Status of Structural Analysis of Substrates and Film Growth 

Inputs for GaN Device Development Program

by Kevin Kirchner

ARL-TR-5427 January 2011

Approved for public release; distribution unlimited. 
NOTICES

Disclaimers

The findings in this report are not to be construed as an official Department of the Army position 

unless so designated by other authorized documents.

Citation of manufacturer’s or trade names does not constitute an official endorsement or 

approval of the use thereof.

Destroy this report when it is no longer needed. Do not return it to the originator.
Army Research Laboratory

Adelphi, MD 20783-1197

ARL-TR-5427 January 2011

Status of Structural Analysis of Substrates and Film Growth 

Inputs for GaN Device Development Program

Kevin Kirchner

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
ii

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently 

valid OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

January 2011

2. REPORT TYPE

Interim

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Status of Structural Analysis of Substrates and Film Growth Inputs for GaN 

Device Development Program

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Kevin Kirchner

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

U.S. Army Research Laboratory

ATTN: RDRL-SED-E

2800 Powder Mill Road

Adelphi, MD 20783-1197

8. PERFORMING ORGANIZATION

 REPORT NUMBER

ARL-TR-5427

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)

11. SPONSOR/MONITOR'S REPORT

 NUMBER(S)

12. DISTRIBUTION/AVAILABILITY STATEMENT

Approved for public release; distribution unlimited.

13. SUPPLEMENTARY NOTES

14. ABSTRACT

This report covers the x-ray diffraction crystallographic analysis of semiconductor wafers involved in our team’s project to 

produce gallium nitride (GaN) wide bandgap devices. The wafers were examined for crystal quality by symmetric and 

asymmetric GaN scans for each quadrant of the 18 wafers. Data comparisons made include the figures of merit (FOM) for 

GaN substrates compared with those of GaN films grown on the substrates, and the homoepitaxial GaN films’ FOMs 

compared with those from heteroepitaxial films. The analysis produced the best FOMs for GaN for our lab to date: 39” (arc 

seconds) symmetric and 58” asymmetric. The good homoepitaxial GaN film quality was ~3 to 8 times better than that of good 

heteroepitaxial films. The heteroepitaxial GaN film quality was shown to be suited for our experimental needs. At a 95% 

confidence level, we were able to show a bias between the quality of the wafer quadrants of the Hydride Vapor Phase 

epitaxially grown GaN substrates. The microstructural quality of the material inputs as measured by x-ray diffraction is 

currently on track to play its part in the development of novel GaN-based devices.

15. SUBJECT TERMS

GaN, homoepitaxial, x-ray diffraction, micro structural analysis, GaN Device Program, Schottky Devices, HEMT, film 

growth, heteroepitaxial 

16. SECURITY CLASSIFICATION OF:

17. LIMITATION

 OF 

 ABSTRACT

UU

18. NUMBER

OF 

 PAGES

36

19a. NAME OF RESPONSIBLE PERSON

Kevin Kirchner

a. REPORT

Unclassified

b. ABSTRACT

Unclassified

c. THIS PAGE

Unclassified

19b. TELEPHONE NUMBER (Include area code)

(301) 394-0093

Standard Form 298 (Rev. 8/98)

Prescribed by ANSI Std. Z39.18
iii

Contents

List of Figures iv

List of Tables iv

Acknowledgments v

1. Introduction and Background 1

2. Kyma GaN Substrates 3

3. SUNY Heteroepitaxial GaN Films on Sapphire Substrates 11

4. GaN Substrates vs. GaN Films Grown On Them 16

5. Homoepitaxial vs. Heteroepitaxial GaN Films 18

6. Observations and Conclusions 21

Appendix. Statistical Bias between Kyma GaN Wafer Quadrants 23

List of Symbols, Abbreviations, and Acronyms 27

Distribution List 28
iv

List of Figures

Figure 1. Ranking of Kyma's GaN substrates by x-ray diffraction. ................................................4

Figure 2. Scans of the monolithic and facetted GaN peaks. The plots are of intensity vs. 

