U.S. patent application number 12/244474 was filed with the patent office on 2009-01-22 for single crystal silicon having improved gate oxide integrity.
This patent application is currently assigned to MEMC ELECTRONIC MATERIALS, INC.. Invention is credited to Francesco Bonoli, Robert J. Falster, Paolo Mutti, Vladimir V. Voronkov.
Application Number | 20090022930 12/244474 |
Document ID | / |
Family ID | 22984626 |
Filed Date | 2009-01-22 |
United States Patent
Application |
20090022930 |
Kind Code |
A1 |
Falster; Robert J. ; et
al. |
January 22, 2009 |
SINGLE CRYSTAL SILICON HAVING IMPROVED GATE OXIDE INTEGRITY
Abstract
A process for producing a single crystal silicon wafer
comprising a front surface, a back surface, a lateral surface
joining the front and back surfaces, a central+ axis perpendicular
to the front and back surfaces, and a segment which is axially
symmetric about the central axis extending substantially from the
front surface to the back surface in which crystal lattice
vacancies are the predominant intrinsic point defect, the segment
having a radial width of at least about 25% of the radius and
containing agglomerated vacancy defects and a residual
concentration of crystal lattice vacancies wherein (i) the
agglomerated vacancy defects have a radius of less than about 70 nm
and (ii) the residual concentration of crystal lattice vacancy
intrinsic point defects is less than the threshold concentration at
which uncontrolled oxygen precipitation occurs upon subjecting the
wafer to an oxygen precipitation heat treatment.
Inventors: |
Falster; Robert J.; (London,
GB) ; Voronkov; Vladimir V.; (Merano, IT) ;
Mutti; Paolo; (Milan, IT) ; Bonoli; Francesco;
(Novara, IT) |
Correspondence
Address: |
Richard A. Schuth (MEMC);Armstrong Teasdale LLP
One Metropolitan Square, Suite 2600
St. Louis
MO
63102-2740
US
|
Assignee: |
MEMC ELECTRONIC MATERIALS,
INC.
St. Peters
MO
|
Family ID: |
22984626 |
Appl. No.: |
12/244474 |
Filed: |
October 2, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11089102 |
Mar 24, 2005 |
7431765 |
|
|
12244474 |
|
|
|
|
10039196 |
Jan 2, 2002 |
6986925 |
|
|
11089102 |
|
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Current U.S.
Class: |
428/64.1 |
Current CPC
Class: |
C30B 29/06 20130101;
C30B 15/203 20130101; Y10T 428/21 20150115; C30B 15/206
20130101 |
Class at
Publication: |
428/64.1 |
International
Class: |
B32B 3/26 20060101
B32B003/26 |
Claims
1. A single crystal silicon wafer comprising a front surface, a
back surface, a lateral surface joining the front and back
surfaces, a central axis perpendicular to the front and back
surfaces, and a segment which is axially symmetric about the
central axis extending substantially from the front surface to the
back surface in which crystal lattice vacancies are the predominant
intrinsic point defect, the segment having a radial width of at
least about 25% of the radius and containing agglomerated vacancy
defects and a residual concentration of crystal lattice vacancies
wherein (i) the agglomerated vacancy defects have a radius of less
than about 70 nm and (ii) the residual concentration of crystal
lattice vacancy intrinsic point defects is less than the threshold
concentration at which uncontrolled oxygen precipitation occurs
upon subjecting the wafer to an oxygen precipitation heat
treatment.
2. The wafer of claim 1 wherein the wafer is capable of having a
concentration of oxygen precipitates of less than 1.times.10.sup.8
cm.sup.-3, upon being subjected to a rapid thermal anneal in which
the wafer is rapidly heated to a temperature of 1200.degree. C. in
the essential absence of oxygen and then cooled, and then subjected
to an oxygen precipitation heat treatment, consisting essentially
of annealing said wafer at 800.degree. C. for 4 hours and then at
1000.degree. C. for 16 hours.
3. The wafer of claim 1 wherein said wafer has a nominal diameter
of at least 200 mm.
4. The wafer of claim 1 wherein the segment has a width of at least
50% of the radius of the wafer.
5. The wafer of claim 1 wherein the segment has a width of at least
75% of the radius of the wafer.
6. The wafer of claim 1 wherein the segment has a width of at least
95% of the radius of the wafer.
7. The wafer of claim 1 wherein the agglomerated vacancy defects
have an average radius of less than 60 nm.
8. The wafer of claim 1 wherein the agglomerated vacancy defects
have an average radius of less than 50 nm.
9. The wafer of claim 1 wherein the agglomerated vacancy defects
have an average radius of less than 40 nm.
10. The wafer of claim 1 wherein the agglomerated vacancy defects
have an average radius of less than 30 nm.
11. The wafer of claim 1 wherein the average void density is less
than 1.times.10.sup.8 cm.sup.-3.
12. The wafer of claim 1 wherein the average void density is less
than 5.times.10.sup.7 cm.sup.-3.
13. The wafer of claim 1 wherein the average void density is less
than 1.times.10.sup.7 cm.sup.-3.
14. The wafer of claim 1 wherein the average void density is less
than 5.times.10.sup.6 cm.sup.-3.
15. The wafer of claim 1 wherein the average void density is
greater than 5.times.10.sup.6 cm.sup.-3.
16. The wafer of claim 1 wherein the average void density is
greater than 1.times.10.sup.7 cm.sup.-3.
17. The wafer of claim 1 wherein the average void density is
greater than 5.times.10.sup.7 cm.sup.-3.
18. The wafer of claim 1 wherein the average void density is
greater than 1.times.10.sup.3 cm.sup.-3.
19. The wafer of claim 1 wherein the oxygen content is less than 13
PPMA.
20. The wafer of claim 19 wherein the carbon concentration is less
than 5.times.10.sup.16 atoms/cm.sup.3.
21. The wafer of claim 20 wherein the nitrogen content is less than
1.times.10.sup.13 atoms/cm.sup.3.
22. The wafer of claim 19 wherein the nitrogen content is less than
1.times.10.sup.13 atoms/cm.sup.3.
23. The wafer of claim 1 wherein the carbon concentration is less
than 5.times.10.sup.16 atoms/cm.sup.3.
24. The wafer of claim 23 wherein the nitrogen content is less than
1.times.10.sup.13 atoms/cm.sup.3.
25. The wafer of claim 1 wherein the nitrogen content is less than
1.times.10.sup.13 atoms/cm.sup.3.
26. The wafer of claim 1 wherein the residual vacancy concentration
is less than 3.times.10.sup.12 cm.sup.-3.
27. The wafer of claim 1 wherein the residual vacancy concentration
is less than 2.times.10.sup.12 cm.sup.-3.
28. The wafer of claim 1 wherein the residual vacancy concentration
is less than 1.times.10.sup.12 cm.sup.3.
29. The wafer of claim 1 wherein the residual vacancy concentration
is less than 5.times.10.sup.11 cm.sup.-3.
30. The wafer of claim 1 wherein the residual vacancy concentration
is less than 1.times.10.sup.11 cm.sup.-3.
31. The wafer of claim 1 wherein the residual vacancy concentration
is less than 5.times.10.sup.10 cm.sup.-3.
32. The wafer of claim 1 wherein the residual vacancy concentration
is less than 1.times.10.sup.10 cm.sup.-3.
33. The wafer of claim 1 wherein the wafer has a homoepitaxial
layer deposited on the front surface thereof.
Description
REFERENCE TO RELATED APPLICATION
[0001] This application is a division of application Ser. No.
11/089,102, filed Mar. 24, 2005, now U.S. Pat. No. 7,431,765, which
is a division of application Ser. No. 10/039,196, filed Jan. 2,
2002, now U.S. Pat. No. 6,986,925, which claims the benefit of U.S.
Provisional Application No. 60/259,362, filed Jan. 2, 2001, all of
which are incorporated in their entirety herein by reference.
BACKGROUND OF THE INVENTION
[0002] In general, the present invention relates to the preparation
of a single crystal silicon ingot according to the Czochralski
method. In particular, the invention relates to a high throughput
process for preparing single crystal silicon wafers having improved
gate oxide integrity, wherein the growth conditions of a single
crystal silicon ingot, from which the wafers are derived, are
controlled. More specifically, the growth conditions of a single
crystal silicon ingot, including the growth velocity, the average
axial temperature gradient and the cooling rate, are controlled in
order to limit the size, and in some cases the density, of
vacancy-related agglomerated defects, and optionally the residual
vacancy concentration, in single crystal silicon wafers derived
therefrom. Additionally, the present invention relates to a more
accurate and reliable method by which to evaluate the gate oxide
integrity of such wafers.
[0003] Single crystal silicon, which is the starting material in
most processes for the fabrication of semiconductor electronic
components, is commonly prepared by the so-called Czochralski
("Cz") method. In this method, polycrystalline silicon
("polysilicon") is charged to a crucible and melted, a seed crystal
is brought into contact with the molten silicon, and then a single
crystal is grown by slow extraction. After formation of a neck is
complete, the diameter of the crystal is enlarged by, for example,
decreasing the pulling rate and/or the melt temperature until the
desired or target diameter is reached. The cylindrical main body of
the crystal which has an approximately constant diameter is then
grown by controlling the pull rate and the melt temperature while
compensating for the decreasing melt level. Near the end of the
growth process but before the crucible is emptied of molten
silicon, the crystal diameter is typically reduced gradually to
form a tail end in the form of an end-cone. The end-cone usually is
formed by increasing the crystal pull rate and heat supplied to the
crucible. When the diameter becomes small enough, the crystal is
then separated from the melt.
[0004] In recent years, it has been recognized that a number of
defects in single crystal silicon form in the growth chamber as the
ingot cools from the temperature of solidification. More
specifically, as the ingot cools intrinsic point defects, such as
crystal lattice vacancies or silicon self-interstitials, remain
soluble in the silicon lattice until some threshold temperature is
reached, below which the given concentration of intrinsic point
defects becomes critically supersaturated. Upon cooling to below
this threshold temperature, a reaction or agglomeration event
occurs, resulting in the formation of agglomerated intrinsic point
defects.
[0005] The type and initial concentration of these intrinsic point
defects in the silicon are determined as the ingot cools from the
temperature of solidification (i.e., about 1410.degree. C.) to a
temperature greater than about 1300.degree. C. (i.e., about
1325.degree. C., 1350.degree. C. or more); that is, the type and
initial concentration of these defects are controlled by the ratio
v/G.sub.0, where v is the growth velocity and G.sub.0 is the
average axial temperature gradient over this temperature range. In
general, a transition from self-interstitial dominated growth to
vacancy dominated growth occurs near a critical value of v/G.sub.0
which, based upon currently available information, appears to be
about 2.1.times.10.sup.-5 cm.sup.2/sK, where G.sub.0 is determined
under conditions in which the axial temperature gradient is
constant within the temperature range defined above. Accordingly,
process conditions, such as growth rate (which affect v), as well
as hot zone configurations (which affect G.sub.0), can be
controlled to determine whether the intrinsic point defects within
the silicon single crystal will be predominantly vacancies (where
v/G.sub.0 is generally greater than the critical value) or
self-interstitials (where v/G.sub.0 is generally less than the
critical value).
[0006] Defects associated with the agglomeration of crystal lattice
vacancies, or vacancy intrinsic point defects, include such
observable crystal defects as D-defects, Flow Pattern Defects
(FPDs), Gate Oxide Integrity (GOI) Defects, Crystal Originated
Particle (COP) Defects, and crystal originated Light Point Defects
(LPDs), as well as certain classes of bulk defects observed by
infrared light scattering techniques (such as Scanning Infrared
Microscopy and Laser Scanning Tomography). Also present in regions
of excess vacancies are defects which act as the nuclei for the
formation of oxidation induced stacking faults (OISF). It is
speculated that this particular defect is a high temperature
nucleated oxygen precipitate catalyzed by the presence of excess
vacancies.
[0007] Agglomerated defect formation generally occurs in two steps;
first, defect "nucleation" occurs, which is the result of the
intrinsic point defects, such as vacancies, being supersaturated at
a given temperature. Once this "nucleation threshold" temperature
is reached, intrinsic point defects, such as vacancies, start to
agglomerate (i.e., void formation begins). The intrinsic point
defects will continue to diffuse through the silicon lattice as
long as the temperature of the portion of the ingot in which they
are present remains above a second threshold temperature (i.e., a
"diffusivity threshold"), below which intrinsic point defects are
no longer mobile within commercially practical periods of time.
