U.S. patent application number 16/016368 was filed with the patent office on 2018-10-18 for multicrystalline silicon brick and silicon wafer therefrom.
The applicant listed for this patent is SINO-AMERICAN SILICON PRODUCTS INC.. Invention is credited to Hung-Sheng CHOU, Sung Lin HSU, Wen-Ching HSU, Chung-Wen LAN, Yu-Ting WONG, Yu-Min YANG, Wen-Huai YU.
Application Number | 20180297851 16/016368 |
Document ID | / |
Family ID | 54334115 |
Filed Date | 2018-10-18 |
United States Patent
Application |
20180297851 |
Kind Code |
A1 |
CHOU; Hung-Sheng ; et
al. |
October 18, 2018 |
MULTICRYSTALLINE SILICON BRICK AND SILICON WAFER THEREFROM
Abstract
Present disclosure provides a multicrystalline silicon (mc-Si)
brick, including a bottom portion starting from a bottom to a
height of 100 mm, a middle portion starting from the height of 100
mm to a height of 200 mm; and a top portion starting from the
height of 200 mm to a top. A percentage of incoherent grain
boundary in the bottom portion is greater than a percentage of
incoherent grain boundary in the top portion. Present disclosure
also provides a multicrystalline silicon (mc-Si) wafer. The mc-Si
wafer includes a percentage of non-.SIGMA. grain boundary from
about 60 to about 75 and a percentage of .SIGMA.3 grain boundary
from about 12 to about 25.
Inventors: |
CHOU; Hung-Sheng; (Hsinchu,
TW) ; YANG; Yu-Min; (Hsinchu, TW) ; YU;
Wen-Huai; (Hsinchu, TW) ; HSU; Sung Lin;
(Hsinchu, TW) ; HSU; Wen-Ching; (Hsinchu, TW)
; LAN; Chung-Wen; (Taipei City, TW) ; WONG;
Yu-Ting; (Taihcung City, TW) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
SINO-AMERICAN SILICON PRODUCTS INC. |
Hsinchu |
|
TW |
|
|
Family ID: |
54334115 |
Appl. No.: |
16/016368 |
Filed: |
June 22, 2018 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
14698615 |
Apr 28, 2015 |
10029919 |
|
|
16016368 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
C30B 29/06 20130101;
C01B 33/02 20130101; C30B 28/06 20130101; C30B 29/64 20130101 |
International
Class: |
C01B 33/02 20060101
C01B033/02; C30B 29/64 20060101 C30B029/64; C30B 29/06 20060101
C30B029/06 |
Foreign Application Data
Date |
Code |
Application Number |
Apr 29, 2014 |
TW |
103115312 |
Claims
1. A multicrystalline silicon brick, comprising: a bottom portion
starting from a bottom to a height of 100 mm; a middle portion
starting from the height of 100 mm to a height of 200 mm; and a top
portion starting from the height of 200 mm to a top; wherein a
percentage of incoherent grain boundary in the bottom portion is
greater than a percentage of incoherent grain boundary in the top
portion.
2. The multicrystalline silicon brick of claim 1, further
comprising a preferred grain orientation of {112} in the bottom
portion, the middle portion, and the top portion.
3. The multicrystalline silicon brick of claim 1, wherein the
incoherent grain boundary comprises non-.SIGMA. grain
boundaries.
4. The multicrystalline silicon brick of claim 1, a percentage of
coherent grain boundary in the bottom portion is lower than a
percentage of coherent grain boundary in the top portion.
5. The multicrystalline silicon brick of claim 4, wherein the
coherent grain boundary comprises .SIGMA.3 grain boundary.
6. The multicrystalline silicon brick of claim 5, the percentage of
.SIGMA.3 grain boundary being lower than the percentage of the
non-.SIGMA. grain boundary and greater than other grain boundary
being more incoherent than the .SIGMA.3 grain boundary.
7. The multicrystalline silicon brick of claim 3, wherein the
percentage of non-.SIGMA. grain boundaries is from about 65 to
about 75 at the bottom portion.
8. The multicrystalline silicon brick of claim 6, wherein the
percentage of non-.SIGMA. grain boundary is greater than a
summation of the percentage of .SIGMA.3 grain boundary and the
percentage of other grain boundary being more incoherent than the
.SIGMA.3 grain boundary.
9. The multicrystalline silicon brick of claim 5, wherein the
percentage of .SIGMA.3 grain boundaries is from about 12 to about
18 at the bottom portion.
10. The multicrystalline silicon brick of claim 1, further
comprising a nucleation promotion layer under the bottom portion,
wherein the nucleation promotion layer comprises a plurality of
beads.
11. The multicrystalline silicon brick of claim 10, wherein the
beads comprises an average diameter smaller than about 10 mm.
12. The multicrystalline silicon brick of claim 10, wherein the
beads comprises single crystalline silicon, multicrystalline
silicon, silicon carbide, or combinations thereof.
13. The multicrystalline silicon brick of claim 12, wherein an
angle between a pole direction of a first single crystalline
silicon bead and a normal to the bottom of the multicrystalline
silicon ingot is different from an angle between a pole direction
of a second single crystalline silicon bead and the normal to the
bottom of the multicrystalline silicon ingot.
14. A multicrystalline silicon brick, comprising a plurality of
non-.SIGMA. grain boundaries; and a plurality of .SIGMA.3 grain
boundaries, wherein a percentage of non-.SIGMA. grain boundaries is
from about 60 to about 75 and a percentage of .SIGMA.3 grain
boundaries is from about 12 to about 25.
15. The multicrystalline silicon brick of claim 14, further
comprising: a bottom portion starting from a bottom to a height of
100 mm; a middle portion starting from the height of 100 mm to a
height of 200 mm; and a top portion starting from the height of 200
mm to a top; wherein a percentage of .SIGMA.3 grain boundaries is
from about 12 to about 18 at the bottom portion.
16. The multicrystalline silicon brick of claim 14, further
comprising a preferred crystal orientation comprises {112}.
17. The multicrystalline silicon brick of claim 14, wherein the
percentage of .SIGMA.3 grain boundaries is lower than the
percentage of the non-.SIGMA. grain boundaries and greater than
other grain boundaries being more incoherent than the .SIGMA.3
grain boundaries.