position.......................................................................................................................................6

Figure 3. Overview of the x-ray scans of Kyma’s GaN wafers......................................................7

Figure 4. Kyma GaN substrates, FWHM vs. quadrant plots. The grouping shows data pattern 

A.................................................................................................................................................8

Figure 5. Kyma GaN substrates plots, FWHM vs. quadrant. The grouping of the plots shows 

data pattern B. Sym scans are blue and asym are red. ...............................................................9

Figure 6. Kyma GaN substrates, FWHM vs. quadrant plots. The grouping of x-ray plots 

shows data pattern C. ...............................................................................................................10

Figure 7. Ranking of SUNY GaN/sapphire samples using x-ray diffraction. ..............................12

Figure 8. Graphical overview of SUNY heteroepitaxial GaN data. The sym scans are blue 

and the asym scans are red.......................................................................................................13

Figure 9. SUNY GaN/sapphire heteroepitaxial films, showing grouping of x-ray plots by data 

pattern A. The sym scans are blue and the asym scans are red. ..............................................14

Figure 10. SUNY GaN/sapphire heteroepitaxial films, showing grouping of x-ray plots by 

data pattern B. The sym scans are blue and the asym scans are red. .......................................15

Figure 11. Graphical comparison of Kyma GaN Substrates and the GaN films grown on 

them, FWHM vs. quadrant plots..............................................................................................17

Figure 12. Comparison of homoepitaxial and heteroepitaxial films using sym scans...................19

Figure 13. Comparison of homoepitaxial and heteroepitaxial films using asym scans.................20

List of Tables

Table 1. GaN substrates vs. GaN films grown on them.................................................................16

Table A-1. Two factor ANOVA without replication....................................................................24

Table A-2. Paired sample T- test for QI and QIII..........................................................................25
v

Acknowledgments

I would like to acknowledge the members of my team: Dr. Ken Jones, Dr. Randy Tomkins, 

Dr. Tim Walsh, Mike Derenge, and Cuong Nguyen for their help, support, and collaboration 

throughout the year. Additional thanks go to Dr. Walsh for his help with the statistical analysis 

contained within this report.
vi

INTENTIONALLY LEFT BLANK.
1

1. Introduction and Background

Solid-state devices based on gallium nitride (GaN) have the potential to have superior electronic 

properties. After the type of material used, the quality of that material is critical. However 

growing and processing better materials is a laborious and very expensive process. An extremely 

useful way of tracking the material improvement process is through the use of x-ray diffraction. 

The wavelengths of the x-rays used are dimensionally on the scale of the smallest component 

(unit cell) of the atom’s long range order. It is because of this relationship that x-ray diffraction is 

able to tell us how repeatable a group of unit cells are with respect to their neighbors. The higher 

the degree of repeatability in a crystalline solid, the higher the quality. The x-ray diffraction unit 

of measure of a material’s quality is the full width at half maximum (FWHM) value. 

This report covers the crystallographic analysis, by x-ray diffraction, of 18 recent wafers 

involved in our team’s project to produce GaN-based wide bandgap (WBG) devices. The 

substrate and film inputs for the project came from Kyma, Crystal Systems, Mike Derenge, and 

our State University of New York (SUNY) partners. Some additional enabling collaborations 

during this period were with Georgia Institute of Technology, Pennsylvania State University, and

Sandia National Laboratory. The wafers were examined by symmetric (sym) GaN (002) and 

asymmetric (asym) GaN (102) scans for each of the sub regions of the 18 wafers.

Besides the analysis of the basic crystalline quality of the project’s inputs, many comparisons 

were made. For example, the figures of merit (FOMs) for GaN substrates were compared with 

the FOMs of GaN films that were grown on those substrates. Some comparisons between 

different FOMs are given in terms of percentage of improvements. So for example, if sample A 

had a FWHM value of 100” (arc seconds) and sample B had a FWHM value of 60”, that 

comparison could be expressed as there being a 40% improvement between sample A and B. 

Also, it is worth noting that smaller FWHM values indicate better crystalline quality of a 

material.