While the ingot remains above this temperature, vacancy intrinsic
point defects, for example, diffuse through the crystal lattice to
sites where agglomerated vacancy defects, or voids, are already
present, effectively causing a given agglomerated defect to grow in
size. This is because these agglomerated defect sites essentially
act as "sinks," attracting and collecting vacancy intrinsic point
defects because of the more favorable energy state of the
agglomeration. Accordingly, the formation and size of such
agglomerated defects are dependent upon the growth conditions,
including v/G.sub.0 (which impacts the initial concentration of
such point defects) and the cooling rate or residence time of the
main body of the ingot over the range of temperatures bound by the
"nucleation threshold" at the upper end and the "diffusivity
threshold" (which impacts the size and density of such defects) at
the lower end.
[0008] Maximizing throughput is a primary concern in the
cost-effective production of single crystal silicon wafers. As a
result, growing single crystal silicon ingots at the highest
possible growth rates is the goal for all silicon manufacturers.
However, until now, there has generally been no clear way to
produce single crystal silicon of an acceptable quality using such
growth conditions. For example, high pull rates/cooling rates
typically mean a high vacancy concentration, which leads to a high
concentration of small, agglomerated defects. Such conditions are
favorable, for example, with respect to light point defects (LPDs)
because integrated circuit manufacturers typically require that the
number of such defects in excess of about 0.2 microns in size not
exceed about 20 for a 200 mm diameter wafer. However, such
conditions are also unfavorable because they have traditionally
been considered to yield wafers having poor gate oxide integrity.
In contrast, when slower pull rates/cooling rates are employed as a
means by which to improve GOI (slow cooling typically resulting in
a few, very large agglomerated vacancy defects being formed), the
resulting size of LPDs is unacceptable.
[0009] An additional area of concern, with respect to high pull
rates/cooling rates, is the residual vacancy concentration. More
specifically, high pull rates typically lead to high vacancy
concentrations in the silicon that is formed, and well as high
cooling rates. High cooling rates, in turn, typically lead to a
high residual vacancy concentration (i.e., the concentration of
silicon lattice vacancies present in the silicon, once it has
cooled to a temperature at which vacancies are essentially no
longer mobile). High residual vacancy concentrations are
problematic because, upon subsequent heating, they can lead to
uncontrolled oxygen precipitation.
[0010] Accordingly, a need continues to exist for a method by which
single crystal silicon ingots may be grown by the Czochralski
process under conditions which maximize not only throughput, but
also the yield of the silicon wafers obtained therefrom. Such a
process would optimize growth conditions such that the fastest
possible pull rate of a given crystal puller could be employed, in
view of the need to limit the size, and in some cases the density,
of agglomerated vacancy defects, as well as the residual vacancy
concentration.
SUMMARY OF THE INVENTION
[0011] Among the several features of the present invention
therefore is the provision of a single crystal silicon ingot, from
which a single crystal silicon wafer may be obtained, having
improved gate oxide integrity, and a process for the preparation
thereof; the provision of such a process wherein the highest
possible pull rates, for a given crystal puller, can be employed,
thus maximizing throughput and yield; the provision of such a
process wherein growth conditions are controlled to limit the size
of agglomerated vacancy defects formed; the provision of such a
process wherein the density of agglomerated vacancy defects is
controlled; and, the provision of such a process wherein the
residual vacancy concentration is limited to avoid uncontrolled
oxygen precipitation.
[0012] Briefly, therefore, the present invention is directed to a
process for growing a single crystal silicon ingot in which the
ingot comprises a central axis, a seed-cone, a tail end, and a
constant diameter portion between the seed-cone and the tail end
having a lateral surface and a radius extending from the central
axis to the lateral surface, the ingot being grown from a silicon
melt and then cooled from the solidification temperature in
accordance with the Czochralski method. The process comprises: (i)
controlling a growth velocity, v, and an average axial temperature
gradient, G.sub.0, during the growth of the constant diameter
portion of the crystal to form a segment which is axially symmetric
about the central axis in which crystal lattice vacancies are the
predominant intrinsic point defect, the segment having a radial
width of at least about 25% of the radius; and, (ii) cooling the
ingot to form in the axially symmetric segment agglomerated vacancy
defects and a residual concentration of crystal lattice vacancy
intrinsic point defects, wherein the agglomerated vacancy defects
have an average radius of less than about 70 nm and the
concentration of residual crystal lattice vacancy intrinsic point
defects is less than the threshold concentration at which
uncontrolled oxygen precipitation occurs upon subjecting the cooled
segment to an oxygen precipitation heat treatment.
[0013] The present invention is further direct to a single crystal
silicon wafer comprising a front surface, a back surface, a lateral
surface joining the front and back surfaces, a central axis
perpendicular to the front and back surfaces, and a segment which
is axially symmetric about the central axis extending substantially
from the front surface to the back surface in which crystal lattice
vacancies are the predominant intrinsic point defect, the segment
having a radial width of at least about 25% of the radius and
containing agglomerated vacancy defects and a residual
concentration of crystal lattice vacancies, wherein (i) the
agglomerated vacancy defects have an average radius of less than
about 70 nm, and (ii) the residual concentration of crystal lattice
vacancy intrinsic point defects is less than the threshold
concentration at which uncontrolled oxygen precipitation occurs
upon subjecting the wafer to an oxygen precipitation heat
treatment.
[0014] The present invention is still further direct to a single
crystal silicon wafer comprising a front surface, a back surface, a
lateral surface joining the front and back surfaces, a central axis
perpendicular to the front and back surfaces, and a segment which
is axially symmetric about the central axis extending substantially
from the front surface to the back surface in which crystal lattice
vacancies are the predominant intrinsic point defect, the segment
having a radial width of at least about 25% of the radius and
containing agglomerated vacancy defects and a residual
concentration of crystal lattice vacancies, wherein (i) the
agglomerated vacancy defects have an average radius of less than
about 70 nm, and (ii) upon being subjected to a rapid thermal
anneal, wherein the wafer is rapidly heated to a temperature of
about 1200.degree. C. in the essential absence of oxygen and then
cooled, and then subjected to an oxygen precipitation heat
treatment, consisting essentially of annealing said wafer at
800.degree. C. for about 4 hours and then at about 1000.degree. C.
for about 16 hours, the concentration of oxygen precipitates formed
will be less than about 1.times.10.sup.8 cm.sup.-3.
[0015] The present invention is further direct to a method of
evaluating gate oxide integrity of a population of single crystal
silicon wafers. The method comprises (i) determining the dielectric
breakdown characteristics of a first subset of said population as a
function of the amount of stress applied to the first subset
wherein the amount of stress is increased at a first rate from an
initial value to a final value, (ii) determining the dielectric
breakdown characteristics of a second subset of said population as
a function of the amount of stress applied to the second subset
wherein the amount of stress is increased at a second rate from an
initial value to a final value and the second rate is different
from the first rate, and (iii) using the dielectric breakdown
characteristics determined in steps (i) and (ii) to predict the
gate oxide failure rate at a given electric field for the
population.
[0016] Other objects and features of the present invention will be
in part apparent and in part pointed out hereinafter.
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] FIG. 1 is a schematic of a cross-section of a segment of a
single crystal silicon wafer having an oxide layer deposited on the
surface thereof, showing in exaggerated detail voids (denoted "A")
at the surface which result in weak spots (denoted "B") in the
oxide layer.
[0018] FIG. 2 is a schematic diagram which illustrates a typical
dielectric breakdown distribution in void-containing and void-free
silicon in a ramped field test.
[0019] FIG. 3 is a schematic diagram comparing the dielectric
breakdown distributions of a "normal" (or high density)
void-containing silicon wafer and an "improved" slow cooled (or low
density) silicon wafer; the total integrated number of breakdown
events up to the arbitrarily defined test field of 8 MV/cm being
lower for the slow cooled crystal (which contains a lower number
density of voids).
[0020] FIG. 4 is a schematic diagram illustrating the Weibull
representation of dielectric breakdown failures in a constant field
(or current) test.
[0021] FIG. 5 is a schematic diagram illustrating the Weibull
representation of dielectric breakdown failures, wherein stress
levels are changed (changing field or current).
[0022] FIG. 6 is a graph illustrating constant field breakdown
distributions for a typical void-related failure mechanism at 5
MV/cm. (Std. void distribution; 0.1 cm.sup.2; 21 nm oxide; tested
166 dev.; 10 V stress; max. time allowed for breakdown: 2000 sec.;
time parameter, a=0.15).
[0023] FIG. 7 is a schematic illustration of a Weibull analysis of
ramped field data.
[0024] FIG. 8 is a graph illustrating variable ramp test results on
void-containing silicon.
[0025] FIG. 9 is a graph illustrating Weibull plots comparing the
ramped field breakdown distributions of typical "normal" (denoted
"SR-STD") and "slow cooled" (denoted "SR-SAC") materials
(defect-free, epi material, denoted "SR-EPI," provided as a
reference).
[0026] FIG. 10 is a schematic diagram illustrating the breakdown
distributions in "normal" (or high density) and "slow cooled" (or
low density) material if the differences between the two were
simply a reduction in defect density.
[0027] FIG. 11 is a schematic diagram illustrating breakdown
distributions in "normal" (or high density) and "slow cooled" (or
low density) material if the differences between the two were
simply a reduction in defect density (plotted in Weibull form).
[0028] FIG. 12 is a schematic illustration of a Weibull analysis
which shows in detail a shift which occurs as a result of void
size; that is, FIG. 12 illustrates a Weibull view of the size
effect of voids on the dielectric breakdown distribution (for
normal, or high density, and slow cooled, or low density,
material).
[0029] FIG. 13 illustrates the results of a calculated oxide
reliability test in void-containing material; that is, FIG. 13
illustrates the predicted reliability from ramp test data for
standard (lower curve) and slow cooled (upper curve) material (21
nm oxide; prediction for 5 V room temperature operation).
[0030] FIG. 14 is a graph illustrating the breakdown distributions
of a given void-containing material (denoted "STD"), as well as,
for comparison, a "slow cooled" (denoted "SAC") and "fast cooled"
(denoted "U97-DDef", obtained from a rapidly cooled tail-end
section of an ingot).
[0031] FIG. 15 is a graph which illustrates the reliability
extrapolations for the standard material (upper curve) and "fast
cooled" (lower curve) material of FIG. 14; that is, FIG. 15
illustrates the predicted reliability from ramp test data comparing
standard and fast cooled void types (21 nm oxide; prediction from 5
V room temperature operation).
[0032] FIG. 16 is a graph which illustrates the production of voids
in a growing crystal under the most typical cooling rates (showing
that, under such conditions, the consumption of vacancies to voids
is efficient enough to reduce their concentration to a value below
the precipitation enhancement threshold by the time vacancies
become bound to oxygen).
[0033] FIG. 17 is a graph which illustrates the production of voids
in a growing crystal which, in comparison to the crystal in FIG.
16, is cooled more rapidly (showing that, by cooling more rapidly
through the void growth regime, anomalously high values of oxygen
precipitation result, due to the high levels of residual vacancies
at the time the crystal enters the binding regime).
[0034] FIGS. 18, 19 and 20 are graphs which illustrate a series of
models for predicting the behavior of the silicon material under
given conditions. Generally, these graphs illustrate that for
different conditions (e.g., growth conditions, cooling rate, etc.),
a certain size of voids and a certain residual vacancy
concentration are obtained. Accordingly, it is to be noted that
while these graphs illustrate general regions for growth conditions
which may yield a given material, further experimentation can be
carried out to refine the conditions within or about these regions.