18. A multicrystalline silicon brick, comprising: a bottom portion
starting from a bottom to a height of 100 mm; a top portion
starting from the height of 200 mm to a top; and a nucleation
promotion layer under the bottom portion, wherein the nucleation
promotion layer comprises a plurality of beads.
19. The multicrystalline silicon brick of claim 18, wherein a
percentage of incoherent grain boundary in the bottom portion is
greater than a percentage of incoherent grain boundary in the top
portion.
20. The multicrystalline silicon brick of claim 18, wherein a
percentage of non-.SIGMA. grain boundaries is from about 60 to
about 75 and a percentage of .SIGMA.3 grain boundaries is from
about 12 to about 25.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of prior-filed
application Ser. No. 14/698,615, filed Apr. 28, 2015, under 35
U.S.C. 120, and incorporates the prior-filed application by
reference in its entirety.
BACKGROUND
[0002] Multi-crystalline silicon (mc-Si) grown by directional
solidification has attracted much attention in photovoltaic
industry because of its low production cost and high throughput.
However, the crystal quality deteriorates as the ingot grows taller
due to the accumulation of impurities and the generation
(multiplication) of dislocations. Because these defects, as well as
crystal properties, are affected by grain morphologies and lattice
orientations, the control of grain structures is important during
crystal growth.
[0003] Different from random grain boundaries, special grain
boundaries are characterized by particular misorientation and
extensive areas of good fit (special grain boundaries are described
by a sigma number (1<.SIGMA.<29), which is defined as the
reciprocal of the fraction of lattice points in the boundaries that
coincide between the two adjoining grains on the basis of the
coincident site lattice (CSL) model.). Thus, there is low
distortion of atomic bonds and relatively little free volume for
special grain boundaries and consequently low boundary energy.
BRIEF DESCRIPTION OF THE DRAWINGS
[0004] The file of this patent or application contains at least one
drawing executed in color. Copies of this patent or patent
application publication with color drawings will be provided by the
Patent and Trademark Office upon request and payment of the
necessary fee.
[0005] Aspects of the present disclosure are best understood from
the following detailed description when read with the accompanying
figures. It is noted that, in accordance with the standard practice
in the industry, various features are not drawn to scale. In fact,
the dimensions of the various features may be arbitrarily increased
or reduced for clarity of discussion.
[0006] FIG. 1A is a schematic illustration of the experimental
setup, in accordance with some embodiments.
[0007] FIG. 1B is a schematic illustration of silicon beads in the
nitride-coated quartz crucible, in accordance with some
embodiments.
[0008] FIG. 2A is a longitudinal cross section of ingots at a
pulling speed of 10 mm/h, and the dashed line indicates the initial
melt/solid interface, in accordance with some embodiments.
[0009] FIG. 2B is a longitudinal cross section of ingots at a
pulling speed of 50 mm/h, and the dashed line indicates the initial
melt/solid interface, in accordance with some embodiments.
[0010] FIG. 2C is a longitudinal cross section of ingots at a
pulling speed of 200 mm/h, and the dashed line indicates the
initial melt/solid interface, in accordance with some
embodiments.
[0011] FIG. 3A is a grain structure (left), EBSD mapping (bottom),
and the inverse pole diagrams (right) at an ingot height 0 mm of
ingot V, in accordance with some embodiments.
[0012] FIG. 3B is a grain structure (left), EBSD mapping (bottom),
and the inverse pole diagrams (right) at an ingot height 7 mm of
ingot V, in accordance with some embodiments.
[0013] FIG. 3C is a grain structure (left), EBSD mapping (bottom),
and the inverse pole diagrams (right) at an ingot height 14 mm of
ingot V, in accordance with some embodiments.
[0014] FIG. 4 is a comparison of major grain orientations at
different growth distances for different pulling speeds; the
inverse pole diagram of the orientation of V20 at h=19 mm is
included for comparison, in accordance with some embodiments.
[0015] FIG. 5 shows the development of major grain boundaries along
the growth direction for ingot V1. The twin boundaries (purple) and
typical grain boundary mappings at the given heights are inserted
for comparison; the results for ingots V5 and V20 are similar. (For
interpretation of the references to color in this figure caption,
the reader is referred to the web version of this paper), in
accordance with some embodiments.
[0016] FIG. 6A shows a grain competition mechanisms (ingot V1,
overgrown), in each figure, from the left to the right are EBSD,
grain boundary mappings, and the inverse pole diagrams from
different ingot positions. The number on the EBSD mapping indicates
the wafer number, which was closed to its height in mm, in
accordance with some embodiments.
[0017] FIG. 6B shows grain competition mechanisms (ingot V1, a
low-interfacial-energy grain formation at the tri-junction), in
each figure, from the left to the right are EBSD, grain boundary
mappings, and the inverse pole diagrams from different ingot
positions. The number on the EBSD mapping indicates the wafer
number, which was closed to its height in mm, in accordance with
some embodiments.
[0018] FIG. 7A shows grain competition mechanisms (ingot V1,
high-interfacial-energy grain from the tri-junction with twin
boundary movement), in each figure, from the left to the right are
EBSD, grain boundary mappings, and the inverse pole diagrams from
different ingot positions. The number on the EBSD mapping indicates
the wafer number, which was closed to its height in mm, in
accordance with some embodiments.
[0019] FIG. 7B shows grain competition mechanisms (ingot V1, twins
movement), in each figure, from the left to the right are EBSD,
grain boundary mappings, and the inverse pole diagrams from
different ingot positions. The number on the EBSD mapping indicates
the wafer number, which was closed to its height in mm, in
accordance with some embodiments.
[0020] FIG. 8 shows the grain size at different heights of Ingot A
and Ingot B, in accordance with some embodiments.
[0021] FIG. 9A shows grain orientation mappings and typical grain
boundary mappings at a given height (95 mm) of Ingot B, in
accordance with some embodiments.
[0022] FIG. 9B shows defect location mapping and typical grain
boundary mappings at a given height (95 mm) of Ingot B, in
accordance with some embodiments.
[0023] FIG. 10A shows grain orientation mappings and typical grain
boundary mappings at a given height (132.5 mm) of Ingot B, in
accordance with some embodiments.
[0024] FIG. 10B shows defect location mapping and typical grain
boundary mappings at a given height (132.5 mm) of Ingot B, in
accordance with some embodiments.
[0025] FIG. 11A shows grain orientation mappings and typical grain
boundary mappings at a given height (170 mm) of Ingot B, in
accordance with some embodiments.