Heteroepitaxially grown GaN films are still, relatively speaking, immature; and homoepitaxial 

GaN films, and the GaN substrates that make their existence possible, have even shorter analysis 

baselines. Because of the small number of good GaN homoepitaxial films currently available to 

us, this report is somewhat interim in nature. That said, my work has uncovered many 

encouraging material attributes. For example, the x-ray work includes the best FWHM numbers 

that I have measured for the GaN (002) peak, 39”. FWHM values correlate with lower defect 

densities, and lower defect densities have been shown to correlate with better device 

characteristics.
2

With new material systems there are always challenges. The asymmetric x-ray scans seem to 

have revealed in plane, material quality issues. Many of these problems are conjectured to be 

caused by small angle grain boundaries (SAGBs).

* SAGBs are thought to be formed by an 

amassing of line defects.

This work, besides documenting the overall quality of the material, also differentiates between 

multiple technologies, different material processing, and interactions between inputs. 

Additionally this work constitutes an initial investment in being able to make “before and after” 

comparisons in the future.

At this stage of the project, I am not sure of what and how patterns in the data will show up, so I 

employ a number of different methods of organizing the data in this report, i.e., graphical, chart 

form, grouping levels, and overlays. Each section of the report includes a short section-specific 

introduction.

This report contains six sections:

1. Introduction and Background

2. Kyma GaN substrates

3. SUNY heteroepitaxial GaN films

4. GaN substrates and film comparisons

5. Homoepitaxial vs. heteroepitaxial GaN films

6. Observations and Conclusions

 

*Callister, W. D. Material Science and Engineering An Introduction, Fourth Edition, John Wiley & Sons: New York 1997, 

p.77.
3

2. Kyma GaN Substrates

Twelve of Kyma’s novel hydride vapor phase epitaxy (HVPE) GaN substrates, enabling 

homoepitaxial growth of GaN films, were analyzed. For analytical purposes, the twelve 1x1 cm 

wafers were divided into a total of 48 quadrants (Cartesian coordinate nomenclature). Each plot 

and major chart entry is labeled with the sample number from which it came. The plot’s abscissa 

values are the quadrant number from which the data was taken; the ordinates are the FWHM

values.

Notes:

• The plots of the x-ray scans were grouped by similarities of pattern. Patterns varied from

having both sym (GaN 002) and asym (GaN 102) scans matching their counterparts to only 

having one of the pairs possess some similarity. There were also a couple of mirror image 

pairings between scans.

• The sym scans contained the best GaN FWHM value (39”) I have seen to date. The asym 

values ranged from decent to poor. Sample 15691 (figure 1) had the best symmetric scans, 

averaging 40” across the four quadrants of its wafer. Quadrant I, for both sym and asym 

scans, had the best results across all samples. This could be caused by an inhomogeneity in 

the wafer’s growth conditions. If an examination of the growth conditions turned up a 

difference it could potentially mean a significant improvement in the quality of the sample 

output as a whole. To be sure, we ran a statistical analysis and there is a statistically 

significant bias between the wafer quarters across the wafers (see the appendix). A level of 

detail of the scans that is not made clear by either the charts or the plots is the effect of an 

amassing of material defects, which create what are called SAGBs (figure 2).
4

Figure 1. Ranking of Kyma's GaN substrates by x-ray diffraction.

In figure 1, the following apply:

• QI through QIV stand for the different wafer quadrants. They are in Cartesian coordinates 

as follows: 

• There are 96 data points over 48 sample regions across 12 wafers.

• The asymmetric rocking curves (RCs) of sample 692.1 consisted of two distinct regions. 

The FWHM for each are included.
5

• For row and column averages, it is the sum of the two values that are used for sample 

692.1.

• The row averages are also the sample average.

In addition to the rankings shown in the charts, the following was observed:

• The sym scans show a remarkable improvement over the industry standard.