As shown: the X axis (log scale, ranging from about 0 to 100) is
the cooling rate (K/min.); the Y axis (ranging from about 0.01 to
0.25) is S.sub.0 (the vacancy concentration when the silicon is
formed, based on the ratio v/G.sub.0); the generally diagonal,
dashed/dotted lines indicate the residual vacancy concentration
(C.sub.res); the generally diagonal, solid lines indicates void
radius (R.sub.v); and, N.sub.v indicates the void density (the
generally "L" shaped lines for each N.sub.v value being isocontours
for void density, each contour having essentially the same lower
limit, below which "defect free" material would be formed). Also,
because of the need to make certain assumptions concerning the
value of certain of the parameters involved in the calculations
required to generate these curves, it should be understood that
these curves are intended to demonstrate the existence of a set of
operating conditions, or space, in which "useful, functionally
perfect" silicon of the present invention may be manufactured;
thus, the boundaries of this space may not precisely define the
boundaries of the operating conditions in which "useful,
functionally perfect" silicon of the present invention may be
manufactured in all crystal pullers. More specifically:
[0035] FIG. 18 is a graph illustrating the relationship between
void size, void density and residual vacancy space as a function of
the incorporated vacancy concentration, S.sub.0, normalized to the
melting point concentration, and cooling rate (void density,
N.sub.v, shown at 1.times.10.sup.5 cm.sup.-3, 1.times.10.sup.6
cm.sup.-3, 1.times.10.sup.7 cm.sup.-3 and 1.times.10.sup.8
cm.sup.-3; residual vacancy concentration, C.sub.res, shown at
1.times.10.sup.12 cm.sup.-3, 3.times.10.sup.12 cm.sup.-3 and
1.times.10.sup.13 cm.sup.-3; and, void radius, R.sub.v, shown at 30
nm and 15 nm).
[0036] FIG. 19 is a graph illustrating an exemplary "window" of
operating conditions under which "useful, functionally perfect"
silicon can be formed under a standard growth model, and assuming a
constant cooling rate is employed (void density, N.sub.v, shown at
1.times.10.sup.5 cm.sup.-3, 1.times.10.sup.6 cm.sup.-3,
1.times.10.sup.7 cm.sup.-3 and 1.times.10.sup.8 cm.sup.-3; residual
vacancy concentration, C.sub.res, shown at 1.times.10.sup.12
cm.sup.-3, 3.times.10.sup.12 cm.sup.-3 and 1.times.10.sup.13
cm.sup.-3; and, void radius, R.sub.v, shown at 30 nm and 15
nm).
[0037] FIG. 20 is a graph illustrating an exemplary "window" of
operating conditions under which "useful, functionally perfect"
silicon can be formed under a modified growth model, wherein a
two-stage cooling rate is employed (void density, N.sub.v, shown at
1.times.10.sup.4 cm.sup.-3, 1.times.10.sup.5 cm.sup.-3,
1.times.10.sup.6 cm.sup.-3, 1.times.10.sup.7 cm.sup.-3 and
1.times.10.sup.8 cm.sup.-3; residual vacancy concentration,
C.sub.res, shown at 3.times.10.sup.12 cm.sup.-3 and
1.times.10.sup.13 cm.sup.-3; and, void radius, R.sub.v, shown at 30
nm and 15 nm).
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0038] Based upon experimental evidence to-date, it appears that
presently accepted practices for determining gate oxide integrity
in single crystal silicon wafers are inaccurate and, as a result,
lead to the disposal and therefore waste of wafers which would
otherwise be acceptable for use. More specifically, gate oxide
integrity requirements are typically presented in terms of a
percent failure at a given electrical field, a field which is
substantially greater than the field at which the integrated
circuit will be operated (e.g., 2.times., 3.times., 4.times., etc.
the operating field). As further explained below, such tests can
and, it is now believed, do result in the rejection of material
which is acceptable for use. This waste is primarily the result of
a test which erroneously leads to the conclusion that a few, large
agglomerated defects in a given wafer are preferable to a number
of, in comparison, relatively small defects.
[0039] Accordingly, the present invention enables more wafers to be
obtained from a given single crystal silicon ingot by engineering
void size, in some cases irrespective of density, by controlling
growth conditions (including growth velocity, v, and the average
axial temperature gradient, G.sub.0, as defined herein), as well as
the cooling rate of the ingot within certain temperature ranges
during the growth process, in order to meet well-defined failure
distribution requirements (i.e., GOI requirements) in both field
and time. Additionally, the cooling rate may be controlled to avoid
residual vacancy concentrations which are so high that a massive
catalysis of subsequent oxygen clustering reactions occurs.
Avoiding such reactions is preferred because such vacancy-catalyzed
oxygen clusters can and usually do grow large enough in the crystal
growth process that they cannot be eliminated by subsequent thermal
treatments (such as, for example, the processes described in U.S.
Pat. No. 5,994,761 and PCT/US99/19301, both of which are
incorporated herein by reference). As a result, oxygen
precipitation performance of such wafers runs out of control,
preventing the formation of a denuded zone under ordinary
conditions; that is, if the residual vacancy concentration is too
high, a wafer subjected to the thermal processes described in U.S.
Pat. No. 5,994,761 and PCT/US99/19301 would not yield the desired
result.
Gate Oxide Integrity Determination
[0040] Referring now to FIG. 1, voids, or agglomerated vacancy
defects, which intersect the silicon-silicon dioxide interface
(denoted "A") create "weak spots" (denoted "B") in the gate oxide,
resulting in dielectric breakdown events that occur at electric
fields generally lower than what is expected from a void-free
interface. The presence of these "weak spots" in the gate oxide has
been a primary issue of concern for silicon material performance
for about the past ten years. Recently, progress has been made in
understanding the detailed nature of void-related breakdown
distributions, in both electric field and stress-time, as a
function of void size distribution and oxide thickness. This
progress has led to a variety of important conclusions which are
described further herein, and which serve as the basis for the
present invention.
[0041] Dielectric Breakdown and Material Reliability--Void-related
Dielectric Breakdown:
[0042] Referring now to FIG. 2, a schematic diagram illustrating
typical distributions of breakdown events in void-containing
silicon and void-free silicon (e.g., epitaxial, substantially
defect-free or interstitial type silicon) are shown. This diagram
illustrates exemplary results in a system with a 20 nm gate oxide
with a relatively large capacitor sampling area (about 0.1
cm.sup.2). Dielectric breakdown tests offer movable "windows" for
the distributions of faults in any given system. The relative
position of the "window" with respect to the defect of interest is
determined by the product of the density of this defect and the
capacitor area. If the product is too large or small, essentially
nothing is observed. Accordingly, in the schematic illustrated in
FIG. 2, it has been assumed that the optimal case has been
selected.
[0043] The effect of the voids in the dielectric breakdown test is
to create a peak of breakdown events in the mid-field range.
Additionally, there is a second class of defects, denoted by a
second peak, beyond the void-related failure peak, which is
responsible for the distribution of breakdown events at higher
fields. It is this second class, or mode, of breakdown which
completes the breakdown process for all devices. This mode is found
to be common for essentially all types of material, including
defect-free material (e.g., epitaxial silicon), and is due to an
effect unrelated to voids. Accordingly, this is generally not a
practically important material characteristic for the present
invention and therefore will not be discussed further; that is, for
purposes of the present invention, we are concerned solely with the
first peak.
[0044] The presence of this first peak implies that void-related
breakdown is a finite effect. The simple reason for this is that
there is a limited number of countable voids in any given sample.
By the time the electric field reaches values higher than that of
the end of second peak, all of the voids in the system have been
"turned on;" that is, all of the voids have been transformed from a
real physical "defect" (i.e., a void) into an observable electrical
defect (i.e., a breakdown site). The integral of electrically
detected defects under the peak is equal to the total number of
physical voids intersecting the interface.
[0045] The reason for this distribution in field of electrical
faults resulting from voids (i.e., the width of the peak) is
believed to be a combination of scatter in actual void size and,
more importantly, scatter in the cross-section of the
void-interface intersection resulting from both the size and
spatial distribution of the voids. It will be seen that the shape
of the peak of the material of the present invention (in addition
to simply the average value) is a significant parameter in material
reliability.
[0046] Breakdown Requirements and Material Screening:
[0047] Semiconductor device manufacturers are generally concerned
with two questions: (i) what is the yield of devices, and (ii) what
is the reliability of the devices over time; in other words, device
manufacturers are concerned with how many defective pieces are
found in short tests of operation (i.e., "yield"), and how many
defective pieces will subsequently develop over the life of a
device (i.e., "reliability"). These questions require further
clarification; for instance, one must consider what are the
operating conditions of the device and what are the allowed levels
of defectiveness as a function of time. Initially, if some
generally standard answers to these questions are assumed, the
operating field would be about 2.5 MV/cm (for 20 nm oxide and 5V
V.sub.dd) and a single bit fail would result in a defective chip.
After yield screening, it is the reliability requirements that are
important. For example, in stringent automotive applications, it is
typically required that the failure rate be less than 1 ppm fail in
10 years.
[0048] Data such as that shown in FIG. 2, however, actually does
not provide much help in coming to conclusions about any of these
questions; FIG. 2 shows no breakdown events at the operating field
(2.5 MV/cm). This means that the yield of operating devices derived
from both void-containing and void-free material when evaluated at
this operating field is actually about 100%. Stated more
stringently, this number must be considered within the context of a
defined statistical "confidence limit" but, even taking this into
consideration, this number should not be significantly different
than about 100% in view of such data.
[0049] In reality, however, one hundred percent of the
void-containing and void-free material will not be free of defects.
In an attempt to deal with yield and reliability, therefore,
semiconductor device manufacturers have subjected the manufactured
semiconductor devices, e.g., capacitors, to fields which are
significantly greater than the operating field. This approach,
sometimes referred to the "burn-in" test, is a standard part of
integrated circuit testing. It is only under such tests that
failure due to voids is seen and becomes important. Referring again
to FIG. 2, it can be seen that applying 10V instead of 5V moves one
directly into the middle of the void failure distribution. The
basic reasoning behind this standard procedure is the belief that,
by eliminating parts defective at fields higher than the operating
field, one will have succeeded in eliminating weak spots which
would have failed at the operating field during the expected life
of operation.
[0050] One of the limitations of the burn-in test is that is
carried out on the finished semiconductor devices. It cannot,
therefore, be used to identify silicon wafers which have a
high-probability of yielding semiconductor devices which, if used
in a semiconductor device manufacturing process, would produce
semiconductor devices having a high incidence of burn-in failure.
In an effort to pre-screen silicon wafers for this purpose,
semiconductor device manufacturers have subjected silicon wafers to
various gate oxide integrity tests, such as ramped field tests
(e.g., "BVOX", wherein the percent pass might be 20%, 70%, etc. up
to a given field, such as 8 mV) or the "QBD" test. In principle,
however, these tests are equivalent to the "burn-in" test in the
sense that the wafers are subjected to an electric field which is
arbitrarily selected.
[0051] The issue is thus one of correlating the "burn-in" field or
equivalent test to the performance specification. Stated another
way, the field which actually and effectively identifies, and thus
screens, those devices that would fail in the required lifetime of
the device, down to the level of the specification (e.g., 1 ppm),
without unnecessarily throwing away those devices that would
actually have survived must be determined. To determine this, one
needs to have reliable information about the time-dependence of the
failure mechanism resulting from the particular class of defect for
which one is screening. This information then needs to be coupled
to the specific field dependence of the distribution with which one
is dealing. Until now, this has not been done; rather, only
standard, "rule of thumb" approaches have been used to-date. As a
result, it can be concluded that: (i) the burn-in field is a
largely arbitrarily chosen stress level which, it is hoped, will
successfully screen devices in order to reduce the failure rate of
devices sold by the integrated circuit manufactures to acceptable
levels; and, (ii) the BVOX requirement is based on an equally
arbitrarily chosen field (a field larger than the burn-in field),
in which the hope is that this screening will produce an acceptable
level of success (i.e., yield) through the burn-in test. The
problem gets compounded even more when these already arbitrary
conditions are then applied to arbitrarily different circumstances,
such as different oxide thicknesses.
[0052] Applying these standard tests, if the results of "normal"
void-containing material are compared to what is conventionally
considered to be an "improved" material (i.e., lower void density,
slow cooled material), the slow-cooled material appears to be
superior. For example, FIG. 3 shows in a schematic way typical
examples of the experimentally-determined, void-related part of the
breakdown distribution of the two types of material. The effective
oxide defect density, as determined by BVOX testing (purely a
matter of definition, rather than an absolute number), scales
approximately with the void density in the silicon in most BVOX
type tests; but it need not.
[0053] In view of FIG. 3, it can be seen that the slow cooled
material has a total number of void-related breakdown events which
is less than the standard material. This is because slow cooling
produces a lower number density of voids, as is commonly understood
and expected. Furthermore, however, it should be noted that there
is a shift in the average field of the distribution between the two
groups.