[0026] FIG. 11B shows defect location mapping and typical grain
boundary mappings at a given height (170 mm) of Ingot B, in
accordance with some embodiments.
[0027] FIG. 12A shows grain orientation mappings and typical grain
boundary mappings at a given height (207.5 mm) of Ingot B, in
accordance with some embodiments.
[0028] FIG. 12B shows defect location mapping and typical grain
boundary mappings at a given height (207.5 mm) of Ingot B, in
accordance with some embodiments.
[0029] FIG. 13 shows the percentage of various grain orientations
at given heights of Ingot B, in accordance with some
embodiments.
[0030] FIG. 14 shows the percentage of various grain boundary types
at given heights of Ingot B, in accordance with some
embodiments.
[0031] FIG. 15A shows grain orientation mappings and typical grain
boundary mappings at a given height (95 mm) of Ingot A, in
accordance with some embodiments.
[0032] FIG. 15B shows defect location mapping and typical grain
boundary mappings at a given height (95 mm) of Ingot A, in
accordance with some embodiments.
[0033] FIG. 16A shows grain orientation mappings and typical grain
boundary mappings at a given height (132.5 mm) of Ingot A, in
accordance with some embodiments.
[0034] FIG. 16B shows defect location mapping and typical grain
boundary mappings at a given height (132.5 mm) of Ingot A, in
accordance with some embodiments.
[0035] FIG. 17A shows grain orientation mappings and typical grain
boundary mappings at a given height (170 mm) of Ingot A, in
accordance with some embodiments.
[0036] FIG. 17B shows defect location mapping and typical grain
boundary mappings at a given height (170 mm) of Ingot A, in
accordance with some embodiments.
[0037] FIG. 18A shows grain orientation mappings and typical grain
boundary mappings at a given height (207.5 mm) of Ingot A, in
accordance with some embodiments.
[0038] FIG. 18B shows defect location mapping and typical grain
boundary mappings at a given height (207.5 mm) of Ingot A, in
accordance with some embodiments.
[0039] FIG. 19 shows the percentage of various grain orientations
at given heights of Ingot A, in accordance with some
embodiments.
[0040] FIG. 20 shows the percentage of various grain boundary types
at given heights of Ingot A, in accordance with some
embodiments.
DETAILED DESCRIPTION
[0041] The following disclosure provides many different
embodiments, or examples, for implementing different features of
the provided subject matter. Specific examples of components and
arrangements are described below to simplify the present
disclosure. These are, of course, merely examples and are not
intended to be limiting. For example, the formation of a first
feature over or on a second feature in the description that follows
may include embodiments in which the first and second features are
formed in direct contact, and may also include embodiments in which
additional features may be formed between the first and second
features, such that the first and second features may not be in
direct contact. In addition, the present disclosure may repeat
reference numerals and/or letters in the various examples. This
repetition is for the purpose of simplicity and clarity and does
not in itself dictate a relationship between the various
embodiments and/or configurations discussed.
[0042] In some embodiments of the present disclosure, special grain
boundaries with sigma numbers smaller than or equal to 3 are
referred to as coherent grain boundaries. On the other hand,
special grain boundaries with sigma numbers greater than 3 are
referred to as incoherent grain boundaries, and special grain
boundaries with sigma numbers greater than 27 are referred to as
non-sigma grain boundaries. In some embodiments, the incoherent
grain boundaries and the non-sigma grain boundaries are
collectively called "non-coherent grain boundary".
[0043] In some embodiments of the present disclosure, a silicon
brick is a portion of a silicon ingot. For example, a silicon brick
can be a 156 mm by 156 mm column separated from a silicon ingot. In
some cases, a silicon ingot can be divided into a 5 by 5 silicon
brick array. For an industrial practice, each of the silicon brick
can be further sliced into about 600 silicon wafers. Polysilicon
has a melting point of about 1,414 degrees Celsius, and the
aforesaid separation operation of the silicon brick from the
silicon ingot or the silicon wafer from the silicon brick can only
generate frictional heat lower than about 100 degrees Celsius.
Hence, said separation can be considered as pure physical change
(decrease in dimension) without the involvement of any chemical
change, for a chemical change can only occurs at a temperature in
proximity to the melting point of the silicon.
[0044] In some embodiments of the present disclosure, three
portions of a silicon ingot, or a silicon brick separated from a
silicon ingot, can be identified according to a height of the ingot
or brick. Generally, a brick of an ingot can be equally divided
into three portions. In some embodiments, a bottom portion ranges
from a bottom to a height of 100 mm; a middle portion ranges from
the height of 100 mm to a height of 200 mm; and a top portion
ranges from the height of 200 mm to a top. Various crystal
properties such as coherency of grain boundary, grain orientations,
or grain size can be separately characterized according to
different aforesaid portions.
[0045] The simplest way to control crystal structure is to use
seeds with given orientations, and the use of mono-crystalline
seeds has become popular in recent years for the production of the
so-called mono-like or quasi-mono ingots. Unfortunately, the grain
competition and new grain formation may spoil the structures and
reduce the production yield. Therefore, it is believed that using a
preferred growth orientation for directional solidification could
increase the structure yield and reduce defect density. This issue
can be discussed based on the twin formation mechanisms, and
concluded that {100} orientation turned out to be the most
difficult one to the growth of mono-like ingots.
[0046] To obtain better crystal properties in mc-Si growth, one of
the approaches is the so-called dendrite casting method, which
controls the initial undercooling to induce [110]/[112] dendrites
and .SIGMA.3 grain boundaries. However, the control of undercooling
is not so easy in a commercial growth station due to the large
thermal resistance from the thick bottom of the quartz crucible and
the imperfect nitride coating. This thus limits the applications of
the method for mass production.
[0047] For growing mc-Si, it is found that the grains seemed to be
oriented randomly, but the relative grain orientation could be
described mostly by special coincidence orientations. This
indicated that the grain structure developed from far fewer
independent nuclei that were decided at the initial stage of
nucleation and crystal growth. It is believed that {111} was the
preferred growth orientation for silicon due to the smaller
interfacial energy. The melt growth behavior of me-Si using an in
situ monitoring system during a thin-film directional
solidification was studied, and it is observed that different
growth behaviors of oriented grains appear in different cooling
conditions.
