Atomic Scale Characterization of Point Defects in the Ultra-Wide Band Gap Semiconductor Β-Ga2o3 DISSERTATION

Atomic Scale Characterization of Point Defects in the Ultra-Wide Band Gap Semiconductor β-Ga2O3

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Jared M Johnson

Graduate Program in Materials Science and Engineering

The Ohio State University

2020

Dissertation Committee:

Professor Jinwoo Hwang, Advisor

Professor Roberto Myers

Professor Wolfgang Windl

Professor Jeff Sharp

Copyrighted by

Jared Michael Johnson

2020

Abstract

Precisely controlled point defects are vital to the manipulation of important electronic properties in semiconductor materials. Point defects and their complexes display a wide range of atomic structures and functional states that critically influence a semiconductor’s unique properties. Therefore, gaining insight on the exact nature of their formation and role in determining properties is key to advancing these materials for application. This type of characterization requires obtaining experimental information on the atomic scale structure of point defects.

The emerging ultra-wide band gap semiconductor β-Ga2O3, which displays excellent properties for high-performance electrical, optical, and power device applications, lacks the detailed understanding of point defects needed for its development. In this work, point defects are characterized in β-Ga2O3 bulk crystals and thin films. Centered around high-resolution scanning transmission electron microscopy

(STEM), several characterization techniques are collectively used to uncover point defect formation and to link theoretical predictions to measured properties.

First, an unusual formation of point defect complexes within the atomic-scale structure of β-Ga2O3 is directly observed using STEM. These complexes, which involve one cation interstitial atom paired with two cation vacancies, correlate directly with structures predicted by density functional theory. The divacancy-interstitial complexes

ii are shown to act as compensating acceptors by a comparison between STEM data and deep level optical spectroscopy results. This comparison also reveals that the development of the complexes is facilitated by Sn doping through increased vacancy concentration. Additionally, a different stable complex is shown to form via the relaxation of a specific Ga atom near two adjacent divacancy-interstitial complexes.

Molecular dynamics simulations confirm the energetic stability of the new structure.

Point defects in β-(AlxGa1-x)2O3 films are investigated using quantitative STEM to explain the inability to achieve epitaxial growth of high Al concentration films. A quantitative STEM analysis of Al site occupancy indicates that 54% of the incorporated

Al occupies the Ga2 site, conflicting with density function theory formation energy calculations. This result suggests that the growth of a higher energy structure leads to the difficulty in β-(AlxGa1-x)2O3 film growth. The aforementioned divacancy-interstitial complexes are also observed in the films, showing an increase in concentration with Al.

Finally, a new STEM technique is proposed for the three-dimensional characterization of vacancies, lighter and heavier dopants. Using multislice STEM simulations of β-Ga2O3, the contrast of vacancies and lighter defects is shown to become enhanced when selecting a small range of low scattering angles. The origin of this effect is the de-channeling of electrons due to the point defect in the atomic column. The three- dimensional characterization of the point defects can be realized by capturing the de- channeling signal in the 20–40 mrad detection angle range.

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To my grandmother, Beulah M. Walker (1943-2005),

for being with me every day.

Acknowledgments

For me, this journey started at the most opportune time; a fortuitous juncture between the beginning of my next academic pursuit and my PhD advisor’s, Prof. Jinwoo

Hwang’s, first position in academia. This timing led to a graduate student – PhD advisor relationship that I am truly grateful for and words cannot express my appreciation for him trusting me to produce at a level that allowed both of us to move forward towards our goals. Above all, I would like to thank Prof. Hwang for his high expectations and ability to help me see the broader picture throughout my research. Additionally, the knowledge that I have gained from our stimulating cultural conversations is something I will always find valuable.

The Hwang research group members have played an instrumental role in my time at The Ohio State University. Not only have they contributed substantially to my research and my knowledge of materials science and engineering, they have also presented an opportunity for me to gain a better understanding of their different cultures. For that, I thank all of the members: Soohyun Im, Gabriel Calderon-Ortiz, Menglin Zhu, Mehrdad

Abbasi Gharacheh, and Hsien-Lien Huang. A special thanks goes to Hsien-Lien for all of his help on beta gallium oxide research. The late nights and prompt data analysis did not go unnoticed. v

I would like to thank the Center for Electron Microsocopy and Analysis

(CEMAS) here at OSU and all of the faculty that has helped me along the way. I also acknowledge funding from the Department of Defense, Air Force Office of Scientific

Research GAME MURI program and Dr. Ali Sayir and thank all of the members of the

MURI team. Finally, thank you Brandon Kemerling for paving the way, providing guidance, and giving me someone to look up to.

Vita

2006 – 2010...... Illinois Valley Central High School Chillicothe, IL

2010 – 2014...... B.S. Physics & Mathematics Monmouth College, Monmouth, IL

2017...... M.S. Materials Science and Engineering The Ohio State University, Columbus, OH

2014 to present ...... Graduate Research Associate, Department of Materials Science and Engineering The Ohio State University, Columbus, OH

Publications

[1] A. F. M. A. U. Bhuiyan, Z. Feng, J. M. Johnson, Z. Chen, H.-L. Huang, J. Hwang and H. Zhao, MOCVD epitaxy of B-(AlxGa1-x)2O3 thin films on (010) Ga2O3 substrates and N-type doping, Appl. Phys. Lett. 115, 120602 (2019).

[2] P. D. Garman, J. M. Johnson, V. Talesara, H. Yang, X. Du, J. Pan, D. Zhang, J. Yu, E. Cabrera, et al., Dual Silicon Oxycarbide Accelerated Growth of Well- Ordered Graphitic Networks for Electronic and Thermal Applications, Adv. Mater. Technol. 4, 1800324 (2019).

[3] P. D. Garman, J. M. Johnson, V. Talesara, H. Yang, D. Zhang, J. Castro, W. Lu, J. Hwang and L. J. Lee, Silicon Oxycarbide Accelerated Chemical Vapor Deposition of Graphitic Networks on Ceramic Substrates for Thermal Management Enhancement, ACS Appl. Nano Mater. 2, 452 (2019).

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[4] J. M. Johnson, Z. Chen, J. B. Varley, C. M. Jackson, E. Farzana, A. R. Arehart, H. Huang, A. Genc, S. A. Ringel, et al., Unusual Formation of Point Defect Complexes in the Ultra-wide Band Gap Semiconductor β-Ga2O3, Phys. Rev. X 9, 041027 (2019).

[5] M. R. Karim, Z. Feng, J. M. Johnson, M. Zhu, J. Hwang and H. Zhao, Low- Pressure Chemical Vapor Deposition of In2O3 Films on Off-Axis c-Sapphire Substrates, research-article, Cryst. Growth Des. 19, American Chemical Society, 1965 (2019).

[6] B. Mazumder, J. Sarker, Y. Zhang, J. M. Johnson, M. Zhu, S. Rajan and J. Hwang, Atomic scale investigation of chemical heterogeneity in β- (AlxGa1−x)2O3 films using atom probe tomography, Appl. Phys. Lett. 115, 132105 (2019).

[7] S. Im, Z. Chen, J. M. Johnson, P. Zhao, G. H. Yoo, E. S. Park, Y. Wang, D. A. Muller and J. Hwang, Direct determination of structural heterogeneity in metallic glasses using four-dimensional scanning transmission electron microscopy, Ultramicroscopy 195, 189 (2018).

[8] S. Rafique, M. R. Karim, J. M. Johnson, J. Hwang and H. Zhao, LPCVD homoepitaxy of Si doped β-Ga2O3 thin films on (010) and (001) substrates, Appl. Phys. Lett. 112, 052104 (2018).

[9] M. Souri, J. Terzic, J. M. Johnson, J. G. Connell, J. H. Gruenewald, J. Thompson, J. W. Brill, J. Hwang, G. Cao, et al., Electronic and optical properties of La-doped Sr3Ir2O7 epitaxial thin films, Phys. Rev. Mater. 2, 024803 (2018).

[10] Y. Zhang, Z. Jamal-Eddine, F. Akyol, S. Bajaj, J. M. Johnson, G. Calderon, A. A. Allerman, M. W. Moseley, A. M. Armstrong, et al., Tunnel-injected sub 290 nm ultra-violet light emitting diodes with 2.8% external quantum efficiency, Appl. Phys. Lett. 112, 071107 (2018).

[11] Y. Zhang, A. Neal, Z. Xia, C. Joishi, J. M. Johnson, Y. Zheng, S. Bajaj, M. Brenner, D. Dorsey, et al., Demonstration of high mobility and quantum transport in modulation-doped β-(AlxGa1-x)2O3/Ga2O3 heterostructures, Appl. Phys. Lett. 112, 173502 (2018).

[12] J. H. Gruenewald, J. Kim, H. S. Kim, J. M. Johnson, J. Hwang, M. Souri, J. Terzic, S. H. Chang, A. Said, et al., Engineering 1D Quantum Stripes from Superlattices of 2D Layered Materials, Adv. Mater. 29, 1603798 (2017).

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[13] J. M. Johnson, S. Im, W. Windl and J. Hwang, Three-dimensional imaging of individual point defects using selective detection angles in annular dark field scanning transmission electron microscopy, Ultramicroscopy 172, 17 (2017).

[14] Y. Kim, S. S. Cruz, K. Lee, B. O. Alawode, C. Choi, Y. Song, J. M. Johnson, C. Heidelberger, W. Kong, et al., Remote epitaxy through graphene enables two- dimensional material-based layer transfer, Nature 544, 340 (2017).

[15] S. Krishnamoorthy, Z. Xia, C. Joishi, Y. Zhang, J. McGlone, J. Johnson, M. Brenner, A. R. Arehart, J. Hwang, et al., Modulation-doped β- (Al0.2Ga0.8)2O3/Ga2O3 field-effect transistor, Appl. Phys. Lett. 111, 023502 (2017).

[16] C. H. Lee, S. Krishnamoorthy, D. J. O’Hara, M. R. Brenner, J. M. Johnson, J. S. Jamison, R. C. Myers, R. K. Kawakami, J. Hwang, et al., Molecular beam epitaxy of 2D-layered gallium selenide on GaN substrates, J. Appl. Phys. 121, 094302 (2017).

[17] Y. Zhang, S. Krishnamoorthy, F. Akyol, J. M. Johnson, A. A. Allerman, M. W. Moseley, A. M. Armstrong, J. Hwang and S. Rajan, Reflective metal/semiconductor tunnel junctions for hole injection in AlGaN UV LEDs, Appl. Phys. Lett. 111, 051104 (2017).

[18] F. Akyol, S. Krishnamoorthy, Y. Zhang, J. Johnson, J. Hwang and S. Rajan, Low-resistance GaN tunnel homojunctions with 150 kA/cm2 current and repeatable negative differential resistance, Appl. Phys. Lett. 108, 131103 (2016).

[19] S. Krishnamoorthy, E. W. Lee, C. H. Lee, Y. Zhang, W. D. McCulloch, J. M. Johnson, J. Hwang, Y. Wu and S. Rajan, High current density 2D/3D MoS2/GaN Esaki tunnel diodes, Appl. Phys. Lett. 109, 183505 (2016).

[20] J. Thompson, J. Nichols, S. Lee, S. Ryee, J. H. Gruenewald, J. G. Connell, M. Souri, J. M. Johnson, J. Hwang, et al., Enhanced metallic properties of SrRuO3 thin films via kinetically controlled pulsed laser epitaxy, Appl. Phys. Lett. 109, 161902 (2016).

[21] Y. Wang, L. Seewald, Y. Y. Sun, P. Keblinski, X. Sun, S. Zhang, T. M. Lu, J. M. Johnson, J. Hwang, et al., Nonlinear Electron-Lattice Interactions in a Wurtzite Semiconductor Enabled via Strongly Correlated Oxide, Adv. Mater. 28, 8975 (2016).

[22] Y. Zhang, S. Krishnamoorthy, J. M. Johnson, F. Akyol, A. Allerman, M. W. Moseley, A. Armstrong, J. Hwang and S. Rajan, Interband tunneling for hole

injection in III-nitride ultraviolet emitters, Appl. Phys. Lett. 106, 141103 (2015).

Fields of Study

Major Field: Materials Science and Engineering

Table of Contents

Abstract ...... ii

Acknowledgments...... v

Vita ...... vii

Publications ...... vii

Fields of Study ...... x

Table of Contents ...... xi

List of Tables ...... xvii

List of Figures ...... xviii

Chapter 1: Introduction ...... 1

Chapter 2: Motivation and Background ...... 7

2.1 Ultra-Wide Band Gap Semiconductor β-Ga2O3 ...... 7

2.1.1 Point Defects...... 9

2.1.1.1 Theoretical Studies...... 10

2.1.1.2 Experimental Studies ...... 14

2.2 Scanning Transmission Electron Microscopy ...... 16 xi

2.2.1 Quantitative STEM ...... 19

2.3 Conclusion ...... 24

Chapter 3: Methods ...... 26

3.1 Crystal Growth ...... 26

3.1.1 EFG ...... 27

3.1.2 MOCVD ...... 28

3.1.3 MBE...... 28

3.2 Experiments ...... 29

3.2.1 TEM Sample Preparation ...... 29

3.2.1.1 Focused Ion Beam...... 30

3.2.1.2 Low Energy Ion Milling ...... 31

3.2.2 STEM...... 32

3.2.2.1 ABF Imaging ...... 34

3.2.2.2 HAADF Imaging ...... 35

3.2.2.3 Quantitative HAADF Imaging ...... 35

3.2.3 DLOS ...... 36

3.3 Simulations ...... 37

3.3.1 Multislice Algorithm ...... 37

3.3.2 DFT ...... 38

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3.3.3 Molecular Dynamics...... 38

Chapter 4: Unusual Formation of Point Defect Complexes in the Ultra-Wide Band Gap

Semiconductor β-Ga2O3 ...... 39

4.1 Abstract ...... 39

4.2 Introduction ...... 40

4.3 Direct Observation of Divacancy-Interstitial Complexes ...... 42

4.4 Effects of Sn Doping ...... 51

4.5 Deep Level Optical Spectroscopy ...... 53

4.6 Cation Interstitial ...... 55

4.7 Conclusions ...... 56

4.8 Acknowledgements ...... 56

4.9 Appendix: Methods ...... 58

Chapter 5: Self-Created Cation Vacancies by Atomistic Relaxation Adjacent to Defect

Complexes in β-Ga2O3 ...... 58

5.1 Abstract ...... 58

5.2 Introduction ...... 59

5.3 Self-Created Cation Vacancies by Atomistic Relaxation ...... 60

5.4 Molecular Dynamics ...... 68

5.5 Effects of Sn Doping ...... 68

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5.6 Functional Behavior ...... 69

5.7 Acknowledgement ...... 71

Chapter 6: Al Distribution and Point Defect Complexes in β-(AlxGa1-x)2O3 Films ...... 72

6.1 Abstract ...... 72

6.2 Introduction ...... 73

6.3 Al Site Distribution ...... 75

6.4 Divacancy-Interstitial Complex ...... 79

6.5 Defect Complex Functional Behavior ...... 83

6.6 Conclusion ...... 83

6.7 Acknowledgement ...... 84

Chapter 7: Three-Dimensional Imaging of Individual Point Defects Using Selective

Detection Angles in Annular Dark Field Scanning Transmission Electron Microscopy . 85

7.1 Abstract ...... 85

7.2 Introduction ...... 86

7.3 Simulation Details ...... 91

7.4 Results ...... 94

7.4.1 Achieving Depth-Dependent Vacancy Contrast Using LAADF STEM ...... 94

7.4.2 3D Imaging of Individual Vacancies Using Selective LAADF Ranges ...... 99

7.4.3 Effect of Probe Convergence Angle ...... 102

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7.4.4 Effect of Crystal Orientation and Thickness ...... 104

7.4.5 3D Imaging of Lighter Dopant Atoms Using LAADF Angles ...... 107

7.4.6 3D Imaging of Heavier Dopant Atoms in β-Ga2O3 ...... 109

7.4.7 Effect of Local Atomic Distortion ...... 111

7.4.8 Verification of the Low Angle Ripple Effect and Vacancy Contrast ...... 113

7.5 Discussion ...... 116

7.5.1 Experimental Realization of Multiple, Narrow ADF Ranges ...... 116

7.5.2 Allowable Experimental Uncertainties ...... 117

7.5.3 The Use of Column Averaged Intensity ...... 118

7.6. Conclusion ...... 119

7.7 Acknowledgement ...... 120

Chapter 8: Summary and Final Conclusions ...... 121

References ...... 125

Appendices ...... 136

A. “Unusual Formation of Point Defect Complexes in the Ultra-Wide Band Gap

Semiconductor β-Ga2O3” ...... 136

A.1 Methods ...... 136

A.2 Statistical Analysis of Column Intensities for Ga1 vs Ga2 with Cation Interstitials

...... 138

A.3 Multislice Image Simulation...... 139

A.4 Estimating the Number of Defect Complexes in the Atomic Column ...... 143

1 A.5 Formation Energies for 2푉퐺푎 – Sni Complexes ...... 145

B. “Al Distribution and Point Defect Complexes in β-(AlxGa1-x)2O3 Films” ...... 146

B.1 Statistical Analysis of Column Intensities for Ga1 vs Ga2 with Cation Interstitials

...... 146

B.2 Quantitative STEM Al Composition Analysis ...... 147

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List of Tables

Table 1. Materials properties of the major semiconductors [1]...... 3

Table 2. Ga1 and Ga2 columns from a defect free region are compared to neighboring Ga1 and Ga2 columns when an interstitial is located in the ib or ic site. Average column intensities are calculated by averaging the intensities located within a circle of radius = 4 pixels centered around the column. The neighboring Ga columns with interstitials present were chosen for this analysis from the indicated interstitials in Figure 19(g). Error bars represent the differences in measurements of different columns...... 139