• Up to their point in the sample stream, samples 8183, 8184, and 8185 were the 2nd, 3rd, and 

1

st

, respectively, in in-plane (parallel to surface to sample) crystal quality. With sample 

8186, the quality changed abruptly. Interestingly, the rankings of the quadrants across all 

samples are the same for both the sym and asym scans.

Figure 2 shows four scans (A through D). Scans A and B, although having similar FWHM 

numbers, show the start of a move from a monolithic to a multifaceted “flat topped” peak. With 

their flat-topped multifaceted peaks, scans C and D show the progression of the effect due to a 

further increase in the density of the SAGB. 

Figure 3 presents a thumbnail overview of the GaN substrate plots. 

Figures 4–6 show the enlarged individual plots.

The data from these x-ray scans of freestanding GaN substrates provides the first sets of data that 

allow subsequent comparisons between substrates and films and a more complete analysis 

between homoepitaxial and heteroepitaxial film growth. Eventually, the information will be

carried forward into the analysis space where the processing and performance of devices is 

analyzed.
`

Figure 2. Scans of the monolithic and facetted GaN peaks. The plots are of intensity vs. position.

6
Figure 3. Overview of the x-ray scans of Kyma’s GaN wafers.

7
Figure 4. Kyma GaN substrates, FWHM vs. quadrant plots. The grouping shows data pattern A.

Note: The sym scans are blue and the asym scans are red.

8
Figure 5. Kyma GaN substrates plots, FWHM vs. quadrant. The grouping of the plots shows data pattern B. Sym scans are blue and asym are red.

9
Figure 6. Kyma GaN substrates, FWHM vs. quadrant plots. The grouping of x-ray plots shows data pattern C.

Note: The sym scans are blue and the asym scans are red.

10
11

3. SUNY Heteroepitaxial GaN Films on Sapphire Substrates

Sym and asym scans were taken of the heteroepitaxial GaN films that were grown on five 2” 

sapphire wafers by our partners at SUNY. There is one x-ray plot per wafer containing both sym 

and asym scans (figure 8). Groupings of x-ray scans were again made on the basis of plot 

similarities (figure 9 and 10). Sample 2093N1 is one-half of a 2” wafer, having Quads I and IV.

The collected data is also presented in chart form (figure 7). The chart shows rankings of the 

wafers and the quadrants across all SUNY wafers. The best wafer in terms of sym x-ray scans is 

2093N. There was a tie for the best sample in terms of the asym scans, between samples 2079 

and 2088. The best quadrant across all the wafers, in sym terms is QII. The best in terms of the 

asym scan analysis across all wafers is QI.

Note: Samples 2080 and 2088 were grown to be high electron mobility transistors (HEMTs) 

structures while the remaining samples were prepared to be Schottky devices. This means that 

the GaN films on 2080 and 2088 are thinner than those on the remaining samples. In 

heteroepitaxial growth, thicker films often show better structural quality than thinner films. 

Therefore if the two HEMT samples have similar or slightly worst FOMs this still signifies films 

of good quality in my opinion. Overall, sample 2080 had the second best scan out of the five 

samples for both sym and asym scans, and sample 2088 was the third best for sym scans and was 

tied for first for asym scans. Therefore, the HEMT samples echo the Schottky data, i.e., all our 

SUNY samples are of good microstructural quality.

These x-ray scans of the heteroepitaxial films are part of my group’s analysis and documentation 

of the input streams for our GaN Device Program. In this report additional analyses are 

presented, for example, I compare the Kyma homoepitaxial films with these heteroepitaxial films 

in section 4. Over time, as we learned the quality of the samples and our expectations for the 

project grew, we increased the number of scans from 8 scans per 2” sample to 32. Our team has 

been developing GaN Schottky diodes and HEMTs with segments of these wafers.
12 Figure 7. Ranking of SUNY GaN/sapphire samples using x-ray diffraction.

12
13

Figure 8. Graphical overview of SUNY heteroepitaxial GaN data. The sym scans are blue and the asym scans are red.

13
14

Figure 9. SUNY GaN/sapphire heteroepitaxial films, showing grouping of x-ray plots by data pattern A. The sym scans are blue and the asym scans are red.