[0048] Conventionally, .SIGMA.3 grain boundaries are more desired
than a non-coherent or non-.SIGMA. grain boundaries in a mc-Si
structure due to the fact that .SIGMA.3 grain boundaries are more
coherent and functions as a less efficient recombination center
compared with the non-coherent counterpart (including incoherent
and non-.SIGMA. grain boundaries). Alternatively stated, .SIGMA.3
grain boundaries are more "electrically inert" than the
non-coherent boundaries. Using conventional means to grow mc-Si,
the percentage of .SIGMA.3 grain boundaries is greater than the
percentage of the non-coherent counterpart in order to retain
sufficient quantum efficiency or conversion efficiency of a
photovoltaic. However, the quantum efficiency of a mc-Si
photovoltaic still hits a limit because the accumulation of the
impurities and multiplication of dislocations not only occurs at
the grain boundary region but also in the grain body. Taking this
fact into consideration, the present disclosure provides a mc-Si
structure having a greater percentage of non-coherent grain
boundaries than that of the coherent grain boundaries, and showing
better conversion efficiency than the me-Si structure prepared
according to conventional means.
[0049] In some embodiments of the present disclosure, the coherency
of the grain boundary can be identified by at least two methods:
(1) by a computer-programmed EBSD, and (2) by photoluminescence
(PL) observing the incoherent/non-.SIGMA. grain boundaries.
[0050] In some embodiments, a structure of mc-Si, which can be a
mc-Si ingot, a me-Si brick, or a me-Si wafer, is disclosed. The
structure of me-Si shows a greater percentage of non-coherent grain
boundaries (for example, a summation of the incoherent grain
boundaries and non-.SIGMA. grain boundary) than that of the
coherent grain boundaries. In some embodiments, the me-Si brick
possesses a greater percentage of non-coherent grain boundary in a
bottom portion than that in a top portion. In some embodiments, the
me-Si wafer possesses a percentage of non-.SIGMA. grain boundary
from about 60 to about 75 and a percentage of .SIGMA.3 grain
boundary from about 12 to about 25. In some embodiments, a
percentage of the non-.SIGMA. grain boundary and a percentage of
.SIGMA.3 grain boundary of a me-Si wafer are substantially
identical.
[0051] A method for obtaining the me-Si structure described herein
is also disclosed. A nucleation promotion layer is utilized to
promote a small grain size at the initial of the me-Si grain
growth. As described in the following, the nucleation promotion
layer can be made of silicon beads with an average dimension of
about less than 10 mm. In some embodiments, the silicon beads can
take spherical shape. In some embodiments, the silicon beads can be
single crystalline silicon, multicrystalline silicon, silicon
carbide, or combinations thereof.
[0052] In some embodiments of the present disclosure, when
preparing a me-Si ingot or brick, {100} and {110} poly-silicon
grains were favored at a high cooling rate, e.g., 30 K/min, as a
result of kinetic control; the growth velocity of {100} was 140.8
cm/h at 30 K./min. On the contrary, at a low cooling rate, e.g., 1
K/min, {111} grains were dominant due to thermodynamic control that
favors the orientation with the lowest interfacial energy. By using
phase field modeling, similar developments can be obtained. The
force balance is further used at the tri-junction to explain the
dominance of {111} grains at the low growth rate. The critical
velocity for facet formation, as a result of morphological
instability, was estimated around 12 cm/h. However, the growth
velocity for {100} dominated growth was unknown. Therefore, for the
grain competition in a normal speed at about 1 cm/h in commercial
mc-Si production, {111} grains should be dominant. Moreover, the
grain competition in silicon is far more complicated than people
having ordinary skill in the art have expected due to twin
formation.
[0053] Referring to FIG. 1A, in some embodiments, mc-Si ingot (70
mm in broadest dimension) is grown by directional solidification in
an apparatus 100. The directional solidification setup using
induction coil 101 for heating is shown, where the crucible 102 is
insulated by graphite felt 103 [to inventor: please verify whether
103 is an aluminum felt or a graphite felt] to better control the
solidification front. Spherical silicon beads 104 (for example,
0.92 mm in diameter from CV 21, Japan) are used as the seed layer.
In some embodiments, the nucleation promotion layer may possess a
height H at a bottom of the crucible. In some embodiments, the
height H is about 20 mm.
[0054] In some embodiments of the present disclosure, spherical
silicon beads can be used as the nucleation promotion layer for
directional solidification of me-Si. However, silicon beads are not
limited to a spherical shape. Any form of silicon scraps with a
characteristic dimension of equal to or smaller than 10 mm is
within the contemplated scope of the present disclosure. For
example, a roughened crucible bottom can be used as the nucleation
promotion layer. In some embodiments, the roughened crucible bottom
can be formed by a blanket physical or chemical etch and thus the
concave and convex patterns being randomly disposed, with a
characteristic dimension (for example, a distance between a vertex
of a convex and a bottom of a concave) being smaller than or equal
to about 10 mm. In other embodiments, the roughened crucible bottom
can be formed by a patterned etch. For example, line features or
dot features with a pitch of smaller than or equal to about 10 mm
can be formed as the nucleation promotion layer.
[0055] In the following description, the experimental setup and
procedure are described briefly, followed by results, discussion,
and conclusion. In some embodiments, the seeds used for directional
solidification mc-Si growth are not limited to spherical beads, as
discussed. Any beads having an average diameter of lower than 50
mm, preferably lower than 10 mm, are suitable for the subsequent
mc-Si growth. In some embodiments, the silicon beads can be made of
single crystalline silicon, multicrystalline silicon, or a mixture
thereof. Other materials such as silicon carbide can also be used,
separately or together, with silicon seeds. In the case of using
single crystalline beads, although all the beads are having a
single orientation, for example, {110}, the pole direction of each
bead is not necessary perpendicular to a normal of the bottom of
the mc-Si ingot or brick. Details of the single crystalline beads
will be further discussed in FIG. 1B.
[0056] Referring to FIG. 1B, in some embodiments with single
crystalline silicon beads, for example, {110} silicon beads, the
pole direction P1 of a first bead 110 and a normal N of the
crucible bottom 102B form an angle .theta.1 greater than zero.
Similarly, the pole direction P2 of a randomly selected second bead
120 (other than the first bead 110) and a normal N of the crucible
bottom 102B form an angle .theta.2 greater than zero. The angles
.theta.1 and .theta.2 can be different. In other words, even if the
beads 110 and 120 are made of single crystalline materials having
an orientation of {110}, the ingot formed thereon can be
multicrystalline with random crystal orientations due to the
randomly disposed pole directions of the single crystalline beads.
