the facets, extend downward along the boundaries, and cluster at
the bottom of the pit.
[0101] FIG. 5 is a plan view of a facet pit formed by facet growth
in which facet pits are maintained to the end of the growth,
illustrating that dislocations propagate in a direction normal to
facets inside the facet pit because the growth direction is
parallel to the dislocation direction, reach the boundaries between
the facets, extend downward along the boundaries, and cluster at
the bottom of the pit.
[0102] FIG. 6 is a partial plan view of a dot mask formed on an
underlying substrate for facet growth in which facet pits are
maintained to the end of the growth and including a dot pattern of
numerous masking portions regularly arranged at a large spacing in
two orthogonal directions.
[0103] FIG. 7 is a perspective view of a GaN crystal formed by dot
facet growth in which the GaN crystal is grown in vapor phase on an
underlying substrate on which a dot mask is formed so as to form
facet pits whose bottoms are located above masking portions.
[0104] FIG. 8 is a plan view of a surface of a GaN crystal formed
by dot facet growth in which the GaN crystal is grown in vapor
phase on an underlying substrate on which a dot mask is formed so
as to form facet pits whose bottoms are located above masking
portions.
[0105] FIGS. 9A to 9F are longitudinal sectional views illustrating
the steps of a facet growth process by which a GaN crystal is grown
in vapor phase on an underlying substrate on which a dot mask is
formed so as to form facet pits whose bottoms are defined by
masking portions, the facet pits are made larger, and crystal
defect cluster regions H are formed above the masking portions.
[0106] FIG. 10 is a partial plan view of a stripe mask formed on an
underlying substrate for facet growth in which facets are
maintained to the end of the growth and including a parallel stripe
pattern of masking portions regularly arranged at a large spacing
in one direction.
[0107] FIG. 11 is a plan view of a GaN crystal formed by stripe
facet growth in which the GaN crystal is grown in vapor phase on an
underlying substrate on which a stripe mask is formed so as to form
a ridge-and-valley structure including valleys above masking
portions, flat top faces midway between the masking portions, and
inclined facets between the top faces and the valleys.
[0108] FIG. 12 is a perspective view of a GaN crystal formed by
stripe facet growth in which the GaN crystal is grown in vapor
phase on an underlying substrate on which a stripe mask is formed
so as to form a ridge-and-valley structure including valleys above
masking portions, flat top faces midway between the masking
portions, and inclined facets between the top faces and the
valleys.
[0109] FIG. 13 is a plan view of a GaN crystal formed by stripe
facet growth in which the GaN crystal is grown in vapor phase on an
underlying substrate on which a stripe mask is formed so as to form
a ridge-and-valley structure including valleys above masking
portions, sharp ridges midway between the masking portions, and
inclined facets between the sharp ridges and the valleys.
[0110] FIG. 14 is a perspective view of a GaN crystal formed by
stripe facet growth in which the GaN crystal is grown in vapor
phase on an underlying substrate on which a stripe mask is formed
so as to form a ridge-and-valley structure including valleys above
masking portions, sharp ridges midway between the masking portions,
and inclined facets between the sharp ridges and the valleys.
[0111] FIGS. 15A to 15F are sectional views illustrating the steps
of a process by which GaN is grown in vapor phase on an underlying
substrate on which a stripe mask is formed so that crystals having
the c-plane and facets are grown above exposed portions, because
the growth proceeds initially in the exposed portions, and so that
low crystal defect cluster regions H are formed above masking
portions, thus forming a parallel ridge-and-valley structure
including valleys directly above the masking portions and ridges
midway between the masking portions.
[0112] FIGS. 16A and 16B are sectional views illustrating the steps
of a process by which the crystal grown by the stripe mask facet
growth process in FIGS. 15A to 15F is further grown so that it has
higher ridges and larger valleys.
[0113] FIG. 17 is a sectional view of a GaN crystal, proposed in
Patent Document 7 (Japanese Patent No. 3826825), that is grown in
the c-axis direction while forming facets so that it can be heavily
doped with oxygen because of the selectivity that oxygen is
absorbed into the crystal negligibly through the c-plane and in
large amounts through the facets.
[0114] FIG. 18 is a sectional view of a GaN crystal, proposed in
Patent Document 7 (Japanese Patent No. 3826825), that is grown on a
crystal having a non-c-plane surface prepared in advance so that it
can be heavily doped with oxygen because of the selectivity that
oxygen is absorbed into the crystal negligibly through the c-plane
and in large amounts through the facets.
[0115] FIG. 19 is a sectional view of an HVPE furnace for producing
a nitride semiconductor crystal according to the present
invention.
[0116] FIG. 20 is a sectional view showing the profile of a type II
nitride semiconductor crystal, having a ridge-and-valley structure,
that is produced by a method according to the present
invention.
[0117] FIG. 21 is a sectional view showing the profile of a type I
nitride semiconductor crystal, having a flat surface, that is
produced by a method according to the present invention.
[0118] FIG. 22 is a graph showing the growth temperatures and the
V/III ratios b of examples of vapor deposition processes disclosed
in the related art, namely, Patent Documents 1 to 11, and examples
of vapor deposition processes according to the present invention in
a coordinate system, where the horizontal axis indicates the growth
temperature (.degree. C.) and the vertical axis indicates the V/III
ratio b in a logarithmic scale.
[0119] FIG. 23 is a graph showing the radii of bow curvature (m) of
invention examples and comparative examples, namely, Samples 1 to
45, along the horizontal axis and the cracking ratios (%) thereof
along the vertical axis, where the numbers are the sample numbers,
the white circles indicate type I, the white triangles indicate
type II, and the multiplication signs indicate the comparative
examples, which are not known examples.
[0120] FIG. 24 is a sectional view showing the profile of a nitride
semiconductor crystal of a mixture of type I and type II, having
flat faces and facets, that is produced by a method according to
the present invention.
[0121] FIG. 25 is a plan view showing the width s and the spacing w
of a stripe mask used in a method according to the present
invention in which a nitride semiconductor is grown in vapor phase
on an underlying substrate on which a stripe mask including
parallel masking portions is formed.
[0122] FIG. 26 is a plan view showing the diameter s and the
spacing w of a dot mask used in a method according to the present
invention in which a nitride semiconductor is grown in vapor phase
on an underlying substrate on which a dot mask including plurality
of dot masking portions arranged in two orthogonal directions is
formed.
[0123] FIG. 27 is a graph showing the silicon concentrations
(cm.sup.-3) in the c-plane of the examples of GaN crystals grown in
vapor phase disclosed herein, namely, Samples 1 to 45, along the
horizontal axis in a logarithmic scale and the resistivities
(.OMEGA.cm) thereof along the vertical axis in a logarithmic scale,
where the numbers are the sample numbers, the white circles
indicate type I, the white triangles indicate type II, and the
multiplication signs indicate the comparative examples.
[0124] FIG. 28 is a graph showing the silicon concentrations
(cm.sup.-3) in the f-plane of the examples of type II GaN crystals
grown in vapor phase disclosed herein, namely, Samples 25 to 39,
along the horizontal axis and the oxygen concentrations (cm.sup.-3)
thereof in the f-plane along the vertical axis, where the white
triangles indicate the points of the samples and the numbers are
the sample numbers.
[0125] FIG. 29 is a graph showing the silicon concentrations
(cm.sup.-3) in the c-plane of the examples of type II GaN crystals
grown in vapor phase disclosed herein, namely, Samples 25 to 39,
along the horizontal axis and the silicon concentrations
(cm.sup.-3) thereof in the f-plane along the vertical axis, where
the white triangles indicate the points of the samples and the
numbers are the sample numbers.
[0126] FIG. 30 is a graph showing the oxygen concentrations
(cm.sup.-3) in the f-plane of the examples of type II GaN crystals
grown in vapor phase disclosed herein, namely, Samples 25 to 39,
and Comparative Examples 44 and 45 along the horizontal axis in a
logarithmic scale and the oxygen concentrations (cm.sup.-3) thereof
in the c-plane along the vertical axis in a logarithmic scale,
where the numbers are the sample numbers, the white triangles
indicate type II, and the multiplication signs indicate the
comparative examples.
[0127] FIG. 31 is a graph showing the oxygen concentrations
(cm.sup.-3) in the f-plane of the examples of type II GaN crystals
grown in vapor phase disclosed herein, namely, Samples 25 to 39,
along the horizontal axis in a logarithmic scale and the
resistivities (.OMEGA.cm) thereof along the vertical axis in a
logarithmic scale, where the numbers are the sample numbers and the
white triangles indicate and the points of the samples.
[0128] FIG. 32 is a graph showing the sums of the silicon
concentrations in the c-plane and the oxygen concentrations in the
f-plane of the examples of type II GaN crystals disclosed herein,
namely, Samples 25 to 39, along the horizontal axis in a
logarithmic scale and the resistivities (.OMEGA.cm) thereof along
the vertical axis in a logarithmic scale, where the numbers are the
sample numbers and the white triangles indicate and the points of
the samples.
[0129] FIG. 33 is a partial enlargement of FIG. 23.
[0130] FIG. 34 is a partial enlargement of FIG. 27.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0131] In a method for producing an n-type nitride semiconductor
substrate according to the present invention, a silicon- and
oxygen-doped conductive nitride semiconductor crystal substrate
having a thickness of 100 .mu.m or more and having little bow, low
cracking ratio, low resistivity, and few local variations in
resistivity is produced by forming a dot mask or a stripe mask on
an underlying substrate, growing a thick nitride semiconductor
crystal on the masked underlying substrate by HVPE at a substrate
temperature of 1,040.degree. C. to 1,150.degree. C. while doping
facets with oxygen and silicon and doping c-plane growth regions
mainly with silicon by supplying ammonia gas, a group III source
gas, a silicon (Si) compound gas, and oxygen (O) in a ratio b of
the group V source gas to the group III source gas of 1 to 10, and
removing the underlying substrate.
[0132] Unlike the related art, two dopants are used, rather than
one dopant, and the facets and the c-plane are doped mainly with
different dopants so that the resistivity is complementarily made
uniform.
[0133] In the related art, there is no example in which GaN is
grown at such a low V/III ratio b, namely, 1 to 10, and such a high
temperature, namely, 1,040.degree. C. to 1,150.degree. C. As shown
in FIG. 22, the V/III ratio b is higher than 10 in many GaN growth
methods (Patent Documents 1, 4, 7, 8, 10 (in part), and 11).
Although GaN is grown in a V/III ratio b of lower than 10 in some
documents (Patent Documents 2, 3, 9(in part), and 10 (in part)),
the temperature is low, namely, below 1,040.degree. C.
[0134] In a V/III ratio b of 1 to 10 and a temperature range of
1,040.degree. C. to 1,070.degree. C., facets appear noticeably,
thus forming sharply inclined faces. A crystal having such a rough
surface is referred to as type II. This type is shown in FIG. 20.
Because the crystal is formed by facet growth on an underlying
substrate U on which masking portions M are formed at a large
pitch, crystal defect cluster regions H are formed above the
masking portions M, and low-dislocation-density single-crystal
regions Z are formed beside the crystal defect cluster regions H so
as to follow facets F. The facets F remain to the end of the
growth. In some cases, the facets F may occupy the entire surface.
In other cases, the c-plane may appear as if the facets F were
partially cut (broken lines) and be followed by c-plane growth
regions Y. Depending on the proportion of the facets F, the c-plane
growth regions Y may be absent between the regions Z, or may be
partially present.
[0135] The present invention employs facet growth because the wide
masking portions M are periodically arranged on the underlying
substrate U and a nitride semiconductor is grown thereon.
Accordingly, numerous facets F are formed so as to extend upward
from the masking portions M. The facet growth proceeds as shown in
FIGS. 9A to 9F and 15A to 15F. The crystal defect cluster regions H
are formed above the masking portions M, and the
low-dislocation-density single-crystal regions Z and the c-plane
growth regions Y are formed above exposed portions E. The
low-dislocation-density single-crystal regions Z are formed below
the facets F, and the c-plane growth regions Y are formed below the
c-plane. For type II, that is, a crystal having a surface with
facets, it grows while the facets F remain predominant. For type I,
that is, a crystal having a flat surface, the c-plane becomes
predominant soon because the temperature is high, finally occupying
the entire surface. In either case, the crystal mainly absorbs
oxygen until sometime because of the facet growth.
[0136] The width (diameter) of the masking portions M is denoted by
s, the spacing between the masking portions M is denoted by w, and
the pitch of the masking portions M is denoted by p. The width s is
10 to 100 .mu.m, and the spacing w is 250 to 10,000 .mu.m. The
masking portions M are regularly formed on the underlying substrate
U. Because of the regularity, s, w, and p can be defined. Typical
examples are an isolated dot pattern of masking portions (dot mask,
as shown in FIG. 26) and a parallel stripe pattern of masking
portions (stripe mask, as shown in FIG. 25). Other patterns having
regularity can also be used.
[0137] In a V/III ratio b of 1 to 10 and a higher temperature
range, namely, 1,090.degree. C. to 1,150.degree. C., the surface
finally becomes a flat c-plane surface. Such a crystal having less
roughness is referred to as type I. FIG. 21 shows a type I crystal.
Even a type I crystal is grown by facet growth until sometime
because the mask is used. The growth process changes to c-plane
growth near the final stage of the growth. Accordingly, the crystal
defect cluster regions H are formed above the masking portions M,
the low-dislocation-density single-crystal regions Z are formed
beside the crystal defect cluster regions H, and the c-plane growth
regions Y are formed midway between the masking portions M.
Although the top surface is the c-plane, this is facet growth
because the crystal is grown after the masking portions M are
formed at a large pitch on the underlying substrate U. The growth
process changes to c-plane growth after the crystal grows to a
sufficient thickness. Thus, type I in the present invention differs
from c-plane growth in the related art. The width (diameter) of the
masking portions M is denoted by s, the spacing between the masking
portions M is denoted by w, and the pitch of the masking portions M
is denoted by p. The width s is 10 to 100 .mu.m, and the spacing w
is 250 to 10,000 .mu.m. The masking portions M are regularly formed
on the underlying substrate U. Because of the regularity, s, w, and
p can be defined. Typical examples are an isolated dot pattern of
masking portions (dot mask, as shown in FIG. 26) and a parallel
stripe pattern of masking portions (stripe mask, as shown in FIG.
25). Other patterns having regularity can also be used.
[0138] In a V/III ratio b of 1 to 10 and the middle temperature
range, namely, 1,070.degree. C. to 1,090.degree. C., a mixed type
having a partially cut mountain shape is formed. FIG. 24 shows a
sectional view of a mixed-type crystal. The crystal is grown by
facet growth because it is grown after the masking portions M are
formed at a large pitch on the underlying substrate U. The portions
directly above the masking portions M are the crystal defect
cluster regions H. The portions following the facets F beside the
crystal defect cluster regions H above the exposed portions E are
the low-dislocation-density single-crystal regions Z. The portions
under the c-plane between the regions Z are grown by c-plane
growth. C-plane growth becomes predominant after the crystal grows
to a sufficient thickness. The portions formed by c-plane growth
are the c-plane growth regions Y. The facets F remain in the
surface to the end. The width (diameter) of the masking portions M
is denoted by s, the spacing between the masking portions M is
denoted by w, and the pitch of the masking portions M is denoted by
p. The width s is 10 to 100 .mu.m, and the spacing w is 250 to
10,000 .mu.m. The masking portions M are regularly formed on the
underlying substrate U. Because of the regularity, s, w, and p can
be defined. Typical examples are an isolated dot pattern of masking
portions (dot mask, as shown in FIG. 26) and a parallel stripe
pattern of masking portions (stripe mask, as shown in FIG. 25).
Other patterns having regularity can also be used.
[0139] In any case, the surface is finally ground and polished into
a flat mirror surface. Thus, the mirror wafer no longer has the
ridge-and-valley structure, that is, the structure immediately
after the crystal growth. The mirror wafer has a thickness of 100
.mu.m or more for use as a free-standing substrate. Any larger
thickness is permitted. In some cases, the thickness may be 300 to
10,000 .mu.m. A thick wafer is cut into a plurality of wafers in a
direction parallel to the plane thereof. The wafer maintains its
original HZYZHZYZ . . . structure and therefore has anisotropy in
the lateral direction. Although the structure is transparent and
invisible to the naked eye, it can be recognized by cathode
luminescence (CL) or fluorescence microscopy.
[0140] Another characteristic of the present invention is double
doping with silicon and oxygen. For type II and the mixed type, the
c-plane and the f-plane (which refers to facets) are mixed in the
surface. Even for type I, the c-plane and the f-plane are mixed
until sometime during the growth. Oxygen has the plane orientation
dependence that the f-plane is more doped with oxygen and the
c-plane is less doped with oxygen. If silicon has the opposite
plane orientation dependence, that is, if the c-plane is more doped
with silicon and the f-plane is less doped with silicon, double
doping with silicon and oxygen allows the amounts of n-type dopants
absorbed into the c-plane and the f-plane to be complementary. In
this case, however, it should be examined whether double doping
with silicon and oxygen results in interference between the two
dopants (interference effect) and, if oxygen and silicon do not
interfere with each other and independently release n-type
carriers, whether oxygen doping and silicon doping can be
considered as being equal (dominance) since the amounts of oxygen
and silicon required may differ because of the difference in
activation rate. In addition, the ratio of the c-plane to the
f-plane (C/F ratio) varies depending on the method for crystal
growth. The ratio of the c-plane to the f-plane varies not only as
a whole, but also in the growth direction (height direction). If
the ratio of the c-plane to the f-plane varies, the resistivity
should vary as a whole. Thus, various factors must be clarified to
enable a design for achieving the intended resistivity by double
doping. Double doping with n-type dopants is not described in
Patent Documents 1 to 11 mentioned above. According to research by
the present inventors, no document discusses double doping.
[0141] As a result of many experiments, the present inventors have
found that silicon has no plane orientation dependence, that is,
the c-plane and the f-plane are equally doped with silicon. The
amount of oxygen absorbed differs considerably between the c-plane
and the f-plane, and the ratio is larger than 50 times, which is
the ratio pointed out in Patent Document 7.
[0142] If a nitride semiconductor crystal is grown in an atmosphere
containing both silicon and oxygen by facet growth, in which the
c-plane and the f-plane coexist, the n-type dopant concentration
can be made uniform in the c-plane and the f-plane, thus reducing
local variations in resistivity. In the present invention, as
described above, the V/III ratio b is low, namely, 1 to 10, and the
substrate temperature is high, namely, 1,040.degree. C. to
1,150.degree. C. For type II (see FIG. 20), in which facets are
predominant and spread over substantially the entire surface during
the growth, oxygen serves as the major dopant. Oxygen can be
introduced into the atmosphere by adding water or oxygen itself to
ammonia, hydrogen, or HCl gas. The c-plane, which is slightly
present, is supplied with n-type carriers by silicon doping.