14

& B
15

Figure 10. SUNY GaN/sapphire heteroepitaxial films, showing grouping of x-ray 

plots by data pattern B. The sym scans are blue and the asym scans are 

red.

2093

2093N1
16

4. GaN Substrates vs. GaN Films Grown On Them

This section presents a comparison of the structural quality of HVPE-grown GaN substrates and

the metalorganic chemical vapor phase deposition (MOCVD) grown homoepitaxial GaN films 

produced on them. The data is represented in both table (table 1) and graphic (figure 11) forms.

The following summary provides an additional examination of the data:

• The graphical output highlights the relationship between the substrates and films.

• The sym substrate and film scans track each other for both samples, but for the asym scans,

they do not track for either sample.

• The sym values for both substrate and film of sample 8183 are excellent (table 1).

• The film values for the asym scans of 8184 contain an extraordinary value of 58”.

• The asym scans for the films are significantly lower than the substrate values, particularly 

for sample 8184.

These were the only homoepitaxial GaN films measured to date until a couple of weeks ago. 

Since then we have received a few samples from Lumilog/SUNY; however, they are not up to 

the level of quality of the Kyma samples examined here. The Lumilog/SUNY film’s sym values 

averaged ~200” and the film’s asym values averaged ~400”.

Table 1. GaN substrates vs. GaN films grown on them.

SAMPLE 8183 SAMPLE 8184

Sym Scan Values Sym Scan Values

Substrate: 49, 83, 65, 54

Film :50, 89, 66, 53

Substrate: 74, 70, 132, 69

Film : 69, 62, 109, 59

Notes

Note: Very close match between substrate and film 

average values Sub 63”, Film 65”

Note: Similar average values, substrate and film: 

Sub 86”, Film 75”.

Asym Scan Values Asym Scan Values

Substrate: 414, 484, 462, 402

Film : 268, 276, 291, 283

Substrate: 477, 564, 670, 545

Film : 58, 106, 86, 71

Notes

Epi film numbers are 37% better than the substrate. 

Film 280” and Substrate 441”. 

Substrate has values similar to 8183. Asym film values 

are very good, including a remarkable value of 58”. As 

a dataset, they are much better than the substrate’s 

asym values.
Figure 11. Graphical comparison of Kyma GaN Substrates and the GaN films grown on them, FWHM vs. quadrant plots

17
18

5. Homoepitaxial vs. Heteroepitaxial GaN Films

Two plots (sym and asym) containing eight scans were used to compare the homoepitaxial film 

data with the very good quality heteroepitaxial films we received, primarily, from our SUNY 

partners. Our team’s principle grower, Mike Derenge, grew the homoepitaxial and 

heteroepitaxial films on the Kyma and the Crystal System’s substrates, respectfully. All the 

SUNY and our principal grower’s films were grown by MOCVD.

The comparisons for the sym scans show the homoepitaxial films improving over their

heteroepitaxial counterparts by from 73% to 77% (figures 12 and 13). For the asym scans, the 

homoepitaxial films improved over their heteroepitaxial films by from 42% to 94%. It is very 

promising having two sym homoepitaxial FWHM values in the 50s, having an asym value in the 

50s is extraordinary (i.e., sample 8184’s 94% improvement). Good FWHM values correlate with 

lower defect densities, and lower defect densities are thought by the technical community to 

correlate with better device characteristics. 

The homoepitaxial films show some remarkable improvements in crystal quality, unfortunately 

the devices that were fabricated on them had some performance issues. However, we do have 

initial data pointing to a solution for the device performance problems. Our group is currently in 

the process of implementing that solution. 
Figure 12. Comparison of homoepitaxial and heteroepitaxial films using sym scans.

19
Figure 13. Comparison of homoepitaxial and heteroepitaxial films using asym scans.

20
21

6. Observations and Conclusions

In this interim report, I have presented the results of the microstructural analysis using x-ray 

diffraction of substrate and film inputs to the GaN WBG Device Program of the Power 

Components Branch.