In other embodiments, the silicon beads can be multicrystalline
silicon, silicon carbide, crystalline material beads other than
silicon, or combinations thereof.
[0057] In some embodiments, before solidification started, silicon
raw material was melted leaving about 5 mm to 10 mm of the
nucleation promotion layer at the bottom. The temperature gradient
of the furnace for crystal growth was about 10 K/cm. Therefore, the
estimated cooling rate was about 3.33 K/min for the crucible speed
of 20 cm/h. However, in a commercial mc-Si production, the
temperature gradient of the furnace is about 1 K/cm and the
crucible speed being around 1 cm/h. Hence the estimated cooling
rate is about 0.0167 K/min in a production setting.
[0058] Referring to FIG. 2A to FIG. 2C, three ingots are grown from
different crucible pulling speeds. The ingots are labeled as V1 for
the crucible speed at 10 mm/h, V5 for 50 mm/h, and V20 for 200
mm/h. After crystal growth, the ingots were cut into wafers and
polished for further analysis. The wafers were also chemically
etched (HNO3:HF=6:1) for subsequent characterizations. The grain
orientation and boundary mappings were carried out by using
electron backscattered diffraction (EBSD) (Horiba Nordlys F+) with
a step size of 10 .mu.m, which was installed in an SEM (Hitachi
S3400).
[0059] The longitudinal cross sections of the grown ingots are
shown in FIG. 2A to FIG. 2C for comparison. As shown, the columnar
grains were grown upward nicely from the nucleation promotion layer
in all cases. The interface shape was nearly flat except near the
crucible wall. This could also be seen from the grain growth
direction. Near the crucible wall (not shown), new grains appeared
and grew inwards. As the pulling speed increased, the interface
became more concave. Again, this could be seen from the convergent
grains toward the center near the upper parts of FIG. 2B and FIG.
2C. After crystal growth, the unmelted silicon beads sintered
together, but the initial solidification front could be determined
from the starting points of the columnar grains.
[0060] The width of the columnar grains grew upward slowly, but the
grain size needed to be analyzed from the cross section grains,
which will be discussed shortly. In some embodiments, the columnar
grains can have an average height of about 3 cm. However, in a
commercial production setting, the columnar grains can have an
average height of from about 25 cm to about 36 cm due to different
ingot growth conditions. An interesting observation was that some
grains were terminated suddenly by other grains due to their tilted
growth orientation from the observed cutting plane. Moreover, some
disoriented grains grew in the direction that was quite different
from the growth direction. This could be explained by the twin
formation from the {111} facets, which will be discussed shortly.
Otherwise, the oriented grains will grow over the disoriented
grains during grain competition
[0061] The horizontal cuts of ingot V1 and their EBSD results are
shown in FIG. 3A-FIG. 3C, respectively, for the positions at ingot
or brick height h=0 mm, 7 mm, and 14 mm from the starting point of
the columnar grains. Although the area near the wafer center (50%
of the diameter), where the grains grew vertically, should be the
better area for orientation analysis, its difference from the
bigger area mapping (80% of the diameter) was found not significant
change. To have more grains for analysis, the present disclosure
still chose the bigger area for orientation comparison. In each
figure, the grains in the dashed box are analyzed. Their
orientation mapping is shown at the bottom of the figure; the
corresponding color to the orientation is indicated at the top
right corner of the photograph in FIG. 3A. In addition, the inverse
pole diagrams, in terms of the frequency counts and their contours,
are shown on the right. As shown in FIG. 3A, the grains are uniform
and round due to the uniform silicon beads are used as the
nucleation promotion layer. The orientations were quite random as
well, although the contours showed some difference, but the
difference of the contour minimum (0.78) shown in blue and maximum
(1.22) shown in red is not large. Also, the horizontal cut did not
follow exactly the initial solidification front. However, as the
position increased to h=7 mm, as shown in FIG. 3B, the grain size
increased. More importantly, the percentage of the orientations
near {112} and {111} increased substantially. This trend continued
to the top of the ingot, where the orientations near {112} being
dominant, as shown in FIG. 3C.
[0062] The reason for the dominance of {112} grains may related to
the factors that this orientation has the lowest interfacial energy
next to {111}, and the angle between {111} and {112} is only
19.471. Some commercial wafers grown by using an incubation layer
also have more {112} grains till the top of the ingot. In other
words, the grain competition remained similar regardless the ingot
height; the percentage of {112} at h=14 mm for V1 was about 15%.
Furthermore, in the development of grain structures in a small
notch, {112} grains became dominant form the initial {110} grains
in a small growth distance of 4 mm. Therefore, in some embodiments,
{112} are the dominance orientation of the grain competition from
random seeds.
[0063] The development of grain structures of ingots V5 and V20 was
similar to ingot V1. However, {111} became more dominant at the end
of the growth. The percentage evolutions of major grain
orientations of the three ingots were compared in FIG. 4. As shown,
{112} grains became dominant for ingot V1, while {111} grains
became dominant for ingots V5 and V20. In fact, {212} grains in V5
were slightly more than {111} grains, but the smallest orientation
difference between them is only 15.81, and this could be caused by
the deflection of the interface. Again, the dominance of {111}
grains was consistent with previous observations. The {110} grains
in V1 and V20 were also more than other grains. Because the {110}
orientation is rather rough, the growth rate in this orientation
could be high at high undercooling. Nevertheless, the distribution
of the grain orientations in all cases was rather wide, but {100}
grains remained few near the end. As will be discussed shortly, the
angle between {100} and {111} is large being about 54.71, which is
easier to generate a higher undercooling for twin formation.
[0064] The average grain sizes are also calculated. For simplicity,
the grain size is calculated by dividing the diagonal distance of
the dashed box by the grain numbers across the distance. The grain
size increased with the growth distance for all velocities; it
increased from 0.92 mm at the bottom to about 1.2, 1.4 and 1.6 mm
at the height of 19 mm for ingots V1, V2, and V3, respectively. In
some embodiments, it is found that the grain growth became more
significant with the increasing crucible pulling velocity.