[0143] Even for type I (see FIG. 21), in which the c-plane spreads
over the surface, the crystal is considerably doped with oxygen
because it grows while maintaining facets until sometime. As the
end of the growth approaches, the c-plane becomes dominant, and
accordingly less oxygen is absorbed. Instead, the crystal is more
doped with silicon.
[0144] For the mixed type (see FIG. 24), in which facet growth
continues to the end, as in type II, oxygen is sufficiently
absorbed through facets. The c-plane is doped with silicon.
[0145] The underlying substrate may be any substrate on which a
nitride semiconductor grows in the c-axis direction, such as a
(111) GaAs wafer, a c-plane sapphire wafer, a c-plane SiC wafer, or
a c-plane GaN wafer. The mask may be formed of SiO.sub.2, SiN, MN,
or a metal film.
[0146] FIG. 19 is a schematic longitudinal sectional view of an
HVPE furnace. A heater 3 is disposed outside a vertically oriented
reactor 2. The heater 3 extends in the vertical direction and is
divided into several segments so that any temperature distribution
can be formed in the vertical direction. The reactor 2 has a hot
wall. A gallium reservoir 4 containing molten gallium is disposed
in the upper middle portion of the reactor 2. A susceptor 5 is
disposed in the lower portion of the reactor 2 and is supported by
a rotating shaft so that it can be rotated and elevated. An
underlying substrate 6 is placed on the susceptor 5. A first source
gas supply pipe 7 supplies hydrogen (H.sub.2) gas and hydrogen
chloride (HCl) gas to the gallium reservoir 4. HCl and gallium
react to produce GaCl gas. The GaCl gas then flows downward. A
second source gas supply pipe 8 supplies hydrogen (H.sub.2) gas and
ammonia (NH.sub.3) gas to the top of the underlying substrate 6.
GaCl and NH.sub.3 react to produce GaN. A third source gas supply
pipe 10 supplies a mixture of a silicon (Si) compound gas (such as
silane (SiH.sub.4)) and a carrier gas (H.sub.2) to the reactor 2.
To add oxygen, water or oxygen itself is mixed in the source gas
(H.sub.2+HCl) from the first source gas supply pipe 7, the source
gas (NH.sub.3+H.sub.2) from the second source gas supply pipe 8, or
the source gas (SiH.sub.4+H.sub.2) from the third source gas supply
pipe 10. The GaN being synthesized is doubly doped with silicon and
oxygen. After the reaction, exhaust gas and unreacted gas are
discharged from a gas exhaust pipe 9.
[0147] Silicon is supplied using a source material such as silicon
chloride, silicon fluoride, or silicon hydride (SiH.sub.4). The
source material, which is gaseous, is blown into the reactor
through the upper gas channel in vapor phase. The source material
is then thermally decomposed and absorbed into the crystal. In the
crystal, oxygen and silicon coexist as n-type dopants.
[0148] The nitride semiconductor substrate, thus produced,
according to the present invention has a cracking ratio K of 22% or
less. The lower limit of the cracking ratio K is about 1%
(0.01.ltoreq.K.ltoreq.0.22). For type II, the cracking ratio is 18%
or less (K.ltoreq.0.18 (type II)). Patent Documents 2 and 3
disclose that free-standing GaN crystals having flat surfaces were
all cracked during polishing. That is, all the GaN substrates
having flat surfaces in Patent Documents 2 and 3 have a cracking
ratio K of 100%.
[0149] The radius of bow curvature U of the nitride semiconductor
substrate according to the present invention after the removal of
the underlying substrate is 3.5 to 7 m (3.5 m.ltoreq.U.ltoreq.7 m).
For type II, which has a surface with facets, the radius of bow
curvature U is 4.2 m.ltoreq.U.ltoreq.7 m. According to Patent
Documents 2 and 3, in which ELO is used, unpolished crystals having
flat surfaces had a radius of curvature of 0.054 to 0.167 m. That
is, these crystals had extremely large bow. In addition, four
unpolished crystals having rough surfaces had a radius of curvature
of 1 to 2.6 m, and one unpolished crystal having a rough surface
had a radius of curvature of 10 m. Because the bow is increased
after polishing, after the unpolished sample having a radius of
curvature of 10 m was polished, the radius of bow curvature U was
decreased to 3.4 m. That is, the substrates having rough surfaces
in Patent Documents 2 and 3 had a radius of curvature U of 3.4 m or
less. The cracking ratio of this sample is not disclosed in Patent
Documents 2 and 3. The substrate temperature is 1,020.degree. C.,
which is lower than that of the present invention. The growth
process is not facet growth, but c-plane growth. The resistivity is
0.05 .OMEGA.cm. The type of dopant is not disclosed in Patent
Documents 2 and 3. In some documents, the bow is expressed as the
radius of curvature U, although in other cases it is expressed as
the height h of the center of a wafer placed on a flat surface so
as to be convex. The height h of the center of a wafer having a
diameter D can be converted to the radius of curvature U on the
basis of the relationship U=D.sup.2/8 h. The radius of curvature U
in the present invention, namely, 3.5 to 7 m, is equivalent to a
height h of 89 to 45 .mu.m for a diameter of two inches (50
mm).
[0150] The nitride semiconductor substrate according to the present
invention has a silicon concentration of 5.times.10.sup.19
cm.sup.-3.gtoreq.[Si].gtoreq.1.times.10.sup.17 cm.sup.-3 and an
oxygen concentration of 1.times.10.sup.19
cm.sup.-3.gtoreq.[O].gtoreq.1.times.10.sup.15 cm.sup.-3, where an
oxygen concentration of 1.times.10.sup.15 cm.sup.-3 is the
detection limit of oxygen, and a lower concentration is possible in
practice. This will be described later.
[0151] The resistivity r of the nitride semiconductor substrate
according to the present invention is 1.times.10.sup.-2 .OMEGA.cm
or less. In the lower range of resistivity r, a resistivity r of
1.5 to 2.times.10.sup.-3 .OMEGA.cm is also achieved. That is, the
resistivity r of the crystal provided by the present invention is
0.0015 .OMEGA.cm.ltoreq.r.ltoreq.0.01 .OMEGA.cm, which is lower
than the resistivity achieved in Patent Document 1, namely, 0.005
.OMEGA.cm.ltoreq.r.ltoreq.0.08 .OMEGA.cm. Thus, a superior nitride
semiconductor crystal having low resistivity, low cracking ratio,
and little bow can be achieved as an n-type substrate.
[0152] The mask is formed of, for example, SiO.sub.2, SiON, SiN,
AlN, or Al.sub.2O.sub.3. The mask may be formed in any periodic
pattern having small masking portions and a large exposed portion.
Although a stripe mask (parallel stripes) and a dot mask (isolated
staggered distribution) will be described here, a mask having
another periodic pattern may also be formed. For a stripe mask, the
width s of the masking portions is 10 to 100 .mu.m, the spacing w
between the masking portions is 250 to 10,000 .mu.m, and the pitch
p (p=s+w) is 260 to 10,100 .mu.m.
[0153] For a dot mask, the diameter s of the masking portions is 10
to 100 .mu.m, the spacing w between the masking portions is 250 to
10,000 .mu.m, and the pitch p is 260 to 10,100 .mu.m.
[0154] At a V/III ratio b of 1 to 10 and a substrate temperature of
1,040.degree. C. to 1,080.degree. C., a ridge-shaped crystal (type
II) grows that have facets F lower above the masking portions and
higher above the exposed portions (see FIG. 20). This is facet
growth because the crystal is lower above the masking portions M
and is higher above the exposed portions E. The facets F (simply
referred to as "f-plane") considerably absorb oxygen. The facets F
are doped with both oxygen and silicon. The facet growth continues
to the end. The portions above the masking portions M are the
crystal defect cluster regions H, and the portions above the
exposed portions E, but near the masking portions M, and directly
below the facets F are the low-dislocation-density single-crystal
regions Z. The amount of oxygen supplied is defined as 0(t), and
the amount of silicon supplied is defined as Si(t). The amounts of
oxygen and silicon supplied may be constant during the growth, that
is, O(t)=C.sub.2 and Si(t)=C.sub.1, respectively (where C.sub.1 and
C.sub.2 are constants).
[0155] FIG. 20 shows an ideal type (type II) composed only of
ridges to contrast it with FIG. 21. The ideal type is a repetition
of ZHZHZH . . . . The ideal type is achieved with a stripe mask
only in special cases. The ideal type is not achieved with a dot
mask because of its geometric limitations; instead, a repetition of
ZHZYZHZYZH . . . is achieved. In practice, for either a dot mask or
a stripe mask, the c-plane often appears midway between the masking
portions M (indicated by the broken lines), and the c-plane growth
regions Y are formed therebelow. Little oxygen is absorbed into the
c-plane, and silicon is instead absorbed. That is, silicon is
necessary for c-plane doping. In the initial stage of the growth,
the masking portions M and, the exposed portion E are influential,
and the facets F are predominant. In the final stage of the growth,
the difference between the masking portions M and the exposed
portion E is not influential, and the c-plane tends to appear
partially. Accordingly, it is possible to initially supply no or
only a slight amount of silicon-containing gas (for example,
SiH.sub.4 gas) and gradually increase the amount of
silicon-containing gas depending on the appearance of the c-plane.
For example, the amount of silicon-containing gas supplied Si(t)
may be determined on the basis of the equation
Si(t)=C.sub.3t+C.sub.4t.sup.2+ . . . (where C.sub.3 and C.sub.4 are
positive constants and t is time). This allows the donor
concentration to be made more uniform in the thickness
direction.
[0156] Type II, in which the facets F (f-plane) are maintained to
the end, is most preferable in view of low cracking ratio, small
bow, robustness, low dislocation density, and ease of oxygen
doping. However, the c-plane may appear somewhere during the
growth. If only oxygen doping is performed, the donor density
(n-type dopant) is lower in those portions. In the present
invention, the c-plane has a considerable donor density because the
crystal is also doped with silicon. Thus, the donor density can be
made uniform by doping the f-plane with oxygen and silicon and
doping the c-plane with silicon. In addition, most of the donor is
oxygen, and the dosage of silicon is low. This ensures safety
because SiH.sub.4, which is hazardous, does not have to be used in
large quantities. A type II crystal is a repetition of ZHZYZHZYZH .
. . as viewed in the lateral direction. This structure results in
stress relaxation because different types of regions, namely, the
regions H and Z or the regions H, Z, and Y, are mixed. This reduces
the internal stress and therefore reduces the cracking ratio.
[0157] At higher substrate temperatures, namely, 1,080.degree. C.
to 1,150.degree. C., a crystal having a surface of constant height
(type I) grows I (see FIG. 21). For type I, the surface is a
substantially flat c-plane surface. In practice, the portions above
the masking portions M may be slightly depressed. The c-plane is
doped with silicon as a donor, although not all of the donor is
silicon; oxygen is important. A considerable proportion of the
donor is oxygen. Even type I is initially grown by facet growth
because the facets F are formed and grown as the growth starts from
the exposed portions E. The crystal defect cluster regions H are
formed above the masking portions M, and the
low-dislocation-density single-crystal regions Z and the c-plane
growth regions Y are formed above the exposed portions E. Because
the temperature is high, the growth process becomes closer to
c-plane growth as the end of the growth approaches. The portions
above the masking portions M are the crystal defect cluster regions
H, and the portions above the exposed portion E are a mixture of
the low-dislocation-density single-crystal regions Z and the
c-plane growth regions Y. The surface is the c-plane. This
structure results in stress relaxation because different types of
regions alternate (HZYZHZYZ . . . ).
[0158] Type I can absorb a large amount of oxygen because it is
initially grown by facet growth and has numerous facets F, and also
absorb silicon through the f-plane because silicon has no
selectivity. The inner portion of the crystal is sufficiently doped
with oxygen. The crystal is simultaneously doped with oxygen and
silicon through the f-plane. As the end of the growth approaches,
however, the facets F are decreased, and the growth process becomes
closer to c-plane growth. Less oxygen is absorbed because the
facets F are decreased, and more silicon is absorbed because the
c-plane is increased. For type I, the effect of silicon doping
becomes significant at the end of the growth, when silicon serves
as a complementary dopant. That is, more silicon is contained in
the surface, and more oxygen is contained in the inner portion.
[0159] It is also possible to introduce silicon as a dopant from
the beginning and maintain a constant amount of silicon supplied
(Si(t)=C.sub.1). In this case, the f-plane is simultaneously doped
with oxygen and silicon in the initial facet growth stage. As the
end of the growth approaches, the c-plane becomes predominant, and
the crystal is doped only with silicon. That is, whereas the rate
at which silicon is absorbed remains constant, the rate at which
oxygen is absorbed decreases. The donor density then varies in the
thickness direction. As a result, the donor density is lower in the
surface, and accordingly the resistivity is higher in the
surface.
[0160] Because facet growth occurs initially and becomes closer to
c-plane growth as the end of the growth approaches, the amount of
silicon supplied may be changed with time. That is, it is possible
to initially supply no silicon-containing gas (for example,
SiH.sub.4 gas), gradually increase the amount of silicon-containing
gas supplied, and maximize the amount of silicon-containing gas
supplied as the end of the growth approaches, as represented by the
equation Si(t)=C.sub.3t+C.sub.4t.sup.2+ . . . (where C.sub.3 and
C.sub.4 are positive constants and t is time). In this case, oxygen
and silicon are absorbed through the f-plane in the initial and
middle stages, when the f-plane is predominant, and silicon is
absorbed through the c-plane in the final stage. This allows the
donor (n-type dopant) concentration to be uniform in the thickness
direction.
[0161] In resistivity measurement, silicon doping is influential
because the measurement is carried out between two points in the
surface. However, if devices are fabricated using the crystal as an
n-type substrate, the oxygen concentration is influential because a
current flows perpendicularly. The resistivity is the average of
local variations in the lateral direction because it is measured
between two separate points. The resistivity in the perpendicular
direction differs from that in the lateral direction. For type II,
if the resistivity is measured on the surface, oxygen doping and
silicon doping are both influential; on the other hand, for type I,
in which the surface is the c-plane, the portions doped with
silicon contribute greatly to resistivity. Accordingly, for type I,
the conductivity is increased (the resistivity is decreased)
substantially in proportion to the dosage of silicon. That is, for
type I, the smaller the dosage of silicon is, the higher the
surface resistivity is. However, this applies only to the surface;
the conductivity is high in the perpendicular direction because the
inner portion of the crystal is doped with oxygen.
[0162] Even for type I, the internal stress can be relaxed because
the inner portion of the crystal has the HZYZHZYZ . . . structure.
Thus, the cracking ratio can be reduced.
[0163] To form type I, a higher temperature and a lower V/III ratio
b are desired. Specifically, a temperature of 1,080.degree. C. to
1,150.degree. C. and a V/III ratio b of 1 to 10 are desired. In
addition, type I can be more reliably formed if the temperature is
1,090.degree. C. to 1,150.degree. C. and the V/III ratio b is about
1 to 5.
[0164] At a V/III ratio b of 1 to 10 and a substrate temperature
around 1,080.degree. C. (1,070.degree. C. to 1,090.degree. C.), a
mixture of type I and type II, that is, a crystal having
trapezoidal tops, is formed (see FIG. 24). This crystal grows
initially by facet growth. The crystal growth starts from the
exposed portions E, and the facets F are formed at the edges of the
exposed portions E. The growth starts later on the masking portions
M. The low-dislocation-density single-crystal regions Z and the
c-plane growth regions Y are formed above the exposed portions E.
The crystal defect cluster regions H are formed above the masking
portions M. Because this is facet growth, oxygen is absorbed
through the facets F (f-plane). Silicon is also absorbed through
the facets F. That is, the f-plane is simultaneously doped with
silicon and oxygen. Although the crystal defect cluster regions H
are formed above the masking portions M and the growth process
changes to c-plane growth as the end of the growth approaches, the
facets F remain to the end. The c-plane is doped with silicon.
Thus, the dopant distribution becomes more uniform. The crystal has
the HZYZHZYZ . . . structure, which reduces the internal stress and
therefore reduces the cracking ratio.
[0165] Although the sectional views of the three types, namely,
type II, type I, and the mixed type, are shown (FIGS. 20, 21, and
24, respectively), phase transition does not occur such that the
cross-sectional shape changes suddenly at a certain temperature; it
changes continuously with the temperature and the V/III ratio b. At
a temperature of 1,090.degree. C. to 1,150.degree. C. and a V/III
ratio b of 1 to 3, the ideal flat type shown in FIG. 21 is formed.
As the temperature is decreased and the V/III ratio b is increased,
the type changes gradually from the flat type in FIG. 21 to the
ridge shape in FIG. 20.
[0166] A substrate temperature of 1,050.degree. C. to 1,150.degree.
C. is relatively high as the growth temperature for vapor
deposition of a nitride semiconductor. The growth of type I
suggests that a crystal having a flat surface can be finally formed
even on large masking portions if the temperature is increased.
[0167] A V/III ratio b of 1 to 10 is extremely low and is close to
the lower limit in the vapor deposition of a nitride semiconductor.
Growing a silicon- and oxygen-doped nitride semiconductor at a low
V/III ratio b and a high growth temperature is the idea of the
present invention.
[0168] By double doping with silicon and oxygen, silicon can be
absorbed into the c-plane to form a highly uniform donor
concentration distribution together with oxygen absorbed into the
f-plane, thus achieving a conductive nitride semiconductor
substrate having a resistivity r of 10.sup.-2 .OMEGA.cm or less.
The lower limit of the resistivity r is 0.0015 .OMEGA.cm. That is,
the range of resistivity r of the substrate of the present
invention is 0.0015 .OMEGA.cm.ltoreq.r.ltoreq.0.01 .OMEGA.cm.
[0169] Because a crystal is grown on an underlying substrate on
which a mask having a large repetition pitch is formed, a structure
including different types of regions, namely, the crystal defect
cluster regions H, the low-dislocation-density single-crystal
regions Z, and the c-plane growth regions Y, is formed in the inner
portion. That is, a structure in which different phases are
sequentially arranged, namely, the ZYZHZYZ . . . structure, is
formed. This structure relaxes the internal stress, thus providing
a crystal having little bow. The radius of bow curvature U can be
controlled to 3.5 m.ltoreq.U.ltoreq.8 m.