Table 3. Ga1 and Ga2 columns from the β-Ga2O3 substrates are compared to the alloyed films. Average column intensities are calculated by averaging the intensities located within a circle of radius = 17 pixels centered around the column. All average column intensities are background subtracted. Ga1 and Ga2 columns were chosen for this analysis from the images in Figures 27(b) and 27(c). Film data error bars represent the differences in column measurements corresponding to the column by column Al composition fluctuation and their random distributions...... 147

Table 4. Experimental data for Ga1 and Ga2 columns in the β-Ga2O3 substrates and alloyed films is compared. Experimental average intensities are normalized to the incident beam. The comparison between experimental and simulated data from Figure 45 yield Al composition and occupancy results. Film data error bars represent the differences in column measurements corresponding to the column by column Al composition fluctuation and their random distributions...... 149

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List of Figures

Figure 1. Relationship between band gap energy and bond length for semiconductors [1]...... 2

Figure 2. Calculated band structure for β-Ga2O3 [17]...... 7

Figure 3. (a) Bandgap dependences of the breakdown field and (b) theoretical limits of breakdown voltage for major semiconductors [19]...... 8

Figure 4. Four inch diameter β-Ga2O3 wafer...... 9

Figure 6. Enthalpy of formation as a function of the alloy composition for the corundum and monoclinic structures [38]...... 13

1 1 Figure 7. Migration mechanism of VGa for the formation of 2VGa - Gai complexes [39]. 14

Figure 8. DLTS and DLOS detected deep level defect states in bulk β-Ga2O3 [44]...... 15

Figure 9. ABF image of β-Ga2O3 along the [010]m zone axis. Ga and O atomic columns are displayed as dark contrast on the bright background...... 18

Figure 10. HAADF STEM image of [110] Sb doped (left) and undoped (right) Si revealing heavier substitutional dopants (bright dots) [56]...... 19

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Figure 11. Quantitative STEM analysis for varying thicknesses of STO with comparison using multislice frozen phonon and bloch wave simulations [59]...... 21

Figure 12. ADF detector efficiency map [65]...... 22

Figure 13. Simulated PACBED patterns for different thicknesses of STO along the [001] direction [66]...... 23

Figure 14. Photograph of a processed 10 x 15 mm2 β-Ga2O3 substrate [20]...... 27

Figure 15. β-Ga2O3 substrate and FIB specimen (red line) orientations. (a) (201) grown crystal providing an [010] cross-section FIB specimen extracted parallel to the [102]. (b) (010) grown crystal providing an [001] cross-section FIB specimen extracted 53.8° from the [102]...... 31

Figure 16. Schematic diagram of the STEM optical configuration [76]...... 33

Figure 17. Schematic diagram of the (a) HAADF and (b) ABF imaging modes [79]. .... 34

Figure 18. Crystal structure and experimental image of β-Ga2O3. (a) Crystal structure of

β-Ga2O3 along the [010]m direction with five possible interstitial sites (ia-e). (b) Atomic resolution HAADF-STEM image of a [010]m Sn-doped β-Ga2O3 bulk crystal from a defect free area...... 43

Figure 19. Direct detection of interstitial defects in Sn-doped β-Ga2O3. (a) HAADF- STEM images from two regions (left and right) with clustered interstitial defects. Magnified locations from the image (a-left) with intensity located in interstitial sites (b) ib, (c) ic, (d) id and (e) ie are marked corresponding to Fig. 1(a). Arrows in (d) and (e) point towards accompanying interstitials in the ib and ic sites. (f) Intensity is evaluated across the red-dashed line demonstrating the significant signal scattered from the cation interstitial atoms located in the ic site (red triangle). (g) Positions of ib (aqua mark) and ic

(red mark) interstitial atoms identified in a larger area of β-Ga2O3. Yellow-dashed

xix outlined areas indicate the interstitials clustering and concentrating in areas of about 10 nm2...... 45

1 1 Figure 20. Migration mechanism of VGa for the formation of 2VGa – Gai complexes. In 1 the presence of a VGa, an adjacent Ga1 relaxes into the (a) ic or the (e) ib site, creating an 1 additional VGa. (b)–(d) Experimental and simulated HAADF images showing multiple 1 c 2VGa - Gai complexes along the [010]m direction. (d) Line profiles from a [(b), green- dashed] defect free and [(c), red-dashed] interstitial containing experimental images show a significant reduction in Ga1 intensity (blue arrows) from vacancies when neighboring ic interstitials (red triangle) are compared to unperturbed Ga1 columns (green arrows). (d) Line profiles from a [(b), green-dashed] simulated defect free and a [(c), red-dashed] simulated 25 nm (~82 atoms) thick crystal containing 10 defect complexes located near the surface, showing similar profiles to the corresponding experimental images. (f)–(h) 1 b Similarly, experimental and simulated HAADF images show multiple 2VGa – Gai complexes along the depth direction. The simulated crystal contains 10 defect complexes located near the surface...... 49

Figure 21. STEM results for point defects and defect complexes in β-Ga2O3. (a) HAADF

STEM image of an atomic column containing Sn dopants (purple triangle) in [010]m bulk

Sn-doped β-Ga2O3. The inset shows the line profile along the dashed line in the figure.

(b) HAADF STEM image of UID β-Ga2O3 showing interstitial defects with red arrows indicating detected Ga interstitials in the ic sites...... 53

Figure 22. DLOS as a function of Sn doping in bulk β-Ga2O3. The trap detected at EC – 2.0 eV shows a positive correlation with Sn concentration...... 54

Figure 23. Crystal structure and experimental HAADF-STEM images of β-Ga2O3. (a)

Crystal structure of β-Ga2O3 along the [010]m direction with five possible interstitial sites

(ia-e). (b) Atomic resolution HAADF-STEM image of a [010]m Sn-doped β-Ga2O3 bulk crystal from a region with (inset) a defect free area and clustered interstitial defects.

Magnified locations from image (b) with combinations of interstitial intensities located in the (c) 2ic – id sites and the (d) 2ib – ie sites...... 62

(c) a Ga2 atom located between the two complexes relaxes into to the id site (blue arrow) 2 and subsequently creates a VGa. (d–f) shows the equivalent mechanism for the formation of 2ib – ie complexes...... 64

1 c Figure 25. (a) The model showing the region of the two neighboring 2VGa – Gai complexes, with the positions of expected cation vacancies according to the mechanism shown in Fig. 2. (b) Experimental HAADF image of a corresponding area. (c) Line profiles from the dashed lines of same colors from (b). Relatively lower intensity of the right Ga2 column (blue arrow) across the blue line confirms the higher concentration of vacancies in that column. Intensities in (d) are lower than the defect free columns (orange line in (c)), indicating Ga1 columns containing vacancies across both green and gray lines in (b). (e–g) Simulated HAADF images using the model shown in (a) shows the same line profile trends. (h–n) Similar analysis for vacancy identification in 2ib – ie complexes...... 66

Figure 26. HAADF STEM images of an (a) β-(Al0.22Ga0.78)2O3 and (b) β-(Al0.4Ga0.6)2O3 film with the β-(AlxGa1-x)2O3//β-Ga2O3 interface marked with a dashed yellow line. Bright contrast above the white dashed line in (b) indicates a rotation or phase transformation region...... 75

Figure 27. (a) Crystal structure of β-Ga2O3 along the [001]m direction. (b) and (c)

HAADF STEM images of (b) β-(Al0.22Ga0.78)2O3 and (c) β-(Al0.4Ga0.6)2O3 films used for the quantitative analysis of Al site occupancy. Inset are the experimental PACBED patterns acquired from the β-Ga2O3 substrate and the corresponding multislice simulated xxi patterns, indicating a 16.8 nm and 18.5 nm thick TEM sample for the β-(Al0.22Ga0.78)2O3 and β-(Al0.4Ga0.6)2O3 films, respectively. (d) Quantitative STEM data showing the Al site occupancy (%) in the Ga1 (red x) and Ga2 (blue x) sites versus the Al composition of the film...... 77

Figure 28. Direct detection of interstitial intensities in β-(AlxGa1-x)2O3 films. (a) Model of

[001]m β-Ga2O3 indicating the position of the ic interstitial site. HAADF images from (b)

β-(Al0.22Ga0.78)2O3 and (c) β-(Al0.4Ga0.6)2O3 films with significant intensities in the ic site

(red arrow). (d) A string of clustered ic interstitials with fluctuating intensities in the β-

(Al0.4Ga0.6)2O3 film...... 80

1 1 c Figure 29. Migration mechanism of VGa for the formation of 2VGa – Gai complexes. (a) A 1 VGa causes the migration of the adjacent Ga1 into the ic site, forming the energetically 1 c stable 2VGa – Gai complex. (b) Significant intensity from interstitials in the ic site (red triangle) and the reduction in Ga1 column intensity (blue triangles) from the presence of vacancies are shown in the HAADF image. Ga2 columns (yellow circles) also show decreased intensity from Al incorporation. (c) High intensity from the interstitial site (red triangle) and the complete disappearance of Ga1 site intensity (blue triangles) reveal a complete column of vacancies and interstitials along the 18.5 nm thickness of the β- 1 c (Al0.4Ga0.6)2O3 film, confirming the observation of 2VGa – Gai complexes...... 82

Figure 30. Crystal structure of β-Ga2O3 in a (a) perspective view, along (b) [010]m, (c)

[001]m, and (d) [100]m view. Green spheres are Ga atoms and red spheres are oxygen atoms...... 94

Figure 31. (a) Schematic of β-Ga2O3 used in the simulation along the [010]m beam direction. Vacancies were placed one-by-one at the positions indicated along the depth, 1 to 11. (b) An example simulated image using a HAADF detection angle (60-170 mrad). The arrow indicates the column containing the vacancy. The red dotted circle shows the area that we averaged to get the intensity of the column. The column intensity as a function of the vacancy depth position (red curve) was plotted against the intensity of the xxii column without a vacancy (blue curve) for ADF angles (c) 60-170 mrad, (d) 100-150 mrad, and (e) 20-100 mrad. The error bars indicate the uncertainty (SDOM) generated from the averaging of ten simulated images, each of which used twenty frozen phonon configurations at 298 K. Probe convergence half angle = 9.6 mrad, and sample thickness = 33 Å...... 97

Figure 32. CBED patterns simulated with a probe positioned at the octahedral Ga column with (a) no vacancy and (b) a vacancy at the 6th position from the top surface without TDS. (c) and (d) show the same simulations but with TDS for (a) and (b) cases, respectively. (e) and (f) are the zoomed-in versions of (c) and (d), respectively, to show the intensities at low scattering angles. The patterns (a) to (d) were presented in linear scale with the intensity saturated at the center to make the higher angle scattering intensities more visible. The patterns in (e) and (f) were presented with γ = 0.5. The inset in (f) shows the annular averaged intensities of the 2D patterns in (e) and (f) to show the differences between them in linear scale. The x-scale of the inset graph matches the x- scale of the 2D pattern in (f). Probe convergence half angle = 9.6 mrad, and sample thickness = 33 Å...... 98

Figure 33. Column-averaged intensity as a function of vacancy depth position (red curve) compared to the column intensity without vacancy (blue curve) for detection angles (a) 0–5 mrad (bright field), (b) 5–9.6 mrad (annular bright field), (c) 10–20 mrad, (d) 20–30 mrad, (e) 30–40 mrad, and (f) 110–120 mrad, for imaging with [010]m orientation. (g) is the simulated image with a vacancy placed at the 6th position (15 Å depth) from the top [see Fig. 31(a)] with 20–30 mrad detection angle. (h) is the simulated image with vacancy placed at the 9th position (25 Å depth) from the top with 30–40 mrad detection angle. All simulations used TDS and probe convergence half angle of 9.6 mrad, and sample thickness = 33 Å...... 100

Figure 34. Column averaged intensity as a function of vacancy depth position (red curve) compared to the intensity without a vacancy (blue curve) for detection angles (a) 20-30

xxiii mrad, (b) 30-40 mrad, and (c) 100-150 mrad using 20 mrad probe half convergence angle. All simulations used TDS...... 103

Figure 35. Column-averaged intensity as a function of vacancy depth position (red curve) compared to the column intensity without a vacancy (blue curve) for detection angles (a)

20–30 mrad and (b) 30–40 mrad, for imaging with [001]m orientation and sample thickness of 60 Å. (c) shows the image simulated for the vacancy placed at the 9th position (46 Å depth) from the top with a 30–40 mrad detection angle. The arrow indicates the column containing the vacancy. (d) Probe channeling oscillation along (top)

[010]m (bottom) [001]m orientations in β-Ga2O3. (e) and (f) are the same simulations as (a) and (b), but with a sample twice as thick (119 Å). For (e) and (f), the intensities for every other vacancy positions were simulated...... 106

Figure 36. Column-averaged intensity as a function of vacancy depth position (red curve) compared to the column intensity without a vacancy (blue curve) for detection angles (a)

20–30 mrad, and (b) 30–40 mrad, for imaging with [010]m orientation and sample thickness of 55 Å. The intensities for every other vacancy position were simulated. .... 107

Figure 37. Column-averaged intensity as a function of Si depth position (red curve) compared to the column intensity without an impurity (blue curve) for detection angles

(a) 20–30 mrad, (b) 30–40 mrad, and (c) 100–150 mrad, for imaging with [010]m orientation. The data with a vacancy (red curve) is the same data presented in Figure 33. All simulations used TDS and a probe convergence half angle of 9.6 mrad...... 108

Figure 38. Column-averaged intensity as a function of Nd dopant depth position (red curve) compared to the column intensity without a vacancy (blue curve) for detection angles (a) 20–30 mrad, and (b) 30–40 mrad, for imaging with [010]m orientation. (d) Probe channeling intensity profiles along the depth direction without point defects (black) and with point defects, including a vacancy (light blue) and a Nd dopant (light green), placed at the 5th position (13 Å depth) from the top...... 110

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Figure 39. (a) Relaxation of the oxygen atoms surrounding a Ga vacancy (located behind the front Ga atom as indicated) from DFT. The arrows indicate the direction of the displacement, and their magnitudes are exaggerated for visual clarity. (b and c) Column intensity as a function of vacancy depth position for the relaxed structure using (b) 20–30 mrad and (c) 30–40 mrad detection angles, compared to the unrelaxed case...... 112

Figure 40. CBED simulated for the Sr column in SrTiO3 with no vacancy, slice thickness = 1.953 Å and (a) 4 × 4 × 8 (in x, y, and z) unit cells and 1024 × 1024 real space pixel sampling, and (b) 20 × 20 × 8 unit cells and 2048 × 2048 pixel sampling. (c) and (d) are the same simulations as (a) and (b), respectively, but with a vacancy positioned in the middle of the column. (e and f) CBED simulated with no vacancy, and slice thickness of (e) 1.3 Å and (f) 0.98 Å. No TDS was used...... 114

풘풊풕풉 풗풂풄풂풏풄풚 (c) and (d) show the intensity ratio ( ) for the normal RMS (pink) and 풘풊풕풉풐풖풕 풗풂풄풂풏풄풚 RMS+15% (blue) data in (a) and (b), respectively...... 115

Figure 42. (a) The difference ratio R = I - I / I between the column intensities with vac 0 0 and without a vacancy along [010]m orientation as a function of vacancy depth. Ivac is the intensity of the vacancy-containing column and I0 is the intensity of the column without a vacancy. (b) Intensity profile across the column containing the vacancy as a function of the depth of the vacancy using 20-30 mrad detection angle...... 119

1 1 Figure 43. HAADF multislice image simulations and analysis for 2VGa – Gai and 2VGa –

Sni complexes. (a) Schematic examples of β-Ga2O3 used in the simulations along the

[010]m beam direction of (a-left) a defect free cell, (a-middle) a cell containing four 1 randomly distributed 2VGa – Gai complexes (positions 2,5,6,10), and (a-right) a cell

xxv

1 containing four clustered 2VGa – Sni complexes (positions 1,2,3,4). (b) Schematic of the 1 c 2VGa – Gai defect complex. (e) Line profiles from a defect free (c, green-dashed) and a 1 c 2VGa – Gai defect complex containing (d, red-dashed) simulated HAADF image showing the decrease in Ga1 intensity (blue arrows) from the incorporated vacancies and increase 1 b in interstitial site intensity (red triangle). (f) Schematic of the 2VGa – Gai defect complex. 1 b (i) Similarly, line profiles from a defect free (g, green-dashed) and a 2VGa – Gai defect complex containing (h, aqua-dashed) simulated HAADF image show similar intensity 1 changes. Plots (j) and (k) show the multislice image simulation analysis for (j) 2VGa – Gai 1 and (k) 2VGa – Sni complexes in a 25 nm (82 atom) thick crystal. Displayed is the fraction of intensity with respect to a defect free Ga1 column versus the number of complexes inserted along the depth direction. Each plot shows a random arrangement of defect complexes and defect complexes clustered at the surface of the crystal...... 142

2 1 Figure 44. Formation energies for SnGa and 2VGa – Sni complexes vacancies in β-Ga2O3, shown in the limit of (a) Ga-rich and (b) O-rich conditions...... 145

Figure 45. HAADF multislice image simulations and analysis for Al composition in (a) 16.8 nm (29 atoms) and (b) 18.5 (32 atoms) thick crystals. Displayed is the column intensity as a fraction of incident beam intensity versus the number of Al atoms in Ga1 and Ga2 columns. Each plot shows the random arrangement along the depth direction of Al in the columns. Also indicated on the plots are the experimental average column intensities and the corresponding Al concentrations...... 149

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Chapter 1: Introduction

Imagine life today without semiconductors. A world without cell phones, televisions, computers, and advanced medical equipment would mean, to many, a lower quality of life. Thankfully, we have today’s electronic technologically, which has emerged from several decades of semiconductor research and development. And, while this progress has led to the frequent fabrication of new devices, the continuous advancement of semiconductors will be vital to the development of novel technologies that could critically impact the planet and its people.