[0065] The development of grain boundaries was further examined,
and the result for ingot V1 is shown in FIG. 5. The mappings of
grain and twin boundaries at different positions are inserted in
the figures for comparison; the twin boundaries are indicated by
the purple lines. As shown, the percentage of non-.SIGMA. grain
boundaries was quit high being about 60-70% at the beginning, but
decreased slowly to about 45% near the end of the growth. In some
embodiments, the percentage of non-.SIGMA. grain boundaries is at
about 70% at the beginning of the growth or at the bottom of the
ingot, and such percentage drops to about 40% within a subsequent
20 mm growth height.
[0066] Still referring to FIG. 5, the percentage of .SIGMA.3 grain
boundaries was only about 20-25% at the beginning, but their
percentage increased with height. Near the top of the ingot, the
percentage was about 40-45%. The percentage of non-.SIGMA. grain
boundaries was about 65-75% at the beginning, but their percentage
decreases with height. Near the top of the ingot, the percentage
was about 40-45%, similar to that of the .SIGMA.3 grain boundaries.
In some embodiments, a percentage of non-.SIGMA. grain boundary and
a percentage of .SIGMA.3 grain boundary of a multicrystalline
silicon (mc-Si) wafer are substantially identical. Further in some
embodiments, the percentage of non-.SIGMA. grain boundary and the
percentage of .SIGMA.3 grain boundary are in a range of from about
40 to about 50. In some embodiments, the aforesaid mc-Si wafer can
be separated from a top portion of an ingot or a brick. In some
embodiments, the twin boundaries and .SIGMA.3 boundaries in a mc-Si
wafer are almost the same based on the computer software of EBSD.
In some embodiments, a preferred grain orientation of a mc-Si wafer
is observed to include {112}.
[0067] Apparently, the high percentage of the non-.SIGMA. or
incoherent boundaries was due to the initial nucleation from the
silicon beads, which had random orientations. Some twins existed
already in the silicon beads due to their formation process. As
crystal growth continued, grain boundaries with a higher symmetry
and a lower interfacial energy, such as the coherent .SIGMA.3 and
twin grain boundaries, are preferred. Ingots V5 and V20 had very
similar grain boundary evolution as ingot V1, as shown in FIG. 5.
However, the coherent .SIGMA.3 grain boundaries increased faster as
the pulling speed increased, and for ingot V3 (not shown in FIG.
5), the coherent .SIGMA.3 grain boundaries increase to more than
40% within 10 mm of growth height. Again, this could be due to the
increase of undercooling in the groove of grain boundaries for twin
nucleation.
[0068] However, in other embodiments where the scale of the
crucible and the temperature gradient are inclined to fit an
industrialized production setting, a percentage of the non-coherent
grain boundary in a bottom portion of a me-Si brick or ingot is
greater than a percentage of the non-coherent grain boundary in a
top portion of a me-Si brick or ingot. In some embodiments, the
non-coherent grain boundary includes non-.SIGMA. grain boundaries
as previously discussed. Moreover, as shown in FIG. 5, the
non-coherent grain boundary herein may include .SIGMA.5, .SIGMA.9,
.SIGMA.27, other .SIGMA., and non .SIGMA. grain boundaries. On the
other hand, a percentage of coherent grain boundary in the bottom
portion of a mc-Si brick or ingot is lower than a percentage of the
coherent grain boundary in a top portion of a me-Si brick or ingot.
In some embodiments, the coherent grain boundary includes .SIGMA.3
grain boundary. As shown in FIG. 5, the coherent grain boundary
herein may include both .SIGMA.3 and twin grain boundaries.
[0069] Grain competition and the development of twin boundaries
from the wafers of ingot V1 is shown in the following description.
Four cases are observed as shown in FIG. 6A, FIG. 6B, FIG. 7A, and
FIG. 7B. The first case is illustrated in FIG. 6A for the grain
bounded by non-coherent boundaries, and an orientation mapping is
shown at the right of the figure. The grain with a higher
interfacial energy, i.e., {115}, is overgrown by others having a
lower interfacial energy as shown by the sequence 6, 7, 8, 9 of the
EBSD mapping and grain boundary (GB) mapping. In the second case,
as shown in FIG. 6B, new grains having a lower interfacial energy
could nucleate from the tri-junction. A {111} grain appeared at the
tri-junction, accompanied by the formation of a twin boundary shown
by the sequence 14, 15, 16, 17 of the EBSD mapping and grain
boundary (GB) mapping. The third case is illustrated in FIG. 7A for
the nucleation of a high-interfacial-energy grain {100} from a
tri-junction. The {221} grain was overgrown, shown by the sequence
7, 8, 9, 10, 11 of the EBSD mapping and grain boundary (GB)
mapping. The last case in FIG. 7B is the formation of grains
between two twin boundaries that appeared and disappeared with the
movement of twin boundaries shown by the sequence 2, 3, 4, 5, 6, 7
of the EBSD mapping and grain boundary (GB) mapping. The formation
of multiple twins was consistent with the in situ observation using
X-ray topography.
[0070] Apparently, the first two cases in FIG. 6A and FIG. 6B led
to the dominance of low-interfacial-energy grains, such as {111},
during grain competition, as well as the formation of twin
boundaries. However, in the last two cases in FIG. 7A and FIG. 7B,
in addition to the formation of twin boundaries, the
high-interfacial-energy grains, such as {100}, could also be
generated. According to calculation, {100} could be generated from
the twining of {221}. Moreover, although the twining process could
generate high-interfacial-energy grains, the twining process could
continue. Because {100} grains have more tilted {111} facets,
54.71, the undercooling could be higher and the twin formation
could be easier. As a result, near the end of the growth, the
percentage of {100} grains was very low. For ingots V5 and V20, the
mechanisms of the development of grain structures were found
similar to that of ingot V1, as shown in FIG. 6A to FIG. 7B. Again,
the increase of twin and non-coherent grain boundaries is
consistent with the twin formation mechanism at the facets. The
wide distribution of the grain orientation might also be explained
by the same mechanism as well.
[0071] The preferred growth orientation of me-Si in directional
solidification by using small silicon beads as the nucleation
promotion layer with random orientations can be observed. It is
found that {112}/{111} became dominant quickly in a short distance
at the low crucible pulling speed of 1 cm/h. As the pulling speed
increased, grains with an orientation near {111} became dominant,
but the distribution was still wide. On the other hand, the
percentage of {100} grains is low in all cases. Due to the random
nucleation promotion layer orientations, the initial percentage of
non-coherent grain boundaries was high being about 70%. As the
crystal growth proceeded, more twin boundaries appeared, and their
growth rate increased slightly with the increasing pulling speed.