[0170] Because a crystal is grown on an underlying substrate on
which a mask having a large repetition pitch is formed, a structure
including different types of regions, namely, the crystal defect
cluster regions H, the low-dislocation-density single-crystal
regions Z, and the c-plane growth regions Y, is formed in the inner
portion. This structure relaxes the internal stress, thus providing
a crystal having low cracking ratio. The cracking ratio K can be
controlled to 1%.ltoreq.K.ltoreq.22%.
[0171] In the facet growth proposed in Patent Documents 8, 9, and
10, a mask for defining a large exposed portion is formed on an
underlying substrate to concentrate crystal defects above the
masking portions, thereby reducing dislocations in the surrounding
regions (Z and Y). This is intended to reduce dislocations.
[0172] If a crystal for use as an n-type substrate is grown, it is
desirable that the crystal have low dislocation density because
dislocations may be increased after a high-density current flows
through the n-type substrate. A direct advantage of facet growth is
to reduce dislocation density, but there is more advantage
thereof.
[0173] In the facet growth proposed in Patent Documents 8, 9, and
10, different regions H, Z, and Y formed in the crystal relax the
stress. It turned out that this also reduces bow and inhibits
cracking. The c-plane growth in Patent Documents 1, 2, and 3 has
little effect of stress relaxation because it forms the same
crystal region. In Patent Documents 1, 2, and 3, crystals having a
flat surface have a radius of bow curvature of several tens of
centimeters and cannot be polished because the cracking ratio is
100%. Some crystals having a rough surface have a radius of bow
curvature of about 1 m and can be polished, but are impractical
because the cracking ratio is high.
[0174] Accordingly, the present invention employs facet growth to
form a GaN crystal doped with an n-type impurity. In some cases, as
in Patent Document 8, facet growth uses no mask, whereas in other
cases, as in Patent Documents 9 and 10, a mask is formed on an
underlying substrate to forcedly form facets from the edges of the
masking portions, thereby designating the positions where the
regions H, Z, and Y are formed. In this case, facets are inevitably
formed, and if the facets are maintained to the end without being
buried, dislocations cluster into the portions above the masking
portions to form the crystal defect cluster regions H above the
masking portions, thus reducing the dislocation density in other
portions.
[0175] If a crystal is grown by facet growth using a mask having a
large pitch for defining a large exposed portion, as in Patent
Documents 9 and 10, a structure in which the crystal defect cluster
regions H, which contain clusters of detects, and the
low-dislocation-density single-crystal regions Z and the c-plane
growth regions Y, which contain few defects, alternate can be
formed, thus relaxing the internal stress.
[0176] It turned out that facet growth using a mask having a large
pitch for defining a large exposed portion provides the
advantageous effect of reducing dislocation density, reducing bow,
and inhibiting cracking.
[0177] To produce a highly conductive GaN crystal, it must be
heavily doped with an n-type impurity. If a single-crystal
structure is heavily doped with an impurity, a strong internal
stress occurs therein, thus increasing the bow, making the crystal
susceptible to cracking, and increasing dislocations. By facet
growth, the HZYZH . . . complex structure can be formed, thereby
reducing the internal stress resulting from the high dosage of
impurity.
[0178] Facet growth is expected to be effective for forming an
n-type conductive crystal. Facet growth, however, has one
disadvantage in view of forming a highly conductive n-type crystal.
Patent Document 6 first revealed that oxygen serves as a donor in
GaN to form an n-type crystal. This document demonstrated that
water, which is safe, can be used for doping with an n-type
impurity (O) and the activation rate is nearly 100%. Patent
Document 7, however, found that oxygen doping has strong plane
orientation dependence, that is, the plane orientation selectivity
that oxygen is absorbed through facets but is not substantially
absorbed through the c-plane. An oxygen-doped n-type crystal formed
by facet growth has not only facets (f-plane), but also the
c-plane. The portions below the f-plane have high conductivity,
whereas the portions below the c-plane have high resistivity. Thus,
facet growth causes significant local variations in the dosage of
oxygen.
[0179] If a crystal is grown on an underlying substrate of a
different material such as GaAs or sapphire, the c-plane may appear
somewhere even in facet growth because the crystal grows in the
c-axis direction. The regions below the c-plane, which are referred
to as the single-crystal low-dislocation-density remaining region Y
or the c-plane growth regions Y, have high resistivity because they
absorb no oxygen. If the HZYZHZYZH . . . structure is formed by
facet growth, the regions H and Z have high conductivity because
they absorb oxygen, and the regions Y have high resistivity because
they absorb no oxygen. That is, the resistivity varies locally and
periodically.
[0180] This is a problem. In addition, this problem occurs only for
facet growth using oxygen as an n-type impurity. Silicon is usually
used as an n-type impurity for a GaN thin film. This problem does
not occur for a normal method that employs c-plane growth using
silicon as an n-type dopant.
[0181] Accordingly, in the present invention, a crystal is grown by
facet growth while simultaneously doping it with oxygen and
silicon. If silicon has c-plane selectivity, it should cancel out
the f-plane selectivity of oxygen, thus forming a uniform donor
concentration distribution. As a result of many experiments, the
present inventors have found that silicon has no plane orientation
dependence and is equally absorbed into both the c-plane and the
f-plane. Therefore, by simultaneous doping with silicon (Si) and
oxygen (O), silicon and oxygen are absorbed into the f-plane, and
silicon is absorbed into the c-plane. That is, the crystal can be
doped with the n-type impurities through all surfaces. If facet
growth is performed on a c-plane underlying substrate (such as
sapphire or GaN) or a (111) GaAs substrate, the HZYZHZ . . .
structure is formed. In this case, silicon is absorbed into the
regions Y so that they have low resistivity. This eliminates
high-resistivity regions. Because no high-resistivity region is
formed, the crystal has smaller local variations in conductivity
and can therefore be used as a highly conductive n-type
substrate.
[0182] The present invention has two characteristics: double doping
with oxygen and silicon and facet growth. Because facet growth has
been described in detail, the doping will be described below. In
the related art, there is no example in which a nitride
semiconductor is doubly doped with oxygen and silicon, and no
document relating thereto was found.
[0183] There is a difference between that a certain element is
n-type for GaN or other nitride semiconductors and that a certain
element serves as an n-type dopant for GaN or other nitride
semiconductors. In addition to oxygen and silicon, some other
n-type impurities are available, including carbon. However, they do
not necessarily serve as n-type dopants. If silicon and oxygen
coexist, they might interfere with each other in the crystal, thus
suppressing and cancelling out the effect of each other. Oxygen
might fail to form a shallow donor level because of the presence of
silicon, or conversely, silicon might fail to form a donor level
because of the presence of oxygen. Even if a donor level is formed,
silicon might capture n-type carriers released by oxygen. That is,
two different types of n-type impurities might cancel out the
effect of each other as a result of interaction. In this case, the
conductivity could not be increased by doping with two different
types of n-type impurities.
[0184] Even if two different types of n-type impurities are
independent of each other without interference and each release one
n-type carrier, their effects should differ because they should
have different activation rates. The conductivity a can be
represented as .sigma.=n.mu.e, where e is the electron charge, .mu.
is the mobility of n-type carriers (free electrons), and n is the
concentration of n-type carriers. The activation rates of oxygen
and silicon are referred to as Mo and Ms, respectively. If silicon
and oxygen are independent, n=Mo[O]+Ms[Si], where [O] is the
concentration of oxygen and [Si] is the concentration of silicon,
and accordingly the conductivity a can be symbolically represented
as .sigma.=.mu.e(Mo[O]+Ms[Si]). In terms of resistivity r,
r=1/.sigma.=1/.mu.e(Mo[O]+Ms[Si]). In other words, if the oxygen
concentration [O], the silicon concentration [Si], and the
resistivity r meet the above relationship, silicon and oxygen are
independent of each other without interfering with each other or
cancelling out the effect of each other.
[0185] The oxygen and silicon concentrations are measured at a
certain point in the c-plane and the f-plane on a sample using a
secondary ion mass spectrometer (SIMS). The measured value may vary
depending on the point where the concentration is measured because
of variations in concentration. The resistivity is determined by
measuring the resistance between two points on the surface. The
resistivity is determined by allowing a current to flow across the
ZHZYZH . . . structure. Because the regions Z and H differ in
resistivity from the regions Y, the measured resistivity is the
weighted average of the resistivity of the regions Z and H and the
resistivity of the regions Y. The resistivity of the regions Y
alone and the resistivity of the regions Z alone are unknown.
[0186] Because the regions H have the same resistivity as the
regions Z and are much smaller than the regions Z, the ratio of the
width of the regions H and Z to the width of the regions Y between
the two points under resistivity measurement is expressed as z:y.
That is, the relationship is normalized to y+z=1. Hence, the
measured resistivity r can be represented by the following
equation:
r=(1/.mu.e){z/(Mo[O].sub.z+Ms[Si].sub.z)+y/(Mo[O].sub.y+Ms[Si].sub.y)}
where [O].sub.z is the oxygen concentration of the regions Z,
[Si].sub.z is the silicon concentration of the regions Z, [O].sub.y
is the oxygen concentration of the regions Y, and [Si].sub.y is the
silicon concentration of the regions Y. The present inventors have
experimentally demonstrated that silicon is equally absorbed into
the c-plane and the f-plane. Silicon absorbed through the c-plane
enters the regions Y, whereas silicon absorbed through the f-plane
enters the regions Z. Hence, [Si].sub.z=[Si].sub.y. The present
inventors have also experimentally demonstrated that oxygen is
absorbed into the f-plane but not into the c-plane. This does not
mean that the difference is about 50 times, as disclosed in Patent
Document 7, but means that [O].sub.y=0. If these two
characteristics are taken into account, [Si].sub.z=[Si].sub.y=[Si]
and [O].sub.z=[O], and the above equation describing the
resistivity is simplified as follows:
r=(1/.mu.e){z/(Mo[O]+Ms[Si])+y/(Ms[Si])}
This allows a more intuitive understanding of the relationship
between the oxygen and silicon concentrations and the resistivity
in the present invention.
[0187] An n-type substrate having a lower resistivity r and a
higher conductivity .sigma. (r.sigma.=1) is desired. According to
the above equation, if [O] and [Si] are fixed, the resistivity is
lowest at z:y=1:0. That is, it is desirable that the f-plane spread
over the entire surface.
[0188] In other words, it is desirable to grow a crystal while
maintaining facets to the end, that is, to minimize the c-plane
growth regions Y.
[0189] Type II meets the above condition. For type II, as shown in
FIG. 20, a ridge-and-valley structure is maintained to the end, and
the low-dislocation-density single-crystal regions Z are
predominant. As the experimental results described later show, type
II (ridge-and-valley structure) tends to have a lower resistivity
than type I (flat).
[0190] Even for type II, if a dot mask is used, the c-plane growth
region Y cannot be eliminated because of its geometric limitations.
In this case, the c-plane growth region Y occurs inevitably midway
between the masking portions, thus increasing the resistivity. If
type II is formed using a stripe mask, the regions Y can be
eliminated because the mask includes parallel masking portions.
Accordingly, a crystal having the lowest resistivity should be
formed if type II is formed using a stripe mask.
[0191] Type II is suitable for forming a low-resistivity,
high-conductivity n-type crystal because it has the minimum
resistivity if [O] and [Si] are fixed. Type II can be formed at a
V/III ratio b of 1 to 10 and a temperature of 1,040.degree. C. to
1,080.degree. C.
[0192] A dot mask, however, has the advantage of low cracking ratio
because of the absence of anisotropy in strength.
[0193] Type II, in which a facet structure is maintained to the
end, has one disadvantage. Most of the facets, including {11-22},
{1-101}, {11-21}, and {1-102} planes, have a sharp angle Y, namely,
about 50.degree. to 60.degree., with reference to the c-plane.
Because ridges are formed with the width w of the exposed portions
E, the height of the ridges is (w/2)tan Y. For example, if
Y=55.degree., tan Y=1.43, and accordingly the height of the ridges
is 0.71 w. If the width w is large, for example, 1,500 .mu.m (1.5
mm), the height of the ridges is 1 mm. The ridges are wasteful
because they are removed by grinding to form a flat surface before
the crystal is polished to form a substrate. Thus, type II, in
which high facets are maintained to the end, has the disadvantage
of including large wasteful portions.
[0194] From this viewpoint, type I, in which a flat c-plane surface
is finally formed, is economically more advantageous because it
includes smaller wasteful portions. Type I can be formed at a V/III
ratio b of 1 to 10 and a temperature of 1,080.degree. C. to
1,150.degree. C. Despite having a flat c-plane surface, type I has
little bow and low cracking ratio and can therefore be processed
into a substrate, unlike the crystals formed by c-plane growth in
Patent Documents 2 and 3 (not facet growth, at 1,030.degree. C. or
less). Because the ratio z:y of type I is ideally 0:1, it has high
resistivity if [O] and [Si] are fixed. However, this applies only
to the surface, and the resistivity is low in the depth direction.
It is important that the resistivity be low in the perpendicular
direction because a current flows perpendicularly through a
substrate used for devices. Type I has sufficiently high
conductivity in the depth direction (perpendicular direction)
because the crystal is initially grown by facet growth and is
therefore doped with a large amount of oxygen in the initial
stage.
[0195] The mixed type (see FIG. 24), formed at 1,070.degree. C. to
1,090.degree. C., have the advantages and disadvantages of the
above two types. For the mixed type, the resistivity, the height of
wasteful portions removed by grinding, and the bow and cracking
ratio are at intermediate levels.
EXAMPLES
[0196] Dot masks or stripe masks were formed on GaAs substrates
having (111)Ga-plane serving as underlying substrates. The masks
were formed of SiO.sub.2 and had a thickness of 60 to 200 nm. The
ranges of dimensions (s, w, and p) of the masks were 10
.mu.m.ltoreq.s.ltoreq.100 .mu.m and 250
.mu.m.ltoreq.w.ltoreq.10,000 .mu.m. The dimensions and shapes of
the masks of the individual samples will be described later. A GaN
film was then grown on the substrates by HVPE. Specifically, a
buffer layer was initially formed, and a thick epitaxial layer was
then formed thereon. A total of 45 different types of samples were
prepared. The growth conditions for the buffer layer were as
follows:
[0197] Substrate temperature: 500.degree. C. to 550.degree. C.
[0198] GaCl partial pressure P.sub.GaCl: 80 Pa (0.0008 atm)
[0199] NH.sub.3 partial pressure P.sub.NH3: 16 kPa (0.16 atm)
[0200] Thickness of buffer layer: 50 nm
[0201] The buffer layer was grown at a V/III ratio b of 200.
Although the growth temperature and the V/III ratio b are important
in the present invention, they are important for epitaxial growth
(growth of the thick film), and the V/III ratio b in the formation
of the buffer layer is not important.
[0202] The term "cracked" means that a linear surface crack having
a length of 2.0 mm or more occurs in the substrate, that three or
more linear surface cracks having a length of 0.5 to 2.0 mm occur
in the substrate, or that 21 or more linear surface cracks having a
length of 0.3 to 0.5 mm occur in the substrate.
[0203] The term "not cracked" means that the number of linear
surface cracks having a length of 2.0 mm or more occurring in the
substrate is zero, that the number of linear cracks having a length
of 0.5 to 2.0 mm occurring in the substrate is two or less, or that
the number of cracks having a length of 0.3 to 0.5 mm occurring in
the substrate is 20 or less.
[0204] The cracking ratio (%) is the number of cracked substrates
divided by the total number of grown substrates and multiplied by
100. The donor density D refers to the concentration of n-type
impurities. That is, the donor density D refers to the
concentration of silicon and oxygen, which form a donor level. The
oxygen concentration [O] and the silicon concentration [Si] were
both measured using SIMS.
[0205] The bow U of a substrate is expressed as the radius of
curvature (m). The curvature is the reciprocal thereof, namely,
U.sup.-1 (m.sup.-1). This radius of curvature is the radius of
curvature of a nitride semiconductor crystal after the removal of
an underlying substrate but before the polishing. The smaller the
radius of curvature is, the larger the bow is. The bow may also be
expressed as the height h of the center of a wafer having a
diameter D. As an approximation to a quadratic curve, the
relationship is h=D.sup.2/8 U. For a 2 inch diameter wafer (D=50
mm), h (.mu.m)=312/U (m).
[0206] Many experiments were repeatedly conducted with varying mask
dimensions and shapes, varying growth temperatures, varying
NH.sub.3 partial pressures, GaCl partial pressures, and SiH.sub.4
partial pressures, and varying amounts of water added. The
substrate size of Sample 1 was 18 mm square, the substrate size of
Sample 3 was three inches (75 mm) in diameter, and the substrates
of the remaining samples were circular substrates having a diameter
of two inches (50 mm).
[0207] The 45 samples will now be described. Serial numbers 1 to 45
were assigned to the individual samples. Samples 1 to 39 are
examples of the present invention. Samples 40 to 45 are comparative
examples. Of the invention examples, namely, Samples 1 to 39,
Samples 1 to 24 are type I (flat surface). For type I, the oxygen
concentration and the silicon concentration were measured in the
c-plane because the surface is flat and the c-plane is exposed
therein. Samples 25 to 39 are type II (ridge-shaped). For type II,
the oxygen concentration and the silicon concentration were
measured both in the c-plane and in the f-plane because the surface
has ridges and valleys formed by inclined faces, namely, facets
(f-plane), and flat faces, namely, the c-plane, and the oxygen
concentration and the silicon concentration differ between the
c-plane and the f-plane. The oxygen concentration and the silicon
concentration in the c-plane are denoted by O.sub.C and Si.sub.C,
respectively, and the oxygen concentration and the silicon
concentration in the f-plane are denoted by O.sub.F and Si.sub.F,
respectively.
[0208] The correspondences with the symbols shown above are as
follows: O.sub.C=[O].sub.y, Si.sub.C=[Si].sub.y, O.sub.F=[O].sub.z,
and Si.sub.F=[Si]. Samples 1 to 18 and 25 to 36 had a stripe
(parallel stripe) mask, where s is the width of the masking
portions, w is the spacing between the masking portions in the
lateral direction, and s+w is the pitch p. Samples 19 to 24 and 37
to 39 had a dot (isolated dot) mask formed on the underlying
substrates, where s is the diameter of the dot masking portions and
w is the spacing between the nearest masking portions. The dot mask
can be completely defined only by s and w because the dot masking
portions are arranged at the center and vertices of a repetitive
pattern of equilateral hexagons.
[0209] For Samples 40 to 43 of comparative examples, no mask was
formed on the underlying substrates, and the crystals were directly
grown on the flat underlying substrates in vapor phase (by c-plane
growth as a whole). Samples 40 to 43 were tested for examining the
effect of a mask and do not belong to the related art. Samples 44
and 45 of comparative examples, which were grown under the same
conditions as the present invention without supplying a silicon
source gas, could not be used as n-type substrates because they had
extremely high resistivity in the c-plane. Samples 44 and 45
demonstrate that a source gas containing silicon is required in
addition to oxygen.