We have observed the following:

• Our best GaN (002) FWHM value to date 39”. This is important because good FWHM 

numbers correlate with lower defect densities and lower defect densities are thought by the 

technical community to correlate with better device characteristics.

• We documented the quality of Kyma’s novel HVPE GaN substrates by wafer and wafer 

quarters (figures 1, 4, 5, and 6).

• We provided a composite thumbnail overview of the sample plots of Kyma’s novel GaN 

substrates (figure 3).

• We showed an example of the effect of peak broadening in x-ray output by SAGB

(figure 2).

• Asym scans of 12 HVPE GaN substrate wafers show a broad range of FWHM values,

~350” to 1750” (figure 1).

• We had excellent asymmetric scan results of the homoepitaxial films (sample 8184) with 

FWHM values of 58” to 106” (table 1).

• We documented the good input quality of SUNY’s heteroepitaxial films by wafer and 

wafer quarters (figure 7).

• The composite thumbnail plots of SUNY scans provided an overview of heteroepitaxial 

film’s sym and asym scans to illustrate the relationships between them (figure 8). 

• Homoepitaxial film quality showed improvement over the substrate it was grown on, in 

some cases by 5 to 7 times (Sample 8184, asym peaks, table 1).

• In sections 2, 3, and 4, we saw the variation in tracking between the sym and asym scans.

• We presented graphical comparisons between good quality GaN heteroepitaxial films and 

novel GaN homoepitaxial films from Kyma (figures 12 and 13).

• Kyma substrates’ micro-structural quality showed a bias across their 12 wafers in favor of 

quadrants I and IV (figure 1 and tables A-1 and A-2). This could be useful information for

our Kyma partners. 
22

There has been a steep learning curve in our team, and the technical community at large, 

regarding GaN quality. Recently, we have also obtained data suggesting we are overcoming a 

major hurdle involving carbon’s negative role in the low-doped GaN films, which we use in

fabricating some of our devices.

As we are able to obtain additional good homoepitaxial films to use for device fabrication, and 

our fabrication techniques and understanding matures, there will likely be additional useful and 

instructive correlations. 

One group in the GaN device community has recently, after five years of hard work, achieved 

the technical community’s target 600-V breakdown voltage. We have also attained 600-V 

breakdown on Kyma substrates and we are working to duplicate these results in our films. 

While x-ray diffraction can help us rate our material input streams, it can also help inform us 

about issues like the material imperfections behind the material consistency issues we are 

working through. Going forward using x-ray diffraction along with scanning electron 

microscopy (SEM), Atomic Force Microscopy (AFM), cathodoluminescence (CL), and etch pit 

techniques, we will try to better understand and control the number and types of material defects 

in our devices to a degree that will help us have good device yields.
23

Appendix. Statistical Bias between Kyma GaN Wafer Quadrants

The present data was examined to determine if the findings present in the report are statistically 

significant. Specifically, our goal was to determine if the mean FWHMs of the 002 (symmetric) 

reflections differed between quadrants of the Kyma samples. Two separate analyses were 

undertaken. First, the four quadrants were compared with the use of a two-factor analysis of 

variance (ANOVA). Second, the quadrants with the largest difference in mean, QI and QIII, 

were compared with a paired sample T-test.

The ANOVA analysis comparing the four quadrants is shown on table A-1. The 002 FWHM 

data are contained in the top table and are organized by wafer (row) and quadrant (column). 

Below the FWHM data is a tabulation of statistics on the individual columns (quadrants) which 

are used in the ANOVA calculation. For each column, the sum (Ta), sum squared (Ta

2

), number 

of observations (na), mean, and standard deviation are calculated. Likewise, statistics are 

calculated by row (wafer) and tabulated to the right of the main data table. Below the table, the 

calculation steps are outlined, including calculation of the grand total T and total number of 

observations n. Sum of squares variation due to factor A (that is, due to variation by column, or 

equivalently by quadrant of the wafer) SSA is calculated, along with the mean square variation 

due to factor A, MSA. Likewise, the sum of squares and mean square variation SSB and MSB are 

calculated for variation due to factor B (that is, variation by row, or equivalently by wafer). The 

sum of squares due to interaction between the two factors SSAB is shown, along with the mean 

square variation MSAB (also known as error variance). Finally, the total sum of squares is given. 