A semiconductor displays electrical conductivity between that of an insulator and a conductor, producing valuable electronic properties for various applications. Research in the field has rapidly progressed from traditional pure element and compound semiconductors to the currently popular wide band gap (WBG) semiconductors. As shown in Figure 1, these materials are defined by their band gap energy and atomic bond length, which are often determining factors when choosing a semiconductor for a specific application. The motivation for researching WBG semiconductors, which display band gaps over ~ 2 eV, comes from their incredible potential for electrical, optical, and power devices, due to their superior properties as compared to typical semiconductors such as Si and GaAs. Essentially, large band gap materials have been proposed to overcome the

1 limitations of traditional semiconductors, and this prospect comes from their increased band gap, which leads to an increased breakdown electric field and short-wavelength emission [1]. A comparison of basic properties for the major semiconductors is shown in

Table 1.

Figure 1. Relationship between band gap energy and bond length for semiconductors [1].

Table 1. Materials properties of the major semiconductors [1].

With high breakdown voltages and a wide emission spectrum, WBG semiconductors display valuable properties for high performance electronic, optical, and power device applications [2–5], including power electronics [6], solid state lighting [7], and photodetectors [8]. To enable applications like these, exact property manipulation is required through the control of its physical source, point defects. Point defects and their complexes display a wide range of atomic scale structures and functional states that critically influence the materials’ unique properties. While controlled point defects, in the form of dopants and alloying elements, have long been utilized to achieve desired properties in WBG materials [9–11], uncontrolled point defects have shown detrimental effects. For instance, large band gap materials have been shown to contain native compensating defects that induce n-type or p-type doping problems [9, 12] and the large critical field strengths supported in WBG semiconductors can be ruined by the presence of point defects [13]. Precise defect control has proven to be critical in currently used materials and will play a key role in the future development of new WBG semiconductors with better properties.

The next-generation of semiconductors will feature the transparent conductive oxide (TCO), beta gallium oxide (β-Ga2O3), and its progression will hinge on the control of point defects. Often described as being in its ‘infancy’, β-Ga2O3 research has intensified over the past ten years due to the demonstration of its successful bulk growth

[14]. Despite the tremendous progress that has been made over that time, the field still lacks the atomic scale characterization of point defects, essential to controlling the material’s unique properties.

This dissertation presents the atomic scale investigation of point defects in β-

Ga2O3 using atomic resolution scanning transmission electron microscopy (STEM). It begins with a thorough review of relevant literature in the field, presented in Chapter 2, providing detailed information on the current state of the material. The motivation to utilize an experimental technique that can reveal atomic scale information, such as

STEM, is exhibited through the evaluation of recent point defect studies. In Chapter 3, the methods used for the study are discussed, including crystal growth, experimental characterization, and theoretical techniques.

Chapters 4 and 5 reveal the direct observation of unusual point defect complex formation that originate from a single gallium vacancy. In Chapter 4, STEM data is correlated with defect spectroscopy data and theoretic calculations to determine the functional state of the complex and ultimately, its role on influencing the properties of β-

Ga2O3. Succeeding these results, an atomistic relaxation near adjacent complexes is described in Chapter 5, employing molecular dynamics simulations for the verification of its stable formation.

Chapter 6 investigates point defects in band gap engineered β-(AlxGa1-x)2O3 thin films. This characterization involves utilizing quantitative STEM to determine the Al site occupancy, which is critical to the epitaxial growth of the films. Additionally, the direct observation of the previously identified point defect complex from Chapter 4 is shown, and its role on the properties of the film is discussed.

Chapter 7 shifts focus to a simulation study performed to develop a new technique for the three-dimensional detection of point defects using STEM. Lastly, Chapter 8

5 summarizes the important results of the work, highlighting the valuable insight gained from one of the first atomic scale characterization studies on point defects in β-Ga2O3.

Chapter 2: Motivation and Background

2.1 Ultra-Wide Band Gap Semiconductor β-Ga2O3

Emerging as the next prominent WBG semiconductor, the crystalline material β-

Ga2O3 has been gaining significant attention for the development of next-generation high-performance electronic, optical, and power devices. Complementing β-Ga2O3’s effectively direct ultra-wide band gap (UWBG) of ~ 4.8 eV (Figure 2) [15] is its optical transparency into the ultraviolet region [16]. As a TCO, β-Ga2O3 demonstrates useful

Figure 2. Calculated band structure for β-Ga2O3 [17]. 7

properties for touch-sensitive displays, electrodes in solar cells, and solid-state light emitters [18]. Furthermore, as shown in Figure 3, β-Ga2O3 exhibits a high breakdown voltage [19] as compared to other semiconductors, establishing itself as a prime candidate for high power device applications. Additionally, recent progress in bulk single crystal

[20–22] and epitaxial film β-Ga2O3 growth techniques [23–25] have presented a realistic opportunity to replace traditional semiconductors like GaN and SiC [26]. High-quality β-

Ga2O3 has been shown to grow with a high growth rate from melt source techniques, resulting in lower production costs as compared to other WBG semiconductors [20].

Figure 4 shows the high-quality single crystal bulk growth of a β-Ga2O3 wafer. Despite these advantages, advancing the material has been hindered from the lack of understanding of point defects and their impact on electrical and optical properties.

Figure 3. (a) Bandgap dependences of the breakdown field and (b) theoretical limits of breakdown voltage for major semiconductors [19].

Figure 4. Four inch diameter β-Ga2O3 wafer.

2.1.1 Point Defects

A better understanding on the exact nature of the point defects present in β-Ga2O3 will be key to answering several of the underlying issues that currently limit the material.

It is imperative to have well-controlled point defects in UWBG TCOs as the intrinsic advantages of a large band gap and optical transparency could be compromised by their presence. For example, the existence of deep-level defects have been shown to severely degrade the optical properties of TCOs [27]. And in β-Ga2O3 devices, defects have been shown to cause threshold voltage instability [28] and drain current lag [29] and have been attributed to decreased mobilities [24]. The control of β-Ga2O3 will require detailed information on the point defects that contribute to these shortcomings as well as its observed intrinsic n-type behavior, difficulty in p-type doping, and low doping efficiency.

Several theoretical and experimental studies have attempted to gain this insight. These studies provide the foundation for microscopic investigations. 9

2.1.1.1 Theoretical Studies

Theoretical studies are reviewed to better understand the possible formation and subsequent electronic function of point defects within β-Ga2O3. Lead by Dr. Joel Varley and Prof. Chris G. Van de Walle, the theoretical studies of β-Ga2O3 have used density function theory (DFT) calculations to describe the electronic and atomic structures of point defects. Using DFT, defect formation energies have been calculated and used to determine their exact atomic positions within the complicated monoclinic structure of β-

Ga2O3 (Figure 5) and concentrations under certain growth conditions. Formation energies of relevant charge states have also been used to acquire a defect’s functional state,

Figure 5. Unit cell of monoclinic β-Ga2O3. Ga1 and Ga2 sites have tetrahedral and octahedral coordination, respectively. O1 and O2 have threefold coordination, while O3 has fourfold coordination. 10 determining its behavior within the band gap. Theoretical calculations have provided prospective point defect structural and functional information that can be combined with experimental information to confirm the existence of point defects, their concentrations, and electronic states.

First, the theoretical study from Varley et al. [17] on the n-type behavior of β-

Ga2O3 is reviewed. Initial speculation attributed the intrinsic n-type conductivity displayed in unintentionally doped (UID) β-Ga2O3 to oxygen vacancies [30]. However,

DFT calculations describing the electronic structure and stability of the oxygen vacancy

(VO) indicated that it is not a contributing factor. Instead, the cause of the n-type conductivity in UID β-Ga2O3 was theorized to result from donor impurities such as silicon (Si) and hydrogen (H). Structurally, it was determined that H incorporates as an interstitial impurity (Hi), bonding with O and behaving as a shallow donor for any Fermi level within the band gap. Likewise, substitutional Si impurities were shown to contribute to n-type behavior. Formation energy calculations revealed that Si impurities prefer the tetrahedrally coordinated Ga1 site. Additionally, several donor elements can be used to drive the material more n-type in doped β-Ga2O3. Formation energies revealed that the important dopants germanium (Ge) and tin (Sn), commonly used for n-type doping in bulk and epitaxial β-Ga2O3 [20, 31], prefer to substitute on the Ga1 site and the octahedrally coordinated Ga2 site, respectively. This theoretical study of n-type UID and doped β-Ga2O3 provides significant insight into the formation and positioning of H interstitials and substitutional dopants.

The theoretical examination of p-type conductivity, or rather the lack thereof, has indicated that shallow acceptors do not exist in β-Ga2O3. Several devices require the ability to achieve both n-type and p-type doping. As alluded to above, n-type doping has been demonstrated with several types of dopants, producing carrier concentrations of up to about 1020 cm-3 [32]. However, theoretical calculations have predicted that conventional doping will not generate p-type conductivity in β-Ga2O3. This result has been derived from calculations that show, even if shallow acceptors can be incorporated, the resulting holes would be more stable localized as small polarons, becoming self- trapped [33]. This behavior has previously been seen in WBG oxide semiconductors [34].

Even so, iron (Fe) dopants, incorporating on the Ga1 site and acting as deep acceptors, have been shown to create semi-insulating β-Ga2O3 [35].

Alloying Ga2O3 with Al2O3 can lead to a desired increase in band gap energy, which can enable the realization of several semiconductor heterostructure designs [36,

37]. Peerlaers et al. have performed theoretical calculations predicting the monoclinic structure is the preferred structure for alloy concentrations lower than 71% Al, as shown in Figure 6 [38]. In these β-(AlxGa1-x)2O3 alloys, the Al was shown to preferentially occupy the octahedrally coordinated Ga2 site. This means, for x = 0.5, Ga and Al should occupy all tetrahedrally coordinated and all octahedrally coordinated, respectively. This theoretical study may be significant to the explanation of β-(AlxGa1-x)2O3 growth difficulties [25], which must result from the incorporation of the Al substitutional point defects.

Figure 6. Enthalpy of formation as a function of the alloy composition for the corundum and monoclinic structures [38].

Lastly, Varley et al. have predicted the unusual formation of point defect complexes that develop from a single cation vacancy (VGa) [39, 40]. As displayed in

Figure 5, the monoclinic crystal structure of β-Ga2O3 contains a tetrahedrally (Ga1) and an octahedrally coordinated (Ga2) cation site. Formation energy calculations have

1 demonstrated that gallium vacancies prefer the Ga1 site (VGa) in both O-rich and Ga-rich

1 conditions. However, the VGa was found to be in a metastable state, with a more stable configuration involving the migration of an adjacent Ga1 into an interstitial octahedrally coordinated site. Figure 7 illustrates this migration and shows the small energy barrier that must be overcome for the relaxation to take place [39]. This complex was termed the divacancy-interstitial complex, and further studies have revealed several possible

1 interstitial sites, all resulting from the migration of a Ga1 adjacent to a VGa [41]. This 13 unusual point defect complex was shown to act as a compensating acceptor and has been suspected as the cause of mobility reduction and low doping efficiency in β-Ga2O3 [24,

32, 42, 43]. The control of this predicted compensating defect complex will be crucial to advancing n-type β-Ga2O3.

1 1 Figure 7. Migration mechanism of VGa for the formation of 2VGa - Gai complexes [39].

2.1.1.2 Experimental Studies

Complementing the knowledge gained from theoretical calculations, recent experimental studies using defect characterization techniques have revealed critical defect information. The most significant experimental work to date utilized deep level

14 optical spectroscopy (DLOS) and deep level transient spectroscopy (DLTS) to detect a rich spectrum of deep level defect states throughout the band gap of bulk grown β-Ga2O3, as illustrated in Figure 8 [44, 45]. Although this data provides important electronic defect state information, it fails to identify the physical source of the traps and to quantitatively determine defect concentrations. Even so, this work will be essential to correlating theory and future microscopic data and will guide the development of β-Ga2O3 through the consideration of the electronically active defects, similar to what has been reported for

GaN transistors [46]. In electron spin resonance [47, 48] and infrared spectroscopy [49,

50] experiments, the presence of proton irradiation induced defects and implanted O-H bonds were attributed to gallium vacancies and consequently, the divacancy-cation interstitial complex discovered by DFT. Essentially, these two experiments have indirectly observed the complex after prompting their formation through defect generation in β-Ga2O3.

Figure 8. DLTS and DLOS detected deep level defect states in bulk β-Ga2O3 [44].

Experimental studies, up to this point, have revealed significant information on defects and their states but all required correlation to theoretical calculations to determine their physical source. What has been missing in the field is the direct detailed experimental information on the atomic scale structure of point defects, which will be essential to bridging the theoretical predictions from DFT studies to the measured properties of β-Ga2O3. This information will be vital to the development of the material through the improvement of growth, alloying, and doping with precise defect control.

However, direct observations have been nearly unattainable due to the atomic scale nature of the defects. Many techniques used for defect characterization, such as positron annihilation spectroscopy (PAS), secondary ion mass spectroscopy (SIMS), DLOS and

DLTS, and X-ray diffraction, display spatial resolution of, at best, greater than 20 nm

[51, 52], which is significantly larger than the atomic scale resolution required for the direct observation of point defects. Detection on the atomic scale requires an experimental technique with unprecedented resolution and chemical sensitivity.

2.2 Scanning Transmission Electron Microscopy

One of the goals of modern electron microscopy has been the direct characterization of point defects in crystalline materials. And, recent advances in

(scanning) transmission electron microscopy (S/TEM) have made this possible by providing viable imaging techniques that combine unprecedented sub-angstrom resolution and chemical sensitivity. Complimenting the advantages of using the short

16 wavelength of electrons, the impressive resolution that is achievable in current STEM comes from the development of aberration correction [53, 54]. When an aberration corrected electron probe is produced and scanned across the sample, the formation of images, displaying the two-dimensional projection of the three-dimensional sample structure, is possible, with approximately 0.7 Å lateral resolution. This resolution combined with select STEM imaging modes can be utilized to reveal point defects’ exact positions, types, and effects on local atomic structure. For example, as shown in Figure 9, the annular bright field (ABF) mode produces images that reveal positions of lighter and heavier atoms. This technique has been used to identify oxygen displacements in perovskites [55]. Perhaps the most widely used technique, high angle annular dark field

(HAADF) STEM produces atomic structure images that are directly interpretable due to contrast that is heavily dependent on the atomic number of the atoms in the columns, scaling as ~Z1.7. The chemical sensitivity of the HAADF method combined with sub- angstrom resolution in probe-corrected STEM has allowed for the direct detection of impurity atoms. The first HAADF STEM direct observation of substitutional heavier dopants (Figure 10) was reported Voyles et al. in 2002 [56]. This technique has also been used to directly observe vacancies on cation sites in perovskites [57]. The HAADF

STEM observations of point defects in the two-dimensional projection of the three- dimensional crystal structure demonstrates the unmatched spatial resolution and chemical sensitivity of the technique that can benefit point defect studies in β-Ga2O3. However, merely assessing point defect formation in two-dimensions neglects critical depth information.

Figure 9. ABF image of β-Ga2O3 along the [010]m zone axis. Ga and O atomic columns are displayed as dark contrast on the bright background.

Figure 10. HAADF STEM image of [110] Sb doped (left) and undoped (right) Si revealing heavier substitutional dopants (bright dots) [56].

2.2.1 Quantitative STEM

A complete characterization of point defects will require obtaining the three- dimensional atomic scale information, such as exact location (depth), distribution, concentration, or clustering and how they affect local structure. Within the last decade, two STEM techniques, focal series imaging and quantitative STEM, have been developed in an effort to reveal this three-dimensional information. While focal series imaging has been deemed impractical due to the current microscopic depth of field limitations [58], quantitative STEM has become a powerful tool used for the interpretation of HAADF

STEM images.

Alone, experimental HAADF STEM data, which is highly sensitive to the atomic number of the atoms in a column, allows for a qualitative examination of the atomic structure. Consequently, variations in structure and contrast from defects may be distinguishable, but the exact details on the nature of the defects may be unexplainable.

Further interpretation requires a quantitative approach, coupling quantitative experimental HAADF STEM imaging with simulation, resulting in image intensities that can be directly compared. Quantitative STEM has shown the capability to assess defect configurations in three-dimensions, extract exact atom types, and determine defect concentrations.

Quantitative STEM places the measured image intensities on an absolute scale by normalizing the intensities to the incident beam [58]. This normalization of the experimental intensities allows for the direct comparison between experiment and simulation. To find the most accurate simulation method, HAADF imaging theories were analyzed by carrying out a quantitative STEM comparison of STO with varying thicknesses [59]. As shown in Figure 11, the multislice frozen phonon model [60] was shown to provide excellent agreement for thin and thick samples. The effectiveness of this method comes from the propagation of the electron wave function with the weak phase approximation through one slice of the material at a time. One of the most widely used multislice simulation packages was created by Kirkland, and details on the theory behind the method and how to effectively and accurately run the programs can be found in Advanced Computing in Electron Microscopy [61].

Figure 11. Quantitative STEM analysis for varying thicknesses of STO with comparison using multislice frozen phonon and bloch wave simulations [59].

To properly compare experimental and simulated data, it is imperative to have exact knowledge of sample thickness because, as seen in Figure 11, atomic column intensity is immensely dependent on the number of atoms within the column. Analyzing thickness by directly comparing experimental and simulated column intensity was found to be inaccurate if experimental uncertainties were not accounted for [62]. The most prominent uncertainty, ADF-detector non-uniformity, has been well documented and potential solutions have been addressed [55, 63]. The efficiency map for a typical ADF detector is shown in Figure 12. Correction for detector variance has been realized by simply incorporating the experimentally measured detector response in simulation [55].