[0210] The term "core" in Table refers to the masking portions or
the crystals grown thereon. Table shows the sample numbers, the
types of pattern, the core spacing w (.mu.m), the core width s
(.mu.m), the growth temperature Tq (.degree. C.), P.sub.Ga (GaCl
partial pressure P.sub.GaCl; kPa), P.sub.N (ammonia partial
pressure P.sub.NH3; kPa), the substrate size (mm or inches ('')),
the thickness (.mu.m), the types of core (type of crystal of the
portions formed on the masking portions; inverted layer J,
polycrystalline layer P, or inclined layer A), the types of crystal
surface (type I or type II), the silicon concentration Sic in the
c-plane (cm.sup.-3), the oxygen concentration O.sub.C in the
c-plane (cm.sup.-3), the silicon concentration Si.sub.F in
facet-plane F (cm.sup.-3), the oxygen concentration O.sub.F in
facet-plane F (cm.sup.-3), the resistivity r (.OMEGA.cm), the
cracking ratio K (%), and the radius of bow curvature U (m). The
radius of bow curvature is the radius of curvature of a crystal
after the removal of an underlying substrate but before the
polishing. The radius of bow curvature U is also simply referred to
as the bow U, although it means the radius of curvature, and the
larger the value is, the smaller the bow is. The resistivity r
(.OMEGA.cm) and the cracking ratio K (%) were measured after the
polishing.
[0211] Oxygen, serving as an n-type impurity, was supplied by
adding water to one of the source gases. Silicon was supplied in
the form of SiH.sub.4 gas. The amount of water added and the
partial pressure of SiH.sub.4 gas were varied, although they were
not measured or shown in Table because they were added in trace
amounts and were therefore difficult to measure. Because the amount
of water added and the SiH.sub.4 partial pressure were varied, the
dosages of silicon and oxygen, the resistivity r, the bow U, and
the cracking ratio K varied from sample to sample even at the same
substrate temperature Tq, the same mask dimensions (s, w, and p),
and the same NH.sub.3 and GaCl partial pressures.
TABLE-US-00009 TABLE Partial pressure Core Core Growth Sample
spacing width temperature P.sub.Ga P.sub.N Substrate Thickness No.
Pattern w (.mu.m) s (.mu.m) Tq (.degree. C.) (kPa) (kPa) size
(.mu.m) Type of core 1 Stripe 500 50 1100 4 10 18 mm 400 Inverted
layer J 2 Stripe 500 50 1100 4 10 2'' 400 Inverted layer J 3 Stripe
500 50 1100 4 10 3'' 400 Inverted layer J 4 Stripe 500 50 1100 10
10 2'' 400 Inverted layer J 5 Stripe 500 50 1100 3.3 10 2'' 400
Inverted layer J 6 Stripe 500 50 1100 4 10 2'' 400 Inverted layer J
7 Stripe 500 50 1100 4 10 2'' 400 Inverted layer J 8 Stripe 500 50
1100 4 10 2'' 400 Polycrystalline layer P 9 Stripe 500 50 1100 4 10
2'' 400 Inclined layer A 10 Stripe 500 10 1100 4 10 2'' 400
Inverted layer J 11 Stripe 500 25 1100 4 10 2'' 400 Inverted layer
J 12 Stripe 500 100 1100 4 10 2'' 400 Inverted layer J 13 Stripe
250 50 1100 4 10 2'' 400 Inverted layer J 14 Stripe 750 50 1100 4
10 2'' 400 Inverted layer J 15 Stripe 1000 50 1100 4 10 2'' 400
Inverted layer J 16 Stripe 1500 50 1100 4 10 2'' 400 Inverted layer
J 17 Stripe 2000 50 1100 4 10 2'' 400 Inverted layer J 18 Stripe
10000 50 1100 4 10 2'' 400 Inverted layer J 19 Dot 500 50 1100 4 10
2'' 400 Inverted layer J 20 Dot 500 50 1100 4 10 2'' 400 Inverted
layer J 21 Dot 500 50 1100 4 10 2'' 400 Inverted layer J 22 Dot
1000 50 1100 4 10 2'' 400 Inverted layer J 23 Dot 2500 50 1100 4 10
2'' 400 Inverted layer J 24 Dot 5000 50 1100 4 10 2'' 400 Inverted
layer J 25 Stripe 500 50 1050 4 10 2'' 400 Inverted layer J 26
Stripe 500 50 1050 4 10 2'' 400 Inverted layer J 27 Stripe 500 50
1050 4 10 2'' 400 Inverted layer J 28 Stripe 500 50 1050 4 10 2''
400 Inverted layer J 29 Stripe 500 50 1050 4 10 2'' 400 Inverted
layer J 30 Stripe 500 50 1050 4 10 2'' 400 Inverted layer J 31
Stripe 500 50 1050 4 10 2'' 400 Inverted layer J 32 Stripe 500 50
1050 4 10 2'' 400 Inverted layer J 33 Stripe 500 50 1050 4 10 2''
400 Inverted layer J 34 Stripe 500 50 1050 4 10 2'' 400 Inverted
layer J 35 Stripe 500 50 1050 4 10 2'' 400 Inverted layer J 36
Stripe 500 50 1050 4 10 2'' 400 Inverted layer J 37 Dot 500 50 1050
4 10 2'' 400 Inverted layer J 38 Dot 500 50 1050 4 10 2'' 400
Inverted layer J 39 Dot 500 50 1050 4 10 2'' 400 Inverted layer J
40 C- Comparative -- -- 1050 4 10 2'' 400 -- plane example 41 C-
Comparative -- -- 1050 4 10 2'' 400 -- plane example 42 C-
Comparative -- -- 1030 4 10 2'' 400 -- plane example 43 C-
Comparative -- -- 1030 4 10 2'' 400 -- plane example 44 Stripe
Comparative 500 50 1050 4 10 2'' 400 Inverted layer J example 45
Stripe Comparative 500 50 1050 4 10 2'' 400 Inverted layer J
example C-plane F-plane Radius of Type of Silicon Oxygen Silicon
Oxygen Cracking bow Sample crystal concentration concentration
concentration concentration Resistivity ratio K curvature No.
surface Si.sub.C (cm.sup.-3) O.sub.C (cm.sup.-3) Si.sub.F
(cm.sup.-3) O.sub.F (cm.sup.-3) r (.OMEGA.cm) (%) U (m) 1 I 1
.times. 10.sup.18 1 .times. 10.sup.15 -- -- 9 .times. 10.sup.-3 1
8.0 2 I 1 .times. 10.sup.18 1 .times. 10.sup.15 -- -- 9 .times.
10.sup.-3 7 6.2 3 I 1 .times. 10.sup.18 1 .times. 10.sup.15 -- -- 9
.times. 10.sup.-3 12 5.2 4 I 1 .times. 10.sup.19 1 .times.
10.sup.15 -- -- 4.7 .times. 10.sup.-3 15 5.0 5 I 1 .times.
10.sup.18 1 .times. 10.sup.15 -- -- 9 .times. 10.sup.-3 13 6.2 6 I
1 .times. 10.sup.17 1 .times. 10.sup.15 -- -- 1 .times. 10.sup.-2 3
6.5 7 I 5 .times. 10.sup.19 1 .times. 10.sup.15 -- -- 1.8 .times.
10.sup.-3 17 4.7 8 I 1 .times. 10.sup.18 1 .times. 10.sup.15 -- --
9 .times. 10.sup.-3 9 6.2 9 I 1 .times. 10.sup.18 1 .times.
10.sup.15 -- -- 9 .times. 10.sup.-3 11 6.2 10 I 1 .times. 10.sup.18
1 .times. 10.sup.15 -- -- 9 .times. 10.sup.-3 11 6.2 11 I 1 .times.
10.sup.18 1 .times. 10.sup.15 -- -- 9 .times. 10.sup.-3 9 6.2 12 I
1 .times. 10.sup.18 1 .times. 10.sup.15 -- -- 9 .times. 10.sup.-3 8
6.4 13 I 1 .times. 10.sup.18 1 .times. 10.sup.15 -- -- 9 .times.
10.sup.-3 6 6.8 14 I 1 .times. 10.sup.18 1 .times. 10.sup.15 -- --
9 .times. 10.sup.-3 8 6.2 15 I 1 .times. 10.sup.18 1 .times.
10.sup.15 -- -- 9 .times. 10.sup.-3 11 5.3 16 I 1 .times. 10.sup.18
1 .times. 10.sup.15 -- -- 9 .times. 10.sup.-3 13 4.7 17 I 1 .times.
10.sup.18 1 .times. 10.sup.15 -- -- 9 .times. 10.sup.-3 17 4.2 18 I
1 .times. 10.sup.18 1 .times. 10.sup.15 -- -- 9 .times. 10.sup.-3
22 4.0 19 I 1 .times. 10.sup.18 1 .times. 10.sup.15 -- -- 9 .times.
10.sup.-3 4 4.8 20 I 4 .times. 10.sup.18 1 .times. 10.sup.15 -- --
7 .times. 10.sup.-3 5 4.2 21 I 7 .times. 10.sup.18 1 .times.
10.sup.15 -- -- 5 .times. 10.sup.-3 7 3.8 22 I 1 .times. 10.sup.18
1 .times. 10.sup.15 -- -- 9 .times. 10.sup.-3 9 3.7 23 I 1 .times.
10.sup.18 1 .times. 10.sup.15 -- -- 9 .times. 10.sup.-3 10 3.7 24 I
1 .times. 10.sup.18 1 .times. 10.sup.15 -- -- 9 .times. 10.sup.-3
13 3.5 25 II 1 .times. 10.sup.18 1 .times. 10.sup.15 1 .times.
10.sup.18 1 .times. 10.sup.18 8 .times. 10.sup.-3 6 6.5 26 II 4
.times. 10.sup.18 1 .times. 10.sup.15 4 .times. 10.sup.18 1 .times.
10.sup.18 6 .times. 10.sup.-3 8 6.3 27 II 7 .times. 10.sup.18 1
.times. 10.sup.15 7 .times. 10.sup.18 1 .times. 10.sup.18 4 .times.
10.sup.-3 11 6.2 28 II 1 .times. 10.sup.19 1 .times. 10.sup.15 1
.times. 10.sup.19 1 .times. 10.sup.18 2 .times. 10.sup.-3 12 6.0 29
II 1 .times. 10.sup.18 1 .times. 10.sup.15 1 .times. 10.sup.18 5
.times. 10.sup.16 8 .times. 10.sup.-3 5 6.4 30 II 1 .times.
10.sup.18 1 .times. 10.sup.15 1 .times. 10.sup.18 1 .times.
10.sup.17 7.9 .times. 10.sup.-3 5 6.3 31 II 1 .times. 10.sup.18 1
.times. 10.sup.15 1 .times. 10.sup.18 5 .times. 10.sup.17 7.5
.times. 10.sup.-3 6 6.2 32 II 1 .times. 10.sup.18 1 .times.
10.sup.15 1 .times. 10.sup.18 5 .times. 10.sup.18 7.5 .times.
10.sup.-3 7 6.0 33 II 1 .times. 10.sup.18 1 .times. 10.sup.15 1
.times. 10.sup.18 1 .times. 10.sup.19 2 .times. 10.sup.-3 10 5.8 34
II 4 .times. 10.sup.18 1 .times. 10.sup.15 4 .times. 10.sup.18 1
.times. 10.sup.19 1.9 .times. 10.sup.-3 11 5.5 35 II 7 .times.
10.sup.18 1 .times. 10.sup.15 7 .times. 10.sup.18 1 .times.
10.sup.19 1.8 .times. 10.sup.-3 14 5.0 36 II 1 .times. 10.sup.19 1
.times. 10.sup.15 1 .times. 10.sup.19 1 .times. 10.sup.19 1.5
.times. 10.sup.-3 18 4.8 37 II 1 .times. 10.sup.18 1 .times.
10.sup.15 1 .times. 10.sup.18 1 .times. 10.sup.18 8 .times.
10.sup.-3 3 5.0 38 II 4 .times. 10.sup.18 1 .times. 10.sup.15 4
.times. 10.sup.18 1 .times. 10.sup.18 6.3 .times. 10.sup.-3 5 4.6
39 II 7 .times. 10.sup.18 1 .times. 10.sup.15 7 .times. 10.sup.18 1
.times. 10.sup.18 4 .times. 10.sup.-3 6 4.2 40 -- 1 .times.
10.sup.18 1 .times. 10.sup.15 -- -- 0.01 75 1.5 41 -- 1 .times.
10.sup.19 1 .times. 10.sup.15 -- -- 4.7 .times. 10.sup.-3 88 1.2 42
-- 1 .times. 10.sup.18 1 .times. 10.sup.15 -- -- 0.01 92 1.3 43 --
1 .times. 10.sup.19 1 .times. 10.sup.15 -- -- 4.7 .times. 10.sup.-3
90 1.0 44 II 1 .times. 10.sup.16 1 .times. 10.sup.15 1 .times.
10.sup.16 4 .times. 10.sup.18 High in c- 30 7.0 plane 45 II 1
.times. 10.sup.16 1 .times. 10.sup.15 1 .times. 10.sup.16 8 .times.
10.sup.18 High in c- 36 6.8 plane
Sample 1 (Invention Example; Stripe; Type I)
[0212] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask (core) width s of 50 .mu.m was formed on 18 mm
square GaAs substrates. Sample 1 is characterized in that 18 mm
square wafers were used as underlying substrates. After a buffer
layer was formed on the substrates, an epitaxial layer was grown
thereon. The epitaxial growth temperature Tq was 1,100.degree. C.,
the NH.sub.3 partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and
the GaCl partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The
epitaxial layer was grown to a thickness of 400 .mu.m or more.
[0213] The GaAs substrates were removed by machining, thus
obtaining free-standing GaN substrates having a thickness of 400
.mu.m. The V/III ratio b was 2.5. The type of core crystal was the
inverted layer J. The type of crystal surface was type I, which was
formed because the growth temperature Tq was high. Because this was
type I, the surface was flat, and only the c-plane was exposed
therein. The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 1%, which is extremely low and was the minimum of all
samples. The bow U was 8 m, indicating that the bow was extremely
small. Thus, these were superior conductive GaN substrates.
Sample 2 (Invention Example; Stripe; Type I)
[0214] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates, which are easily available.
After a buffer layer was formed on the substrates, an epitaxial
layer was grown thereon. The epitaxial growth temperature Tq was
1,100.degree. C., the NH.sub.3 partial pressure P.sub.NH3 was 10
kPa (0.1 atm), and the GaCl partial pressure P.sub.GaCl was 4 kPa
(0.04 atm). The epitaxial layer was grown to a thickness of 400
.mu.m or more.
[0215] The GaAs substrates were removed by machining, thus
obtaining free-standing GaN substrates having a thickness of 400
.mu.m. The V/III ratio b was 2.5. The type of core crystal was the
inverted layer J. The type of crystal surface was type I, which was
formed because the growth temperature Tq was high. Because this was
type I, the surface was flat, and only the c-plane was exposed
therein. The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3
.OMEGA.cm.
[0216] That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 7%, which is low. The bow U was 6.2 m, indicating that
the bow was small. Thus, these were superior conductive GaN
substrates.
Sample 3 (Invention Example; Stripe; Type I)
[0217] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 3 inch (75 mm)
diameter circular GaAs substrates. Sample 3 is characterized in
that large 3 inch GaN wafers were used as underlying substrates.
After a buffer layer was formed on the substrates, an epitaxial
layer was grown thereon. The epitaxial growth temperature Tq was
1,100.degree. C., the NH.sub.3 partial pressure P.sub.NH3 was 10
kPa (0.1 atm), and the GaCl partial pressure P.sub.GaCl was 4 kPa
(0.04 atm). The epitaxial layer was grown to a thickness of 400
.mu.m or more.
[0218] The GaAs substrates were removed by machining, thus
obtaining free-standing GaN substrates having a thickness of 400
.mu.m. The V/III ratio b was 2.5. The type of core crystal was the
inverted layer J. The type of crystal surface was type I, which was
formed because the growth temperature Tq was high. Because this was
type I, the surface was flat, and only the c-plane was exposed
therein. The silicon concentration Sic in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 12%, which is low. The bow U was 5.2 m, indicating that
the bow was small. Thus, these were superior conductive GaN
substrates having a large area.
Sample 4 (Invention Example; Stripe; Type I)
[0219] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,100.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 10 kPa (0.1 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more. Sample 4 is
characterized in that the GaCl partial pressure was high.
[0220] The GaAs substrates were removed by machining, thus
obtaining free-standing GaN substrates having a thickness of 400
.mu.m. The V/III ratio b was 1. The type of core crystal was the
inverted layer J. The type of crystal surface was type I, which was
formed because the growth temperature Tq was high. Because this was
type I, the surface was flat, and only the c-plane was exposed
therein. The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.19 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.4. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 4.7.times.10.sup.-3
.OMEGA.cm. That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 15%, which is low. The bow U was 5 m, indicating that
the bow was small. Thus, these were superior conductive GaN
substrates.
Sample 5 (Invention Example; Stripe; Type I)
[0221] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,100.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 3.3 kPa (0.033 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0222] The V/III ratio b was 3. The GaAs substrates were removed by
machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 13%, which is low. The bow U was 6.2 m, indicating that
the bow was small. Thus, these were superior conductive GaN
substrates.
Sample 6 (Invention Example; Stripe; Type I)
[0223] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,100.degree. C., the NH.sub.3
partial pressure P.sub.3 was 10 kPa (0.1 atm), and the GaCl partial
pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial layer was
grown to a thickness of 400 .mu.m or more.
[0224] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.17 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio(Si/O ratio) (q) in the c-plane was
10.sup.2. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 1.times.10.sup.-2 .OMEGA.cm,
which was the highest among all samples. Still, these were
conductive substrates with satisfactorily low resistivity r.
Silicon was the main donor responsible for releasing n-type
carriers (conduction electrons). The cracking ratio K was 3%, which
is extremely low. The bow U was 6.5 m, indicating that the bow was
small. Thus, these were superior conductive GaN substrates.
Sample 7 (Invention Example; Stripe; Type I)
[0225] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,100.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0226] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
5.times.10.sup.19 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
5.times.10.sup.4. The amount of oxygen absorbed was small because
of the c-plane growth. The resistivity r was 1.8.times.10.sup.-3
.OMEGA.cm. That is, the substrates had extremely low resistivity r
and were conductive. Silicon was the main donor responsible for
releasing n-type carriers (conduction electrons). The cracking
ratio K was 17%, which is satisfactorily low. The bow U was 4.7 m,
indicating that the bow was satisfactorily small. Thus, these were
superior conductive GaN substrates.