[0054] The "yield" of slow cooled material is generally better than
standard material, based on the assumption that the device under
consideration is statistically sensitive at all to the problem
(which is a question of the relationship of total gate area and
effective defect density; i.e., the "window" problem described
herein). Additionally, the material which is essentially free of
such agglomerated defects (e.g., epitaxial silicon, or
alternatively "low defect density silicon," as described in
PCT/US98/07365 and PCT/US98/07304 which are incorporated herein by
reference) is generally better than them both. However, such a
conclusion is based entirely upon the field chosen for the test to
define the yield which, as noted above, has been selected somewhat
arbitrarily to-date. For example, in the present case, if the field
is changed from 8 to 4 MV/cm, then all three types of silicon
appear to be acceptable. Additionally, at a slightly larger field,
the performances of the slow cooled and standard materials are
actually reversed. All of this leads one to question just what is
actually the best way to define material quality.
[0055] Breakdown Statistics:
[0056] To resolve this issue, and ultimately determine the best way
to evaluate the silicon material for performance, statistical
methods have been employed here. The purpose of such an approach is
to predict the time dependence of device failure in a system with a
given set of defects at a given stress level, and then to assess
the effectiveness of the "screening" of the device distribution by
a particular burn-in procedure. The stress level of interest is the
operating field (e.g., 2.5 mV/cm) and the failure requirements are
for extremely low failure rates over very long times (e.g., failure
of 1 ppm/10 years). Clearly, a coherent method is needed to
extrapolate data which can be taken in a convenient and cost
effective way, and this involves the application of statistics.
[0057] The first basic assumption is that defects are randomly
distributed. Thus, Poisson statistics are employed. "Yield" is
simply the probability of not finding a defect in a group of
samples. These defects have a density D and the samples (i.e.,
capacitors) have an individual area A. The yield is given by
equation (1):
Y=1-F=exp(-AD) (1)
where Y is yield and F is the number of failures.
[0058] The cause of the electrical defects of interest are voids
that intersect the wafer surface. They have an area density
approximately equal to their volume density, , times their average
diameter, d. Since the oxide thicknesses of interest are generally
small, ranging for example from a few nanometers (e.g., 2, 4, 6,
etc.) to a few tens of nanometers (e.g., 10, 20, 30, etc.),
compared to the amount of silicon consumed during the oxidation
process, it is believed to be reasonable to ignore this small
correction here.
[0059] It is important to keep in mind that dielectric breakdown
tests do not detect voids, rather they detect oxide failures. The
only physical or potential defect density is pd. This is not equal
to D in the above expression; rather, D is the electrical defect
density which is something different from the void density. A
physical defect only becomes an electrical defect when it is
"turned-on" by electrical stress. In order to describe and utilize
data from electrical stress tests, an approximate mathematical form
is needed for this conversion from physical defect to electrical
defect.
[0060] Constant Field Or Current Stress:
[0061] There are two main stress variables for the case of
dielectric breakdown: electric field (or current) and time. The
Weibull approach to this statistical problem assumes a simple power
law relation for whatever variable is under test, which usually
means just time. However, our case is slightly more complicated
than the usual case, in that it is a two-parameter distribution and
combines two different power laws for each variable. In this
regard, it is to be noted that the Weibull distribution makes no
claim to describing or modeling any physical mechanism; rather, it
is just a statistical method and a simple, useful and powerful way
of dealing with complex data.
[0062] To begin then, first consider the simplest kind of applied
stress, that of constant field stress E. For this case, the Weibull
description of the increase of effective defect density with time
is shown in equations (2) and (3):
AD=Ct.sup.aE.sup.b (2)
and thus
1-F=exp(-Ct.sup.aE.sup.b). (3)
The density and probe area are contained in the "C" parameter, the
field dependence in the "b" and the time dependence in the "a"
parameter (where t=time). These parameters are easily obtained by
taking a double logarithm of yield data and plotting this against
the logarithm of time. The "Weibull" plot is thus expressed in
equation (4):
ln(-ln(1-F))=a ln(t)+b ln(t)+b ln(E)+ln C. (4)
This is a simple linear, and hence useful, equation in ln(t), and
it appears to works well in describing the experimental data. The
number ln(-ln(1-F)) is referred to as the Weibull number.
[0063] Once determined, these parameters give a complete
description of the rates of failure in a system at arbitrary fields
and times. It is, however, only valid for a single type of
distributed defect. If there is more than one type of defect
present, as is almost always the case, then the parameter set for
this distribution is determined independently and then added to the
other distribution. In addition to voids, there is a second, higher
field class of defect activated by the electrical stress.
Fortunately, this class may be clearly separated from the void part
of the distribution and analyzed separately.
[0064] The parameter set: C, a and b give a kind of "fingerprint"
for particular distributions of defects. An example of a typical
case is shown schematically in FIG. 4. Such plots are very useful.
For instance, they allow for result scaling to arbitrary capacitor
areas; C is proportional to A, and thus the scaling factor is
simply ln(A.sub.1/A.sub.2). The "a" or time parameter for each mode
of breakdown is read directly off the chart. In order to determine
the "b" or field parameter, multiple measurements at different
stress levels must be performed. This produces another simple
scaling factor, b(lnE.sub.1/E.sub.2), which is analogous to the
area factor. The difference between these area and field parameters
is that the area scaling parameter is constant over all defect
types (assuming random distribution), whereas the field parameter
will in general be unique to each particular defect distribution or
breakdown mode. Field scaling is illustrated schematically in FIG.
5 for a bi-modal case.
[0065] An example of a real and rather typical time dependent
response for a void-dominated system is shown in FIG. 6. The time
dependence for electrical damage accumulation by voids is
relatively weak. The "a" parameter is found to be about 0.15. On
average, it takes a relatively long time for a void which is not
already broken down at the test field to transform itself into an
electrical defect. Another consequence of this weak time dependence
is that, in reliability terms, the failure rate decreases with time
as devices fail by this mechanism. In this regard it is to be noted
that it is only under these conditions that burn-in screening
works.
[0066] FIG. 6, however, shows only a part of the breakdown picture.
Another significant, but non-void related, breakdown mechanism is
not seen, simply because the test did not last long enough. Based
on other measurements, this mode exhibits a different time
dependence in comparison to the void-related mechanism. The "a"
parameter of the non-void related mechanism is greater than one
(i.e., about 3), and thus this mode is quite different, both
physically and statistically (i.e., the reliability
perspective).
[0067] The problem with conventional test procedures described
above is two-fold. First, they are extremely time consuming and,
second, they offer a very narrow range of field investigation. Even
at mid-range fields, such tests can require weeks. Since
extrapolation down to low fields is the goal, this is not a
particularly satisfactory method. A more convenient and highly
complementary test is to extract the parameters necessary to
predict reliability from a test which rapidly scans a wide range of
fields. It is indeed possible to extract all of the parameters
solely by means of ramped field tests.
[0068] Ramped Field Stress:
[0069] Ramped field testing of dielectric breakdown behavior is a
popular method of testing. The hypothetical data of FIGS. 1 and 2
come from such a hypothetical test. The general belief about such
tests is that they give information only about the field dependence
of the breakdown distribution. In reality, however, they can yield
very powerful information about the time dependence as well.
Importantly, these tests can rapidly reveal the time dependence of
individual modes of breakdown over a very wide range of fields.
[0070] In ramped field tests, both the field and time are varied
simultaneously, unlike constant field tests. In order to
disentangle the two parameters, one needs a model of how damage
builds up or integrates as the field builds up over time. It has
now been found that a simple additive damage build up model (see,
e.g., R. Falster, The Phenomenology of Dielectric Breakdown in Thin
Silicon Dioxide Films, J. Appl. Phys., 66, 3355 (1989)) does not
describe the data from void-related breakdown for polysilicon
cathodes, and that in order to explain the data of both ramped
field and constant field stress a new model for damage (W) build
up, as expressed in equation (7), is to be applied:
W=p[.intg.E(t).sup.ddt]a (7)
where
d=b/a.
[0071] Upon integration of Equation (7) for a linearly ramped
field, this equation produces the "Weibull" description of
dielectric breakdown for ramped field tests, in terms of the same
"a" and "b" parameters of the constant field test, as indicated in
equation (8):
1-F=exp{-C[a/(a+b)].sup.a(dE/dt).sup.-aE.sup.a+b} (8).
Taking the double logarithm to produce the Weibull ramped test plot
yields equation (9):
ln(-ln(1-F))=(a+b)ln(E)-a ln(dE/dt)+ln C+a ln {a/(a+b)} (9).
This is linear in ln(E). The slope of the line is equal to the sum
of the parameters a+b.
[0072] Accordingly, it is to be noted that a change in ramp rate
produces a simple shift in the Weibull plot in the amount of a ln
[(dE.sub.1/dt)/(dE.sub.2/dt)]. By simply performing variable ramped
rate measurements on the same defect population, one obtains a set
of parameters and conformation of these parameters over a wide
range of fields. With this formulation, it is possible to go back
and forth between data, constant stress and ramped stress tests,
which is very useful.
[0073] Referring now to FIGS. 7 and 8, FIG. 7 is a schematic
illustration of this procedure, while FIG. 8 illustrates real data
for void-containing systems. If the "a" parameter is extracted from
the ramp test results, using the methods above from the data of
FIG. 8 (and other similar plots), the same results as simple
constant field test (cf. FIG. 5) are obtained. The ramp test
results, however, confirm that this value is valid over the entire
range of fields in which voids dominate the breakdown distribution;
in other words, the time dependence of void-related breakdown has
the same form over the range of electric field under which it is
active. Experimental evidence obtained to-date demonstrates that
the "a" parameter, for void-related breakdown, is typically in the
range of about 0.15 to about 0.18. With this information, it is
possible to derive reliability performance from simple ramped test
results using the statistical formalisms discussed above.
[0074] One aspect of the present invention, therefore, is a method
of evaluating gate oxide integrity of a population of single
crystal silicon wafers. This method comprises several steps: (i)
determining the dielectric breakdown characteristics of a first
subset of the population as a function of the amount of stress
(e.g., an electric field), applied to the first subset wherein the
amount of stress is increased at a first rate from an initial value
to a final value, (ii) determining the dielectric breakdown
characteristics of a second subset of said population as a function
of the amount of stress applied to the second subset wherein the
amount of stress is increased at a second rate from an initial
value to a final value and the second rate is different from the
first rate, and (iii) using the dielectric breakdown
characteristics determined in steps (i) and (ii) to predict the
gate oxide failure rate under a defined set of conditions for the
population. Preferably, the first and second rates differ by a
factor of at least 5, more preferably at least 10, and for some
applications, by at least 100. In addition, in some embodiments it
is preferred that three, four or even more subsets of wafers be
evaluated at different ramp rates (which preferably differ from
each other by a factor of at least 10). For example, in one
embodiment each of four subsets of wafers of the population are
subjected to an applied electric field which is linearly increased
at a rate of 0.05, 0.5, 5 and 50 megavolts/cm/sec.,
respectively.
[0075] In one embodiment of the present invention, the population
of wafers upon which the gate oxide integrity test is carried out
may be wafers from a specific ingot (or portion thereof), a
specific crystal growth process, or even a cassette or a plurality
of cassettes of wafers. The subsets are selected from this
population and thus may comprise a whole or fractional part of one
or more wafers of the population. For example, each of the subsets
may comprise a fractional part of the same wafer or wafers.
Alternatively, each of the subsets may comprise a fractional part
of different wafers. In yet a further alternative, the subsets
comprise a fractional part of a partially overlapping set of
wafers, i.e., each set comprises a fractional part of the same
wafer or wafers and a whole or fractional part of different
wafers.
[0076] Void-Related Dielectric Breakdown Revisited:
[0077] Returning to the question of void-related breakdown
distributions, a schematic view is illustrated in FIG. 2 of typical
distributions in electric field of void-related breakdowns for
"normal" and "slow cooled" types of crystal. Referring now to FIG.
9, actual data comparing the two types of material presented in the
Weibull format is illustrated (results for void-free, epitaxial
material is included as a reference, as is the "standard" BVOX
reference field of 8 MV/cm). Viewed in this way, the usual
differences between "slow cooled" and normal material (BVOX
percentages) are self-evident. Furthermore, all three materials
exhibit an identical behavior independent of the distribution of
voids in the materials (again, noting that the very different
high-field breakdown distribution is unrelated to voids).