Even so, an independent method for thickness determination was demonstrated to verify image simulations. The position averaged convergent beam electron diffraction

(PACBED) technique has shown high sensitivity to small changes in crystal thickness, as 21 shown in Figure 13, and can be obtained simultaneously acquired with HAADF-STEM images in both experiment and simulation [64]. By comparing experimental and simulated PACBED patterns, sample thickness can be determined with high accuracy.

Thus, the observed crystal structure can be accurately modeled and simulated for comparison.

Figure 12. ADF detector efficiency map [65].

Figure 13. Simulated PACBED patterns for different thicknesses of STO along the [001] direction [66]. 23

Pivotal to the quantitative assessment of point defects at the atomic scale in three- dimensions was the realization of a defect’s depth dependency. When a crystalline sample was oriented along a high-symmetry zone axis, a defect’s depth position (along the beam direction) was shown to greatly affect the amount of electron scattering by influencing the electron channeling [67, 68]. Ultimately, understanding the electron probe oscillation through the crystal has allowed for the determination of point defect depth information because of the atomic column intensity variations. This method was utilized to determine the depth positions and clustering of heavier dopants to within an uncertainty of 1 unit cell [67, 69, 70]. Recent studies have shown that a defect’s depth dependence can be enhanced by incorporating variable-angle measurements [70].

Currently, this method has only been established for the depth determination of heavier point defects.

2.3 Conclusion

Essential to advancing semiconductors for successful application is the manipulation of important properties through well-controlled point defects. This will continue to be true for the emerging ultra-wide band gap semiconductor β-Ga2O3, which displays properties superior to those semiconductors currently used for electronic, optical, and power device applications. However, β-Ga2O3 remains underdeveloped due to the lack of understanding of its key properties and ultimately, the point defects that control them. Several point defects and their functional states have been realized through

24 theoretical and experimental studies, but what has been missing in the field is the direct experimental information, which has been elusive due to their atomic scale nature.

Providing unmatched spatial resolution and chemical sensitivity, electron microscopy must be utilized for the direct observation and complete characterization of point defects in β-Ga2O3. Specifically, HAADF STEM imaging possesses the capability to assess the atomic structures of defects. And, when combined with simulation, can be used quantitatively to extract three-dimensional information such as location, concentration, and influence on the local structure. A microscopic study will be essential to connecting the theoretical predictions from DFT studies, the previous experimental defect studies, and the measured properties of β-Ga2O3. This information will provide important guidance to achieving desired properties through the synthesis, alloying, and doping of the material with precise defect control, and will be influential to the characterization of defects in future semiconductor materials for their development and application.

Chapter 3: Methods

From fabrication to characterization, it is important to understand the role of each method in contributing to and establishing the critical structure-property relationship that is essential for materials development. This is particularly important in β-Ga2O3 where several techniques are viable for its growth and characterization. Here, the growth and experimental and simulation characterization methods used in the investigation of point defects in β-Ga2O3 are reported.

3.1 Crystal Growth

β-Ga2O3 crystals were grown using three different techniques: edge-defined film- fed growth (EFG), metalorganic chemical vapor deposition (MOCVD), and molecular beam epitaxy (MBE). These methods were used to produce unintentionally doped (UID),

Sn doped, and Al alloyed β-Ga2O3. High-quality UID and Sn-doped β-Ga2O3 single crystals were fabricated by the EFG process, and epitaxial β-(AlxGa1-x)2O3 thin films were grown by MOCVD and MBE on the EFG β-Ga2O3 substrates.

3.1.1 EFG

UID and Sn-doped β-Ga2O3 bulk crystals were grown using the EFG process [20,

71]. In this melt source technique, high-grade Ga2O3 powder, used as the source material, was heated to the melting point temperature of β-Ga2O3 in a growth atmosphere of 98% nitrogen and 2% oxygen and pushed into contact with a β-Ga2O3 seed crystal. From here, the crystal growth, set to the orientation of (201), was initiated, and continued into the shape determined by the top surface of the die. To produce Sn-doped crystals and subsequently drive the material more n-type, tin dioxide (SnO2) powder was added to the

Ga2O3 powder. The UID and Sn-doped crystals were then processed into semiconductor substrates by annealing in nitrogen ambient at 1450 °C, which reduces residual stress in the crystal and activates donors. The resulting β-Ga2O3 crystals were reported to exhibit carrier concentrations (n) of about 2.4 x 1017 cm-3 and 8.2 x 1018 cm-3 for UID and Sn doped substrates, respectively. A photograph of a processed substrate, identical to those investigated, is shown in Figure 14. These substrates were produced by Novel Crystal

Technology, Inc. and the Tamura Corporation [20].

Figure 14. Photograph of a processed 10 x 15 mm2 β-Ga2O3 substrate [20].

3.1.2 MOCVD

(010) β-(Al0.4Ga0.6)2O3 thin films were grown on Fe-doped semi-insulating (010)

EFG β-Ga2O3 substrates via MOCVD [25]. The epitaxial growth of these thin films was achieved by the systematic tuning of the trimethylaluminum (TMAI)/triethylgallium

(TEGa) molar flow rate ratio and growth temperature. Specifically, at a temperature of

880 °C, the TMAI molar flow rate was increased to produce higher Al concentration

(010) β-(AlxGa1-x)2O3 thin films. This method was used to incorporate an Al-alloying composition of 40% while maintaining the beta phase. (010) β-(Al0.4Ga0.6)2O3 thin films were grown with a thickness of about 10 nm.

3.1.3 MBE

Lower Al content (010) β-(AlxGa1-x)2O3 thin films were grown on Fe-doped (010)

EFG β-Ga2O3 substrates by MBE. These films were produced in a Riber M7 system equipped with a Veeco oxygen plasma source. Prior to growth an oxygen plasma cleaning was carried out on the substrate at a temperature of 800 °C for 15 minutes. The epitaxial growth utilized slightly oxygen rich conditions involving a Ga beam equivalent pressure (BEP) of 8 x 10-8 Torr, Al BEP of 1 x 10-8 Torr, oxygen pressure of 1.5 x 10-5

Torr, substrate temperature of 610 °C (temperature read from pyrometer calibrated to Si emissivity) and RF oxygen plasma power of 300 W. For the sample of interest, the entire heterostructure consisted of a 30 nm buffer layer of β-Ga2O3 and a layer of β-(AlxGa1-

28 x)2O3 grown on an Fe-doped β-Ga2O3 (010) substrate. Using these parameters, a 20 nm thick β-(Al0.22Ga0.78)2O3 film was produced, with concentration determined by high resolution XRD.

3.2 Experiments

For the characterization of the aforementioned β-Ga2O3 substrates and films, the experimental techniques, TEM and DLOS, were exploited to obtain select point defect information vital to establishing structure-property relationships. As the primary characterization technique used in these studies, TEM was utilized in the scanning

(S)TEM setup with specific microscope arrangements for the atomic scale direct observation of defects. As a complementary technique, DLOS was used to reveal defect trap states.

3.2.1 TEM Sample Preparation

Key to obtaining high-quality data is TEM sample preparation, which requires attention to specimen thickness and damage. Here, a common two-step ion milling process was utilized to produce ideal samples for STEM imaging. First, the focused ion beam (FIB) was used to select, extract, and thin desired regions of the samples. Second, the specimens underwent a low energy milling procedure for further thinning and reduction in any damage from the FIB.

3.2.1.1 Focused Ion Beam

The FIB instrument consists of both an electron and an ion beam column, positioned to allow the probes to be focused at the same location on the sample surface.

While the electron column is a scanning electron microscope used to create images of the sample surface at high magnifications, the Ga+ ion beam is primarily used to remove the sample material. Utilizing this ability, sufficiently thin samples can be produced for

STEM imaging [72].

STEM samples were prepared using a Thermo Fischer Scientific Helios dual- beam FIB. Before beginning the FIB procedure, the thin film samples were sputter coated with gold for protection against ion beam damage. The first step in the FIB preparation of the aforementioned β-Ga2O3 samples was the consideration of advantageous STEM imaging orientations. Identified by the growth directions and cleavage planes of the β-

Ga2O3 samples, the (201) and (010) substrates were oriented to produce cross-sectional

[010]monoclinic (m) and [001]m imaging directions, respectively (Figure 15). Once the sample was aligned, the ion beam was used to produce a 28 휇m by 6 휇m rectangular specimen with 1 휇m thickness along the imaging direction. The specimen was then attached to a thin needle by platinum (Pt) deposition and extracted from the bulk of the sample. Next, the specimen was attached to a TEM omniprobe lift-out grid. To produce ideal specimens for STEM imaging, the sample was then thinned with the ion beam to a sufficient thickness (< 30 nm). During this step, the sample was tilted to an incidence angle of 1.5° and initially thinned with an ion beam at an accelerating voltage of 30 kV. A final

30 thinning at an accelerating voltage of 5 kV was completed to reduce ion damage [73].

The significant remaining damaged layer was further reduced by low energy ion milling.

3.2.1.2 Low Energy Ion Milling

Post FIB preparation, STEM samples underwent a final low energy milling procedure to reduce damage induced by the higher energy FIB, which includes amorphization, ion implantation, and redeposition [74]. This step was carried out using a

Fischione 1040 NanoMill equipped with a focused argon (Ar) ion beam. Ar ion beam milling was first performed at an accelerating voltage of 900 V and then at 500 V. Lower energy milling has proven to be critical to acquiring high-quality STEM images at the atomic scale [74].

3.2.2 STEM

STEM was performed using aberration corrected Thermo Fisher Scientific Titan or Titan Themis instruments, all operated at 300 kV. For the TEM to function in STEM mode, a series of lenses are used to focus the accelerated electrons into a probe at the sample plane. When the probe is formed with large convergence angles (10–30 mrad) and aberration correction, sub-angstrom resolution can be achieved. In this study, resolution of about 0.7 Å was achieved using large convergence angles. To form atomic structure images, the probe is scanned over the specimen in a raster, and for each probe position, the electrons that pass through the thin specimen are collected by an ADF detector and used to construct images. A schematic diagram of the STEM optical configuration is shown in Figure 16. For further information on STEM and imaging modes, refer to Refs.

[75–78].

Here, desired structural information was revealed by utilizing the ABF and

HAADF imaging modes. As shown in Figure 17, these modes are differentiated by the

ADF detector position relative to the transmitted electrons, meaning specific electrons scattered to particular angles are used to form atomic resolution images with varying contrast, dependent on the elements in the atomic column. HAADF STEM was used as the primary imaging mode, while ABF was used as a complimentary technique to detect

O positions. Additionally, quantitative HAADF STEM was performed for the direct interpretation of experimental images by comparison to simulation.

Figure 16. Schematic diagram of the STEM optical configuration [76].

Figure 17. Schematic diagram of the (a) HAADF and (b) ABF imaging modes [79].

3.2.2.1 ABF Imaging

ABF imaging was performed on the [001]m cross-sectional β-(AlxGa1-x)2O3 thin films. This method was executed by increasing the camera length and positioning the

ADF detector in the path of the direct beam. The arrangement is shown in Figure 17(b).

In this setup, the ADF detector functioned as an ABF detector, collecting transmitted electrons from the outer region of the direct beam near the optic axis enabling the visualization of atomic columns composed of light atoms. The captured signal was then used to construct atomic resolution phase contrast images with O columns and Ga columns appearing as dark spots on a bright background.

3.2.2.2 HAADF Imaging

All bulk and thin film β-Ga2O3 samples were investigated using HAADF-STEM imaging. Using short camera lengths, the ADF detector was positioned at high angles, allowing for the detection of electrons that are scattered over an angle range of about 60–

400 mrad [Figure 17(a)]. These electrons are incoherently (Rutherford) scattered electrons [80] that, when collected by an ADF detector, produce dark field images with contrast highly sensitive to the atomic number of the atoms in the sample. In the bulk β-

Ga2O3 samples, HAADF images were collected from areas of interest such as regions that displayed noticeable contrast as a result of defect formation. Similarly, HAADF images were acquired at β-(AlxGa1-x)2O3//β-Ga2O3 interfaces and from film regions in β-(AlxGa1- x)2O3 thin films.

3.2.2.3 Quantitative HAADF Imaging

For a more detailed understanding of point defect structures in β-(AlxGa1-x)2O3, quantitative STEM was performed by obtaining three requisite pieces of information:

HAADF atomic resolution images, the incident beam intensity, and sample thickness.

This process was completed by following the quantitative STEM method developed and described by LeBeau et al. in Ref. [63]. First, the signal from the incident beam was collected by scanning the electron beam directly on the HAADF detector. This scan produced a spatial intensity map of the detector and the vacuum, which was later

35 analyzed to determine the incident beam intensity and the background intensity, respectively. After, the beam was aligned on the optic axis and the HAADF detector was centered to ensure that the convergent beam electron diffraction pattern (CBED) was symmetrical to the detector geometry. Without varying any microscope parameters,

HAADF images were then acquired for normalization and a direct comparison to simulated images. Immediately following image acquisition, PACBED patterns were obtained from the same area for thickness determination. This acquisition involved replacing the HAADF detector with a charge-coupled device (CCD) camera and rapidly scanning the STEM probe while collecting CBED patterns. The resulting diffraction pattern is the averaged pattern from each probe position, termed PACBED pattern [64].

3.2.3 DLOS

For the determination of defect states and their concentrations in bulk β-Ga2O3,

DLOS was performed on Ni/Ga2O3 Schottky diodes on four different β-Ga2O3 substrates: n ~1 x 1017 cm-3 UID (010), n ~1.5 x 1018 cm-3 Sn-doped (201), n ~3.5 x 1018 cm-3 Sn- doped (010), and n ~5 x 1018 cm-3 Sn-doped (010). DLOS utilizes monochromatic sub- bandgap light to observe optically stimulated photoemission transients as a function of incident light energy [44, 45]. Here, light from a 1000W Xe-lamp was dispersed through a high-resolution monochromator to provide incident light from 1.2 eV to 5.0 eV in 0.02 eV steps, and photoemission transients were measured for 300 seconds.

3.3 Simulations

Essential to the confirmation of point defect formations and their correlation to measured properties are theoretical calculations. Here, image and diffraction simulations were performed to quantitatively assess defect formation in experimental HAADF images and to determine optimal STEM imaging conditions to uncover point defects. In addition,

DFT and molecular dynamics were used to calculate point defect and defect complex formation energies and functional states.

3.3.1 Multislice Algorithm

All STEM ADF image and diffraction simulations were performed using the multislice algorithm [60, 61] and carried out through the Ohio Supercomputer Center.

The spherical aberration coefficients, Cs3 = 0.002 mm and Cs5 = 1.0 mm, and the 300 kV accelerating voltage were used as microscope input parameters in the simulations. Other inputs, such as the modeled structure, convergence angle, and ADF detection angles, were specific to the individual studies and can be found in their respective chapters.

For the study of bulk β-Ga2O3, HAADF images of point defect complexes were simulated with various arrangements. HAADF simulations were also used in the quantitative STEM analysis of Al incorporation into β-(AlxGa1-x)2O3 thin films.

Additionally, PACBED simulations were utilized in the study. Furthermore, an entire examination of ADF image and diffraction simulations was carried out to identify

37 optimal imaging conditions for point defect observations. The methods used in this study are fully described in Chapter 6.

3.3.2 DFT

DFT calculations were utilized for identifying point defect complex formation energies and functional states. DFT atomistic simulations were based on hybrid functional calculations performed using the methodology as described in Ref. [41].

Arrangements of interstitial atoms and vacancies were modelled with a 160-atom supercell of bulk β-Ga2O3 and used in the simulations.

3.3.3 Molecular Dynamics

Similarly, the molecular dynamics (MD) method was applied to calculate the formation energies of point defect complexes in the β-Ga2O3 structure. These simulations were carried out using the LAMMPS package [81]. In this method, the short-range

Buckingham-type potential together with the Coulomb law are used to describe the interionic interactions for Ga and O rigid ions. The development, description, and application of the method can be found in Refs. [82, 83]. Formation energies were determined by calculating the energy difference of the system with and without the defect complexes. The MD simulations are fully described in Chapter 5.

Chapter 4: Unusual Formation of Point Defect Complexes in the Ultra-

Wide Band Gap Semiconductor β-Ga2O3

This chapter is presented in the form of the peer-reviewed journal article, J. M.

Johnson, Z. Chen, J. B. Varley, C. M. Jackson, E. Farzana, A. R. Arehart, H. Huang, A.

Genc, S. A. Ringel, C. G. Van de Walle, D. A. Muller, and J. Hwang, Unusual Formation of Point Defect Complexes in the Ultra-wide Band Gap Semiconductor β-Ga2O3, Phys.

Rev. X 9, 041027 (2019). The supplementary material is included in Appendix A.

4.1 Abstract

Understanding the unique properties of ultra-wide band gap semiconductors requires detailed information about the exact nature of point defects and their role in determining the properties. Here, we report the first direct microscopic observation of an unusual formation of point defect complexes within the atomic scale structure of β-Ga2O3 using high resolution scanning transmission electron microscopy (STEM). Each complex involves one cation interstitial atom paired with two cation vacancies. These divacancy- interstitial complexes correlate directly with structures obtained by density functional theory, which predicts them to be compensating acceptors in β-Ga2O3. This prediction is

39 confirmed by a comparison between STEM data and deep level optical spectroscopy results, which reveals that these complexes correspond to a deep trap within the band gap, and that the development of the complexes is facilitated by Sn doping through increased vacancy concentration. These findings provide new insight on this emerging material’s unique response to the incorporation of impurities that can critically influence their properties.

4.2 Introduction

Controlling point defects in crystalline materials can critically influence their properties, and it is therefore imperative to have well-controlled point defects to advance the materials for successful application. Point defects can be very diverse, both in terms of their structure and function. In particular, understanding the formation of point defect complexes, which may occur in response to impurity incorporation within the structure, is of great importance because of their versatile formations and influence on the materials’ properties. This is particularly the case in wide band gap semiconductors, where the intrinsic advantages of a large band gap and the possibility of high optical transparency

(e.g., in transparent conductive oxides or TCOs) are severely impaired by the presence of defects. For example, the large critical field strengths that can theoretically be supported in wide band gap semiconductors for applications in next-generation power electronics can be ruined by the presence of defects [84], and the existence of significant deep-level defect concentrations can severely degrade the optical properties of TCOs [27].