Sample 8 (Invention Example; Stripe; Type I)
[0227] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,100.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0228] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the
polycrystalline layer P. The type of crystal surface was type I,
which was formed because the growth temperature Tq was high.
Because this was type I, the surface was flat, and only the c-plane
was exposed therein. The silicon concentration Si.sub.C in the
c-plane was 1.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.3. The amount of oxygen
absorbed was small because of the c-plane growth. The resistivity r
was 9.times.10.sup.-3 .OMEGA.cm. That is, the substrates had low
resistivity r and were satisfactorily conductive. Silicon was the
main donor responsible for releasing n-type carriers (conduction
electrons). The cracking ratio K was 9%, which is low. The bow U
was 6.2 m, indicating that the bow was small. Thus, these were
superior conductive GaN substrates.
Sample 9 (Invention Example; Stripe; Type I)
[0229] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,100.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0230] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inclined
layer A. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 11%, which is low. The bow U was 6.2 m, indicating that
the bow was small. Thus, these were superior conductive GaN
substrates.
Sample 10 (Invention Example; Stripe; Type I)
[0231] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask width s of 10 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. Sample 10 is characterized in
that the mask width s was extremely small. After a buffer layer was
formed on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,100.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0232] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 11%, which is low. The bow U was 6.2 in, indicating
that the bow was small. Thus, these were superior conductive GaN
substrates. In this way, an n-type conductive substrate having a
desired structure can be formed even if the mask width s is as
small as 10 .mu.m.
Sample 11 (Invention Example; Stripe; Type I)
[0233] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask width s of 25 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. Sample 11 is characterized in
that the mask width s was small. After a buffer layer was formed on
the substrates, an epitaxial layer was grown thereon. The epitaxial
growth temperature Tq was 1,100.degree. C., the NH.sub.3 partial
pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl partial
pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial layer was
grown to a thickness of 400 .mu.m or more.
[0234] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.0 cm. That is, the
substrates had low resistivity r and were satisfactorily
conductive. Silicon was the main donor responsible for releasing
n-type carriers (conduction electrons). The cracking ratio K was
9%, which is low. The bow U was 6.2 m, indicating that the bow was
small. Thus, these were superior conductive GaN substrates. In this
way, an n-type conductive substrate having a desired structure can
be formed even if the mask width s is as small as 25 .mu.m.
Sample 12 (Invention Example; Stripe; Type I)
[0235] A parallel stripe mask having a stripe core spacing w of 500
.mu.m and a mask width s of 100 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. Sample 12 is characterized in
that the mask width s was large. After a buffer layer was formed on
the substrates, an epitaxial layer was grown thereon. The epitaxial
growth temperature Tq was 1,100.degree. C., the NH.sub.3 partial
pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl partial
pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial layer was
grown to a thickness of 400 .mu.m or more.
[0236] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 8%, which is low. The bow U was 6.4 m, indicating that
the bow was small. Thus, these were superior conductive GaN
substrates. In this way, an n-type conductive substrate having a
desired structure can be formed even if the mask width s is as
large as 100 .mu.m.
Sample 13 (Invention Example; Stripe; Type I)
[0237] A parallel stripe mask having a stripe core spacing w of 250
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. Sample 13 is characterized in
that the stripe core spacing w was small. After a buffer layer was
formed on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,100.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0238] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 6%, which is very low. The bow U was 6.8 m, indicating
that the bow was small. Thus, these were superior conductive GaN
substrates. In this way, an n-type conductive substrate having a
desired structure can be formed even if the stripe core spacing w
is as small as 250 .mu.m.
Sample 14 (Invention Example; Stripe; Type I)
[0239] A parallel stripe mask having a stripe core spacing w of 750
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. Sample 14 is characterized in
that the stripe core spacing w was large. After a buffer layer was
formed on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,100.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0240] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 8%, which is low. The bow U was 6.2 m, indicating that
the bow was small. Thus, these were superior conductive GaN
substrates. In this way, an n-type conductive substrate having a
desired structure can be formed even if the stripe core spacing w
is as large as 750 .mu.m.
Sample 15 (Invention Example; Stripe; Type I)
[0241] A parallel stripe mask having a stripe core spacing w of
1,000 .mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50
mm) diameter circular GaAs substrates. Sample 15 is characterized
in that the stripe core spacing w was large. After a buffer layer
was formed on the substrates, an epitaxial layer was grown thereon.
The epitaxial growth temperature Tq was 1,100.degree. C., the
NH.sub.3 partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the
GaCl partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The
epitaxial layer was grown to a thickness of 400 .mu.m or more.
[0242] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 11%, which is low. The bow U was 5.3 m, indicating that
the bow was small. Thus, these were superior conductive GaN
substrates. In this way, an n-type conductive substrate having a
desired structure can be formed even if the stripe core spacing w
is as large as 1,000 .mu.m (1 mm).
Sample 16 (Invention Example; Stripe; Type I)
[0243] A parallel stripe mask having a stripe core spacing w of
1,500 .mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50
mm) diameter circular GaAs substrates. Sample 16 is characterized
in that the stripe core spacing w was large. After a buffer layer
was formed on the substrates, an epitaxial layer was grown thereon.
The epitaxial growth temperature Tq was 1,100.degree. C., the
NH.sub.3 partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the
GaCl partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The
epitaxial layer was grown to a thickness of 400 .mu.m or more.
[0244] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 13%, which is low. The bow U was 4.7 m, indicating that
the bow was small. Thus, these were superior conductive GaN
substrates. In this way, an n-type conductive substrate having a
desired structure can be formed even if the stripe core spacing w
is as large as 1,500 .mu.m (1.5 mm).
Sample 17 (Invention Example; Stripe; Type I)
[0245] A parallel stripe mask having a stripe core spacing w of
2,000 .mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50
mm) diameter circular GaAs substrates. Sample 17 is characterized
in that the stripe core spacing w was large. After a buffer layer
was formed on the substrates, an epitaxial layer was grown thereon.
The epitaxial growth temperature Tq was 1,100.degree. C., the
NH.sub.3 partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the
GaCl partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The
epitaxial layer was grown to a thickness of 400 .mu.m or more.
[0246] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 pin. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3
.OMEGA.cm.
[0247] That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 17%, which is satisfactorily low. The bow U was 4.2 m,
indicating that the bow was satisfactorily small. Thus, these were
superior conductive GaN substrates. In this way, an n-type
conductive substrate having a desired structure can be formed even
if the stripe core spacing w is as large as 2,000 .mu.m (2.0
mm).
Sample 18 (Invention Example; Stripe; Type I)
[0248] A parallel stripe mask having a stripe core spacing w of
10,000 .mu.m and a mask width s of 50 .mu.m was formed on 2 inch
(50 mm) diameter circular GaAs substrates. Sample 18 is
characterized in that the stripe core spacing w was large. After a
buffer layer was formed on the substrates, an epitaxial layer was
grown thereon. The epitaxial growth temperature Tq was
1,100.degree. C., the NH.sub.3 partial pressure P.sub.NH3 was 10
kPa (0.1 atm), and the GaCl partial pressure P.sub.GaCl was 4 kPa
(0.04 atm). The epitaxial layer was grown to a thickness of 400
.mu.m or more.
[0249] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 22%, which is satisfactorily low. The bow U was 4 m,
indicating that the bow was satisfactorily small. Thus, these were
superior conductive GaN substrates. In this way, an n-type
conductive substrate having a desired structure can be formed even
if the stripe core spacing w is as large as 10,000 .mu.m (10
mm).
[0250] A comparison between Samples 16, 17, and 18 reveals that an
conductive substrate having a desired structure can be formed if
the mask spacing w is up to about 10,000 .mu.m and that as the mask
spacing w is increased, the cracking ratio K is increased, and the
bow is also gradually increased. Accordingly, an excellent crystal
structure can be achieved over a wide range of stripe mask spacing
w, namely, 250 to 10,000 .mu.m.
[0251] Samples 1 to 18 above are type I (flat surface) crystals
grown on stripe masks. Next, invention examples using dot masks,
namely, Samples 19 to 24, will be described.
Sample 19 (Invention Example; Dot; Type I)
[0252] A dot mask having a dot core spacing w of 500 .mu.m and a
mask diameter s of 50 .mu.m was formed on 2 inch (50 mm) diameter
circular GaAs substrates. The dot mask had an isolated dot pattern
of masking portions formed at positions with six-fold symmetry.
That is, the masking portions were arranged at the vertices of
regular triangles tiled together. Hence, the mask can be defined
only by s and w. This sample demonstrates that the present
invention can be applied either to a stripe mask or to a dot mask.
After a buffer layer was formed on the substrates, an epitaxial
layer was grown thereon. The epitaxial growth temperature Tq was
1,100.degree. C., the NH.sub.3 partial pressure P.sub.NH3 was 10
kPa (0.1 atm), and the GaCl partial pressure P.sub.GaCl was 4 kPa
(0.04 atm). The epitaxial layer was grown to a thickness of 400
.mu.m or more.
[0253] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 4%, which is extremely low. The bow U was 4.8 m,
indicating that the bow was satisfactorily small. Thus, these were
superior conductive GaN substrates. In this way, a dot mask can be
used to form a highly conductive GaN substrate having a similar
structure.
Sample 20 (Invention Example; Dot; Type I)
[0254] A dot mask having a dot core spacing w of 500 .mu.m and a
mask diameter s of 50 was formed on 2 inch (50 mm) diameter
circular GaAs substrates. This sample demonstrates that the present
invention can be applied either to a stripe mask or to a dot mask.
After a buffer layer was formed on the substrates, an epitaxial
layer was grown thereon. The epitaxial growth temperature Tq was
1,100.degree. C., the NH.sub.3 partial pressure P.sub.NH3 was 10
kPa (0.1 atm), and the GaCl partial pressure P GaCl was 4 kPa (0.04
atm). The epitaxial layer was grown to a thickness of 400 .mu.m or
more.
[0255] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
4.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
4.times.10.sup.3. The amount of oxygen absorbed was small because
of the c-plane growth. The resistivity r was 7.times.10.sup.-3
.OMEGA.cm. That is, the substrates had low resistivity r and were
conductive. Silicon was the main donor responsible for releasing
n-type carriers (conduction electrons). The cracking ratio K was
5%, which is extremely low. The bow U was 4.2 m, indicating that
the bow was satisfactorily small. Thus, these were superior
conductive GaN substrates. In this way, a dot mask can be used to
form a highly conductive GaN substrate having a similar
structure.
Sample 21 (Invention Example; Dot; Type I)
[0256] A dot mask having a dot core spacing w of 500 .mu.m and a
mask diameter s of 50 .mu.m was formed on 2 inch (50 mm) diameter
circular GaAs substrates. This sample demonstrates that the present
invention can be applied either to a stripe mask or to a dot mask.
After a buffer layer was formed on the substrates, an epitaxial
layer was grown thereon. The epitaxial growth temperature Tq was
1,100.degree. C., the NH.sub.3 partial pressure P.sub.NH3 was 10
kPa (0.1 atm), and the GaCl partial pressure P.sub.GaCl was 4 kPa
(0.04 atm). The epitaxial layer was grown to a thickness of 400
.mu.m or more.
[0257] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
7.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
7.times.10.sup.3. The amount of oxygen absorbed was small because
of the c-plane growth. The resistivity r was 5.times.10.sup.-3
.OMEGA.cm. That is, the substrates had low resistivity r and were
conductive. Silicon was the main donor responsible for releasing
n-type carriers (conduction electrons). The cracking ratio K was
7%, which is low. The bow U was 3.8 m, indicating that the bow was
satisfactorily small. Thus, these were superior conductive GaN
substrates. In this way, a dot mask can be used to form a highly
conductive GaN substrate having a similar structure.
Sample 22 (Invention Example; Dot; Type I)
[0258] A dot mask having a dot core spacing w of 1,000 .mu.m and a
mask diameter s of 50 .mu.m was formed on 2 inch (50 mm) diameter
circular GaAs substrates. Sample 22 is characterized in that the
dot core spacing w was large. After a buffer layer was formed on
the substrates, an epitaxial layer was grown thereon. The epitaxial
growth temperature Tq was 1,100.degree. C., the NH.sub.3 partial
pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl partial
pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial layer was
grown to a thickness of 400 .mu.m or more.
[0259] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 9%, which is low. The bow U was 3.7 m, indicating that
the bow was satisfactorily small. Thus, these were superior
conductive GaN substrates. In this way, a dot mask having a large
dot spacing (w=1,000 .mu.m) can be used to form a highly conductive
GaN substrate having a similar structure.
Sample 23 (Invention Example; Dot; Type I)
[0260] A dot mask having a dot core spacing w of 2,500 .mu.m and a
mask diameter s of 50 .mu.m was formed on 2 inch (50 mm) diameter
circular GaAs substrates. Sample 23 is characterized in that the
dot core spacing w was large. After a buffer layer was formed on
the substrates, an epitaxial layer was grown thereon. The epitaxial
growth temperature Tq was 1,100.degree. C., the NH.sub.3 partial
pressure P.sub.N3 was 10 kPa (0.1 atm), and the GaCl partial
pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial layer was
grown to a thickness of 400 .mu.m or more.
[0261] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 10%, which is low. The bow U was 3.7 m, indicating that
the bow was satisfactorily small. Thus, these were superior
conductive GaN substrates. In this way, a dot mask having a large
dot spacing (w=2,500 .mu.m) can be used to form a highly conductive
GaN substrate having a similar structure.
Sample 24 (Invention Example; Dot; Type I)
[0262] A dot mask having a dot core spacing w of 5,000 .mu.m and a
mask diameter s of 50 .mu.m was formed on 2 inch (50 mm) diameter
circular GaAs substrates. Sample 24 is characterized in that the
dot core spacing w was extremely large (5 mm). After a buffer layer
was formed on the substrates, an epitaxial layer was grown thereon.
The epitaxial growth temperature Tq was 1,100.degree. C., the
NH.sub.3 partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the
GaCl partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The
epitaxial layer was grown to a thickness of 400 .mu.m or more.
[0263] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type I, which was formed
because the growth temperature Tq was high. Because this was type
I, the surface was flat, and only the c-plane was exposed therein.
The silicon concentration Si.sub.C in the c-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
10.sup.3. The amount of oxygen absorbed was small because of the
c-plane growth. The resistivity r was 9.times.10.sup.-3 .OMEGA.cm.
That is, the substrates had low resistivity r and were
satisfactorily conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 13%, which is low. The bow U was 3.5 m, indicating that
the bow was satisfactorily small. Thus, these were superior
conductive GaN substrates. In this way, a dot mask having a large
dot spacing (w=5,000 .mu.m) can be used to form a highly conductive
GaN substrate having a similar structure.
[0264] According to the results of the samples using a dot mask,
namely, Samples 19 to 24, an excellent GaN substrate having a
predetermined structure can be formed with low cracking ratio and
little bow if the dot mask spacing w is 500 to 5,000 .mu.m.
According to the results of Samples 22 to 24, the cracking ratio
tends to increase as the dot mask spacing w is increased. A larger
dot mask spacing w is preferred for lesser spatial constraints on
the fabrication of devices on the substrate. Even if the dot mask
spacing w is 10,000 the cracking ratio is acceptable. As for the
lower limit, a GaN substrate with superior properties can be formed
even if the dot mask spacing w is 250 .mu.m. In view of the
substrate properties, a GaN substrate crystal having conductivity,
low cracking ratio, and little bow can be produced over a wide
range of dot mask spacing w, namely, about 250 to 10,000 .mu.m.
[0265] Whereas Samples 1 to 24, described above, are crystal
substrates grown at a higher growth temperature Tq, namely,
1,100.degree. C., Samples 25 to 45, described below, are crystals
grown at a lower growth temperature Tq, namely, 1,050.degree. C. or
lower. A crystal grown at 1,050.degree. C. has a surface with a
concavity and convexity of ridges and valleys (stripe mask) or a
concavity of conical pits. The concavo-convex surface has numerous
inclined facets exposed therein. This is type II. The flat faces
are the c-plane, and the inclined faces are facets. Type II has
anisotropy in oxygen doping. For type II, the facets are doped with
a large amount of oxygen. Accordingly, the oxygen concentration
O.sub.F in the facets differs from the oxygen concentration O.sub.C
in the c-plane. Therefore, both the oxygen concentration O.sub.F in
the facets and the oxygen concentration O.sub.C in the c-plane were
measured. As a result, the oxygen concentration in the facets was
higher than the oxygen concentration in the c-plane
(O.sub.F>O.sub.C). Similarly, the silicon concentration was
measured both in the facets and the flat c-plane faces. As a
result, no selectivity was found between the silicon concentration
in the c-plane and the silicon concentration in the f-plane.
Sample 25 (Invention Example; Stripe; Type II)
[0266] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0267] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a serrated structure in which ridges and
valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 1.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.3. The silicon concentration
Si.sub.F in the f-plane was 1.times.10.sup.18 cm.sup.-3, and the
oxygen concentration O.sub.F in the f-plane was
1.times.10.sup.18/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 1. The amount of oxygen absorbed was
small in the c-plane and was large in the f-plane. Thus, the amount
of oxygen absorbed differed significantly between the c-plane and
the f-plane, showing strong anisotropy. On the other hand, the
c-plane and the f-plane were nearly equally doped with silicon and
had no difference in the amount of silicon absorbed. Thus, oxygen
has selectivity between the c-plane and the f-plane, whereas
silicon has no such selectivity. For Sample 25, the oxygen
concentration and the silicon concentration were nearly equal in
the f-plane. The resistivity r was 8.times.10.sup.-3 .OMEGA.cm and
was equal in the f-plane and the c-plane. That is, the substrates
had low resistivity r and were uniformly conductive. Silicon was
the main donor responsible for releasing n-type carriers
(conduction electrons) in the c-plane, whereas oxygen and silicon
contributed equally thereto in the f-plane. The cracking ratio K
was 6%, which is very low. The bow U was 6.5 m, indicating that the
bow was small. Thus, these were superior conductive GaN substrates.
In this way, a uniformly conductive substrate crystal having the
same resistivity in the f-plane and the c-plane can be formed by
doping a type II crystal having a superimposed mountain range
structure with oxygen through the f-plane and silicon through the
c-plane so as to complementarily supply carriers.