Below these, the F value is given for variation due to factor A (data column or quadrant) and 

factor B (data row or wafer). The F value is given by Fx = MSx/MSAB, where x is A or B. Next to 

the F value for both factors, the probability (from the F distribution) is given. The probability PA

for factor A is interpreted as the probability that the four columns share the same mean. The 

value is 0.053, or equivalently there is a 1 – PA = 0.947 probability that the four columns 

(quadrants) do not have the same mean. Thus we have rigorously shown that there is a 

statistically significant difference in the mean value of the 002 FWHM depending on the 

quadrant of the wafer for these Kyma wafers.
24

Table A-1. Two factor ANOVA without replication.

Table A-2 shows the T-test analysis. The two quadrants were chosen because they have the 

largest difference in mean value, 73.58 (QI) compared with 96.67 (QIII). The table shows the 

002 FWHMs organized by wafer (row) and quadrant (column). To the right of the FWHM data, 

the mean for each row is given, as well as the difference d between the QI and QIII values for 
25

each wafer. Below the table, statistics are calculated for each column (quadrant), including the 

mean, standard deviation, variance, and total number of observations n. The test statistic t is 

given by

s n

d

t

d

avg

/



(A.1)

where davg is the average difference between QI and QIII, sd is the standard deviation of the 

difference, and n is the number of observations. From the test statistic, the t-distribution yields a 

probability of 0.024 that the two samples (quadrants I and III) have the same mean, that is, there 

is a 97.6% chance that they come from populations with different means. Thus, we can 

rigorously conclude that there is a significant difference in the means of the 002 FWHMs for 

quadrants I and III in the Kyma-grown GaN samples. Furthermore, from the t value 

corresponding to a probability of 0.05, the 95% confidence interval for the mean difference 

between QI and QIII is found to be 19.34. Thus, we can say at a 95% confidence level that the 

difference between the mean values of QI and QIII is 23.08 ± 19.34. Further testing should help 

to narrow down the confidence window allowing us to more precisely determine the mean 

difference between the 002 FWHM of QI and QIII.

Table A-2. Paired sample T- test for QI and QIII.
26

INTENTIONALLY LEFT BLANK.
27

List of Symbols, Abbreviations, and Acronyms

ANOVA analysis of variance

Asym asymmetric x-ray scan 

CL cathodoluminescence

FOM figure of merit

FWHM full width at half maximum

GaN gallium nitride

HEMT high electron mobility transistors

HVPE hydride vapor phase epitaxy

MOCVD metalorganic chemical vapor phase deposition

SAGB small angle grain boundary

SEM scanning electron microscopy

SUNY State University of NY

Sym symmetric x-ray scan

WBG wide bandgap
28

No. of

Copies Organization

1 ADMNSTR

ELEC DEFNS TECHL INFO CTR

ATTN DTIC OCP

8725 JOHN J KINGMAN RD STE 0944

FT BELVOIR VA 22060-6218

1 HC US ARMY RSRCH LAB

ATTN RDRL CIM G T LANDFRIED

BLDG 4600

ABERDEEN PROVING GROUND MD 

21005-5066

3 HCS US ARMY RSRCH LAB

ATTN IMNE ALC HRR 

MAIL & RECORDS MGMT

ATTN RDRL CIM L TECHL LIB

ATTN RDRL CIM P TECHL PUB 

ADELPHI MD 20783-1197

10 HCS US ARMY RSRCH LAB

1 CD ATTN RDRL SED

ED SHAFFER

ATTN RDRL SED E

BRUCE GEIL

PAUL BARNES

KEN A JONES

TIM WALSH

RANDY TOMPKINS

CUONG NGUYEN

KEVIN KIRCHNER (1 CD, 3 HCS)

TOTAL: 16 (1 ELEC, 1 CD, 14 HCS)