[0078] With respect to FIG. 9, two features of these distributions
should be particularly noted: [0079] 1. There is a "saturation" in
the breakdown fails at a certain percentage for each distribution
(related to the fact that there is a "peak" in the distribution, as
described above). The simple reason for this result is that, by the
time some characteristic field is reached, all of the voids in the
system have been used up or "turned-on." This difference in the
saturation failure percentages is a result of reducing the number
density of voids by the "slow cooling" process. It should be noted
that such a saturation effect does not exist for the other main
mode of dielectric breakdown at high fields (here, the underlying
physical defects are not countable). It is, of course, this
saturation value that all BVOX tests, for example, actually
measure. They thus directly measure the effective area density of
the voids only. [0080] 2. However, the result of the "slow cooling"
process is not simply to reduce the number density of the voids,
which can be shown by another schematic plot. Referring now to
FIGS. 10 and 11, illustrated are what the fail distributions of the
two cases would have to look like if the difference between the two
were simply a result of density reduction. This is not observed.
Instead, they take a form similar to that illustrated in FIG. 2.
What this means is that, while the overall density of defects has
been reduced by the "slow cooled" treatment, on average, "slow
cooled" voids result in breakdowns at lower fields; that is, the
distribution is shifted.
[0081] In general, voids produced by slow cool-type processes are
larger. This is for the simple reason that in slow cool-type
processes a smaller number of void sites consume the same number of
vacancies as do the larger number of voids in "normal" processes.
It is concluded then that the reason for this shift, illustrated in
FIG. 12, is due to the increased average size of the voids in the
slow cool distribution.
[0082] The Consequences of the Void Size Dependence of Dielectric
Breakdown Distributions:
[0083] On the surface of things, the application of "burn-in"
voltage rules leads one to the straight forward conclusion that the
slow cool-type material, with its lower saturated fail percentages,
is the better material. Of course, as pointed out herein, this
result is not surprising because the very application of this test
makes the outcome pre-determined. But, the real question is, what
result would be obtained if a different criterion was applied? For
example, assume one applies a test which is simply an application
of real reliability criteria to the material system; that is,
assume one applies a stress at the operating field, rather than
some arbitrary field significantly higher than the operating field,
and then sees which system has the most fails after, for example,
10 years.
[0084] Calculating Extrapolated Reliability:
[0085] In order to calculate extrapolated reliability, the system
described above is used and extrapolate from ramped field data to
constant field operation at a defined operating field. Manipulating
equations (4) and (9) above, a simple expression can be written
(equation 10) in Weibull form which allows the solution for the
device wear-out to be determined at essentially any operating
field:
F'(t,E.sub.op)=a ln(t)+F''(E.sub.op,dE/dt)-a ln
[E.sub.op/(dE/dt)]-a ln [a/(a+b)] (10)
where [0086] 1. F'(t,E.sub.op), which is to be determined, is the
Weibull number {=ln(-ln(1-F)} of the time dependent failure
distribution, at the (operating) field, E.sub.op; [0087] 2.
F''(E.sub.op,dE/dt) is the Weibull number extrapolated to the
(operating) field, E.sub.op, from a ramp test result performed at
the ramp rate dE/dt; this number is simply a linear extrapolation
of the data and can be expressed as follows in equation (11):
[0087]
F''(E.sub.op,dEdt)=F''(E.sub.sample,dE/dt)-(a+b)ln(E.sub.sample/E-
.sub.op) (11) [0088] where E.sub.sample is some field value in the
range where the slope a+b is valid, and F'' (E.sub.sample,dE/dt) is
the Weibull number at this point; [0089] 3. a+b is the slope in ln
E of the void-related part of the breakdown distribution from the
ramp test results; and, [0090] 4. "a" is the time parameter deduced
from variable ramp rate tests on the same distribution, or from
sample constant field/current tests.
[0091] Comparison of Standard and "Slow Cool" Materials:
[0092] Referring again to FIG. 9, and in view of the foregoing, a
comparison of the extrapolated reliability of the two material
systems at an operating voltage of 5V over a period of several
years can be performed; this is done by applying equation (10) to
data taken from FIG. 9. FIG. 13 illustrates the surprising results,
surprising in that the standard material with a higher overall
density of voids and corresponding worse BVOX results is actually
the better material.
[0093] In this regard it is to be noted that, while the results
illustrated in FIG. 13 are surprising, they are in fact moot in
this case because neither material would meet the reliability
requirement of 1 ppm failure in ten years (where 10 years equals
about 3.15.times.10.sup.8 seconds). Clearly, the devices made from
both materials have to be screened (i.e., burned-in) in order to
meet these requirements. However, it is still to be noted here that
the application of the burn-in test picks the wrong answer, and
accordingly would have resulted in the waste of acceptable silicon
in the process.
[0094] In view of the foregoing, it can be seen that conventional
screening procedures incorrectly identify the slow-cooled material
as superior by measuring in the saturation regime. Because the
number of failures are so small, the difference in this regime
never enters into the real reliability question, or rather it would
not enter in until perhaps about 10,000 years or so of device
operation. The real issue therefore lies in the initial part of the
breakdown distribution; in particular, it lies in the intercept of
the rising portion of the curve with the operating field (adjusted
by a couple of constants from equation (9)).
[0095] "Functionally" Defect-free Silicon According to the process
of the present invention, it has been discovered that, once a
method of analysis for gate oxide integrity has been properly
defined and applied, it is clearly preferable to grow single
crystal silicon under conditions which yield wafers having voids
which are smaller in size and higher in concentration (or number
density), in contrast to what has heretofore been deemed acceptable
(based on conventional GOI methods of analysis). Stated another
way, it has been discovered that, once gate oxide integrity is more
accurately defined and measured, single crystal silicon wafers
having a higher concentration of smaller voids is preferably to
material having, in comparison, a lower concentration of larger
voids (as further described herein). Experience to-date indicates
that such wafers, from a functional standpoint, are in most cases
of a quality comparable to substantially defect-free silicon.
[0096] Specifically, the present invention enables the engineering
or preparation of "functionally defect-free" silicon, which is a
material designed to meet two basic criteria: [0097] 1. The
material meets the stated requirement for reliability, whatever
that requirement may be for a given application (e.g., 1 ppm fail
in 10 years of device operation); and (optionally), [0098] 2. The
material has essentially no detectable fails at the burn-in
voltage. With respect to the second criterion, it is to be noted
that this is not technically a requirement; that is, true
"functional perfection" is met completely by the first criterion.
However, the burn-in criterion (2) is nevertheless important, since
the material will typically have to meet burn-in test requirements
of integrated circuit manufacturer. Accordingly, even if this is
not necessarily a rational test for gate oxide integrity, it is
nonetheless a kind of function, if not an operating one.
Furthermore, there may be other reasons, beyond the control of the
silicon manufacturers, for users to perform this specific test at a
particular value of burn-in voltage. As a result, this requirement
should preferably be met also by the silicon material.
[0099] Void Size Distribution and "Functional Perfection:"
[0100] It was noted above, in the discussion of FIGS. 10 through
12, that the initial part of the Weibull curve is determined less
by the density of the voids than by their size distribution.
Accordingly, this is a key to "functional perfection." It is quite
a different approach, as compared to all conventional attempt to
improve material. More specifically, in all other proposed material
improvement methods (e.g., slow cooling, defect-free silicon,
epitaxial silicon), the idea has been to reduce the density of
voids, whereas in the present invention the focus is on reducing
the size of the voids (control of void density being optional here
and, in at least some embodiments, a minimum void density actually
being required).
[0101] Generally speaking, the size of voids is reduced by fast
cooling ("fast" cooling being described in greater detail below).
There are two components to this approach: [0102] 1. Through
kinetic limitations, fast cooling reduces the efficiency of vacancy
transport, and thus reduces the effects of vacancy "sinking" to
voids. As a result, voids do not become as big. [0103] 2. Fast
cooling produces a higher density of voids. As a result, given a
fixed concentration of vacancies, there is a smaller number of
available vacancies per void (this, of course, is where "slow cool"
material does poorly in the present context). With this in mind,
consider that fastest cooling in conventional CZ silicon is usually
found in the tail-end region, where the pulling rate typically
increases sharply to make the tail-end. This also has the effect of
changing the cooling rate of the crystal in regions cooler than the
melt interface. Here we are particularly interested in the cooling
rate of the crystal in the void nucleation temperature region,
which typically ranges from about 1000.degree. C. to about
1200.degree. C., and the void growth temperature region, which
typically ranges from about 1100.degree. C. to about 900.degree. C.
(both of which are described in greater detail below). The axial
positions of these temperatures, relative to the melt-solid
interface, are determined by the hot zone design or
configuration.
[0104] Referring now to FIG. 14, a comparison is provided of the
breakdown distribution of a given or standard material, relative to
silicon materials obtained from comparably "slow cooled" and "fast
cooled" (denoted "U97") processes. These results are rather
striking, within the context of the present discussion. More
specifically, it is to be noted: [0105] 1. The larger void density
of the fast cooled material is clearly seen in the larger saturated
fail percentage (less striking). A 8 MV/cm BVOX test result would
yield about 85% fail for the fast cooled material, 65% fail for the
standard material and 45% for the slow cooled material; in short,
by standard test methods, the material of the present invention
appears to be inferior. [0106] 2. The smaller void sizes of the
fast cooled material results in a shift of the initial part of the
distribution toward higher fields. Furthermore, the slope of this
part of the distribution becomes steeper. A large slope is much
more powerful than a mere parallel shift in the distribution
because it will drive the intercept at the operating field to
significantly lower values. The reason for this increase in the
slope (and hence tightening of the distribution of failures in
field) is understood to be due to a smaller range in void
cross-sectional area available at the silicon-oxide interface.
Accordingly, in spite of the notable failure of the BVOX test, the
fast cooled material is exceptionally good when it comes to
reliability performance. Referring now to FIG. 15, a comparison is
provided of the predicted reliability of this material with that of
the (better BVOX performing) standard material. It should be note
that, from these results, it can been that in ten years of
operation the fast cooled material produces better than about 0.001
ppm fails, which greatly exceeds even the most stringent of
requirements. It is to also be noted that, at a burn-in field of,
for example, 5 MV/cm (which is twice the operating voltage), there
is essentially no measurable yield loss (i.e., much less than about
1% fail).
[0107] Crystal Growth Considerations for "Functionally Perfect"
Material:
[0108] The framework for the models which describe the density and
size of voids produced in silicon as a function of growth
conditions have been described in several recent publications.
(See, e.g., V. V. Voronkov et al., J. Cryst. Growth, 194, 76
(1998); V. V. Voronkov, J. Cryst. Growth, 204, 462 (1999); and, R.
Falster et al., On the Properties of the Intrinsic Point Defect in
Silicon, Phys. Stat. Sol., (B) 222, 219 (2000). See also PCT
Application Nos. PCT/US98/07304, 07305 and 07365, all of which are
incorporated herein by reference.) Generally speaking, however, the
concentration of the vacancies which compose the voids is
determined by the parameter v/G.sub.0 at the melt/solid interface,
wherein v is the growth velocity and G.sub.0 is the average axial
temperature gradient over a temperature range bound by the
solidification temperature and a temperature greater than about
1300.degree. C. (e.g., about 1325.degree. C., 1350.degree. C. or
even 1375.degree. C.). The larger this value, in excess of the
critical value for v/G.sub.0, the larger the vacancy concentration
incorporated into the growing crystal. These vacancies become
critically supersaturated at some "nucleation" temperature (which
itself is dependent upon the concentration of vacancies, in that
the higher the vacancy concentration, the higher this temperature),
and thus voids are formed. The density of voids produced is
essentially proportional to the factor:
q 3 / 2 C v 1 / 2 ##EQU00001##
where
[0109] q is the cooling rate at the nucleation temperature;
and,
[0110] C.sub.v is the vacancy concentration at the point of
nucleation.