Additionally, the presence of impurities and the formation of various types of complexes in TCOs have been suggested to contribute to the observed intrinsic n-type behavior, difficulty in p-type doping, and low doping efficiency [33, 85, 86]. What has been missing in the field is direct experimental information on the detailed atomic scale structure of such complexes. Gaining this information is essential to exactly crosslinking theoretical predictions of complexes to measured properties of wide band gap semiconductors, which will then provide important guidance to the synthesis and doping of the material with precisely controlled properties. However, such information has been nearly unattainable because of the small (atomic scale) nature of the defect complexes, especially when they are buried within the three-dimensional material. These challenges have led to the lack of experimental information on how the complexes incorporate within the atomic scale structure and the inability to discover any unknown complexes that may critically affect the properties of the material.

Here, we present the first direct scanning transmission electron microscopy

(STEM) observation of the unusual formation of point defect complexes within the atomic scale structure of β-Ga2O3. Note that β-Ga2O3 is an excellent candidate for high performance electronic, optical, power device and sensor applications [1, 26, 87–94] due to its unique properties including an ultra-wide band gap of about 4.8 eV [15], optical transparency into the ultraviolet region [16], and high breakdown voltage [19]. However, advancing the material has been hampered by the lack of a detailed understanding of the formation of point defect complexes [17, 33, 39–41, 95, 96] and their impact on electrical and optical properties [35, 44, 97–99]. Using STEM, we discovered a new type of point

41 defect complex that involves one cation interstitial atom, which can be positioned at two of the five possible interstitial sites, paired by two cation vacancies. The structure of this unusual cation interstitial-divacancy complex is consistent with the predictions made by density functional theory (DFT). DFT also shows that this defect acts as a deep level and is the dominant compensating acceptor in β-Ga2O3; since β-Ga2O3 is n-type-doped for most applications, this defect therefore has a crucial impact on device performance.

Comparing the STEM data to deep level optical spectroscopy (DLOS) shows that formation of the defects is enhanced by increased Sn doping, confirming the compensating-acceptor character, with a defect level at EC – 2.0 eV. The present atomic scale investigation identifies this unusual defect as the origin of a number of previously unexplained phenomena in β-Ga2O3, and also sheds light on this material’s unique response to the incorporation of impurities that can critically influence its properties.

4.3 Direct Observation of Divacancy-Interstitial Complexes

First, we explain the observation of interstitial defects and defect complexes in

Sn-doped β-Ga2O3 bulk crystals (doping concentration of 8.5 x 1018 cm-3 yielding a carrier concentration of 8.2 x 1018 cm-3 [20, 100]). The unit cell of monoclinic β-Ga2O3 contains two crystallographically different Ga (Ga1, Ga2), and three oxygen atom positions (O1, O2, O3) as shown in Figure 18(a). The structure is oriented along [010]m, which is the orientation used throughout this study. Note that Ga1 and Ga2 have

Figure 18. Crystal structure and experimental image of β-Ga2O3. (a) Crystal structure of β-Ga2O3 along the [010]m direction with five possible interstitial sites (ia-e). (b) Atomic resolution HAADF-STEM image of a [010]m Sn-doped β-Ga2O3 bulk crystal from a defect free area.

tetrahedral and octahedral coordination, respectively. And, O1 and O2 have threefold coordination, while O3 has fourfold coordination. Figure 18(a) also shows five potential cation interstitial sites (ia-e). As will be explained in detail, these interstitial sites have been derived from both our experimental observation and DFT calculations [39, 40]. A high angle annular dark field (HAADF) STEM image (see Appendix A.1 for details) from the [010]m Sn-doped sample of a defect free region is shown in Figure 18(b). As

HAADF intensity depends on the atomic number, high intensity in this image mostly 43 arises from the scattering of the Ga1 and Ga2 columns while only very weak intensity is observed from O positions. Figure 19 shows the direct detection of interstitial defects and defect complexes in the same Sn-doped β-Ga2O3 bulk crystal. In the sample areas shown in Figure 19(a) (left and right), significant intensities were observed in multiple interstitial sites, in addition to Ga columns that are still positioned at their regular positions. Specifically, these noticeable intensities appeared in four distinct interstitial sites, termed ib-e [Figures 19(b)–19(e)]. Amongst them, the most prominent intensities were located in the ic site [Figures 19(c) and 19(f)]. We also note that these interstitial intensities were found to be clustered and concentrated in about 10 nm2 areas [Figure

19(g)]. Clustering likely happens along the direction parallel to the electron beam as well, which can be evidenced by the high interstitial column intensity [e.g., Figure 19(f)] indicating that there are likely multiple cation interstitial atoms along the column [56,

101]. Previous works have identified extended defects (e.g., twin boundaries and screw dislocations) [102–104] and some atomic scale defects [27, 105] in β-Ga2O3, but our present data from aberration corrected STEM provides the first direct identification of the exact positions of interstitial defects.

Figure 19 continued

Next, we identify the unique formation of point defect complexes from the

HAADF STEM intensities by directly correlating them with DFT calculations (see

Appendix A.1 for details). DFT calculations [17, 39, 41] have shown that cation vacancies have low formation energies under O-rich growth conditions, with tetrahedral

1 VGa being the most favorable. However, the vacancy on the tetrahedral Ga1 site was identified as metastable; the presence of the vacancy causes a neighboring Ga atom to leave its tetrahedral site (creating a second vacancy) and move towards an interstitial site

1 midway between the two vacancies, effectively resulting in a 2VGa – Gai complex (Figure

20). This complex is lower in energy than the isolated vacancy, and acts as a deep acceptor. Figure 20(a) shows how the adjacent Ga1 atom relaxes to the ic site, becoming

1 octahedrally coordinated and creating an additional VGa, which can be formed easily due to the relatively small energy barrier [39, 40]. These DFT results have also been utilized in recent β-Ga2O3 defect studies using electron spin resonance [47, 48] and infrared spectroscopy [49, 50] to attribute the presence of proton irradiation induced defects and implanted O-H bonds to the same point defect complexes. However, the direct

1 c confirmation of 2VGa – Gai complexes by STEM in β-Ga2O3 requires the detection of not only the cation interstitial atoms (explained above) but also the vacancies in the neighboring Ga columns. Identifying a single vacancy within an atomic column may not be trivial [106], however, the presence of several vacancies within a Ga column will decrease the overall HAADF STEM signal due to the loss of scattering from the absent

Ga atoms [107]. Image simulations performed using the multislice method [60] (see

Appendix A.1 for details) confirmed that the signal increases at interstitial sites from

47 cation interstitials and decreases at Ga1 sites from vacancies [Figures 20(b)–20(d)]. The loss of intensity for Ga1 columns neighboring interstitials was in fact observed in our experimental data. Individual line profiles in Figure 20(d) illustrate the reduced intensity of Ga1 columns adjacent to interstitials [Figure 20(c)] compared to Ga1 columns in a defect free region [Figure 20(b)]. The reduced intensity of Ga1 columns adjacent to interstitials was substantially more significant than the overall intensity decrease in the area (including the Ga2 columns that are not expected to be involved in the relaxation process) that may be caused by the strain [108] due to the interstitials (see Appendix A.2,

Table 2). Image simulations indicate that the effect of electron channeling from interstitials is minimal due to the considerable gap (~0.18 nm) between the interstitials and the adjacent Ga columns. Therefore, the substantial intensity decrease apart from the overall decrease due to strain in the Ga1 columns adjacent to interstitials suggests that vacancies are most likely present in those columns. Similarly, vacancy – interstitial

1 b complexes surrounding ib sites (2VGa – Gai ) were also observed [Figures 20(e)–20(h)].

Quantitative comparison of atomic column intensity to the image simulation can provide information on the number of defects located within each column (e.g., Ref. [101]).

Based on the experimental and simulation data (see Appendix A [109], Figure 43), the estimated number of complexes within these columns is about 10 (see Appendix A [109] for details).

Figure 20 continued

Considering the near-equilibrium growth condition of the edge-defined, film-fed growth (EFG) process used to grow these bulk crystals, the formation energy (ic < ib < ia), predicted by DFT [39], may directly correspond to the number density of each of those point defects within the material. Despite small sampling in STEM images [such as in

Figure 19(g)] the number densities of interstitials observed in the sampled region (ic = 1.6 x 1020 cm-3 > ib = 3.9 x 1019 cm-3 > ia = 0) appear to be consistent with the energetic favorability found in the DFT calculation. In fact, we have not observed any interstitial ia intensity above the threshold value in the sampled areas, which suggests the formation of ia interstitials may be much less likely than ib or ic. Based on the analysis of images with visible interstitials [e.g., Figure 19(g)], the estimated concentration of defect complexes is about 2 x 1020 cm-3 (see Appendix A [109] for details).

Although lesser in signal and fewer in total number, the interstitials observed in sites id and ie found in Sn-doped β-Ga2O3 display unexplored interstitial complexes that may be important in understanding the material’s properties. Interestingly, interstitial intensities in id and ie sites are always observed to be accompanied by interstitial

1 intensities in nearby ib and ic sites [Figures 19(d) and 19(e)]. This may imply that 2VGa –

b,c Gai complexes may facilitate the formation of other complexes that occupy the id and ie sites. The exact formation mechanism of id and ie defects and their implication to the properties remain to be further explored in the near future.

4.4 Effects of Sn Doping

The next question is then how Sn doping affects the formation of the interstitial point defect complexes shown above. In general, Sn impurities have been shown to contribute to the n-type behavior of β-Ga2O3, producing controllable carrier concentrations from 1016 up to 1019 cm-3 [20, 110]. Formation energy calculations have

51 indicated that Sn can easily be incorporated into β-Ga2O3 acting as a shallow donor and preferring to substitute in the octahedrally coordinated Ga2 site [17, 100]. In fact, our

STEM investigation has revealed several of these Sn substitutional atoms based on the high atomic column intensity in the HAADF mode [e.g., Figure 21(a)]. In addition to incorporating it as a substitutional dopant, Sn, when in high concentration, may promote the formation of the vacancy-interstitial complexes shown above. To verify this hypothesis, we first investigate unintentionally doped (UID) β-Ga2O3 (carrier concentration of 2.4 x 1017 cm-3 [20]) using HAADF STEM. UID β-Ga2O3 images revealed cation interstitials in the ic site [Figure 21(b)], which implies that the interstitials

1 may also be created via the same VGa migration mechanism explained above. A larger sampling resulted in the conclusion that these complexes exist lesser in quantity and smaller in intensity in comparison to Sn-doped β-Ga2O3. This result is consistent with the expectations that the incorporation of Sn donors that drive the material more n-type simultaneously stimulates the formation of the compensating acceptor species like the

1 2VGa – Gai complexes through the subsequent increase in vacancy concentration [39, 41].

Presuming a reduction in vacancy formation energy for increased Fermi level energy

[39], Sn doping facilitates this increase in vacancy concentration through the increase in

Fermi level energy. Additionally, Sn may also be incorporated as the cation interstitial,

1 forming 2VGa – Sni complexes. Its exact role will be discussed among the succeeding results.

Figure 21. STEM results for point defects and defect complexes in β-Ga2O3. (a) HAADF STEM image of an atomic column containing Sn dopants (purple triangle) in [010]m bulk Sn-doped β-Ga2O3. The inset shows the line profile along the dashed line in the figure. (b) HAADF STEM image of UID β-Ga2O3 showing interstitial defects with red arrows indicating detected Ga interstitials in the ic sites.

4.5 Deep Level Optical Spectroscopy

DLOS can reveal the rich spectrum of defect states throughout the large band gap

[44], by using monochromatic incident light as a function of energy to photo-emit trapped carriers to a band edge, which enables the determination of energy levels, concentrations, and optical cross-sections of deep states (see Appendix A.1 [44, 111, 112]).

Accompanying our STEM results and DFT calculations, the DLOS results are consistent with the role of Sn dopant concentration and the number of vacancy-interstitial complexes present. Most importantly, the concentration of the trap detected at EC – 2.0 eV shows a positive correlation with Sn concentration (Figure 22) and the trap has been shown to act as a deep acceptor [45]. This defect behavior is consistent with the

1 electronic state of the 2VGa – Gai complexes predicted by DFT, where levels associated with the expected ε(–2/–3) charge-state transition levels have been predicted to fall between EC – 1.9 and EC – 2.5 eV [39, 41]. The analogous ε(–/–2) levels calculated for

1 the 2VGa – Sni complexes are found to be in a similar energy range, at EC – 2.34 and EC –

2.89 eV for the ib and ic sites, respectively. The apparent defect concentrations obtained from DLOS represent the average over large areas (as opposed to the relatively smaller area observations of STEM) and are limited by the finite time response of the defects

[45]. Nonetheless, the positive correlation between the DLOS detected trap and doping concentration, along with the detection of this trap in UID β-Ga2O3, directly coincide with the observation of interstitials by STEM imaging, which affirms the physical source of the EC – 2.0 eV defect state to be the divacancy – interstitial complex.

Figure 22. DLOS as a function of Sn doping in bulk β-Ga2O3. The trap detected at EC – 2.0 eV shows a positive correlation with Sn concentration. 54

4.6 Cation Interstitial

It would be highly valuable to be able to distinguish whether the observed entities are

1 1 2VGa – Gai (spatially separated from donor impurities), or actual 2VGa – Sni complexes, since it could help identify strategies for controlling the compensating acceptor. The

1 proposed 2VGa – Sni acceptor complexes have also been suggested to contribute to compensation in Sn-doped β-Ga2O3 [113]. Our calculations show that these complexes

1 can readily form when VGa are nearby (calculated barriers less than 0.3 eV for an SnGa to be displaced to octahedrally coordinated interstitials adjacent to VGa1) and are quite stable, with calculated binding energies of at least 1.4 eV relative to isolated VGa and

SnGa species (see Appendix A [109], Figure 44). However, we expect that these complexes would need to form during growth, as Sn is not expected to be appreciably incorporated on the tetrahedral sites which is a prerequisite for their formation post- growth [17]. As mentioned above, determining the species of cation interstitials in Sn- doped β-Ga2O3 via HAADF STEM is difficult because variations in number and location make Ga and Sn interstitials indistinguishable (see Appendix A [109], Figure 43).

However, because DLOS results reveal the same trap (EC – 2.0 eV) in both UID and Sn-

1 doped β-Ga2O3 while DFT calculations predict different electronic states for 2VGa – Gai

1 and 2VGa – Sni complexes, the observed compensating acceptors correlate with native

1 2VGa – Gai complexes.

4.7 Conclusions

In summary, the STEM results provide the first observation of unusual divacancy- cation interstitial complexes, and the structure of the identified complexes matches with

DFT predictions that classify them as compensating acceptors. DLOS results further validated the formation of these complexes as the detected EC – 2.0 eV defect state shows a positive correlation with Sn doping. Sn was determined to facilitate the divacancy – interstitial complex development by increasing the Fermi level energy and subsequently increasing the vacancy concentration. These STEM results provide new important insight on the material’s unique response to the impurity incorporation that can significantly affect their properties, which can ultimately offer important guidance to the development of growth and doping of TCOs for novel applications. The observed complex is in essence a low-symmetry configuration of a cation vacancy. It will be highly interesting to explore, using computational theory and/or microscopy, whether vacancies in other materials can also spontaneously undergo such symmetry-breaking distortions.

4.8 Acknowledgements

S. A. R., C. V., and J. H. acknowledge support by the Department of Defense, Air

Force Office of Scientific Research GAME MURI Program (Grant No. FA9550-18-1-

0479). This work was performed in part at the Cornell PARADIM Electron Microcopy

Facility, as part of the Materials for Innovation Platform Program, which is supported by

56 the NSF under Grant No. DMR-1539918 with additional infrastructure support by Grants

No. DMR1719875 and DMR-1429155. S. A. R. acknowledges additional support from the DTRA under Grant No. HDTRA1-17-1-0034. DFT work was partially performed under the auspices of the U.S. DOE by Lawrence Livermore National Laboratory under

Contract No. DE-AC52-07NA27344, and partially supported by the Critical Materials

Institute, an Energy Innovation Hub funded by the U.S. DOE, Office of Energy

Efficiency and Renewable Energy, Advanced Manufacturing Office.

Chapter 5: Self-Created Cation Vacancies by Atomistic Relaxation

Adjacent to Defect Complexes in β-Ga2O3

This chapter is presented in the form of the Applied Physics Letters submission,

J. M. Johnson, H. Huang, J. Shi, Z. Chen, D. A. Muller, S. Graham, and J. Hwang, Self-

Created Cation Vacancies by Atomistic Relaxation Adjacent to Defect Complexes in β-

Ga2O3.

5.1 Abstract

We report the direct experimental observation of the creation of cation vacancies by atomistic relaxation adjacent to multiple point defects in β-Ga2O3. Combining the detailed analysis of scanning transmission electron microscopy data with molecular dynamics simulations, a stable complex is shown to form via the relaxation of a specific

Ga atom near the previously confirmed divacancy-cation interstitial complexes. The role of Sn-doping on the concentration of the complexes is discussed, along with their compensating-acceptor character. The detailed structure of the complexes revealed in this work can provide important guidance to the understanding of self-creation of point defects and their functional roles in β-Ga2O3.

5.2 Introduction

Essential to advancing crystalline materials for application is the manipulation of important properties through well-controlled point defects. This is particularly key in wide band gap semiconductors where point defects and their complexes display a wide range of atomic structures and functional states that critically influence the materials’ unique properties. Such is the case when large band gap materials contain native compensating defects that induce n-type or p-type doping problems [9, 12] or when optically transparent semiconductors (e.g., transparent conductive oxides or TCOs) have their optical properties compromised by the presence of deep-level defects [27].