Sample 26 (Invention Example; Stripe; Type II)
[0268] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0269] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a serrated structure in which ridges and
valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 4.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 4.times.10.sup.3. The silicon
concentration Si.sub.F in the f-plane was 4.times.10.sup.18
cm.sup.-3, and the oxygen concentration O.sub.F in the f-plane was
1.times.10.sup.18/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 4. The amount of oxygen absorbed was
small in the c-plane and was large in the f-plane. Thus, the amount
of oxygen absorbed differed significantly between the c-plane and
the f-plane, showing strong anisotropy. On the other hand, the
c-plane and the f-plane were nearly equally doped with silicon and
had no difference in the amount of silicon absorbed. Thus, oxygen
has selectivity between the c-plane and the f-plane, whereas
silicon has no selectivity between the c-plane and the f-plane. The
resistivity r was 6.times.10.sup.-3 .OMEGA.cm and was equal in the
f-plane and the c-plane. That is, the substrates had low
resistivity r and were uniformly conductive. Silicon was the main
donor responsible for releasing n-type carriers (conduction
electrons) both in the c-plane and in the f-plane. The cracking
ratio K was 8%, which is low. The bow U was 6.3 m, indicating that
the bow was small. In this way, a type II crystal having a mountain
range structure can be nearly equally doped with silicon through
the f-plane and the c-plane to supply n-type carriers so that it
has the same resistivity in the f-plane and the c-plane. Thus, a
uniformly conductive substrate crystal can be formed.
Sample 27 (Invention Example; Stripe; Type II)
[0270] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0271] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a serrated structure in which ridges and
valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane.
[0272] The silicon concentration Si.sub.C in the c-plane was
7.times.10.sup.18 cm.sup.-3, and the oxygen concentration O.sub.C
in the c-plane was 1.times.10.sup.15/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (q) in the c-plane was
7.times.10.sup.3. The silicon concentration Si.sub.F in the f-plane
was 7.times.10.sup.18 cm.sup.-3, and the oxygen concentration
O.sub.F in the f-plane was 1.times.10.sup.18/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (g) in the f-plane was 7. The
amount of oxygen absorbed was small in the c-plane and was large in
the f-plane. On the other hand, the c-plane and the f-plane were
nearly equally doped with silicon and had no difference in the
amount of silicon absorbed. Thus, oxygen has selectivity between
the c-plane and the f-plane, whereas silicon has no selectivity
between the c-plane and the f-plane. The resistivity r was
4.times.10.sup.-3 .OMEGA.cm and was equal in the f-plane and the
c-plane. That is, the substrates had low resistivity r and were
uniformly conductive. Silicon was the main donor responsible for
releasing n-type carriers (conduction electrons) both in the
c-plane and in the f-plane. The cracking ratio K was 11%, which is
low. The bow U was 6.2 m, indicating that the bow was small. In
this way, a type II crystal having a parallel mountain range
structure can be nearly equally doped with silicon through the
f-plane and the c-plane to supply n-type carriers so that it has
the same resistivity in the f-plane and the c-plane. Thus, a
uniformly conductive substrate crystal can be formed.
Sample 28 (Invention Example; Stripe; Type II)
[0273] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0274] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 1.times.10.sup.19 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.4. The silicon concentration
Si.sub.F in the f-plane was 1.times.10.sup.19 cm.sup.-3, and the
oxygen concentration O.sub.F in the f-plane was
1.times.10.sup.18/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 10. The amount of oxygen absorbed was
small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 2.times.10.sup.-3 .OMEGA.cm and was
equal in the f-plane and the c-plane. That is, the substrates had
extremely low resistivity r and were uniformly conductive. Silicon
was the main donor responsible for releasing n-type carriers
(conduction electrons) both in the c-plane and in the f-plane. The
cracking ratio K was 12%, which is low. The bow U was 6 m,
indicating that the bow was small. In this way, a type II crystal
having a parallel mountain range structure can be nearly equally
doped with silicon through the f-plane and the c-plane to supply
n-type carriers so that it has the same resistivity in the f-plane
and the c-plane. Thus, a uniformly conductive substrate crystal can
be formed.
Sample 29 (Invention Example; Stripe; Type II)
[0275] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0276] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 1.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.3. The silicon concentration
Si.sub.F in the f-plane was 1.times.10.sup.18 cm.sup.-3, and the
oxygen concentration O.sub.F in the f-plane was
5.times.10.sup.16/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 20. The amount of oxygen absorbed was
small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 8.times.10.sup.-3 .OMEGA.cm and was
equal in the f-plane and the c-plane. That is, the substrates had
low resistivity r and were uniformly conductive. Silicon was the
main donor responsible for releasing n-type carriers (conduction
electrons) both in the c-plane and in the f-plane. The cracking
ratio K was 5%, which is extremely low. The bow U was 6.4 m,
indicating that the bow was small. In this way, a type II crystal
having a parallel mountain range structure can be nearly equally
doped with silicon through the f-plane and the c-plane to supply
n-type carriers so that it has the same resistivity in the f-plane
and the c-plane. Thus, a uniformly conductive substrate crystal can
be formed.
Sample 30 (Invention Example; Stripe; Type II)
[0277] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C.; the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0278] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 1.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.3. The silicon concentration
Si.sub.F in the f-plane was 1.times.10.sup.18 cm.sup.-3, and the
oxygen concentration O.sub.F in the f-plane was
1.times.10.sup.17/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 10. The amount of oxygen absorbed was
small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 7.9.times.10.sup.-3 .OMEGA.cm and
was equal in the f-plane and the c-plane. That is, the substrates
had low resistivity r and were uniformly conductive. Silicon was
the main donor responsible for releasing n-type carriers
(conduction electrons) both in the c-plane and in the f-plane. The
cracking ratio K was 5%, which is extremely low. The bow U was 6.3
m, indicating that the bow was small. In this way, a type II
crystal having a parallel mountain range structure can be nearly
equally doped with silicon through the f-plane and the c-plane to
supply n-type carriers so that it has the same resistivity in the
f-plane and the c-plane. Thus, a uniformly conductive substrate
crystal can be formed.
Sample 31 (Invention Example; Stripe; Type II)
[0279] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0280] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 1.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.3. The silicon concentration
Si.sub.F in the f-plane was 1.times.10.sup.18 cm.sup.-3, and the
oxygen concentration O.sub.F in the f-plane was
5.times.10.sup.17/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 2. The amount of oxygen absorbed was
small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 7.5.times.10.sup.-3 .OMEGA.cm and
was equal in the f-plane and the c-plane. That is, the substrates
had low resistivity r and were uniformly conductive. Silicon was
the main donor responsible for releasing n-type carriers
(conduction electrons) both in the c-plane and in the f-plane. The
cracking ratio K was 6%, which is very low. The bow U was 6.2 m,
indicating that the bow was small. In this way, a type II crystal
having a parallel mountain range structure can be nearly equally
doped with silicon through the f-plane and the c-plane to supply
n-type carriers so that it has the same resistivity in the f-plane
and the c-plane. Thus, a uniformly conductive substrate crystal can
be formed.
Sample 32 (Invention Example; Stripe; Type II)
[0281] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0282] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 1.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.3. The silicon concentration
Si.sub.F in the f-plane was 1.times.10.sup.18 cm.sup.-3, and the
oxygen concentration O.sub.F in the f-plane was
5.times.10.sup.18/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 0.2. The amount of oxygen absorbed
was small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 7.5.times.10.sup.-3 .OMEGA.cm and
was equal in the f-plane and the c-plane. That is, the substrates
had low resistivity r and were uniformly conductive. Silicon was
the main donor responsible for releasing n-type carriers
(conduction electrons) in the c-plane, whereas oxygen was the main
donor in the f-plane. The cracking ratio K was 7%, which is low.
The bow U was 6 m, indicating that the bow was small. In this way,
a type II crystal having a parallel mountain range structure can be
nearly equally doped with silicon through the f-plane and the
c-plane to supply n-type carriers so that it has the same
resistivity in the f-plane and the c-plane. Thus, a uniformly
conductive substrate crystal can be formed.
Sample 33 (Invention Example; Stripe; Type II)
[0283] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0284] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 1.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.3. The silicon concentration
Si.sub.F in the f-plane was 1.times.10.sup.18 cm.sup.-3, and the
oxygen concentration O.sub.F in the f-plane was
1.times.10.sup.19/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 0.1. The amount of oxygen absorbed
was small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 2.times.10.sup.-3 .OMEGA.cm and was
substantially equal in the f-plane and the c-plane. That is, the
substrates had extremely low resistivity r and were uniformly
conductive. Silicon was the main donor responsible for releasing
n-type carriers (conduction electrons) in the c-plane, whereas
oxygen was the main donor in the f-plane. The cracking ratio K was
10%, which is low. The bow U was 5.8 m, indicating that the bow was
small. In this way, a type II crystal having a parallel mountain
range structure can be nearly equally doped with silicon through
the f-plane and the c-plane and can be predominantly doped with
oxygen through the f-plane so that the crystal is conductive both
in the f-plane and in the c-plane.
Sample 34 (Invention Example; Stripe; Type II)
[0285] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0286] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 4.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 4.times.10.sup.3. The silicon
concentration Si.sub.F in the f-plane was 4.times.10.sup.18
cm.sup.-3, and the oxygen concentration O.sub.F in the f-plane was
1.times.10.sup.19/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 0.4. The amount of oxygen absorbed
was small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 1.9.times.10.sup.-3 .OMEGA.cm and
was equal in the f-plane and the c-plane. That is, the substrates
had remarkably low resistivity r and were uniformly conductive.
Silicon was the main donor responsible for releasing n-type
carriers (conduction electrons) in the c-plane, whereas oxygen was
the main donor in the f-plane. The cracking ratio K was 11%, which
is low. The bow U was 5.5 m, indicating that the bow was small. In
this way, a type II crystal having a parallel mountain range
structure can be nearly equally doped with silicon through the
f-plane and the c-plane and can be heavily doped with oxygen
through the f-plane to form a substrate crystal highly conductive
both in the c-plane and in the f-plane.
Sample 35 (Invention Example; Stripe; Type II)
[0287] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0288] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 7.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 7.times.10.sup.3. The silicon
concentration Si.sub.F in the f-plane was 7.times.10.sup.18
cm.sup.-3, and the oxygen concentration O.sub.F in the f-plane was
1.times.10.sup.19/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 0.7. The amount of oxygen absorbed
was small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 1.8.times.10.sup.-3 .OMEGA.cm and
was equal in the f-plane and the c-plane. That is, the substrates
had remarkably low resistivity r and were uniformly conductive.
Silicon was the main donor responsible for releasing n-type
carriers (conduction electrons) in the c-plane, whereas oxygen was
the main donor in the f-plane. The cracking ratio K was 14%, which
is satisfactorily low. The bow U was 5 m, indicating that the bow
was small. In this way, a type II crystal having a parallel
mountain range structure can be nearly equally doped with silicon
through the f-plane and the c-plane and can be heavily doped with
oxygen through the f-plane to form a substrate crystal highly
conductive both in the c-plane and in the f-plane.
Sample 36 (Invention Example; Stripe; Type II)
[0289] A stripe mask having a stripe mask core spacing w of 500
.mu.m and a mask width s of 50 .mu.m was formed on 2 inch (50 mm)
diameter circular GaAs substrates. After a buffer layer was formed
on the substrates, an epitaxial layer was grown thereon. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0290] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 1.times.10.sup.19 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.4. The silicon concentration
Si.sub.F in the f-plane was 1.times.10.sup.19 cm.sup.-3, and the
oxygen concentration O.sub.F in the f-plane was
1.times.10.sup.19/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 1. The amount of oxygen absorbed was
small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 1.5.times.10.sup.-3 .OMEGA.cm and
was equal in the f-plane and the c-plane. Heavily doped with both
oxygen and silicon, the substrates had remarkably low resistivity r
and were uniformly conductive. Silicon was the main donor
responsible for releasing n-type carriers (conduction electrons) in
the c-plane, whereas oxygen and silicon were the main donors in the
f-plane. The cracking ratio K was 18%, which is satisfactorily low.
The bow U was 4.8 m, indicating that the bow was fairly small. In
this way, a type II crystal having a parallel mountain range
structure can be nearly equally doped with silicon through the
f-plane and the c-plane and can be heavily doped with oxygen
through the f-plane to form a substrate crystal highly conductive
both in the c-plane and in the f-plane.
[0291] Samples 25 to 36, described above, are type II crystals
formed on stripe masks. The present invention can also be applied
to form a similar type II crystal on a dot mask formed on an
underlying substrate. Samples 37 to 39 are type II crystals formed
on dot masks.
Sample 37 (Invention Example; Dot; Type II)
[0292] A dot mask having a dot mask core spacing w of 500 .mu.m and
a dot diameter s of 50 .mu.m was formed on 2 inch (50 mm) diameter
circular GaAs substrates. After a buffer layer was formed on the
substrates, an epitaxial layer was grown thereon. The epitaxial
growth temperature Tq was 1,050.degree. C., the NH.sub.3 partial
pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl partial
pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial layer was
grown to a thickness of 400 .mu.m or more.
[0293] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 1.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.3. The silicon concentration
Si.sub.F in the f-plane was 1.times.10.sup.18 cm.sup.-3, and the
oxygen concentration O.sub.F in the f-plane was
1.times.10.sup.18/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 1. The amount of oxygen absorbed was
small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 8.times.10.sup.-3 .OMEGA.cm and was
equal in the f-plane and the c-plane. That is, the substrates had
low resistivity r and were uniformly conductive. Silicon was the
main donor responsible for releasing n-type carriers (conduction
electrons) in the c-plane, whereas oxygen and silicon were the main
donors in the f-plane. The cracking ratio K was 3%, which is
extremely low. The bow U was 5 m, indicating that the bow was
fairly small. In this way, a type II crystal having numerous
isolated defect cluster regions H at regular intervals can be
nearly equally doped with silicon through the f-plane and the
c-plane and can be more heavily doped with oxygen through the
f-plane to form a substrate crystal highly conductive both in the
c-plane and in the f-plane.
Sample 38 (Invention Example; Dot; Type II)
[0294] A dot mask having a dot mask core spacing w of 500 .mu.m and
a dot diameter s of 50 .mu.m was formed on 2 inch (50 mm) diameter
circular GaAs substrates. After a buffer layer was formed on the
substrates, an epitaxial layer was grown thereon. The epitaxial
growth temperature Tq was 1,050.degree. C., the NH.sub.3 partial
pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl partial
pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial layer was
grown to a thickness of 400 .mu.m or more.
[0295] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 4.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 4.times.10.sup.3. The silicon
concentration Si.sub.F in the f-plane was 4.times.10.sup.18
cm.sup.-3, and the oxygen concentration O.sub.F in the f-plane was
1.times.10.sup.18/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 4. The amount of oxygen absorbed was
small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 6.3.times.10.sup.-3 .OMEGA.cm and
was equal in the f-plane and the c-plane. That is, the substrates
had low resistivity r and were uniformly conductive. Silicon was
the main donor responsible for releasing n-type carriers
(conduction electrons) both in the c-plane and in the f-plane. The
cracking ratio K was 5%, which is extremely low. The bow U was 4.6
m, indicating that the bow was fairly small. In this way, a type II
crystal having numerous isolated defect cluster regions H at
regular intervals can be nearly equally doped with silicon through
the f-plane and the c-plane and can be more heavily doped with
oxygen through the f-plane to form a substrate crystal highly
conductive both in the c-plane and in the f-plane.
Sample 39 (Invention Example; Dot; Type II)
[0296] A dot mask having a dot mask core spacing w of 500 .mu.m and
a dot diameter s of 50 .mu.m was formed on 2 inch (50 mm) diameter
circular GaAs substrates. After a buffer layer was formed on the
substrates, an epitaxial layer was grown thereon. The epitaxial
growth temperature Tq was 1,050.degree. C., the NH.sub.3 partial
pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl partial
pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial layer was
grown to a thickness of 400 .mu.m or more.
[0297] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The type of core crystal was the inverted
layer J. The type of crystal surface was type II, which was formed
because the growth temperature Tq was low (1,050.degree. C.).
Because this was type II, the surface included facets and flat
c-plane faces and had a mountain range structure in which ridges
and valleys alternated. That is, the surface was a mixture of the
c-plane and the f-plane. The silicon concentration Si.sub.C in the
c-plane was 7.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 7.times.10.sup.3. The silicon
concentration Si.sub.F in the f-plane was 7.times.10.sup.18
cm.sup.-3, and the oxygen concentration O.sub.F in the f-plane was
1.times.10.sup.18/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (g) in the f-plane was 7. The amount of oxygen absorbed was
small in the c-plane and was large in the f-plane. On the other
hand, the c-plane and the f-plane were nearly equally doped with
silicon and had no difference in the amount of silicon absorbed.
Thus, oxygen has selectivity between the c-plane and the f-plane,
whereas silicon has no selectivity between the c-plane and the
f-plane. The resistivity r was 4.times.10.sup.-3 .OMEGA.cm and was
equal in the f-plane and the c-plane. That is, the substrates had
low resistivity r and were uniformly conductive. Silicon was the
main donor responsible for releasing n-type carriers (conduction
electrons) both in the c-plane and in the f-plane. The cracking
ratio K was 6%, which is extremely low. The bow U was 4.2 m,
indicating that the bow was fairly small. In this way, a type II
crystal having numerous isolated defect cluster regions H at
regular intervals can be nearly equally doped with silicon through
the f-plane and the c-plane and can be more heavily doped with
oxygen through the f-plane to form a substrate crystal highly
conductive both in the c-plane and in the f-plane.
Sample 40 (Comparative Example; No Mask; C-Plane Growth)
[0298] After a buffer layer was formed on 2 inch (50 mm) diameter
circular GaAs substrates without forming a mask, an epitaxial layer
was grown thereon. This is not an invention example, but a
comparative example, because no mask was formed. This comparative
example is not a known example. The epitaxial growth temperature Tq
was 1,050.degree. C., the NH.sub.3 partial pressure P.sub.NH3 was
10 kPa (0.1 atm), and the GaCl partial pressure P.sub.GaCl was 4
kPa (0.04 atm). The epitaxial layer was grown to a thickness of 400
.mu.m or more.
[0299] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. No core was present because no mask was
formed. A flat surface was formed by c-plane growth. The surface
was neither type I nor type II, but was a uniform c-plane surface
in which no f-plane was present. The silicon concentration Si.sub.C
in the c-plane was 1.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.3. The resistivity r was 0.01
.OMEGA.cm. That is, the substrates had high resistivity r and were
insufficiently conductive. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 75%, which is extremely high. The bow U was 1.5 m,
indicating that the bow was very large. Because these substrates
have high cracking ratio and large bow, they cannot be used as a
substrate on which devices are to be fabricated.