[0111] The nucleation process for agglomerated intrinsic point
defects typically occurs at a temperature greater than about
1000.degree. C. (e.g., about 1050.degree. C., 100.degree. C.,
1125.degree. C., 1150.degree. C., 1175.degree. C., or even
1200.degree. C.). However, it is to be noted that the temperature
at which nucleation of the predominant intrinsic point defects
occurs can be experimentally determined for a given crystal puller
and process as follows. It is believed that silicon
self-interstitials in a defined region of the ingot remain as point
defects and do not nucleate to form agglomerated defects until that
region passes through the section of the hot zone where the silicon
reaches the temperature of nucleation. That is, under typical
Czochralski growth conditions, the region is originally formed at
the solid/liquid interface and has a temperature of approximately
the melt temperature of silicon. As the region is pulled away from
the melt during the growth of the remainder of the ingot, the
temperature of the region cools as it is pulled through the hot
zone of the crystal puller. The hot zone of a particular crystal
puller typically has a characteristic temperature profile,
generally decreasing with increasing distances from the melt solid
interface, such that at any given point in time, the region will be
at a temperature approximately equal to the temperature of the
section of the hot zone occupied by the region. Accordingly, the
rate at which the region is pulled through the hot zone affects the
rate at which the region cools. Accordingly, an abrupt change in
the pull rate will cause an abrupt change in the cooling rate
throughout the ingot. Significantly, the rate at which a particular
region of the ingot passes through the temperature of nucleation
affects both the size and density of agglomerated defects formed in
the region. Thus, the region of the ingot which is passing through
the nucleation temperature at the time the abrupt change is made
will exhibit an abrupt variation in the size and density of
agglomerated intrinsic point defects, hereinafter referred to as a
nucleation front. Because the nucleation front is formed at the
time the pull rate is varied, the precise location of the
nucleation front along the axis of the ingot can be compared to the
position of the ingot, and correspondingly the nucleation front
within the hot zone at the time the abrupt change in pull rate was
made, and compared with the temperature profile of the hot zone, to
determine the temperature at which the nucleation of agglomerated
intrinsic point defects occurs for the type and concentration of
intrinsic point defects in the location of the nucleation
front.
[0112] Thus, persons skilled in the art can grow a silicon ingot by
the Czochralski method under process conditions designed to produce
an ingot which is either vacancy rich or silicon self-interstitial
rich by making abrupt changes in the pull rate and, then by (i)
noting the position of the ingot with respect to the temperature
profile in the hot zone at the point in time in which the pull rate
is changed, and (ii) observing the axial location of the nucleation
front, an approximation can be made as to the temperature of
nucleation for the concentration of intrinsic point defects present
along the nucleation front. Additionally, since the temperature and
intrinsic point defect concentration varies radially along the
nucleation front, the temperature and intrinsic point defect
concentration can be determined at several points along the
nucleation front and the temperature of nucleation can be plotted
against the intrinsic point defect concentration to determine the
temperature of nucleation as a function of intrinsic point defect
concentration. The temperature of the silicon along the nucleation
front can be determined using any thermal simulation method known
in the art which is capable of estimating the temperature at any
location within a Czochralski reactor, such as for example, the
thermal simulation described in Virzi, Computer Modeling of Heat
Transfer in Czochralski Silicon Crystal Growth, Journal of Crystal
Growth, 112, 699 (1991). The concentration of silicon
self-interstitials may be estimated along the nucleation front
using any point defect simulation method known in the art which is
capable of estimating the concentration of intrinsic point defects
at any point in the ingot, such as for example, the point defect
simulation described in Sinno et al., Point Defect Dynamics and the
Oxidation-Induced Stacking-Fault Ring in Czochralski-Grown Silicon
Crystals, Journal of Electrochemical Society. 145, 302 (1998).
Finally, the temperature of nucleation verses intrinsic point
defect concentration can be obtained for an expanded range of
temperatures and concentration by growing additional ingots under
varying growth parameters to produced ingots with increased or
decreased initial concentrations of intrinsic point defects, and
repeating the cooling experiment and analysis described above.
[0113] The nucleation process quickly stops once the temperature is
within a few Kelvin (e.g., about 2, 4, 6, 8 or more) of the
nucleation temperature. Once this temperature is reached, no new
voids are produced, but existing voids can continue to grow in size
until the diffusion of vacancies becomes so slow as to stop the
growth process; that is, once void nucleation stops, void growth
will continue as long as vacancies are capable of diffusing to void
sites within a commercially practical period of time. In oxygen
containing Czochralski silicon, vacancies are bound to oxygen at a
characteristic temperature of about 1000.degree. C. (e.g., about
1010.degree. C., 1015.degree. C., 1025.degree. C., or even
1050.degree. C.). In the bound state, the vacancies are effectively
immobile on the time scale of void growth. By the time a
temperature of about 900.degree. C. (e.g., about 910.degree. C.,
925.degree. C., 950.degree. C. or even 975.degree. C.) is reached,
essentially all void growth stops.
[0114] In view of the foregoing, the process of the present
invention is focused upon the cooling rate of the crystal over two,
and optionally three, distinct temperature ranges (optional
because, in reference to FIGS. 18-20, if the cooling rate changes,
the "window" of acceptable operating conditions gets bigger):
[0115] 1. The first temperature range is near the melt-solid
interface, where v/G.sub.0 is established over a temperature range
of about 1300.degree. C. to about 1400.degree. C. (i.e., over a
temperature ranging from the solidification temperature to about
1300.degree. C., 1325.degree. C., 1350.degree. C., or even about
1375.degree. C.). The cooling rate within this range influences
whether vacancies are the predominant intrinsic point defect from
about the central axis of the ingot to about the lateral surface of
the ingot for the particular segment of interest. [0116] 2. The
second range of temperatures is that over which void nucleation
occurs. Void nucleation generally occurs at temperatures ranging
from about 1000.degree. C. to about 1200.degree. C., from about
1025.degree. C. to about 1175.degree. C., from about 1050.degree.
C. to about 1150.degree. C., or from about 1075.degree. C. to about
1125.degree. C. Controlling the rate of cooling over this
temperature range influences void density. [0117] 3. The third
range of temperatures is that over which void growth occurs; that
is, the temperature range over which silicon lattice vacancies are
still mobile, for commercially practical periods of time, after
nucleation has occurred. Void growth, or vacancy diffusion,
typically occurs over a temperature range of about 900.degree. C.
to about 1100.degree. C., from about 925.degree. C. to about
1075.degree. C., or from about 950.degree. C. to about 1050.degree.
C. Exemplary details for how such growth conditions may be achieved
are further described herein below.
[0118] In addition to controlling void nucleation and growth, it
may also be important, in certain circumstances, to control the
cooling rate through the temperature range over which vacancies are
mobile, either alone or in combination with the control of
v/G.sub.0 (which determines the initial vacancy concentration), in
order to limit the residual vacancy concentration in the silicon
segment. More specifically, it is currently believed that when
silicon having concentrations of vacancies in excess of about
3.times.10.sup.12 cm.sup.-3 (as determined by, for example, the
platinum diffusion method described herein below) is exposed to
temperatures commonly employed in integrated circuit manufacturing
processes (e.g., temperatures ranging of about 600.degree. C. to
800.degree. C.), a form of catalyzed oxygen precipitation will
occur. This oxygen precipitation can be beneficial or detrimental,
depending upon the degree of precipitation that occurs. For
example, such precipitation is beneficial when it can be controlled
by thermal treatments such as those described in U.S. Pat. No.
5,994,761 (incorporated herein by reference), in order to form
wafers which have controlled vacancy profiles (which in turn lead
to a controlled oxygen precipitation profile). In contrast, this
precipitation is detrimental when it cannot be controlled, because
it can cause oxygen precipitation in crystals to run out of control
(in the sense that a subsequent thermal treatment, such as those
disclosed in for example U.S. Pat. No. 5,994,761 and PCT
Application No. PCT/US99/19301 (incorporated herein by reference),
cannot erase or dissolve the oxygen clusters which form as the
crystal cools). A common example of a situation wherein
precipitation typically runs out of control can be found in the
extreme tail-end of crystals wherein very rapid cooling occurs.
[0119] In normal crystal growth regimes, voids are such effective
consumers of vacancies that practically none, certainly far fewer
than the 3.times.10.sup.12 cm.sup.-3 threshold for the enhanced
precipitation effect, remain as the crystal enters the vacancy
binding regime. If, however, the crystal is cooled rapidly, such as
described herein, then there is some risk that insufficient
vacancies are consumed during the growth phase. Schematically, this
situation is illustrated in FIGS. 16 and 17. More specifically,
FIG. 16 illustrates the production of voids in a growing crystal in
the most typical case. Under such conditions, the consumption of
vacancies to voids is efficient enough to reduce the vacancy
concentration to a value below the enhanced precipitation threshold
by the time vacancies become bound to oxygen. In contrast, FIG. 17
illustrates the production of voids in a growing crystal which is
more rapidly cooled through the void growth regime. The more rapid
cooling results in "anomalously" high values of oxygen
precipitation, due to the high levels of residual vacancies at the
time the crystal enters the binding regime.
[0120] In order to produce "functionally perfect" (i.e.,
"functionally defect-free") silicon, voids must be sufficiently
small in size, such that the requirements described above with
respect to reliability are met. This necessitates relatively high
cooling rates. On the other hand, for a useful product, oxygen
precipitation must also be controllable; that is, one should be
capable of producing denuded zone-type (see, e.g., U.S. Pat. No.
5,994,761) or non-oxygen precipitating-type (see, e.g., PCT
Application No. PCT/US99/19301) behavior in the silicon. These two
requirements are not necessarily met simultaneously. Accordingly,
one aspect of the present invention is the simultaneous meeting of
these two requirements and the description of the conditions under
which this can be achieved.
[0121] Additionally, it is to be noted that, in some instances,
there is a possibility that the voids themselves will hinder or
prevent the formation of an acceptable denuded zone if sufficiently
numerous. In some circumstances, therefore, it may be preferred
that the density of voids be less than about 1.times.10.sup.8
cm.sup.-3.
[0122] In those situations where all of the above described
limitations are met, a silicon material referred to herein as
"useful, functionally perfect" silicon is formed.
[0123] Calculations of the Crystal Growth Conditions for "Useful,
Functionally Perfect" Silicon:
[0124] The calculations which are used to define the operating
conditions for such material are relatively complex and
multi-dimensional, involving the coupling of several crystal growth
parameters. Using the model elements (herein the "standard" model)
developed in the references cited above, these can be estimated and
then further refined, for example, empirically or by additionally
modeling (using means described herein or which are standard in the
art). The results are summarized in the complex chart sketched in
FIG. 18. More specifically, FIG. 18 is an exemplary illustration of
a calculation of the void size/void density/residual vacancy space
as a function of incorporated vacancy concentration (wherein
S.sub.0 is the vacancy concentration, Cv, normalized to the melting
point concentration, Cv.sub.m) and constant cooling rate (e.g.,
constant cooling from about 1400.degree. C. to some temperature at
which, for a given vacancy concentration, vacancies are no longer
mobile within a commercially practical period of time). These
calculations provide the values of the parameters important to the
formation of "useful, functionally perfect" silicon. These
parameters are:
TABLE-US-00001 1. Void density: N.sub.v (cm.sup.-3) 2. Void Size:
R.sub.v (average radial distance, in nm, from about the center of
the void to the outer edge) 3. Residual vacancy C.sub.res
(cm.sup.-3) concentration:
In general, the space of these parameters is given as a function of
two crystal growth parameters: [0125] 1. The incorporated vacancy
concentration (identified as S.sub.0 in FIG. 18). S.sub.0 is the
concentration of vacancies incorporated in the crystal normalized
to the melting point solubility of vacancies. This number is
related to the v/G.sub.0 conditions under which the crystal was
grown. A simple analytical expression linking the two has been
previously discussed, for example, by V. V. Voronkov et al., J.
Appl. Phys., 86, 5975 (1999), which is incorporated herein by
reference. Generally speaking, this relationship may be expressed
as follows:
[0125]
S.sub.0=Cv.sub.0/Cv.sub.m.about.0.23.times.(v/v.sub.c-1)/(v/v.sub-
.c+0.15)
where [0126] Cv0 is the "installed" vacancy concentration; that is,
the vacancy concentration as determined by v/G.sub.0; [0127] Cvm is
the vacancy concentration at the melting point; that is, the
vacancy concentration based on the melting point solubility of
vacancies; [0128] v is the growth velocity; and [0129] v.sub.c is
the critical growth velocity; that is, v.sub.c=G.xi..sub.cr, where
.xi..sub.cr is (v/G).sub.critical. [0130] 2. The cooling rate of
the crystal--In these calculations, the cooling rate is assumed to
be constant through both the void nucleation and the void growth
regimes (as described above). The intersection of these parameter
spaces in the chart represents a map of the conditions under which
a desired result may be achieved. While the precise values for the
crystal growth parameters necessary to meet the requirements for
the formation of "useful, functionally perfect" silicon may vary in
some instances, experimental evidence to-date suggest the
approximate values are: [0131] 1. N.sub.v less than about
1.times.10.sup.8 cm.sup.-3 (in some embodiments, preferably less
than about 5.times.10.sup.7 cm.sup.-3, 1.times.10.sup.7 cm.sup.-3,
or even about 5.times.10.sup.6 cm.sup.-3); [0132] 2. R.sub.v: less
than about 70 nm (in some embodiments, preferably less than about
60, 50, 40, or even 30 nm);
[0133] 3. C.sub.res: less than about 3.times.10.sup.12 cm.sup.-3
(in some embodiments, preferably less than about 2.times.10.sup.12
cm.sup.-3, 1.times.10.sup.12 cm.sup.-3, 5.times.10.sup.11
cm.sup.-3, 1.times.10.sup.11 cm.sup.-3, 5.times.10.sup.10
cm.sup.-3, or even less than about 1.times.10.sup.10
cm.sup.-3).