These observations were explained by the minimization of
interfacial energy, as well as the twin nucleation/growth from
{111} facets.
[0072] Referring to FIG. 8 and Table 1, two ingots (ingot A and
ingot B) are prepared according to the method disclosed herein.
Table 1 records the grain sizes measured at different heights and
FIG. 8 demonstrates the measurement result from a brick separated
from ingot A and ingot B, respectively. A grain size distribution
at different brick heights is shown. In both ingot A and ingot B,
the grain size monotonically increases from a bottom portion of the
brick to a top portion of the brick. For ingot A, the grain size
(15.76 mm) at a brick height of 245 mm is 50% more than the grain
size (10.26 mm) at a brick height of 95 mm. For ingot B, the grain
size (16.97 mm) at a brick height of 207.5 mm is 45% more than the
grain size (11.61 mm) at a brick height of 95 mm.
[0073] Referring to FIGS. 9A, 10A, 11A, 12A, and Table 1, a grain
orientation mapping and a grain boundary mapping at a given height
(95 mm in FIG. 9A, 132.5 mm in FIG. 10A, 170 mm in FIG. 11A, 207.5
mm in FIG. 12A) of Ingot B are shown. Table 1 records the ratio (in
percentage) of grain orientations at different heights of a brick
separated from ingot B. Grain orientations and grain boundary types
are color-coded according to the annotations on the right of the
figures. Referring to FIGS. 9B, 10B, 11B, 12B, and Table 1, a
defect location mapping and a grain boundary mapping at a given
height (95 mm in FIG. 9B, 132.5 mm in FIG. 10B, 170 mm in FIG. 11B,
207.5 mm in FIG. 12B) of Ingot B are shown. Table 1 records the
ratio (in percentage) of grain boundary types at different heights
of a brick separated from ingot B. Defects (shown in black) and
grain boundary types are color-coded according to the annotations
on the right of the figures.
[0074] Referring to FIG. 13, FIG. 13 shows a quantitative summary
diagram in accordance with FIGS. 9A, 10A, 11A, and 12A.
Distribution of the grain orientations at different heights of
Ingot B is shown in FIG. 13. In some embodiments, the preferred
orientation at various heights of Ingot B is {112}.
[0075] Referring to FIG. 14, FIG. 14 shows a quantitative summary
diagram in accordance with FIGS. 9B, 10B, 11B, and 12B.
Distribution of grain boundary types at different height of Ingot B
is shown in FIG. 14. The ratio (in percentage) of high-angle grain
boundary (for example, non-.SIGMA. grain boundary) decreases as
moving to a higher portion of the ingot (i.e. greater brick
height). In some embodiments, the percentage of non-.SIGMA. grain
boundary is from about 65 to about 75 at the bottom portion of an
ingot. The percentage of more coherent grain boundary (for example,
.SIGMA.3 grain boundary) increases as moving to a higher portion of
the ingot. In some embodiments, the percentage of .SIGMA.3 grain
boundary is from about 12 to about 18 at the bottom portion of an
ingot. There are grain boundaries for which the coherency is in
between .SIGMA.3 grain boundary and non-.SIGMA. grain boundary, for
example, .SIGMA.5, .SIGMA.9, .SIGMA.27, other .SIGMA. (collectively
other grain boundary more incoherent than the .SIGMA.3 grain
boundary). As shown in FIG. 14, the percentage of .SIGMA.3 grain
boundary being lower than the percentage of the non-.SIGMA. grain
boundary and greater than other grain boundary being more
incoherent than the .SIGMA.3 grain boundary. In some embodiments,
the percentage of non-.SIGMA. grain boundary is greater than a
summation of the percentage of .SIGMA.3 grain boundary and the
percentage of other grain boundary being more incoherent than the
.SIGMA.3 grain boundary.
[0076] Referring to FIGS. 15A, 16A, 17A, 18A, and Table 1, a grain
orientation mapping and a grain boundary mapping at a given height
(95 mm in FIG. 15A, 132.5 mm in FIG. 16A, 170 mm in FIG. 17A, 207.5
mm in FIG. 18A) of Ingot B are shown. Table 1 records the ratio (in
percentage) of grain orientations at different heights of a brick
separated from ingot B. Grain orientations and grain boundary types
are color-coded according to the annotations on the right of the
figures. Referring to FIGS. 15B, 16B, 17B, 18B, and Table 1, a
defect location mapping and a grain boundary mapping at a given
height (95 mm in FIG. 15B, 132.5 mm in FIG. 16B, 170 mm in FIG.
17B, 207.5 mm in FIG. 18B) of Ingot B are shown. Table 1 records
the ratio (in percentage) of grain boundary types at different
heights of a brick separated from ingot B. Defects (shown in black)
and grain boundary types are color-coded according to the
annotations on the right of the figures.
[0077] Referring to FIG. 19, FIG. 19 shows a quantitative summary
diagram in accordance with FIGS. 15A, 16A, 17A, and 18A.
Distribution of the grain orientations at different heights of
Ingot B is shown in FIG. 19. In some embodiments, the preferred
orientation at various heights of Ingot B is {112}.
[0078] Referring to FIG. 20, FIG. 20 shows a quantitative summary
diagram in accordance with FIGS. 15B, 16B, 17B, and 18B,
Distribution of grain boundary types at different heights of Ingot
B is shown in FIG. 14. The ratio (in percentage) of high-angle
grain boundary (for example, non-.SIGMA. grain boundary) decreases
as moving to a higher portion of the ingot (i.e. greater brick
height). The position of a multicrystalline silicon (mc-Si) wafer
on an ingot can be determined according to resistance analysis. In
general, a mc-Si wafer in proximity to a bottom of an ingot or a
brick has a greater resistance than a mc-Si wafer in proximity to a
top of the ingot or the brick. In some embodiments, the percentage
of non-.SIGMA. grain boundary is from about 65 to about 75 in a
mc-Si wafer. In other embodiments, the percentage of .SIGMA.3 grain
boundary is from about 12 to about 25 in a mc-Si wafer.
Furthermore, the aforesaid wafer may be separated from a bottom
portion of an ingot or brick. Referring back to FIG. 5, in addition
to .SIGMA.3 grain boundary, another type of coherent grain
boundary, namely twin boundary, can be observed in a mc-Si wafer
prepared according to the method described herein. In some
embodiments, the percentage of the .SIGMA.3 grain boundary is
substantially the same as a percentage of the twin boundary in a
me-Si wafer. The aforesaid wafer may be separated from a bottom
portion of an ingot or brick.