Sample 41 (Comparative Example; No Mask; C-Plane Growth)
[0300] After a buffer layer was formed on 2 inch (50 min) diameter
circular GaAs substrates without forming a mask, an epitaxial layer
was grown thereon. This is not an invention example, but a
comparative example, because no mask was formed. This comparative
example is not a known example. The epitaxial growth temperature Tq
was 1,050.degree. C., the NH.sub.3 partial pressure P.sub.NH3 was
10 kPa (0.1 atm), and the GaCl partial pressure P.sub.GaCl was 4
kPa (0.04 atm). The epitaxial layer was grown to a thickness of 400
.mu.m or more.
[0301] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. No core was present because no mask was
formed. A flat surface was formed by c-plane growth. The surface
was neither type I nor type II, but was a uniform c-plane surface
in which no f-plane was present. The silicon concentration Si.sub.C
in the c-plane was 1.times.10.sup.19 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.4. The resistivity r was
4.7.times.10.sup.-3 .OMEGA.cm. That is, the substrates had low
resistivity r and were satisfactorily conductive. Silicon was the
main donor responsible for releasing n-type carriers (conduction
electrons). The cracking ratio K was 88%, which is extremely high.
The bow U was 1.2 m, indicating that the bow was extremely large.
Because these substrates have high cracking ratio and large bow,
they cannot be used as a substrate on which devices are to be
fabricated.
Sample 42 (Comparative Example; No Mask; C-Plane Growth)
[0302] After a buffer layer was formed on 2 inch (50 mm) diameter
circular GaAs substrates without forming a mask, an epitaxial layer
was grown thereon. This is not an invention example, but a
comparative example, because no mask was formed. This comparative
example is not a known example. The epitaxial growth temperature Tq
was 1,030.degree. C., the NH.sub.3 partial pressure P.sub.NH3 was
10 kPa (0.1 atm), and the GaCl partial pressure P.sub.GaCl was 4
kPa (0.04 atm). The epitaxial layer was grown to a thickness of 400
.mu.m or more.
[0303] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. No core was present because no mask was
formed. A flat surface was formed by c-plane growth. The surface
was neither type I nor type II, but was a uniform c-plane surface
in which no f-plane was present. The silicon concentration Si.sub.C
in the c-plane was 1.times.10.sup.18 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.3. The resistivity r was 0.01
.OMEGA.cm, which is high. Silicon was the main donor responsible
for releasing n-type carriers (conduction electrons). The cracking
ratio K was 92%, which is extremely high. The bow U was 1.3 m,
indicating that the bow was extremely large. Because these
substrates have high cracking ratio and large bow, they cannot be
used as a substrate on which devices are to be fabricated.
Sample 43 (Comparative Example; No Mask; C-Plane Growth)
[0304] After a buffer layer was formed on 2 inch (50 mm) diameter
circular GaAs substrates without forming a mask, an epitaxial layer
was grown thereon. This is not an invention example, but a
comparative example, because no mask was formed. This comparative
example is not a known example. The epitaxial growth temperature Tq
was 1,030.degree. C., the NH.sub.3 partial pressure P.sub.NH3 was
10 kPa (0.1 atm), and the GaCl partial pressure P.sub.GaCl was 4
kPa (0.04 atm). The epitaxial layer was grown to a thickness of 400
.mu.m or more.
[0305] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. No core was present because no mask was
formed. A flat surface was formed by c-plane growth. The surface
was neither type I nor type II, but was a uniform c-plane surface
in which no f-plane was present. The silicon concentration Si.sub.C
in the c-plane was 1.times.10.sup.19 cm.sup.-3, and the oxygen
concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10.sup.4. The resistivity r was
4.7.times.10.sup.-3 .OMEGA.cm, which is low. Silicon was the main
donor responsible for releasing n-type carriers (conduction
electrons). The cracking ratio K was 90%, which is extremely high.
The bow U was 1 m, indicating that the bow was extremely large.
Because these substrates have high cracking ratio and large bow,
they cannot be used as a substrate on which devices are to be
fabricated.
Sample 44 (Comparative Example; Stripe; Type II)
[0306] A stripe mask having a stripe mask spacing w of 500 .mu.m, a
stripe width s of 50 .mu.m, and a pitch of 550 .mu.m was formed on
2 inch (50 mm) diameter circular GaAs substrates. After a buffer
layer was formed on the substrates, the supply of SiH.sub.4 gas was
interrupted, and a GaN layer was epitaxially grown thereon. This is
not an invention example because the silicon source gas was not
supplied. This comparative example is not a known example. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0307] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. These substrates had a periodic structure
with the same period as the mask. The type of the crystals on the
cores was the inverted layer J. The crystal type was type II. The
silicon concentration Si.sub.C in the c-plane was 1.times.10.sup.16
cm.sup.-3, and the oxygen concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10. The resistivity r was high in the
c-plane. The silicon concentration Si.sub.F in the f-plane was
1.times.10.sup.16 cm.sup.-3, and the oxygen concentration O.sub.F
in the f-plane was 4.times.10.sup.18/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (g) in the f-plane was 1/400.
Because silicon was contained in a concentration of
1.times.10.sup.16 cm.sup.-3 despite the fact that no silicon source
material was supplied, silicon remaining in the furnace might have
been absorbed into the crystal, or the above concentration might
have been the detection limit of silicon. These substrates were not
conductive, but semi-insulating. The cracking ratio K was 30%,
which is low. The bow U was 7 m, indicating that the bow was small.
Because these substrates have high resistivity, they cannot be used
as a conductive substrate.
Sample 45 (Comparative Example; Stripe; Type II)
[0308] A stripe mask having a stripe mask spacing w of 500 .mu.m, a
stripe width s of 50 .mu.m, and a pitch of 550 .mu.m was formed on
2 inch (50 mm) diameter circular GaAs substrates. After a buffer
layer was formed on the substrates, the supply of SiH.sub.4 gas was
interrupted, and a GaN layer was epitaxially grown thereon. This is
not an invention example because the silicon source gas was not
supplied. This comparative example is not a known example. The
epitaxial growth temperature Tq was 1,050.degree. C., the NH.sub.3
partial pressure P.sub.NH3 was 10 kPa (0.1 atm), and the GaCl
partial pressure P.sub.GaCl was 4 kPa (0.04 atm). The epitaxial
layer was grown to a thickness of 400 .mu.m or more.
[0309] The V/III ratio b was 2.5. The GaAs substrates were removed
by machining, thus obtaining free-standing GaN substrates having a
thickness of 400 .mu.m. The crystal regions had a periodic
structure with the same period as the mask. The type of the
crystals on the cores was the inverted layer J. The portions above
the unmasked regions included the low-dislocation-density
single-crystal regions Z and the c-plane growth regions Y, thus
having the ZYZ structure. The crystal type was type II. The silicon
concentration Si.sub.C in the c-plane was 1.times.10.sup.16
cm.sup.-3, and the oxygen concentration O.sub.C in the c-plane was
1.times.10.sup.15/cm.sup.3. The silicon-to-oxygen ratio (Si/O
ratio) (q) in the c-plane was 10. The resistivity r was high in the
c-plane. The silicon concentration Si.sub.F in the f-plane was
1.times.10.sup.16 cm.sup.-3, and the oxygen concentration O.sub.F
in the f-plane was 8.times.10.sup.18/cm.sup.3. The
silicon-to-oxygen ratio (Si/O ratio) (g) in the f-plane was 1/800.
Because silicon was contained in a concentration of
1.times.10.sup.16 cm.sup.-3 despite the fact that no silicon source
material was supplied, silicon remaining in the furnace might have
been absorbed into the crystal, or the above concentration might
have been the detection limit of silicon. These substrates were not
conductive, but semi-insulating. The cracking ratio K was 36%,
which is low. The bow U was 6.8 m, indicating that the bow was
small. Because these substrates have high resistivity in the
c-plane, they cannot be used as a conductive substrate.
[0310] The growth temperatures (substrate temperatures) and the
V/III ratios b of the examples in the cited patent documents have
been mentioned in the description of the related art and are
indicated by the black dots and the circled black dots in FIG. 22.
Similarly, the substrate temperatures and the V/III ratios b of the
invention examples and the comparative examples are shown in FIG.
22 to clarify the growth conditions unique to the present
invention.
[0311] The points at the temperatures and the V/III ratios b of the
type II crystals of the present invention are indicated by the
white triangles. There are 15 white triangles at a temperature of
1,050.degree. C. and a V/III ratio b of 2.5.
[0312] The points at the temperatures and the V/III ratios b of the
type I crystals of the present invention are indicated by the white
circles. There are 22 white circles at a temperature of
1,100.degree. C. and a V/III ratio b of 2.5, one white circle at a
temperature of 1,100.degree. C. and a V/III ratio b of 3, and one
white circle at a temperature of 1,100.degree. C. and a V/III ratio
b of 1.
[0313] The ranges of substrate temperature and V/III ratio b of the
present invention are surrounded by the broken line, where
1,080.degree. C. is a temperature at which the intermediate mixed
type is formed.
[0314] FIG. 23 shows the radii of bow curvature (m) and the
cracking ratios (%) of Samples 1 to 45 in a two-dimensional
coordinate system, where the horizontal axis indicates the radius
of bow curvature (m) and the vertical axis indicates the cracking
ratio (%). The numbers are the sample numbers. Type I is indicated
by the white circles. Sample 1 was the best sample, having a bow U
of 8 m and a cracking ratio K of 1%. The bow U was 3.5 m for Sample
24 and was 3.7 m for Samples 22 and 23. For type I, the bow U
ranged from 3.5 to 8 m. The cracking ratio K was 22% for Sample 18.
For type I, the cracking ratio K ranged from 1% to 22%.
[0315] Type II is indicated by the white triangles. The bow U of
Sample 39 was 4.2 m. For type II, the bow U ranged from about 4.2
to 6.5 m. The cracking ratio K was lower for type II than for type
I. The cracking ratio K was 18% for Sample 36 and was 3% for Sample
37. For the invention examples, namely, Samples 1 to 39, the bow U
was 3.5 m U 8 m. For type II alone, the bow U was 4.2
m.ltoreq.U.ltoreq.6.5 m, and the cracking ratio K was
3%.ltoreq.K.ltoreq.18%. Thus, type II is superior to type I in
terms of cracking ratio K and bow U, although they have no
remarkable difference.
[0316] The comparative examples are indicated by the multiplication
signs. Samples 40 to 43 had high cracking ratio and large bow. This
shows that a crystal having superior mechanical properties,
including little internal stress, low cracking ratio, and little
bow, can be formed by facet growth using an underlying substrate on
which a mask (masking portions) is formed. Samples 44 and 45 had
small bow and low cracking ratio, although they are comparative
examples because of the high resistivity.
[0317] FIG. 27 shows the dosages of silicon in the c-plane
(cm.sup.-3) and the surface resistivities (.OMEGA.cm) of the
samples in a logarithmic scale in a two-dimensional coordinate
system, where the white circles indicate type I, the white
triangles indicate type II, the multiplication signs indicate the
comparative examples, and the numbers are the sample numbers.
Samples 1, 2, 3, 5, 8 to 19, and 22 to 24, which are type I, are
plotted at a silicon concentration in the c-plane of
1.times.10.sup.18 cm.sup.-3 and a resistivity r of 0.009 .OMEGA.cm.
The number of samples is 19. For type II, Samples 25, 29, 30, 31,
32, and 37 lie around the above coordinates. The total number of
samples is 25. It is reasonable that the samples of type I having
the same silicon concentration had the same resistivity because the
resistivity was measured on the surfaces of the samples and the
number of silicon atoms was counted on the surfaces of the samples
using SIMS. This is because type I, which can absorb only silicon
because the surface is the c-plane, is not subjected to the effect
of oxygen near the surface. For type II (Samples 25, 29, 30, 31,
and 37), which has the f-plane in the surface, the oxygen
concentration in the f-plane (facets) was equal to the silicon
concentration in the f-plane (Samples 25 and 37) or was lower than
the silicon concentration in the f-plane (Samples 29, 30, and 31).
Hence, if the silicon concentration in the c-plane (equal in the
f-plane) is 1.times.10.sup.18 cm.sup.-3, the resistivity r is about
0.007 to 0.008 .OMEGA.cm. It is assumed that the slight differences
from a resistivity r of 0.009 .OMEGA.cm resulted from oxygen doping
in the f-plane.
[0318] Sample 32 had a resistivity r of 0.0075 .OMEGA.cm despite
the fact that the oxygen concentration in the f-plane was
5.times.10.sup.18 cm.sup.-3, which was higher than the silicon
concentration. This is probably due to a measurement error.
[0319] Because the resistivity should be inversely proportional to
the carrier concentration, if the mobility is constant, coordinate
points of silicon concentration and resistivity should lie along a
line connecting the point at a silicon concentration of
1.times.10.sup.18 cm.sup.-3 and a resistivity r of 0.009 .OMEGA.cm
and the point at a silicon concentration of 1.times.10.sup.19
cm.sup.-3 and a resistivity r of 0.0009 .OMEGA.cm (indicated by the
broken line in FIG. 27) in the logarithmic graph. For type I,
Samples 20, 21, 4, and 7 are located above the broken line. That
is, the resistivity is not decreased (the conductivity is not
increased) proportionally as the dosage of silicon is increased.
This is probably because a higher dosage results in more
scattering, thus decreasing the carrier mobility. For type II, the
resistivity should be decreased by the contribution of oxygen.
Nevertheless, Samples 26, 38, 27, and 39, which are type II, are
located above the broken line. This is probably because the
contribution of oxygen was weak since the oxygen concentration was
lower than the silicon concentration.
[0320] The dosage of silicon of Sample 7, which is type I, was
extremely high, namely, 5.times.10.sup.19 cm.sup.-3, and
accordingly the resistivity r thereof was 0.0018 .OMEGA.cm. Thus,
Sample 7 serves as an excellent substrate with high conductivity.
The above dosage of silicon was the highest of all samples. Despite
such a high dosage, Sample 7 had a bow U of 4.7 m and a cracking
ratio K of 17%, which are both high but acceptable. Thus, Sample 7
was structurally maintained despite such a high dosage of silicon
because the internal stress was reduced by the hybrid HZYZH . . .
structure. That is, whereas a sample formed by c-plane growth so
that it has a flat surface is impractical because the cracking
ratio K is 100%, as disclosed in Patent Documents 2 and 3, a
crystal of the present invention having a flat surface is
structurally robust after being heavily doped with silicon because
the crystal is a type I crystal formed by facet growth after
forming masking portions so that a flat surface is finally formed.
This was demonstrated by Sample 7, which is separated toward the
right end in FIG. 27.
[0321] Sample 36, which is type II, had a silicon concentration of
1.times.10.sup.19 cm.sup.-3 and a resistivity r of 0.0015
.OMEGA.cm, which was the lowest of all samples. Accordingly, the
conductivity was the highest. The oxygen concentration in the
f-plane was 1.times.10.sup.19 cm.sup.-3. That is, both the oxygen
concentration and the silicon concentration were high. The high
conductivity, namely, .sigma.=667/.OMEGA.cm, was the result of the
high oxygen concentration and the high silicon concentration, where
the conductivity .sigma. is the reciprocal of resistivity, that is,
.sigma.=r.sup.-1. Sample 36 had a cracking ratio K of 18% and a bow
U of 4.8 m, which are rather inferior but acceptable.
[0322] The importance of oxygen for type II is well understood by
comparing Samples 28 and 36. These samples had the same silicon
concentration, namely, 1.times.10.sup.19 cm.sup.3, but had
different oxygen concentrations, namely, 1.times.10.sup.18
cm.sup.-3 for Sample 28 and 1.times.10.sup.19 cm.sup.-3 for Sample
36. It is assumed that the difference between the resistivity r of
Sample 28, namely, 0.002 .OMEGA.cm, and the resistivity r of Sample
36, namely, 0.0015 .OMEGA.cm, is due to the difference in the
amount of oxygen.
[0323] Sample 33 had a silicon concentration of 1.times.10.sup.18
cm.sup.-3 and a resistivity r of 0.002 .OMEGA.cm, which was about
one fifth those of the 25 samples having the same silicon
concentration (Samples 1, 2, 3 . . . ). This low resistivity is due
to the effect of oxygen. That is, such a low resistivity was
achieved because the oxygen concentration was 1.times.10.sup.19
cm.sup.-3, which was ten times the silicon concentration.
[0324] Sample 6 had the maximum resistivity r, namely, 0.01
.OMEGA.cm. This sample is type I and had a silicon concentration of
1.times.10.sup.17 cm.sup.-3. Because the silicon concentration was
one tenth those of the above 25 samples having silicon
concentrations around 1.times.10.sup.18 cm.sup.-3 (Samples 1, 2, 3
. . . ), the resistivity r should have been about 0.09 .OMEGA.cm;
however, the measured resistivity r was 0.01 .OMEGA.cm. Because
Sample 6 had a cracking ratio K of 3% and a radius of bow curvature
U of 6.5 m, it should have had a low dosage of silicon. It is
therefore assumed that the measured silicon concentration, namely,
1.times.10.sup.17 cm.sup.-3, is correct. The average silicon
concentration might have been higher because of varying silicon
concentrations because the silicon concentration was measured at
one fixed point using SIMS. Alternatively, the resistivity
measurement might have been erroneous. The range of resistivity r
of the substrates of the present invention was 0.0015
.OMEGA.cm.ltoreq.r.ltoreq.0.01 .OMEGA.cm.
[0325] FIG. 28 is a graph showing the silicon concentrations
(cm.sup.-3) in the f-plane (facets) of the type II crystals,
namely, Samples 25 to 39, along the horizontal axis and the oxygen
concentrations (density) (cm.sup.-3) thereof in the f-plane along
the vertical axis, where Samples 25 to 39 are indicated by the
white triangles.
[0326] For Samples 25, 37, and 36, which are located on a diagonal
line, the silicon concentration in the f-plane was equal to the
oxygen concentration in the f-plane. For Samples 25 and 37, the
silicon and oxygen concentrations were both 1.times.10.sup.18
cm.sup.-3, and the resistivity r was 8.times.10.sup.-3
.OMEGA.cm.