Using these values as an exemplary guide, the chart of FIG. 18 can
then be used to map out the crystal growth conditions under which
these values can be met, for a given crystal puller and crystal
pulling process (as further described herein).
[0134] It is to be noted, with respect to these values, that in
some instances, in order to achieve the desired residual vacancy
concentrations and void size, some minimum void density may be
necessary. Stated another way, depending upon the initial vacancy
concentration and the cooling rate, among other things, there may
be a minimum density of voids which is necessary in order for the
residual vacancy concentration to be below the desired level (the
voids acting as "sinks," to which the vacancies can diffuse and be
consumed), and for the void size to be below the desired level (too
few voids and too many vacancies resulting in voids which are too
large). In such instances, typically the void density will be at
least about 5.times.10.sup.6 cm.sup.-3, 1.times.10.sup.7 cm.sup.-3,
5.times.10.sup.7 cm.sup.-3, 1.times.10.sup.8 cm.sup.-3, or
more.
[0135] "Standard Model"
[0136] Referring now to FIG. 19, there is illustrated an exemplary
operating window for meeting the above-described values using a
"standard" model and assuming that the cooling rate is constant
(from solidification to a temperature at which vacancies are no
longer mobile within a commercially practical period of time). The
values contained in the cross-hatched area are achieved at
relatively high cooling rates and large values of v/G.sub.0; that
is, these values are achieved at fast pull rates and in hot zones
designed to produce large axial temperature gradients. It is to be
noted here that, if these temperature gradients are adjusted
appropriately, there is essentially no upper limit to the pull
rates in which these conditions can be met. Accordingly, it is for
this reason that "useful, functionally perfect" silicon can be
produced under essentially the fastest pull rates possible for a
given crystal puller, and thus under the most cost-effective
conditions known to-date.
[0137] Additionally, it is to be noted that there is a further
degree of freedom in the growth of "useful, functionally perfect"
silicon that is not illustrated in the already complex diagram of
FIG. 19. More specifically, if the criterion of constant cooling
rate through both the void nucleation temperature range and the
void growth temperature range is relaxed, the hatched region can be
increased in size. For example, if the cooling rates of the x-axis
of the chart are interpreted to mean the cooling rate through the
void nucleation range (e.g., from about 1080.degree. C. to about
1150.degree. C.) only, and then allow the cooling rate through the
growth regime (e.g., from about 950.degree. C. to about
1050.degree. C.) to be less than this value, then the lower
boundary of this area (i.e., constant C.sub.res) will drop
vertically on the chart. Based upon experimental evidence to-date,
it is estimated that a change in the cooling rate of the second
regime of only about 10% lower than that of the first range will
remove this lower limit effectively entirely, without changing the
other limits appreciably. Without being held to a particular
theory, it is generally believed that the residual vacancies are
being allowed sufficient extra time to be completely consumed by
the voids of a density determined by the first regime cooling rate.
Under the required conditions of a large v/G.sub.0, the
concentration of the residual vacancies is small compared to the
initially incorporated vacancy concentration. Hence, the size of
the voids is not changed in a meaningful or significant way.
[0138] "Modified Model"
[0139] Referring now to FIG. 20, a second exemplary model for the
void/vacancy consumption phenomena is considered. More
specifically, FIG. 20 illustrates the results produced under a
modified model, wherein only a slight but significant change has
been made in the first, or standard, model. Here, "useful,
functionally perfect silicon" can only be produced under conditions
of a two stage cooling rate (as opposed to the constant cooling
rate of the standard model). The operating conditions are
highlighted.
[0140] In this example, the process space for the operating
conditions to produce "useful, functionally perfect" silicon under
the modified model are generally too small and at values of S.sub.0
which are, in most cases, impractical. In order to produce silicon
under such a model, therefore, we then require two stage cooling to
eliminate the lower C.sub.res limit.
[0141] Control of v/G.sub.0 and Cooling Rates
[0142] The general details for controlling v/G.sub.0, in order to
obtain vacancy-dominated silicon over an appreciable length of the
constant diameter portion of a single crystal silicon ingot, are
generally known by those of ordinary skill in the art and are
described, for example, in PCT Application Nos. PCT/US98/07304,
07305, and 07365. Typically, however, in accordance with the
present invention the growth velocity, v, and the average axial
temperature gradient, G.sub.0, will be controlled such that, for at
least a segment of the constant diameter portion of the ingot
(e.g., 10%, 20%, 40%, 60%, 80%, 90%, 95% or more, as measured along
the central axis of the ingot), vacancies will be the predominant
intrinsic point defect in an axially symmetric region having a
width, as measured from about the central axis of the ingot toward
the circumferential edge, or lateral surface, of the ingot, of at
least about 25%, 50%, 75%, 85%, 95% or more, relative to the length
of the radius of the ingot. In some embodiments, however, this
region will preferably extend from the central axis to the lateral
surface of the ingot; that is, preferably the width of the region
will be essentially equal to the width of the constant diameter
portion of the ingot. However, in those instances wherein this
region does not extend from the central axis to the lateral
surface, it may optionally be surrounded by another axially
symmetric region, wherein silicon self-interstitials are the
predominant intrinsic point defect and which is substantially free
of agglomerated intrinsic point defects, as described in, for
example, PCT/US98/07365.
[0143] It is to be noted in this regard that, prior to a thermal
treatment, a single crystal silicon wafer, obtained from a single
crystal silicon ingot grown in accordance with the present
invention, will having a substantially uniform oxygen
concentration, void concentration and vacancy concentration
(excluding the near-surface region of the wafer). Stated another
way, the axially symmetric, vacancy-dominated region of the present
invention will extend substantially from the front surface of the
wafer to the back surface of the wafer (i.e., the vacancy-dominated
region will have a thickness of at least about 90%, 92%, 94%, 96%,
98%, or even about 100%, relative to the overall thickness of the
wafer), the oxygen, void and residual vacancy concentration being
substantially uniform throughout this region (i.e., from about top
to bottom).
[0144] Given that the process of the present invention enables
essentially the fastest possible growth rates for a given crystal
puller to be employed, essentially any value in excess of the
critical value of v/G may be employed. Referring again, for
example, to FIGS. 18-20, it is to be noted in this regard that
S.sub.0 generally represents upward deviations from the critical
value of v/G.sub.0. In addition, FIGS. 18-20 provide exemplary data
on the cooling rates; that is, for a given value of v/G (i.e.,
S.sub.0), these graphs can be used to determine an approximate
cooling rate needed in order to achieve the material of the present
invention.
[0145] Control of the average axial temperature gradient, G.sub.0,
may be achieved through the design of the "hot zone" of the crystal
puller, i.e. the graphite (or other materials) that makes up the
heater, insulation, heat and radiation shields, among other things.
Although the design particulars may vary depending upon the make
and model of the crystal puller, in general, G.sub.0 may be
controlled using any of the means currently known in the art for
controlling heat transfer at the melt/solid interface, including
reflectors, radiation shields, purge tubes, light pipes, and
heaters (side or bottom heaters). In general, radial variations in
G.sub.0 are minimized by, in most cases, positioning such an
apparatus within about one crystal diameter above the melt/solid
interface. G.sub.0 can be controlled further by adjusting the
position of the apparatus relative to the melt and crystal. This is
accomplished either by adjusting the position of the apparatus in
the hot zone, or by adjusting the position of the melt surface in
the hot zone. In addition, when a heater is employed, G.sub.0 may
be further controlled by adjusting the power supplied to the
heater. Any, or all, of these methods can be used during a batch
Czochralski process in which melt volume is depleted during the
process.
[0146] It is to be noted that, in accordance with the present
invention, cooling is controlled through the temperature range over
which nucleation of agglomerated vacancy defects occurs. Once this
is achieved, as indicated by FIGS. 18-20 (and the discussion
relating thereto), the cooling rate can be maintained (i.e., can be
kept constant), or it can be increased.
[0147] In general, the single crystal silicon may be cooled through
the nucleation temperature for agglomerated vacancy defects, and
optionally the temperature at which vacancies are no longer mobile
for commercially practical periods of time, by means of at least
two alternative approaches. In the first approach, the entire ingot
(or at least those portions of the ingot which are desired to
possess the improved gate oxide integrity of the present invention)
is maintained at a temperature in excess of the nucleation
temperature until the ingot tail is completed. The ingot is then
detached from the melt, the heat input to the hot zone is shut
down, and the single crystal silicon is moved from the hot zone of
the Czochralski reactor to a chamber separate from the hot zone,
such as a crystal receiving or other cooling chamber, where the
entire crystal (or at least those above-noted portions) can be
cooled in accordance with the present invention. The cooling
chamber may be jacketed with a heat exchanging device designed to
utilize a cooling medium, for example cooling water, to remove heat
from the cooling chamber at a rate sufficient to cool the single
crystal silicon ingot at the desired rate, without directly
contacting the single crystal silicon with the cooling medium.
Alternatively, or in addition to using a cooling jacket, a
pre-cooled gas such as, for example, helium may be used to
continuously purge the crystal receiving or other cooling chamber
to facilitate more rapid cooling. Methods for removing heat from a
process vessel are well know in the art, such that persons skilled
in the art could employ a variety of means for removing heat from
the crystal receiving or other cooling chamber without requiring
undue experimentation.
[0148] In a second approach, a portion, preferably a large portion,
of the ingot is cooled during crystal growth. In this approach, the
hot zone of the crystal puller is designed to (i) achieve a desired
value (or range of values) for v/G.sub.0 across the entire radius
of the growing crystal, (ii) provide adequate diffusion of vacancy
intrinsic point defects at temperatures intermediate of the
temperature of solidification and the nucleation temperature for
agglomerated intrinsic point defects, and (iii) cool the ingot
through the nucleation temperature for agglomerated vacancy defects
in the grown crystal by applying an appropriate axial temperature
gradient over a range of temperatures containing the nucleation
temperature, and optionally through the temperature at which
vacancies no longer diffuse within a commercially practical period
of time.
[0149] For an ingot prepared in accordance with the process of the
present invention (i.e., an ingot containing material which is
vacancy dominated), in some instances a low oxygen content material
(i.e., less than about 13 PPMA (parts per million atomic, ASTM
standard F-121-83), less than about 12 PPMA, less than about 11
PPMA oxygen, or even less than about 10 PPMA oxygen), may be
preferred. This is because, in medium to high oxygen contents
wafers (i.e., about 14 PPMA to about 18 PPMA), the formation of
oxygen-induced stacking faults and bands of enhanced oxygen
clustering may become more pronounced. Each of these are a
potential source for problems in a given integrated circuit
fabrication process.
[0150] The effects of enhanced oxygen clustering may be further
reduced by a number of methods, used singularly or in combination.
For example, oxygen precipitate nucleation centers typically form
in silicon which is annealed at a temperature in the range of about
350.degree. C. to about 750.degree. C. For some applications,
therefore, it may be preferred that the crystal be a "short"
crystal, that is, a crystal which has been grown in a Czochralski
process until the seed end has cooled from the melting point of
silicon (about 1410.degree. C.) to about 750.degree. C. after which
the ingot is rapidly cooled. In this way, the time spent in the
temperature range critical for nucleation center formation is kept
to a minimum and the oxygen precipitate nucleation centers have
inadequate time to form in the crystal puller.
[0151] Preferably, however, oxygen precipitate nucleation centers
formed during the growth of the single crystal are dissolved by
annealing the single crystal silicon. Provided they have not been
subjected to a stabilizing heat-treatment, oxygen precipitate
nucleation centers can be annealed out of silicon by rapidly
heating the silicon to a temperature of at least about 875.degree.