Likewise, low doping efficiency and impurity contribution to intrinsic n-type behavior has been linked to the formation of defect complexes in TCOs [33, 85]. The crucial information needed to characterize these defects is the direct experimental information on their atomic structure, which has been challenging. This information is vital to bridging the theoretical predictions of complexes and a materials’ measured properties and ultimately, advancing wide band gap semiconductors through point defect control [114].

β-Ga2O3 is an ultra-wide band gap (UWBG) TCO primed for next generation high performance electronic, optical, and power device applications [87–90, 93, 94, 115, 116] but lacks the necessary insight into point defects needed for its development [117]. Its main advantages include a high breakdown voltage (6-8 MV/cm) [19] and a large band gap (~4.8 eV) [15] that produces optical transparency into the ultraviolet region [16].

Additionally, recent progress in bulk single crystal [20–22] and epitaxial film [23–25] β-

Ga2O3 growth techniques have presented a realistic opportunity to replace traditional semiconductors like GaN and SiC [26]. Despite these advantages, the lack of understanding and control of point defect complexes inhibits its progression. Theorized complexes in β-Ga2O3 [17, 33, 39, 40, 95, 96] are predicted to significantly impact its electrical and optical properties [35, 44, 99], but their detailed formations are largely unknown due to the absence of an atomic scale experimental characterization.

In this letter, we present the scanning transmission electron microscopy (STEM) direct observation of unusual defect complexes formed from atomistic relaxation adjacent to multiple point defects in β-Ga2O3. These new complexes result from the clustering of the previously theorized [39, 40] and recently directly detected [118] divacancy-cation interstitial complex. Here, we couple STEM and molecular dynamics simulations to reveal a stable complex, formed from the relaxation of a specific Ga atom near divacancy-cation interstitial complexes. We then discuss the role of Sn doping on facilitating their formation, explaining an increase in concentration due to an increase in the Fermi level energy. Finally, we describe the compensating-acceptor character of these defect complexes.

5.3 Self-Created Cation Vacancies by Atomistic Relaxation

First, we examine the STEM observation of interstitial defects in (2̅01) Sn-doped

β-Ga2O3 bulk crystals (doping concentration of 8.5 x 1018 cm-3 and carrier concentration of 8.2 x 1018 cm-3) fabricated by edge-defined, film-fed growth [20, 100]. The monoclinic

60 crystal structure of β-Ga2O3 is made up of two inequivalent Ga sites and three inequivalent O sites. The Ga sites have tetrahedral (Ga1) and octahedral (Ga2) coordination, and the O sites have threefold (O1, O2) and fourfold (O3) coordination. In

Figure 23(a), a β-Ga2O3 crystal orientated along the [010]m displays these sites along with potential cation interstitial sites (ia-e) that have emerged from theoretical predictions [39] and experimental observation [118]. Inset in the high angle annular dark field (HAADF)

STEM image of Sn-doped β-Ga2O3 in Figure 23(b) is a defect free region displaying high intensity from Ga columns and weak intensity from O columns as HAADF signal depends on atomic number. In the rest of the sample area in Figure 23(b), significant interstitial intensities were detected in sites ib-e, and their clustering revealed a compelling trend of id and ie interstitials accompanied by adjacent ic and ib interstitials, respectively.

Higher magnification examples of this notable coupling are also shown in Figure 23(c)

(for ic – id), and Figure 23(d) (for ib – ie). The trend of these coupling and their similar intensities suggests that there must be some type of interaction between these interstitial defects during their formation.

Figure 23. Crystal structure and experimental HAADF-STEM images of β-Ga2O3. (a) Crystal structure of β-Ga2O3 along the [010]m direction with five possible interstitial sites (ia-e). (b) Atomic resolution HAADF-STEM image of a [010]m Sn-doped β-Ga2O3 bulk crystal from a region with (inset) a defect free area and clustered interstitial defects. Magnified locations from image (b) with combinations of interstitial intensities located in the (c) 2ic – id sites and the (d) 2ib – ie sites.

Next, we analyze the HAADF-STEM interstitial and neighboring column intensities to determine the unique formation of point defect complexes. As explained above, seemingly necessary to the development of id and ie interstitials is the arrangement of two neighboring ic or ib interstitials. Previous DFT calculations have revealed ib and ic interstitials are created from the migration mechanism of cation vacancies that occupy the

1 energetically favorable tetrahedral Ga1 site [39, 41]. The presence of the VGa causes the neighboring Ga1 atom to migrate into the interstitial site (ib,c), halfway between the two

1 b,c Ga1 sites. The resulting 2VGa – Gai complex was shown to be stable as compared to a

1 lone VGa. In our recent report, these divacancy-cation interstitial complexes were directly observed by STEM through the detection of ib and ic interstitials and vacancies in

1 b,c neighboring Ga1 columns [118]. Using the previous confirmation of 2VGa – Gai complexes and the experimental HAADF STEM images that revealed the specific combinations of interstitials (Figure 23), we postulate an atomic scale formation for the

1 new complexes, 2ic – id and 2ib – ie (Figure 24). For 2ic – id [Figure 24(a)], two 2VGa –

c Gai complexes formed adjacent to each other [Figure 24(b)] cause a Ga2 atom, located between the complexes, to relax into the id site and subsequently produce an additional vacancy in the Ga2 site [(Figure 24(c)]. An equivalent mechanism is also suggested for

2ib – ie in Figures 24(d)–24(f). As the formation of 2ic – id and 2ib – ie would involve vacancies located in different Ga columns, the direct confirmation of these individual vacancies, in addition to the cation interstitials shown in Figure 23, is also necessary to confirm the suggested formation of the complexes. This verification is achieved through the analysis of the HAADF intensity as explained below. 63

Figure 24. (a–c) Formation of 2ic – id complexes. (a) A perfect lattice with the ic and id 1 positions identified. (b) A VGa (green font) induces the migration of the adjacent Ga1 into 1 1 the ic site (red arrow), creating an additional VGa (red font). When the resulting 2VGa – c 1 c Gai complex (yellow oval) is adjacent to another 2VGa – Gai complex of the same type, (c) a Ga2 atom located between the two complexes relaxes into to the id site (blue arrow) 2 and subsequently creates a VGa. (d–f) shows the equivalent mechanism for the formation of 2ib – ie complexes.

Figure 25(a) shows the model indicating the positions of the columns containing cation vacancies (columns with V) suggested by the mechanism shown in Figure 24. We plot line profiles of the intensity from the raw experimental HAADF image, shown in

Figure 25(b), to determine the differences in the intensity among the columns indicated in

Figure 25(a). Note that the intensity profiles shown here are averaged over the 20 defect areas marked in Figure 23. First, the profile across the orange line in Figure 25(b) (same as the line shown in [Figure 25(a)]) shows nearly equal intensity for both Ga2 columns

[Figure 25(c)], which is reasonable because both columns are not expected to be involved in the relaxation process. Meanwhile, the profile across the blue line shows the decreased intensity of the right Ga2 column (blue arrow), suggesting that the column contains vacancies, confirming the modeled relaxation suggested in Figure 25(a). Similarly, the profiles across the green and gray lines were lower than the orange line (defect-free), indicating vacancies within the Ga1 columns [Figure 25(d)]. And, the green and gray line profiles matching the right Ga2 column profile (blue arrow) suggests a similar concentration of vacancies exists in the Ga1 columns and the Ga2 column, which again confirms the formation of the 2ic – id complex modeled in Figure 25(a). Multislice image simulations [60] based on the model in Figure 25(a) were performed using a 25 nm thick crystal, as determined by PACBED, and 10 clustered defect complexes as described in

Ref. [118]. These simulations produced profiles similar to the experimental data [Figures

25(e)–25(g)]. The same trend was observed for the formation of 2ib – ie complexes

[Figures 25(i)–25(n)].

Figure 25 continued

5.4 Molecular Dynamics

Molecular dynamics simulations were carried out to gain insight on the formational stability of the modeled atomic arrangements. Utilizing the LAMMPS package, the short-range Buckingham-type potential together with the Coulomb law [82,

83] was used to describe the interionic interactions for Ga and O rigid ions and to ultimately, obtain formation energies for each complex. Formation energies were determined by calculating the energy difference of the system with and without vacancies

1 c [119]. For two 2VGa – Gai complexes formed adjacent to each other without the relaxation of the adjacent Ga2, as shown in Figure 24(b), the calculated formation energy was 46.365 eV, which was greater than the formation energy of 44.407 eV calculated for the 2ic – id complex modeled in Figure 24(c). This calculation confirms the energetic stability of the atomic relaxation producing a 2ic – id complex. The formation energies for

1 b two 2VGa – Gai complexes formed adjacent to each other [Figure 24(e)] and 2ib – ie

[Figure 2(f)] were nearly the same, 44.3649 and 44.3647 eV, respectively, showing a difference of only 0.0002 eV meaning the relaxation is possible but not as likely as the 2ic

– id.

5.5 Effects of Sn Doping

The defect complexes shown above were observed in Sn-doped β-Ga2O3, and we discuss the role of Sn doping to the formation of the complexes. Sn doping has been

68 shown to contribute to the n-type behavior in β-Ga2O3 [20, 100], but its effect on the formation of the complexes presented above arises from its influence on the vacancy concentration. DFT calculations have indicated that Sn prefers to substitute on the octahedrally coordinated Ga2 site [17], and STEM results have confirmed this theoretical prediction [118]. As a substitutional dopant, Sn acts as a shallow donor producing controllable carrier concentrations up to 1019 cm-3 [20, 110]. However, while increasing the carrier concentration, Sn doping is expected to simultaneously induce the increase in vacancy concentration. As the incorporation of Sn drives the material more n-type, the formation energy for cation vacancies decreases through the increase in Fermi level energy [39], thus, facilitating the increase in vacancy concentration. Additionally, recent experimental data comparing Sn-doped to unintentionally doped β-Ga2O3 has indicated that the defect complex concentration increases with Sn doping [118]. This evidence results in the conclusion that Sn doping stimulates the formation of the 2ic,b – id,e

1 complexes through the increase in VGa that initiate the complexes’ development. Yet,

1 b,c 2VGa – Gai complexes must be clustered (i.e. adjacent to each other) for the new complex to form. And, while the increase in vacancy concentration makes their formation more likely, the source of their clustering requires further investigation.

5.6 Functional Behavior

Understanding the functional behavior of 2ic,b – id,e complexes is key to gaining insight on the influence of doping on β-Ga2O3’s unique properties. In our previous work,

1 b,c the defect behavior of 2VGa – Gai complexes was identified by correlating STEM, DFT,

1 b,c and deep level optical spectroscopy (DLOS) results [118]. The 2VGa – Gai complex was determined to be the physical source of an EC – 2.0 eV defect state [45], which acts as a compensating acceptor in β-Ga2O3. Now, the eminent question is how does the relaxation of the Ga2 site atom into the id,e site affect the 2ic,b – id,e defect’s electronic state. As

1 b,c depicted above, a Ga2 atom located between two 2VGa – Gai complexes has moved into the id,e and created a residual vacancy in the Ga2 site. This migration likely acts to both break original oxygen bonds and eliminate dangling oxygen bonds that were created from the initial cation vacancy and Ga1 migration, preserving the octahedral coordination of

1 b,c the relaxed Ga2 atom. Consequently, the 2VGa – Gai complexes are still expected to contribute to compensation in β-Ga2O3.

In summary, STEM data was analyzed to reveal the structure of new 2ic,b – id,e defect complexes that form when two adjacent divacancy-cation interstitial complexes cause an atomistic relaxation. Molecular dynamics simulations validated the formation of these complexes, establishing their stable configuration. The creation of the defect complexes was determined to be facilitated by Sn doping through the increase in vacancy concentration. Counteracting donor Sn, the 2ic,b – id,e defect complex likely shows the

1 b,c same compensating acceptor behavior as the 2VGa – Gai complexes. Interestingly, these complexes are the energetically stable configuration of cation vacancies. This type of

STEM study provides critical information on atomic scale defect structures that can be used to observe new types of defect complexes in TCOs and wide band gap materials. It will continue to be imperative to establish the connection between point defects and 70 defect complexes, like those described here, to properties to advance these materials for application.

5.7 Acknowledgements

S.G. and J.H acknowledge support by the Department of Defense, Air Force

Office of Scientific Research GAME MURI Program (Grant No. FA9550-18-1-0479).

This work was performed in part at the Cornell PARADIM Electron Microcopy Facility, as part of the Materials for Innovation Platform Program, which is supported by the NSF under DMR-1539918 with additional infrastructure support from DMR1719875 and

DMR-1429155.

Chapter 6: Al Distribution and Point Defect Complexes in β-(AlxGa1-

x)2O3 Films

This chapter is presented in the form of the Applied Physics Letters submission,

J. M. Johnson, H. Huang, A. F. M. A. U. Bhuiyan, Z. Feng, N. K. Kalarickal, S. Rajan,

H. Zhao, and J. Hwang, Al Distribution and Point Defect Complexes in β-(AlxGa1-x)2O3

Films. The supplementary material is included in Appendix B.

6.1 Abstract

Band gap engineering in semiconductor materials requires a detailed understanding of the point defects that play a key role in determining their properties.

Here, point defects in β-(AlxGa1-x)2O3 films are investigated at the atomic scale using quantitative STEM to explain its growth difficulties. A quantitative STEM analysis of atomic column intensity indicates that 54% of the incorporated Al substitutes on the octahedrally coordinated Ga2 site. This result evidences higher energy structures, leading to the inability to grow β-(AlxGa1-x)2O3 films at high Al concentrations. Additionally, divacancy-interstitial complexes are observed, showing potentially detrimental effects to the film’s properties.

6.2 Introduction

Fundamental to band gap engineering in semiconductor materials is the precise control of point defects. Point defects critically influence the important transport and optical properties in semiconductors, and their incorporation is particularly vital to developing tunable band gaps through alloying. Decades of progress has proven the viability of alloying to achieve semiconductor materials with desired band gaps for various electronic and photonic applications. Still, exact control of point defects in these materials, such as the alloying element distribution and segregation [120–122] and alloying induced point defect creation [123, 124], remains pivotal to their advancement.

Stemming from their atomic scale nature, a detailed understanding of the point defects in alloyed semiconductors has been limited due to the lack of direct experimental information needed for their characterization. Obtaining this information will provide guidance to the synthesis of band gap engineered semiconductor materials with desired properties.

Emerging as the next semiconductor material for electronic, optical, and power device applications [1, 87, 88, 90, 92–94], the transparent conductive oxide β-Ga2O3 exhibits tremendous potential because of its unique properties and tunable band gap.

Arising from its wide band gap of 4.8 eV [15], β-Ga2O3 shows optical transparency into the ultraviolet region [16] and a high breakdown field[19]. These unique properties make

β-Ga2O3 a candidate material for high power electronics [88, 89] and deep ultraviolet photodetectors [125]. However, realizing its full potential as a semiconductor material

73 requires the manipulation and control of its band gap, which could enable novel heterostructure designs for carrier confinement and field effect transistors or deep UV optoelectronic devices.

To widen its band gap, β-Ga2O3 can be alloyed with Al2O3 [38, 126]. While exhibiting a bandgap of 8.8 eV, Al2O3’s ground state crystal structure is the corundum phase [127], much different than the monoclinic (β) phase of ground state Ga2O3 [128].

Despite their difference in crystal structure, (AlxGa1-x)2O3 is expected to prefer the monoclinic phase for up to 71% Al incorporation [38]. Recent efforts to grow β-(AlxGa1- x)2O3 with high Al composition have resulted in poor film quality or phase transformations [25, 37, 117, 129–133], ultimately demonstrating the inability to control point defects and to incorporate the theoretical maximum Al content while maintaining the β phase. These limitations have evidenced the need for a direct point defect characterization in β-(AlxGa1-x)2O3 thin films.

In this letter, we report the quantitative scanning transmission electron microscopy (STEM) analysis of point defects in β-(AlxGa1-x)2O3 thin films. To start, we analyze the substitutional Al-alloy incorporation in molecular beam epitaxy (MBE) and metal organic chemic vapor deposition (MOCVD) grown films using the quantitative

STEM method. The Al concentration at each substitutional cation atomic site is quantitatively determined to understand their distribution and effect on growth. Next, we show the direct observation of the previously identified unusual point defect complex

[118], resulting from the migration mechanism of a Ga vacancy, and discuss its role as a compensating-acceptor in the β-(AlxGa1-x)2O3 thin films.

6.3 Al Site Distribution

First, the epitaxial growth of (010) β-(AlxGa1-x)2O3 thin films is confirmed using

STEM. As determined by XRD, an (010) β-(Al0.22Ga0.78)2O3 and an (010) β-

(Al0.4Ga0.6)2O3 thin film were produced by MBE and MOCVD [25], respectively, on Fe- doped (010) β-Ga2O3 substrates. In Figure 26, high angle annular dark field (HAADF)

STEM images show the epitaxial growth of the (010) β-(AlxGa1-x)2O3 thin films. The film layer, which exhibits the same orientation as the substrate, displays dark contrast, confirming Al incorporation. However, while the β-(Al0.22Ga0.78)2O3 film displayed a complete epitaxial growth of 20 nm [Figure 26(a)], the β-(Al0.4Ga0.6)2O3 film showed an average thickness of 10 nm before undergoing a rotation or a phase transformation, which produced the bright contrast seen above the film in Figure 26(b).

Next, we analyze the Al distribution in cation sites using quantitative STEM to explain the abrupt discontinuation of the (010) β-(Al0.4Ga0.6)2O3 film growth and the general inability to grow epitaxial β-(AlxGa1-x)2O3 thin films at high Al concentrations.

The monoclinic crystal structure of β-Ga2O3 consists of two inequivalent cation environments: a tetrahedrally coordinated (Ga1) and an octahedrally coordinated (Ga2) site. In Figure 27(a), a β-Ga2O3 crystal oriented along the [001]m displays their positions.