[0327] For Samples 31, 30, 29, 38, 26, 27, 39, and 28, which are
located below the diagonal line, the silicon concentration in the
f-plane was higher than the oxygen concentration in the f-plane
(Si.sub.F>O.sub.F). For Samples 39 and 27, the silicon
concentration was 7.times.10.sup.18 cm.sup.-3, the oxygen
concentration was 1.times.10.sup.18 cm.sup.-3, and the resistivity
r was 4.times.10.sup.-3 .OMEGA.cm. These results suggest that a
substrate whose silicon and oxygen concentrations are the same in
the f-plane often have the same resistivity r. Samples 25, 37, 31,
30, and 29, which had a silicon concentration of 1.times.10.sup.18
cm.sup.-3, had oxygen concentrations of 1.times.10.sup.18 cm.sup.-3
or lower and resistivities r of 8.times.10.sup.-3,
8.times.10.sup.-3, 7.5.times.10.sup.-3, 7.9.times.10.sup.-3, and
8.times.10.sup.-3 .OMEGA.cm, respectively. That is, the resistivity
r was largely determined by the silicon concentration because the
oxygen concentration was lower.
[0328] Samples 33, 34, 35, and 36, which had an oxygen
concentration of 10.times.10.sup.18 cm.sup.-3, had low
resistivities r, namely, 2.times.10.sup.-3, 1.9.times.10.sup.-3,
1.8.times.10.sup.-3, and 1.5.times.10.sup.-3 .OMEGA.cm,
respectively. That is, the resistivity r was low (the conductivity
was high) because of the high oxygen concentration. The differences
in resistivity r are due to the differences in silicon
concentration. Samples 33, 34, 35, and 36 had silicon
concentrations of 1.times.10.sup.18, 4.times.10.sup.18,
7.times.10.sup.18, and 10.times.10.sup.18 cm.sup.-3, respectively.
This demonstrates that the resistivity r is decreased as the
silicon and oxygen concentrations are increased.
[0329] Samples having the same silicon concentration and different
oxygen concentrations will now be compared. For Samples 36 and 28,
the silicon concentration was 10.times.10.sup.18 cm.sup.-3, and the
difference in oxygen concentration was ten times. The resistivities
r of Samples 36 and 28 were 1.5.times.10.sup.-3 and
2.times.10.sup.-3 .OMEGA.cm, respectively, and the difference
therebetween was 1.3 times. For Samples 35 and 27, the silicon
concentration was 7.times.10.sup.18 cm.sup.-3, and the difference
in oxygen concentration was ten times. The resistivities r of
Samples 35 and 27 were 1.8.times.10.sup.-3 and 4.times.10.sup.-3
.OMEGA.cm, respectively, and the difference therebetween was 2.2
times. For Samples 33 and 25, the silicon concentration was
1.times.10.sup.18 cm.sup.-3, and the difference in oxygen
concentration was ten times. The resistivities r of Samples 33 and
25 were 2.times.10.sup.-3 and 8.times.10.sup.-3 .OMEGA.cm,
respectively, and the difference therebetween was four times. These
results suggest that for type II, as the silicon and oxygen
concentrations in the f-plane are increased, the resistivity r is
decreased so as to be inversely proportional to the square roots of
the silicon and oxygen concentrations, rather than linearly
inversely proportional to the silicon and oxygen
concentrations.
[0330] FIG. 29 is a graph showing the silicon concentrations in the
c-plane of the type II crystals, namely, Samples 25 to 39, along
the horizontal axis and the silicon concentrations thereof in the
f-plane along the vertical axis. For Samples 25, 29, 30, 31, 32,
33, and 37, the silicon concentration was 1.times.10.sup.18
cm.sup.-3 and was equal in the c-plane and the f-plane. For Samples
26, 34, and 38, the silicon concentration was 4.times.10.sup.18
cm.sup.-3 and was equal in the c-plane and the f-plane. For Samples
27, 35, and 39, the silicon concentration was 7.times.10.sup.18
cm.sup.-3 and was equal in the c-plane and the f-plane. For Samples
36 and 28, the silicon concentration was 10.times.10.sup.18
cm.sup.-3 and was equal in the c-plane and the f-plane. These
coordinate points are located on the diagonal line at 45.degree.,
meaning that the same amount of silicon was absorbed into the
c-plane and the f-plane, that is, Si.sub.F.lamda.Si.sub.C, which is
equivalent to the equation [Si].sub.z.dbd.[Si].sub.y described
above. This demonstrates that silicon has no plane orientation
dependence, in other words, no plane selectivity.
[0331] FIG. 30 is a graph showing the oxygen concentrations in the
f-plane of the type II crystals, namely, Samples 25 to 39, along
the horizontal axis and the oxygen concentrations thereof in the
c-plane along the vertical axis. The horizontal axis indicates the
oxygen concentration (cm.sup.-3) in the f-plane. The vertical axis
indicates the oxygen concentration (cm.sup.-3) in the c-plane. For
Samples 33, 34, 35, and 36, the oxygen concentration in the f-plane
was 1.times.10.sup.19 cm.sup.-3, and the oxygen concentration in
the c-plane was 1.times.10.sup.15 cm.sup.-3. For Samples 25, 26,
27, 28, and 37 to 39, the oxygen concentration in the f-plane was
1.times.10.sup.18 cm.sup.-3, and the oxygen concentration in the
c-plane was 1.times.10.sup.15 cm.sup.-3. For Samples 29 and 30, the
oxygen concentration in the f-plane was 5.times.10.sup.16 cm.sup.-3
for Sample 29 and 1.times.10.sup.17 cm.sup.-3 for Sample 30, and
the oxygen concentration in the c-plane was 1.times.10.sup.15
cm.sup.-3. Because the c-plane and the f-plane were exposed to the
same atmosphere, it appears unreasonable that the amount of oxygen
absorbed into the c-plane was 1.times.10.sup.15 cm.sup.-3 for every
sample despite the fact that the difference in the amount of oxygen
absorbed into the f-plane was as large as 100 times or 200 times.
The amount of oxygen absorbed into the c-plane is supposed to be
proportional to the amount of oxygen absorbed into the f-plane.
[0332] It is assumed that the above oxygen concentration, namely,
1.times.10.sup.15 cm.sup.-3, was the oxygen detection limit of the
SIMS used, that is, the SIMS read 1.times.10.sup.15 cm.sup.-3 for
amounts of oxygen below 1.times.10.sup.15 cm.sup.-3. If an oxygen
concentration in the f-plane of 1.times.10.sup.19 cm.sup.-3 and an
oxygen concentration in the c-plane of 1.times.10.sup.15 cm.sup.-3
are correct, the ratio is 10.sup.4 times. For the samples having
the lower concentration in the f-plane, as indicated by the broken
line at 45.degree. in FIG. 30, the concentration in the c-plane
should be located lower from the point of concentration in the
f-plane, as indicated by the arrow. Specifically, because Samples
25, 26, 27, 28, and 37 to 39 had an oxygen concentration in the
f-plane of 1.times.10.sup.18 cm.sup.-3, the oxygen concentration in
the c-plane should have been 1.times.10.sup.14 cm.sup.-3, which was
unknown because it was below the detection limit. That is, the
oxygen concentrations in the c-plane shown in Table, which were all
1.times.10.sup.15 cm.sup.-3, are incorrect, and the actual oxygen
concentrations in the c-plane could not be measured because they
were below the detection limit. Accordingly, the oxygen
concentration in the f-plane can be assumed to be zero. Thus, the
oxygen concentration in the c-plane growth regions Y is zero,
namely, O.sub.C.dbd.[O].sub.y=0.
[0333] Type II has four concentration parameters: the silicon
concentration in the c-plane, the oxygen concentration in the
c-plane, the silicon concentration in the f-plane, and the oxygen
concentration in the f-plane. According to the above results, the
oxygen concentration in the c-plane was zero (O.sub.C=0), and the
silicon concentration in the c-plane was equal to the silicon
concentration in the f-plane (Si.sub.C.dbd.Si.sub.F). That is,
there are two free parameters: the oxygen concentration in the
f-plane (O.sub.F=[O].sub.Z) and the common silicon concentration
(Si.sub.F=[Si].sub.z.dbd.Si.sub.C.dbd.[Si].sub.y), which are simply
written as [O] and [Si], respectively. For type I, [Si] is the only
parameter because the surface is the c-plane, which corresponds to
the fact that Samples 1, 2, 3, 5, 8 to 19, and 22 to 24, indicated
by the white circles in FIG. 27, are located at the point of a
silicon concentration of 1.times.10.sup.18 cm.sup.-3 and a
resistivity r of 9.times.10.sup.-3 .OMEGA.cm. Samples 20, 21, 4,
and 7 are type I and had higher silicon concentrations and lower
resistivities r. If these points are approximated by a straight
line passing through the point of a silicon concentration of
1.times.10.sup.18 cm.sup.-3 and a resistivity r of
9.times.10.sup.-3 .OMEGA.cm, the one-dot chain line passing through
the point of a silicon concentration of 1.times.10.sup.19 cm.sup.-3
and a resistivity r of 4.4.times.10.sup.-3 .OMEGA.cm is obtained.
If the relationship between the resistivity r and the silicon
concentration is determined by the straight line passing through
the above two points, the following approximate equation can be
obtained for type I:
log r=3.55-0.311 log [Si]
If the unit of resistivity is 1.times.10.sup.-3 .OMEGA.cm and is
denoted by r', r=r'.times.10.sup.-3. If the unit of silicon
concentration is 1.times.10.sup.18 cm.sup.-3 and is denoted by Si',
[Si'].times.10.sup.18=[Si]. For type I, the relationship between
the resistivity r' and the silicon concentration Si' is as
follows:
log r'=-0.311 log [S']+0.954
This is the approximate equation of the broken line in FIG. 27.
Sample 7 (r'=1.8, Si'=50) and Sample 6 (r'=10, Si'=0.1) deviate
downward from the line. These samples can be included if the
constant term is +0.689 or more. Sample 20 (r'=7, Si'=4) and Sample
4 (r'=4.7, Si'=10) deviate downward from the line. These samples
can be included if the constant term is 1.032 or less. That is, all
samples of type I can be included by the following equation:
0.689.ltoreq.log r'+0.311 log [Si'].ltoreq.1.032
The resistivity r' is inversely proportional to the silicon
concentration raised to the power of 0.311, rather than linearly
inversely proportional to the silicon concentration. It is unknown
why the resistivity r' is not inversely proportional to the first
power of the silicon concentration. This may be due to a decrease
in electron mobility as a result of an increase in silicon
concentration, although it remains unclear. Still, the case of type
I is simpler because only silicon is present on the surface.
[0334] The case of Type II is more complicated. In FIG. 27, the
samples of type II (white triangles) having the same silicon
concentrations had different resistivities. Samples 25, 29, 30, 31,
32, 33, and 37 had the same silicon concentration, namely,
1.times.10.sup.18 cm.sup.-3, but had different resistivities.
Samples 38, 26, and 34 had the same silicon concentration, namely,
4.times.10.sup.18 cm.sup.-3, but had different resistivities. Thus,
the resistivity is not determined only by the silicon
concentration; the oxygen concentration is important.
[0335] FIG. 31 shows the oxygen concentration (cm.sup.-3) in the
f-plane and the resistivity (.OMEGA.cm) in a two-dimensional
coordinate system. Samples 33, 34, 35, and 36, which had an oxygen
concentration of 1.times.10.sup.19 cm.sup.-3, had low
resistivities, namely, 2.times.10.sup.-3, 1.9.times.10.sup.-3,
1.8.times.10.sup.-3, and 1.5.times.10.sup.-3 .OMEGA.cm,
respectively. Thus, the samples having the highest oxygen
concentration had the lowest resistivities. Although Samples 33,
34, 35, and 36 were heavily doped with oxygen, they had cracking
ratios of 10%, 11%, 14%, and 18%, respectively, which are lower
than 22% and are satisfactory. The differences in resistivity and
cracking ratio between the four samples are due to the differences
in silicon concentration.
[0336] Samples 37, 25, 38, and 26 had an oxygen concentration of
1.times.10.sup.18 cm.sup.-3 and a resistivity of 6 to
8.times.10.sup.-3 .OMEGA.cm. These differences are due to the
differences in silicon concentration. The silicon concentration was
1 to 4.times.10.sup.18 cm.sup.-3. If the unit of oxygen
concentration is 1.times.10.sup.18 cm.sup.-3 and is denoted by O'
and the coefficient for type I, namely, -0.311, is used, the
following equation is obtained:
log r'=-0.311 log(1.6[O']+[Si'])+1.032
This applies to oxygen concentrations below 1.times.10.sup.18
cm.sup.-3.
[0337] Samples 33, 34, 35, and 36 had an oxygen concentration of
1.times.10.sup.19 cm.sup.-3, silicon concentrations [Si'] of 1, 4,
7, and 10, respectively, and resistivities r' of 2, 1.9, 1.8, and
1.5, respectively. If the above coefficient, -0.311, is used, the
following equation is obtained:
log r'=-0.311 log([O']+[Si'])+0.62
This applies to oxygen concentrations above 1.times.10.sup.19
cm.sup.-3.
[0338] Accordingly, all samples of type II are included by the
following equation:
log r'=-0.311 log(.kappa.[O']+[Si'])+S
where .kappa. is 1 to 1.6 and S is 0.62 to 1.032. This is a
phenomenological equation, and .kappa. may be 1.1, 1.3, or 1.5. The
coefficient used is 0.311 for consistency with type I. For type II,
the coefficient may vary between 0.3 and 0.5.
[0339] .kappa. serves as a measure of the effectiveness of silicon
and oxygen as a dopant. If .kappa.=1, oxygen and silicon release
the same number of n-type carriers. If .kappa.=1.6, silicon
releases only 0.625 times as many n-type carriers as oxygen.
[0340] FIG. 32 is a graph showing the sums of the silicon
concentrations (cm.sup.-3) in the c-plane and the oxygen
concentrations (cm.sup.-3) in the f-plane of the type II samples
along the horizontal axis and the resistivities (.OMEGA.cm) thereof
along the vertical axis. That is, the horizontal axis indicates
[Si].sub.C+[O].sub.F. This graph is intended to examine the
assumption that oxygen and silicon each independently release one
n-type carrier. If the sums of the silicon and oxygen
concentrations and the resistivities r of the samples are plotted
in a logarithmic graph, it reveals that the above assumption is
correct to some extent. The assumption that the two dopants are
independent is supported by Sample 36, which was most heavily doped
with silicon and oxygen and had the lowest resistivity. The graph
also shows that Samples 35, 34, 39, 27, 26, and 38 are located on
the same straight line, namely, line AB, drawn from the point of
Sample 36. For Sample 36 (point A), the sum of the silicon and
oxygen concentrations was 20.times.10.sup.18 cm.sup.-3, and the
resistivity r was 1.5.times.10.sup.-3 .OMEGA.cm. For Sample 26
(point B), the sum of the silicon and oxygen concentrations was
5.times.10.sup.18 cm.sup.-3, and the resistivity r was
6.times.10.sup.-3 .OMEGA.cm. In the same manner as above, the units
of silicon and oxygen concentrations are 1.times.10.sup.18
cm.sup.-3 and are denoted by Si' and O', respectively, and the unit
of resistivity is 1.times.10.sup.-3 .OMEGA.cm and is denoted by r'.
With Si', O', and r', the coordinates of points A and B are
represented as follows:
Point A [Si']+[O']=20
r'=1.5
Point B [Si']+[O']=5
r'=6
Line AB is a line inclined downward to the right exactly at
45.degree., meaning that the resistivity is exactly inversely
proportional to the sum of the silicon and oxygen concentrations.
Line AB is represented by the following equation:
log r'=1.478-log {[Si']+[O']} (AB)
where log is a common logarithm. If the equation is expressed as a
normal inversely proportional equation, a simple and clear equation
is obtained as follows:
r'=30/{[Si']+[O']} (AB')
The fact that the coefficient of the silicon concentration is equal
to that of the oxygen concentration means that they have the same
activation rates. The fact that there is a simple inversely
proportional relationship means that a simple free electron model
(Drude model) holds, that is, 1/r=.sigma.=ne.mu., where n is the
n-type carrier concentration, e is the electron charge, and .mu. is
the mobility. Because the silicon and oxygen concentrations have
the same coefficient, they have nearly the same activation rate
.nu., that is, .nu..sub.Si=.nu..sub.O=.nu..
[0341] Hence, the n-type carrier concentration n is .nu.{[Si]+[O]}.
Accordingly,
r=1/[e.nu..mu.{[Si]+[O]}]
Because r=r'.times.10.sup.-3 .OMEGA.cm and
[Si]+[O]={[Si']+[O']}.times.10.sup.18 cm.sup.-3,
r'.times.10.sup.-3=1/[e.nu..mu.{[Si']+[O']}.times.10.sup.18]
If this is equal to equation AB' above,
e.nu..mu.=10.sup.3/30.times.10.sup.18=33.times.10.sup.-18
where e is 1.6.times.10.sup.-19. Dividing this by e gives the
following equation:
.nu..mu.=206 cm.sup.2/Vs
The value of .nu. is unknown from the above data alone. If the
activation rate .nu. is close to 1, the mobility is 200
cm.sup.2/Vs.
[0342] The equation indicating that the product of the resistivity
r' and the sum of the silicon and oxygen concentrations
([Si']+[O']) is 30 is an approximate equation that applies well to
Samples 36, 35, 34, 39, 27, 26, and 38 in FIG. 32. However, Samples
25, 37, 31, 30, 29, 28, and 33 deviate from the line. For these
samples, the resistivity should also be expressed as a function of
the sum of the silicon and oxygen concentrations. For Sample 30
(point C), the sum of the silicon and oxygen concentrations was
1.1.times.10.sup.18 cm.sup.-3, and the resistivity r was
7.9.times.10.sup.-3 .OMEGA.cm. The equation of line AC connecting
point A (Sample 36) and point C (Sample 30) will now be considered.
Points A and C have the following coordinates:
Point A [Si']+[O']=20
r'=1.5
Point C [Si'][O']=1.1
r'=7.9
Hence, line AC is represented by the following equation:
log r'=0.9213-0.5728 log {[Si']+[O']} (AC)
If this is expressed as an exponential equation, rather than a
logarithmic equation,
r'=8.34257/{[Si']+[O']}.sup.0.5728
[0343] The type II samples other than Sample 32 are located between
line AC and line AB. That is, the resistivity is given by the
following inequality:
0.9213-0.5728 log {[Si']+[O']}.ltoreq.log r'.ltoreq.1.478-log
{[Si']+[O']}
This represents the relationship between the concentrations and the
resistivities of all type II samples other than Sample 32. If this
is expressed as an exponential inequality,
8.34257/{[Si']+[O']}.sup.0.5728.ltoreq.r'.ltoreq.30/{[Si']+[O']}
The fact that this relationship holds for type II suggests that
silicon and oxygen each release one n-type carrier as a donor
without interfering with each other. Thus, double doping with
silicon and oxygen has advantageous properties.
* * * * *