C., and preferably continuing to increase the temperature to at
least 1000.degree. C., at least 1100.degree. C., 1200.degree. C. or
more. By the time the silicon reaches 1000.degree. C.,
substantially all (e.g., >99%) of such defects have annealed
out. It is important that the wafers be rapidly heated to these
temperatures, i.e., that the rate of temperature increase be at
least about 10.degree. C. per minute and more preferably at least
about 50.degree. C. per minute. Otherwise, some or all of the
oxygen precipitate nucleation centers may be stabilized by the
heat-treatment. Equilibrium appears to be reached in relatively
short periods of time, i.e., on the order of about 60 seconds or
less. Accordingly, oxygen precipitate nucleation centers in the
single crystal silicon may be dissolved by annealing it at a
temperature of at least about 875.degree. C., preferably at least
about 950.degree. C., and more preferably at least about
1100.degree. C., for a period of at least about 5 seconds, and
preferably at least about 10 minutes.
[0152] The dissolution may be carried out in a conventional furnace
or in a rapid thermal annealing (RTA) system. The rapid thermal
anneal of silicon may be carried out in any of a number of
commercially available rapid thermal annealing ("RTA") furnaces in
which wafers are individually heated by banks of high power lamps.
RTA furnaces are capable of rapidly heating a silicon wafer, e.g.,
they are capable of heating a wafer from room temperature to
1200.degree. C. in a few seconds. One such commercially available
RTA furnace is the model 610 furnace available from AG Associates
(Mountain View, Calif.). In addition, the dissolution may be
carried out on silicon ingots or on silicon wafers, preferably
wafers.
[0153] The atmosphere during the rapid thermal annealing and
cooling steps is generally any non-oxidizing atmosphere; oxidation
of the silicon surface has been found to suppress the vacancy
concentration during the rapid thermal annealing step. Preferably,
therefore, the atmosphere has a total absence of oxygen or a
partial pressure of oxygen which is insufficient to inject
sufficient quantities of silicon self-interstitial atoms which
suppress the build-up of vacancy concentrations. While the lower
limit of oxygen concentration at which the vacancy concentration is
unacceptably suppressed has not been precisely determined, it is
generally preferred that the atmosphere during the rapid thermal
annealing step have less than 2,000 ppm (0.002 atm.) and more
preferably less than about 1,000 ppm (0.001 atm.) of oxygen. The
atmosphere may be, for example, a nitriding atmosphere such as
nitrogen or ammonia, a non-nitriding atmosphere such as helium,
neon, carbon dioxide or argon, or combinations thereof. Preferably,
it is argon.
[0154] Substitutional carbon, when present as an impurity in single
crystal silicon, has the ability to catalyze the formation of
oxygen precipitate nucleation centers. For this and other reasons,
therefore, it is preferred that the single crystal silicon ingot
have a low concentration of carbon. That is, the concentration of
carbon in the single crystal silicon is preferably less than about
5.times.10.sup.16 atoms/cm.sup.3, more preferably less than
1.times.10.sup.16 atoms/cm.sup.3, and still more preferably less
than 5.times.10.sup.15 atoms/cm.sup.3.
[0155] Additionally, it is preferred in at least some embodiments
that the single crystal silicon wafer be substantially free of
nitrogen; that is, in some embodiments it is preferred that the
wafers of the present invention be non-nitrogen doped. As used
herein, the terms "non-nitrogen doped" and "substantially free of
nitrogen" refers to silicon have a nitrogen content less than about
1.times.10.sup.13 atoms/cm.sup.3, 5.times.10.sup.12 atoms/cm.sup.3,
1.times.10.sup.12 atoms/cm.sup.3, 5.times.10.sup.11 atoms/cm.sup.3,
or less.
[0156] Accordingly, the present, "non-nitrogen doped" wafers are
distinguishable from wafers which are "nitrogen doped" because, if
both are subjected to a heat treatment (e.g., rapid heating to
about 1200.degree. C. in the essential absence of oxygen), cooled,
and then subjected to an oxygen precipitation heat treatment (e.g.,
heating to about 800.degree. C. for about 4 hours and then to about
1000.degree. C. for about 16 hours), the concentration of oxygen
precipitates in the present "non-nitrogen doped" wafers will be
less than about 1.times.10.sup.8 per cm.sup.3 (e.g., less than
about 5.times.10.sup.7, 1.times.10.sup.7, 5.times.10.sup.6,
1.times.10.sup.6, or less), while the concentration of the
"nitrogen doped" wafers will not.
[0157] It is to be noted that, as further described herein below,
wafers which are sliced from ingots grown in accordance with the
present invention are suitable for use as substrates upon which an
epitaxial layer may be deposited. Epitaxial deposition may be
performed by any means common in the art. Wafers which are sliced
from ingots grown in accordance with the present invention are also
suitable for use as substrates for semiconductor on insulator
structures (e.g., SIMOX or bonded applications). The semiconductor
on insulator composite may be formed, for example, as described in
Iyer et al., U.S. Pat. No. 5,494,849. The present wafers may be
employed in such applications as the substrate wafer or the device
layer.
[0158] Furthermore, it is also to be noted that wafers prepared in
accordance with the present invention are suitable for use in
combination with hydrogen or argon annealing treatments, such as
the treatments described in European Patent Application No. 503,816
A1.
[0159] Epitaxial Wafers
[0160] Generally speaking, silicon wafers prepared in accordance
with the present invention are suitable for use as substrates upon
which an epitaxial layer may be deposited. Homoepitaxial deposition
may be performed by any means common in the art. In certain of
these embodiments, however, control of void size and density are
not narrowly critical because the epitaxial deposition process will
"fill in" voids present at the wafer surface which would otherwise
hinder gate oxide integrity; in these embodiments, the residual
vacancy concentration would still be controlled to avoid excessive
oxygen precipitation (as described in detail above in reference to
"usable, functionally perfect" silicon).
[0161] Detection of Agglomerated Defects
[0162] Agglomerated defects may be detected by a number of
different techniques. For example, flow pattern defects, or
D-defects, are typically detected by preferentially etching the
single crystal silicon sample in a Secco etch solution for about 30
minutes, and then subjecting the sample to microscopic inspection.
(see, e.g., H. Yamagishi et al., Semicond. Sci. Technol. 7, A135
(1992)). Although standard for the detection of agglomerated
vacancy defects, this process may also be used to detect
agglomerated interstitial defects. When this technique is used,
such defects appear as large pits on the surface of the sample when
present.
[0163] Agglomerated defects may also be detected using laser
scattering techniques, such as laser scattering tomography, which
typically have a lower defect density detection limit that other
etching techniques.
[0164] Additionally, agglomerated intrinsic point defects may be
visually detect by decorating these defects with a metal capable of
diffusing into the single crystal silicon matrix upon the
application of heat. Specifically, single crystal silicon samples,
such as wafers, slugs or slabs, may be visually inspected for the
presence of such defects by first coating a surface of the sample
with a composition containing a metal capable of decorating these
defects, such as a concentrated solution of copper nitrate. The
coated sample is then heated to a temperature between about
900.degree. C. and about 1000.degree. C. for about 5 minutes to
about 15 minutes in order to diffuse the metal into the sample. The
heat treated sample is then cooled to room temperature, thus
causing the metal to become critically supersaturated and
precipitate at sites within the sample matrix at which defects are
present.
[0165] After cooling, the sample is first subjected to a non-defect
delineating etch, in order to remove surface residue and
precipitants, by treating the sample with a bright etch solution
for about 8 to about 12 minutes. A typical bright etch solution
comprises about 55 percent nitric acid (70% solution by weight),
about 20 percent hydrofluoric acid (49% solution by weight), and
about 25 percent hydrochloric acid (concentrated solution).
[0166] The sample is then rinsed with deionized water and subjected
to a second etching step by immersing the sample in, or treating it
with, a Secco or Wright etch solution for about 35 to about 55
minutes. Typically, the sample will be etched using a Secco etch
solution comprising about a 1:2 ratio of 0.15 M potassium
dichromate and hydrofluoric acid (49% solution by weight). This
etching step acts to reveal, or delineate, agglomerated defects
which may be present.
[0167] In an alternative embodiment of this "defect decoration"
process, the single crystal silicon sample is subjected to a
thermal anneal prior to the application of the metal-containing
composition. Typically, the sample is heated to a temperature
ranging from about 850.degree. C. to about 950.degree. C. for about
3 hours to about 5 hours. This embodiment is particularly preferred
for purposes of detecting B-type silicon self-interstitial
agglomerated defects. Without being held to a particular theory, it
is generally believed that this thermal treatment acts to stabilize
and grow B-defects, such that they may be more easily decorated and
detected.
[0168] Measurement of Crystal Lattice Vacancies
[0169] The measurement of crystal lattice vacancies in single
crystal silicon can be carried out by platinum diffusion analysis.
In general, platinum is deposited on the samples and diffused in a
horizontal surface with the diffusion time and temperature
preferably being selected such that the Frank-Turnbull mechanism
dominates the platinum diffusion, but which is sufficient to reach
the steady-state of vacancy decoration by platinum atoms. For
wafers having vacancy concentrations which are typical for the
present invention, a diffusion time and temperature of 730.degree.
C. for 20 minutes may be used, although more accurate tracking
appears to be attainable at a lesser temperature, e.g., about
680.degree. C. In addition, to minimize a possible influence by
silicidation processes, the platinum deposition method preferably
results in a surface concentration of less than one monolayer.
[0170] Platinum diffusion techniques are described elsewhere, for
example, by Jacob et al., J. Appl. Phys., 82, 182 (1997);
Zimmermann and Ryssel, The Modeling of Platinum Diffusion In
Silicon Under Non-Equilibrium Conditions, J. Electrochemical
Society, 139, 256 (1992); Zimmermann, Goesele, Seilenthal and
Eichiner, Vacancy Concentration Wafer Mapping In Silicon, Journal
of Crystal Growth, 129, 582 (1993); Zimmermann and Falster,
Investigation Of The Nucleation of Oxygen Precipitates in
Czochralski Silicon At An Early Stage, Appl. Phys. Lett., 60, 3250
(1992); and Zimmermann and Ryssel, Appl. Phys. A, 55, 121 (1992);
all of which are incorporated herein by reference
DEFINITIONS
[0171] As used herein, the following phrases or terms shall have
the given meanings: "agglomerated intrinsic point defects" mean
defects caused by the reaction in which vacancies agglomerate to
produce D-defects, flow pattern defects, gate oxide integrity
defects, crystal originated particle defects, crystal originated
light point defects, and other such vacancy related defects, or
(ii) by the reaction in which self-interstitials agglomerate to
produce dislocation loops and networks, and other such
self-interstitial related defects; "agglomerated interstitial
defects" shall mean agglomerated intrinsic point defects caused by
the reaction in which silicon self-interstitial atoms agglomerate;
"agglomerated vacancy defects" shall mean agglomerated vacancy
point defects caused by the reaction in which crystal lattice
vacancies agglomerate; "radius," in the context of a silicon wafer
or ingot, means the distance measured from a central axis to a
lateral surface of a wafer or ingot; "substantially free of
agglomerated intrinsic point defects" shall mean a concentration of
agglomerated defects which is less than the detection limit of
these defects, which is currently about 10.sup.3 defects/cm.sup.3,
and, "vacancy dominated" and "self-interstitial dominated" mean
material in which the intrinsic point defects are predominantly
vacancies or self-interstitials, respectively.
[0172] Additionally, as used herein, the following phrases or terms
shall have the given meanings: "residual vacancy concentration"
refers to the vacancy concentration, as determined by means
described herein, of the silicon material obtained for a single
crystal silicon ingot grown in accordance with the present
invention, after the ingot has been cooled below a temperature at
which vacancies are no longer mobile for commercially practical
periods of time (i.e., after void growth and/or vacancy diffusion
to sites where they may be consumed or annihilated has stopped);
and, "uncontrolled oxygen precipitation," as well as variations
thereof, refers to oxygen precipitation which cannot be prevented
or "erased" by thermal treatment typically used to dissolve
pre-existing oxygen clusters or precipitate nucleii, such as by
those methods described or referenced herein; more specifically,
this refers to oxygen precipitation which cannot be dissolved by a
thermal treatment wherein the silicon is rapidly heated (e.g., at a
rate of at least 1.degree. C./sec.) to a temperature not in excess
of 1300.degree. C. (e.g. a temperature of 1250.degree. C.,
1225.degree. C., or even 1200.degree. C.), as described in, for
example, U.S. Pat. No. 5,994,761.
[0173] In view of the above, it will be seen that the several
objects of the invention are achieved.
[0174] As various changes could be made in the above material and
processes without departing from the scope of the invention, it is
intended that all matter contained in the above description be
interpreted as illustrative and not in a limiting sense.
* * * * *