The atomic resolution HAADF STEM images used to quantitatively assess the Al incorporation in our β-(AlxGa1-x)2O3 films are shown in Figures 27(b) and 27(c). These images reveal the Ga1 and Ga2 columns, which display high intensity as compared to the

O columns due to the HAADF intensity dependence on atomic number. The decrease in column intensity from the lighter substitutional Al in the β-(AlxGa1-x)2O3 films is clearly visible in the images. To quantitatively analyze each column intensity, we performed quantitative STEM, as described in Ref. [63], utilizing multislice simulations [60]. Inset in Figure 27(b) and 27(c), position averaged convergent beam electron diffraction

(PACBED) patterns revealed the cross-sectional thickness of the β-(Al0.22Ga0.78)2O3 and

β-(Al0.4Ga0.6)2O3 films to be about 16.8 and 18.5 nm, respectively. The quantitative comparison between experimental and multislice simulated column intensities (see

Appendix B for details) indicated that the average Ga2 site contained 24.0% Al in the β-

(Al0.22Ga0.78)2O3 film and 44.5% Al in the β-(Al0.4Ga0.6)2O3 film, while the Ga1 site contained 20.5% and 38.0% Al in the respective films. This result reveals that the overall concentrations of the films are x = 0.22 and 0.41, verifying the XRD measurements. The site preference for Al substitution versus the Al composition of the film is shown in

Figure 27(d). Most importantly, the quantitative STEM comparison indicated that Al only slightly prefers the octahedrally coordinated Ga2 site, at an occupancy of 54% in both films, regardless of the overall Al composition.

Figure 27. (a) Crystal structure of β-Ga2O3 along the [001]m direction. (b) and (c) HAADF STEM images of (b) β-(Al0.22Ga0.78)2O3 and (c) β-(Al0.4Ga0.6)2O3 films used for the quantitative analysis of Al site occupancy. Inset are the experimental PACBED patterns acquired from the β-Ga2O3 substrate and the corresponding multislice simulated patterns, indicating a 16.8 nm and 18.5 nm thick TEM sample for the β-(Al0.22Ga0.78)2O3 and β-(Al0.4Ga0.6)2O3 films, respectively. (d) Quantitative STEM data showing the Al site occupancy (%) in the Ga1 (red x) and Ga2 (blue x) sites versus the Al composition of the film.

Figure 27 continued

The nearly equal distribution of Al in the cation sites suggests that the lack of control of Al inhibits β-(AlxGa1-x)2O3 film growth. Recent density functional theory

(DFT) calculations have suggested that Al energetically prefers the octahedral coordination of the Ga2 site and is expected to completely inhabit the position in β-

AlGaO3 alloys, only occupying the Ga1 site for x > 50%. This arrangement of Ga and Al in alloyed films was predicted to produce stable β-(AlxGa1-x)2O3 for up to x = 0.71 [38].

However, we show that Al only slightly favors the Ga2 site in both the β-(Al0.22Ga0.78)2O3 and β-(Al0.4Ga0.6)2O3 films [Figure 27(d)], with about 45% of the Al occupying the energetically unfavorable Ga1 site. As the Al concentration or the film thickness increases, the total number of Al substituting on the Ga1 site increases, leading to a structure with higher energy. Thus, we conclude that the lack of control of the Al is what likely leads to the phase transformations or rotations of the films and ultimately, the

78 inability to grow β-(AlxGa1-x)2O3 films with high Al concentrations. We note that the growth method does not affect the Al site occupancy.

6.4 Divacancy-Interstitial Complex

Here, we explain the direct observation of interstitial defects and defect complexes that form in the β-(AlxGa1-x)2O3 films. Figure 28(a) shows the β-Ga2O3 crystal structure along the [001]m imaging orientation, with the position of the most probable interstitial defect, which has been derived from theoretical studies [39, 40] and our previous experimental observations [118]. Termed ic, this interstitial site is located directly between two Ga1 atoms. Note that in the [001]m cross-section, the ib interstitial site, also theorized and observed, displays the same position as the ic site, making the ability to distinguish between the two challenging. Throughout this study, we refer to the site as the more probable ic but acknowledge the possibility of ib site interstitial defects.

HAADF images in Figures 28(b) and 28(c) show significant intensities in the ic site in both films. Additionally, a string of ic site intensities were observed in the β-

(Al0.4Ga0.6)2O3 film [Figure 28(d)]. Unlike the interstitial intensities in Figures 28(b) and

28(c), several ic interstitials amongst the string display high intensities and show distinct decreases in adjacent Ga1 site intensity. We also note that clustering of interstitial defects likely occurs along the direction parallel to the electron beam, due to the observed high interstitial column intensities.

Figure 28. Direct detection of interstitial intensities in β-(AlxGa1-x)2O3 films. (a) Model of [001]m β-Ga2O3 indicating the position of the ic interstitial site. HAADF images from (b) β-(Al0.22Ga0.78)2O3 and (c) β-(Al0.4Ga0.6)2O3 films with significant intensities in the ic site (red arrow). (d) A string of clustered ic interstitials with fluctuating intensities in the β- (Al0.4Ga0.6)2O3 film.

The direct identification of the interstitial defect positions and their influence on neighboring column intensities correlates to our previous work, where we observed the unique formation of point defect complexes in β-Ga2O3. Discovered by DFT calculations, the ic interstitial originates from the migration mechanism of energetically favorable Ga1 vacancies [39]. As shown in Figure 29(a), a Ga1 vacancy initiates the migration of the

1 c adjacent Ga1 atom into the ic site, producing an energetically stable 2VGa – Gai complex.

Several β-Ga2O3 studies have attributed their defect detection to the same point defect complex [47–50], and our recent work has provided the direct observation of the complex

[118]. Previously, the complex was observed in bulk β-Ga2O3 along the [010]m imaging orientation through the detection of not only the interstitials, but also the vacancies in corresponding columns. Here, confirming the decrease in Ga column HAADF STEM signal due to the presence of vacancies becomes problematic because of the Al incorporation. As vacancies and Al positioned in Ga columns both act to decrease the overall intensity of the column and because Al is shown to occupy the Ga1 site, it is challenging to determine the origin of the intensity decrease in Ga1 columns next to interstitial intensities. Such is the case in Figure 29(b), where the neighboring Ga1 columns display decreased intensity and Al containing Ga2 sites nearby (yellow circles) also show a reduction in column intensity. However, the presence of vacancies was confirmed by observing an entire column of defects as shown in Figure 29(c). The increased intensity of the ic interstitial coupled with the complete loss of neighboring Ga1 column intensity confirms the presence of vacancies and reveals an entire column of

81 defects through the 18.5 nm thickness of the sample. Therefore, we confirm the existence

1 c of the 2VGa – Gai complex in the β-(AlxGa1-x)2O3 films.

6.5 Defect Complex Functional Behavior

Lastly, we discuss the significance of the complex on the properties of β-(AlxGa1-

1 c x)2O3 films and what factors influence its concentration. Previously, the 2VGa – Gai complex was determined to be the physical source of a deep trap, acting as a compensating acceptor in β-Ga2O3 [118]. In high concentrations the complex may significantly reduce the conductivity of the film and thus, it is critical to identify the influence of Al incorporation on its development. Based on images acquired over several different areas, the concentration of the defect complex was found to be greater in the β-

(Al0.4Ga0.6)2O3 film as compared to the β-(Al0.22Ga0.78)2O3 film, signifying the increase in cation vacancies with increasing Al concentration. This type of response to alloying has previously been reported in wide band gap semiconductors [124, 134]. Additionally, the same response is expected for n-type doping of the film, which will be required for

1 c application. The high concentration of the 2VGa – Gai complex in the β-(Al0.4Ga0.6)2O3 film, expected to increase with higher Al incorporation and doping, could be detrimental to the properties of the film.

6.6 Conclusion

In conclusion, the STEM investigation of point defects in β-(AlxGa1-x)2O3 films at the atomic scale revealed two important results: (i) an almost equal distribution of Al between the Ga1 and Ga2 sites, and (ii) the formation of a point defect complex that varies

83 with Al composition. The quantitative STEM Al site occupancy analysis indicated that

54% of the incorporated Al occupied the octahedrally coordinated Ga2 site, conflicting with theoretical calculations and likely leading to the inability to grow epitaxial β-

1 c (AlxGa1-x)2O3 films at high Al concentrations. Additionally, the 2VGa – Gai complex was directly observed in the films and showed an increase in concentration with Al. Acting as a compensating acceptor, the complex may be detrimental to the films properties when doping for application. This type of STEM study provides critical atomic scale information on point defect incorporation in band gap engineered semiconductors that can ultimately be used to guide the synthesis of the materials with desired properties.

See Appendix B for details about the quantitative STEM comparison of experimental and multislice simulated images.

6.7 Acknowledgements

S.R., H.Z. and J.H. acknowledge support by the Department of Defense, Air

Force Office of Scientific Research GAME MURI Program (Grant No. FA9550-18-1-

0479). This work was performed in part at the Penn State University Materials

Characterization Lab.

Chapter 7: Three-Dimensional Imaging of Individual Point Defects

Using Selective Detection Angles in Annular Dark Field Scanning

Transmission Electron Microscopy

This chapter is presented in the form of the peer-reviewed journal article, J. M.

Johnson, S. Im, W. Windl, and J. Hwang, Three-Dimensional Imaging of Individual

Point Defects using Selective Detection Angles in Annular Dark Field Scanning

Transmission Electron Microscopy, Ultramicroscopy 172, 17 (2017). The supplementary material is included in Appendix B.

7.1 Abstract

We propose a new scanning transmission electron microscopy (STEM) technique that can realize the three-dimensional (3D) characterization of vacancies, lighter and heavier dopants with high precision. Using multislice STEM imaging and diffraction simulations of β-Ga2O3 and SrTiO3, we show that selecting a small range of low scattering angles can make the contrast of the defect-containing atomic columns substantially more depth-dependent. The origin of the depth-dependence is the de- channeling of electrons due to the existence of a point defect in the atomic column, which 85 creates extra “ripples” at low scattering angles. The highest contrast of the point defect can be achieved when the de-channeling signal is captured using the 20-40 mrad detection angle range. The effect of sample thickness, crystal orientation, local strain, probe convergence angle, and experimental uncertainty to the depth-dependent contrast of the point defect will also be discussed. The proposed technique therefore opens new possibilities for highly precise 3D structural characterization of individual point defects in functional materials.

7.2 Introduction

Recent advances in transmission electron microscopy (TEM), such as aberration correction, have enabled imaging of materials with sub-Angstrom lateral resolution, and delivered significant impact to many disciplines of science. The next phase of electron microscopy must involve fully understanding the complex process of electron-sample interaction and developing new ways to extract maximal information about the materials’ structure from the data. For example, modern electron microscopy can significantly benefit the direct characterization of point defects in materials. Point defects have played a major role in tuning the electronic and optical properties of semiconductors over the last few decades, and the ability to control individual point defects will continue to be an essential part of the development of the next-generation functional materials (e.g., [135,

136]). To control individual point defects, it is required to determine the exact location, distribution, segregation, or clustering of the point defects, and understand how they

86 affect the local structure and properties. While there are indirect spectroscopic methods that can estimate point defect concentrations (e.g., [137]), establishing the direct relationship between the detailed structural aspects of point defects and the properties of the material has been challenging. With unmatched spatial resolution, TEM-based techniques, including scanning TEM (STEM) [56, 67, 138–142] and electron energy loss spectroscopy [143–146], have been able to detect the impurity atoms in crystals. The remaining important task is to obtain the exact depth information of the point defect along the beam direction in TEM. The depth information is required to determine the 3D positions of individual point defects, which, for example, is necessary to reveal their clustering or segregation at surfaces or interfaces that may decide whether they are electronically active or not. The aforementioned 3D information is also important to determine how the point defects are related to other important aspects in the structure, such as bonding distances, local lattice distortion, and extended defects in crystals.

Acquiring the true 3D information of atomic scale defects using electron microscopy can therefore significantly advance our knowledge in many areas of materials research.

Efforts have been made to acquire the depth information of individual atoms in the past using STEM [67–69, 147]. In STEM, increasing the probe convergence angle should ideally increase the depth resolution and therefore STEM imaging using highly converged probes should be able to provide 3D atomic scale information. However, even with the largest convergence half angle currently possible (~ 30 mrad), the depth resolution still remains above ~ 5 nm, far greater than the size of an atom. To increase the limit of depth information in STEM, focal series imaging with confocal configurations

87 have been studied [148–152]. An alternative approach is to utilize the incident electron channeling effect in the crystal to obtain important depth information. When a converged probe enters a crystal matrix, the probe intensity oscillates as the electrons pass through the sample along the depth direction [67, 68, 153, 154]. The oscillation results in the difference in the amount of electron scattering that occurs at the position of each atom along the depth direction. Therefore, the exact understanding of how probe channeling occurs in a certain crystal should allow for identifying the depth position of the atomic scale object based on the final image intensity. In other words, the probe oscillation can provide the ability to “resolve” the depth information of the atomic scale object. This method has been used to visualize the atomic structure buried at interfaces [155], and to determine the depth positions of the individual heavier dopants in a crystal [67, 70]. One of the key advantages of this method is that it only needs a single scan of the probe on the sample, hence it can minimize the complications that arise due to multiple scans of the probe in focal series imaging, such as sample drift or radiation damage. Furthermore, while a thin TEM sample is still necessary, the sample can be as thick as a few to ten nanometers, depending on the material [56, 67, 70, 156]. Recent reports have demonstrated that preparing such high quality thin TEM samples from a bulk (or thin film) would require the mechanical wedge polishing technique [67, 70, 156] or gentle crushing (or cleaving) method [69], rather than the use of the more popular focused ion beam method.

In general, the 3D characterization of point defects using probe oscillation information should satisfy two main experimental requirements: (i) a fully quantitative

88 comparison between the experimental and theoretical image intensities, and (ii) the exact knowledge about the thickness of the sample area that is being scanned. The former has been realized using the quantitative STEM technique [59] based on the exact calibration of the annular dark field (ADF) detector and multislice STEM simulations, and the latter is possible by simultaneously acquiring position averaged convergent electron beam diffraction patterns [64] during imaging. Recently, using probe oscillation information combined with quantitative STEM, Hwang et al. have shown that the depth of individual

Gd dopant atoms in the Sr columns of SrTiO3 could be determined with depth uncertainty less than ±1 unit cell [67]. Among the atomic number (Z) based heavier dopant imaging, this has shown the smallest Z-number ratio between the dopant (64Gd) and the host (38Sr) so far. The authors also found that ultimately the dopant depth precision is limited by the experimental errors, which may include sample drift, surface roughness, scan distortion, and Poisson noise. A subsequent report by Zhang et al. [70] has shown that the depth precision can be further increased using the signals from multiple ADF detection angles, as the dopants in different depths may scatter in different angles. These results have a couple of important implications: first, the ADF detection angles can be optimized to maximize the depth dependence of the point defect contrast in the image, and second, theoretical calculation of the image intensity and probe channeling behavior should play a critical role in the prediction and interpretation of the point defect imaging.

While detecting heavier dopants has been possible using Z-contrast imaging combined with probe oscillation information, detecting vacancies and lighter dopants, including their 3D positions, has remained difficult, as the exact understanding of the

89 contrast of the atomic columns including them has been lacking. In this paper, we report a new STEM imaging mode that can realize the 3D characterization of vacancies, lighter and heavier dopants. Using multislice STEM image and diffraction simulations, we show that selecting a small range of detection angles (with about 10 mrad in width) can make the contrast of the defect-containing atomic columns substantially more depth-dependent.

We also show that the low angle ADF (LAADF) signals (e.g., 20-40 mrad) are particularly sensitive to the depth of vacancies and lighter dopants, while high angle ADF

(HAADF) (e.g., 100-150 mrad) signals are more sensitive to the depth of heavier dopants. The simulated images from the atomic model, relaxed using ab initio calculation, also show that our new method is largely robust against the local distortion

(the displacement of nearby atoms) surrounding the point defect. We will also discuss potential ways to realize such selective detection angles in real experimental setups, and consider the maximum allowable experimental uncertainty that can enable indisputable identification of the depth positions of individual point defects.

We used β-Ga2O3 and SrTiO3 for this simulation study. β-Ga2O3 is a transparent conductive oxide (TCO) with an ultra-wide band gap (UWBG) of about 4.9 eV [15]. β-

Ga2O3 is effectively a direct band gap material [17] that shows transparency up to ultraviolet (UV) regions [16] and has a high break down voltage [19]. It is also available as a high quality single crystal substrate that can be prepared using conventional bulk growth methods [157]. Due to these unique advantages, β-Ga2O3 has recently gained significant attention for high-performance, high-efficiency UWBG applications, such as

UV transparent electrodes, high-power and high-voltage field effect transistors, and

90 photodetectors (e.g., [91, 92]). As in other TCOs, the transport and doping properties of

β-Ga2O3 is significantly affected by the types of point defects in it [44]. Undoped β-

Ga2O3 typically shows n-type behavior. Unlike in some other TCOs, however, the oxygen vacancies may not be the direct reason for the intrinsic n-type behavior because they are deep donors in β-Ga2O3 [17, 39, 96]. Instead, unintentionally doped (UID) impurity atoms, such as Si [99] and H [39, 95], may be the source of the n-type behavior.

Such UID impurities can also have close relationship to cation (Ga) vacancies.

Understanding the details of the point defect complexes and how they are connected to the local lattice distortion [33] and electronic properties can therefore open new possibilities of tuning the material’s properties for many important UWBG applications.