[0079] Table 1 below provides complementary information for FIG. 8,
FIG. 13, FIG. 14, FIG. 19, and FIG. 20 of the present disclosure.
The information encompassed in figures listed above is presented in
the context of a Table for clarity.
TABLE-US-00001 TABLE 1 Complementary Data of FIG. 8, FIG. 13, FIG.
14, FIG. 19, and FIG. 20 Ingot A Grain boundary type ratio Grain
orientation ratio Position (mm) Grain size (mm) .SIGMA.3 .SIGMA.5
.SIGMA.9 .SIGMA.27 Other .SIGMA. Non .SIGMA. (001) (115) (113)
(112) (111) (313) (101) (315) 95 10.26 15% 1% 4% 2% 5% 73% 1% 14%
10% 23% 12% 10% 6% 24% 132.5 12.25 18% 0% 4% 3% 7% 68% 1% 14% 7%
23% 14% 13% 6% 22% 170 12.98 19% 1% 6% 2% 4% 68% 2% 14% 9% 25% 10%
13% 4% 23% 207.5 15.21 17% 0% 6% 2% 6% 69% 1% 19% 9% 23% 12% 14% 4%
18% 245 15.76 20% 1% 8% 4% 5% 62% 3% 17% 8% 23% 15% 12% 4% 18%
Ingot B Grain boundary type ratio Grain orientation ratio Position
(mm) Grain size (mm) .SIGMA.3 .SIGMA.5 .SIGMA.9 .SIGMA.27 Other
.SIGMA. Non .SIGMA. (001) (115) (113) (112) (111) (313) (101) (315)
95 11.61 14% 0% 5% 3% 6% 72% 0% 16% 8% 30% 11% 8% 3% 24% 132.5
12.25 15% 0% 4% 4% 6% 71% 0% 15% 9% 30% 13% 6% 5% 22% 170 13.37 16%
1% 6% 4% 5% 68% 1% 18% 9% 28% 16% 6% 3% 19% 207.5 16.97 18% 1% 5%
3% 5% 68% 1% 20% 11% 25% 17% 6% 3% 17%
[0080] Some embodiments of the present disclosure provides a
multicrystalline silicon (mc-Si) brick, including a bottom portion
starting from a bottom to a height of 100 mm, a middle portion
starting from the height of 100 mm to a height of 200 mm; and a top
portion starting from the height of 200 mm to a top. A percentage
of incoherent grain boundary in the bottom portion is greater than
a percentage of incoherent grain boundary in the top portion.
[0081] In some embodiments, the me-Si brick further including a
preferred grain orientation of {112} in the bottom portion, the
middle portion, and the top portion.
[0082] In some embodiments, the incoherent grain boundary includes
non-.SIGMA. grain boundaries.
[0083] In some embodiments, a percentage of coherent grain boundary
in the bottom portion is lower than a percentage of coherent grain
boundary in the top portion.
[0084] In some embodiments, the coherent grain boundary includes
.SIGMA.3 grain boundary.
[0085] In some embodiments, the percentage of .SIGMA.3 grain
boundary being lower than the percentage of the non-.SIGMA. grain
boundary and greater than other grain boundary being more
incoherent than the .SIGMA.3 grain boundary.
[0086] In some embodiments, the percentage of non-.SIGMA. grain
boundaries is from about 65 to about 75 at the bottom portion.
[0087] In some embodiments, the percentage of non-.SIGMA. grain
boundary is greater than a summation of the percentage of .SIGMA.3
grain boundary and the percentage of other grain boundary being
more incoherent than the .SIGMA.3 grain boundary.
[0088] In some embodiments, the percentage of .SIGMA.3 grain
boundaries is from about 12 to about 18 at the bottom portion.
[0089] In some embodiments, the mc-Si brick further including a
nucleation promotion layer under the bottom portion, wherein the
nucleation promotion layer includes a plurality of beads.
[0090] In some embodiments, the beads include an average diameter
smaller than about 10 mm.
[0091] In some embodiments, the beads include single crystalline
silicon, multicrystalline silicon, silicon carbide, or combinations
thereof.
[0092] In some embodiments, an angle between a pole direction of a
first single crystalline silicon bead and a normal to the bottom of
the multicrystalline silicon ingot is different from an angle
between a pole direction of a second single crystalline silicon
bead and the normal to the bottom of the multicrystalline silicon
ingot.
[0093] Some embodiments of the present disclosure provide a
multicrystalline silicon (mc-Si) wafer. The me-Si wafer includes a
percentage of non-.SIGMA. grain boundary from about 60 to about 75
and a percentage of .SIGMA.3 grain boundary from about 12 to about
25.
[0094] In some embodiments, a preferred crystal orientation of the
mc-Si wafer includes {112}.
[0095] In some embodiments, the me-Si wafer further includes a twin
boundary, wherein the percentage of the .SIGMA.3 grain boundary is
substantially the same as a percentage of the twin boundary.
[0096] Some embodiments of the present disclosure provide a
multicrystalline silicon (mc-Si) wafer. A percentage of non-.SIGMA.
grain boundary and a percentage of .SIGMA.3 grain boundary in the
mc-Si wafer are substantially identical.
[0097] In some embodiments, the percentage of non-.SIGMA. grain
boundary and the percentage of .SIGMA.3 grain boundary in the mc-Si
wafer are in a range of from about 40 to about 50.
[0098] In some embodiments, a preferred crystal orientation of the
mc-Si wafer includes {112}.
[0099] In some embodiments, the mc-Si wafer further includes a twin
boundary, wherein the percentage of the .SIGMA.3 grain boundary is
substantially the same as a percentage of the twin boundary.
[0100] The foregoing outlines features of several embodiments so
that those skilled in the art may better understand the aspects of
the present disclosure. Those skilled in the art should appreciate
that they may readily use the present disclosure as a basis for
designing or modifying other processes and structures for carrying
out the same purposes and/or achieving the same advantages of the
embodiments introduced herein. Those skilled in the art should also
realize that such equivalent constructions do not depart from the
spirit and scope of the present disclosure, and that they may make
various changes, substitutions, and alterations herein without
departing from the spirit and scope of the present disclosure.
* * * * *