From a structural point of view, the low-symmetry (monoclinic) structure of β-Ga2O3 provides a unique opportunity to study the effects of orientation on probe channeling and dopant contrast in the STEM image. Here we studied the change in the LAADF and

HAADF intensities of the columns in β-Ga2O3 containing cation vacancies, or common impurity atoms, such as the substitutional Si and Nd [158]. Some of the important results that we acquired, such as the ripple effect at low scattering angles, were also confirmed using a more widely studied higher-symmetry crystal, SrTiO3.

7.3 Simulation Details

All STEM ADF image simulations were performed using the multislice algorithm

[60] with thermal diffuse scattering (TDS) based on the frozen phonon approximation at

298 K. The root mean square (RMS) deviation values of the thermal vibration of β-Ga2O3 were taken from Ahman et al. [128]. For each image simulation with TDS, ten images, each having twenty frozen phonon configurations, were first simulated in parallel, and then averaged to increase statistical reliability, unless stated otherwise. This should be statistically equivalent to simulating one image with two hundred phonon configurations, but ten times faster. The uncertainty of the averaging is presented with the standard deviation of the mean (SDOM) [159]. The image simulations used 1024 by 1024 real and reciprocal space sampling, with the aberration parameters of our probe corrected FEI

Titan STEM (Cs3=0.002 mm, Cs5=1.0 mm) at an acceleration voltage of 300 kV. Two convergence half angles, 9.6 and 20.0 mrad, were tested. The convergent beam electron diffraction (CBED) simulations were performed with and without TDS. For CBEDs with

TDS, 1,000 frozen phonon configurations were used.

β-Ga2O3 has space group C 2/m (monoclinic) (Figure 30a). Among the three

<100> axes, we selected the monoclinic [010] [Figure 30(b)] and [001] [Figure 30(c)]

(therefore [010]m and [001]m, respectively) as the imaging orientations for this study.

[100]m was not used because the atomic columns in the image would overlap significantly and may complicate the analysis [Figure 30(d)]. As shown in Figure 30, the

[010]m orientation will have the largest gap between the Ga atoms in the image

(interatomic distance ~3.3 Å), but it will have a relatively short (3.04 Å) interatomic distance along the column (beam direction). The [001]m orientation has tighter distances between the columns in the image [Figure 30(c)] but has longer interatomic distance along the beam direction (5.8 Å). As we will discuss in Section 7.4.4, the interatomic

92 distance along the beam direction significantly affects the probe channeling oscillation and therefore affects the usable sample thickness range in point defect imaging. Ga atoms exist in two different positions in β-Ga2O3: one in the octahedral and the other in the tetrahedral [Figure 30(b)]. While such distinction in Ga positions may be important for studying point defect complexes (e.g., [96]), it carries little importance for the present study as we found that those two positions do not show a significant difference in point defect contrast or probe channeling oscillation. Therefore, we only show the results from the point defects positioned at the octahedral Ga positions in this paper. Sample thicknesses of 33 and 55 Å were used for [010]m orientation, and 60 and 119 Å were used for [001]m orientation.

Figure 30. Crystal structure of β-Ga2O3 in a (a) perspective view, along (b) [010]m, (c) [001]m, and (d) [100]m view. Green spheres are Ga atoms and red spheres are oxygen atoms. 7.4 Results

7.4.1 Achieving Depth-Dependent Vacancy Contrast Using LAADF STEM

We first show the image simulation along the [010]m orientation (Figure 31).

Simulations were carried out using different ADF detection angles for single vacancies placed in the Ga atomic column [Figure 31(a)] at each depth position (1-11). An example of the resulting HAADF STEM image is shown in Figure 31(b). The white arrow indicates the column containing the vacancy. The dotted red circle indicates the area where we averaged the intensity for the column. This column-averaged intensity is 94 especially useful for the analysis of experimental images, as it tends to reduce the random experimental errors [67, 160]. Column-averaged intensity is also independent from how we select the area. Here we selected the circular area that covers the Ga atomic column, but not the nearby oxygen columns. The intensity is unit-less since it is a fraction of the incident beam. Figures 31(c)–31(e) show the column-averaged intensity as a function of the depth position of the vacancy along the column (red curve), as compared to the intensity of the column with no vacancy (blue curve). Figure 31(c) shows column- averaged intensity vs. depth using the typical HAADF detection angle range, which is also the range used in previous quantitative STEM work [59, 67, 70] (the actual range used in the experiment was 60–380 mrad, but there is almost no intensity beyond 170 mrad). While the vacancy-containing column intensity is significantly lower than that of normal columns (without vacancy), the intensity profile is essentially independent of the vacancy depth position. This is in fact a problem, because it will be impossible to distinguish the vacancy in the bulk from the vacancy on the surface, which is not even distinguishable from the atomic scale surface roughness that may be present on the sample surface. The trend shown in Figure 31(c) is also different from the heavier atom

(Gd) in a lighter host (Sr) observed previously [67, 70], where the column intensity increases monotonically as a function of the dopant depth position. The dissimilar trends between the heavier dopant and vacancy is due to the difference in the way they affect the probe channeling oscillation, which we will discuss in Section 7.4.6. On the other hand, when using a smaller angle range in HAADF, 100 to 150 mrad [Figure 31(d)], the profile becomes slightly more depth-dependent, showing a small decrease at ~24 Å depth. The

95 amount of the intensity decrease is about 7%, which may be detectable depending on the amplitude of experimental errors. However, when LAADF angles (20–100 mrad) are used, the intensity decrease is more prominent than in HAADF. At ~20 Å depth, the intensity drops by about 10% of the intensity of the cases where the vacancies are positioned at either surface. This implies that, unlike detecting heavier dopants using

HAADF imaging [56, 67, 69, 70, 152], vacancies in the bulk can be more easily detected using LAADF angles. In Section 7.4.2, we will show that the contrast of the defect- containing column can be further enhanced if we choose a smaller detection angle range in LAADF. But first, we will show why the LAADF signal can be more sensitive to vacancy depth position using CBED simulation.

Figure 31. (a) Schematic of β-Ga2O3 used in the simulation along the [010]m beam direction. Vacancies were placed one-by-one at the positions indicated along the depth, 1 to 11. (b) An example simulated image using a HAADF detection angle (60-170 mrad). The arrow indicates the column containing the vacancy. The red dotted circle shows the area that we averaged to get the intensity of the column. The column intensity as a function of the vacancy depth position (red curve) was plotted against the intensity of the column without a vacancy (blue curve) for ADF angles (c) 60-170 mrad, (d) 100-150 mrad, and (e) 20-100 mrad. The error bars indicate the uncertainty (SDOM) generated from the averaging of ten simulated images, each of which used twenty frozen phonon configurations at 298 K. Probe convergence half angle = 9.6 mrad, and sample thickness = 33 Å.

The cause of the LAADF’s dependence on the vacancy depth can be found in

CBED patterns simulated with the probe positioned at the Ga column (Figure 32). We first look at the CBED patterns without TDS for columns (a) without a vacancy and (b) with a vacancy positioned at the 6th position from the top (15 Å depth) along [010]m orientation. The two patterns show similar Higher Order Laue Zone (HOLZ) intensities

beyond ~100 mrad but show remarkably different patterns at lower angles (20–100 mrad). The extra “ripples” at lower angles shown in Figure 32(b) must be the result of the de-channeling of the electron due to the existence of the vacancy in the column. It has been well known that any abnormality or defect (e.g., dislocation) in a crystal can result

98 in the strong de-channeling of the electron, which can be captured using LAADF [161–

163]. The result here indicates that similar de-channeling can happen by the perturbation from the vacancy. When TDS is used in the simulations for the columns (c) without a vacancy and (d) with a vacancy, we see in both most of the HOLZ patterns are diffused, but the low angle ripple effect caused by the vacancy still remains. Figures 32(e) and

32(f) show that the difference between the patterns with and without vacancy caused by the ripple effect is most significant in the angle range between 20 and 40 mrad. The

CBED simulation result implies that, if the ADF detection angle is limited to 20–40 mrad, the contrast of the column containing a vacancy can be highly enhanced.

7.4.2 3D Imaging of Individual Vacancies Using Selective LAADF Ranges

Here we show that accurate determination of the 3D position of individual vacancies should be possible using multiple, narrowly selected LAADF angles. Figures

33(a)–33(f) show the column-averaged intensities of the columns that contain the vacancy as a function of vacancy depth from the top surface (red curves) as compared to the intensity of the column without a vacancy (blue curves), all with 9.6 mrad probe convergence half angle but with different ADF detection angles. The result shows that, the bright field [Figure 33(a)] and annular bright field [Figure 33(b)] intensities have essentially no dependence on the vacancy depth, meaning the identification of bulk vacancy will be difficult if these angles are used. However, consistent to the CBED results shown in Figure 32, the most variation in column intensity occurs when the

20–30 mrad angle range, the vacancy in the bulk can drop the column intensity by about

20% of the intensity of the column without a vacancy (blue curve) or the column with surface vacancies (both ends of the red curve), which means the accurate identification of bulk vacancies should be possible. However, the 20–30 mrad angle shows a symmetric profile along the vacancy depth, so distinguishing between the vacancy at the upper part and the vacancy at the lower part of the sample, for example, one placed at the 3rd position (6 Å depth) and the other at the 8th position (22 Å depth) from the top, may be difficult. However, incorporating the information from the 30–40 mrad angles can resolve this problem, because it shows significantly different intensities for those positions. The 30–40 mrad range in fact shows the most significant decrease in the intensity when the vacancy is at the 9th position from the top, where the intensity is almost half the intensity of the column without a vacancy [see Figure 33(h)]. It is also worth pointing out that, with 30–40 mrad angles, the intensity of the vacancy-containing column can even be higher than that of the column without vacancy, which happens near

~10 Å depth. This “contrast reversal” indicates that the signal intensity in this angle range is dominated by the de-channeling ripple effect shown in Figure 32. In addition, the 20–

30 mrad range may also be useful to study how the point defect changes the nearby Ga-O bonding, as the diffraction contrast reveals the oxygen positions as well [Figure 33(g)].

The high diffraction contrast of oxygen columns at LAADF must be due to the complexity of the β-Ga2O3 structure that generates many extra diffraction peaks. This is not the case, for example, in the image simulated for a higher symmetry crystal such as

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SrTiO3, where the oxygen columns are nearly invisible when the 20-30 mrad detection angle range is used. The HAADF angle, 110–120 mrad [Figure 33(f)], basically shows the same trend as the 100–150 mrad range [Figure 31(d)], which indicates minimal dependence on the vacancy depth position. The result shows that the detection of the vacancy in the bulk with precise depth information should be possible by combining the information of multiple selective LAADF signals. We have proposed the idea of combining information from multiple ADF detectors to increase the depth precision in

Zhang et al. [70], but the present work reveals that the depth sensitivity of the column intensity can be greatly increased by limiting the width of the annular detector to about

10 mrad and by optimizing the detection angle range depending on the type of point defects. Using LAADF signals is also beneficial because LAADF typically has much higher scattering intensity compared to HAADF, and therefore a greater signal-to-noise ratio can be achieved.

7.4.3 Effect of Probe Convergence Angle

We tested how the high depth sensitivity of 20–40 mrad scattering angles changes when a higher probe half convergence angle, 20 mrad, is used (Figure 34). The result shows that, while the overall column intensities increase with a higher convergence angle, the trend of the intensity versus the depth profile does not significantly vary

[Figures 34(a) and 34(b)] in comparison to the profiles with a 9.6 mrad half-convergence angle [Figures 33(d) and 33(e)]. The result indicates that, for very thin samples such as

102 the one shown here, the low angle ripple effect is not significantly affected by the increased convergence angle, which we also confirmed in the CBED simulation using a

20 mrad convergence half angle (not shown). The small difference between the 9.6 mrad data (Figure 33) and the 20 mrad data (Figure 34) must be because of the change in the probe channeling oscillation due to the change in the convergence angle, as it alters the relative contribution from each atom position along the depth to the image intensity, either in terms of scattering or de-channeling. Nevertheless, the results imply that convergence angles as high as ~ 20 mrad can also be used for vacancy depth imaging using this method as long as the vacancy contrast as a function of depth can be simulated.

Figure 34. Column averaged intensity as a function of vacancy depth position (red curve) compared to the intensity without a vacancy (blue curve) for detection angles (a) 20-30 mrad, (b) 30-40 mrad, and (c) 100-150 mrad using 20 mrad probe half convergence angle. All simulations used TDS.

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7.4.4 Effect of Crystal Orientation and Thickness

Here we show the vacancy-containing column intensities as compared to the normal column intensities using the other orientation, [001]m. As explained in Section

7.3, the interatomic distance along the depth direction of the [001]m orientation (5.8 Å) is nearly twice as long as the [010]m orientation (3.04 Å). Figure 35 shows the results simulated using the [001]m orientation with a sample thickness of 60 Å, which is almost twice as thick as the thickness used in the simulation along [010]m orientation shown in

Figure 33. However, the number of atoms along [001]m direction in this model is almost equal to the number of atoms along [010]m direction in the 33 Å thick sample shown in

Figure 33 because of the difference in the interatomic spacing. Despite the significant difference in sample thickness, the intensities simulated using detection ranges 20–30 mrad [Figure 35(a)] and 30–40 mrad [Figure 35(b)] along the [001]m orientation show similar trends as compared to the simulations along the [010]m orientation shown in

Figure 33. This can be explained through the simulation of the probe oscillation shown in

Figure 35(d). The oscillation along the [010]m shows almost linear increase until the first maximum at a depth of ~35 Å, while the oscillation along [001]m shows the same trend until the maximum at a depth of ~65 Å. This indicates that the number of atoms directly affects the probe channeling oscillation along the depth, not the actual thickness of the sample. Therefore, the simulations using 33 Å thick [010]m and 60 Å thick [001]m models must have similar de-channeling ripple effects, which results in similar trends in the depth dependence of the vacancy-containing column intensity, despite the differences in

104 thickness. The result also suggests that, depending on which imaging orientation is chosen, the usable sample thickness for 3D vacancy imaging can increase, which is a benefit because thicker TEM samples are easier to prepare in general.

We also performed the same simulation using a 119 Å thick sample along the

[001]m orientation [Figures 35(e) and 35(f)]. The results show that the depth dependency of the vacancy-containing column intensity becomes rather complicated, especially in

30–40 mrad detection angles. Because of the complicated profile, the 119 Å thickness may be too thick for vacancy depth imaging.

The effect of thicker samples on the contrast of vacancy-containing columns were also tested using the [010]m orientation. Figure 36 shows the simulation that is identical to the one shown in Figure 33, but with a thicker sample (55 Å). The intensities of the vacancy-containing columns in both the 20–30 and 30–40 mrad detection ranges show a different and slightly more complex trend as compared to that of the 33 Å thick sample shown in Figure 33. However, because the trends differ, together the individual profiles of both 10 mrad width detection ranges can be used to determine the vacancy depth position. Therefore, we conclude that the usable sample thickness for the 3D imaging of individual vacancies in β-Ga2O3 is about 6 nm, in both the [010]m and [001]m orientations.

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Figure 35. Column-averaged intensity as a function of vacancy depth position (red curve) compared to the column intensity without a vacancy (blue curve) for detection angles (a) 20–30 mrad and (b) 30–40 mrad, for imaging with [001]m orientation and sample thickness of 60 Å. (c) shows the image simulated for the vacancy placed at the 9th position (46 Å depth) from the top with a 30–40 mrad detection angle. The arrow indicates the column containing the vacancy. (d) Probe channeling oscillation along (top) [010]m (bottom) [001]m orientations in β-Ga2O3. (e) and (f) are the same simulations as (a) and (b), but with a sample twice as thick (119 Å). For (e) and (f), the intensities for every other vacancy positions were simulated. 106

Figure 36. Column-averaged intensity as a function of vacancy depth position (red curve) compared to the column intensity without a vacancy (blue curve) for detection angles (a) 20–30 mrad, and (b) 30–40 mrad, for imaging with [010]m orientation and sample thickness of 55 Å. The intensities for every other vacancy position were simulated.

7.4.5 3D Imaging of Lighter Dopant Atoms Using LAADF Angles

In the previous sections, we have demonstrated that the 3D imaging of vacancies should be possible using selective LAADF angles (20–40 mrad). Here we show that the

3D imaging of lighter dopants with accurate depth information should also be possible using the same selective LAADF angles. We chose Si as the lighter dopant, as it is one of the most commonly used dopants in β-Ga2O3 [85, 99], and controlling the unintentional doping of Si in pure β-Ga2O3 is also an important issue [39, 97]. Si has a Z- number that is less than a half of the host Ga atom (Z = 14 vs. 31). Figure 37 shows that the intensity profile along the [010]m direction as a function of Si dopant atom depth essentially follows the same trend as the vacancy case that we showed earlier. However, the absolute amplitude of the column intensity change is about half that of the vacancy 107 cases in both the 20–30 and 30–40 mrad ranges. This means that, with the presence of experimental uncertainty, the accurate determination of the Si atom along the depth should be possible, but more challenging. It is also important to point out that, it may not be completely possible to determine whether the impurity is a Si dopant or vacancy, as their intensities in both detection ranges are too close to each other in some cases (for example, the positions at 3–6 Å depth range) as shown in Figures 37(a) and 37(b). In such cases, incorporating the signal from the 3rd detector can help the distinction between a Si dopant and vacancy. For example, if the 3rd detector is placed in a HAADF range

100-150 mrad, the intensity of the Si-containing column is consistently higher than that of the vacancy-containing column throughout the entire depth range [Figure 37(c)].

Figure 37. Column-averaged intensity as a function of Si depth position (red curve) compared to the column intensity without an impurity (blue curve) for detection angles (a) 20–30 mrad, (b) 30–40 mrad, and (c) 100–150 mrad, for imaging with [010]m orientation. The data with a vacancy (red curve) is the same data presented in Figure 33. All simulations used TDS and a probe convergence half angle of 9.6 mrad.

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7.4.6 3D Imaging of Heavier Dopant Atoms in β-Ga2O3

Figure 38 shows the intensity as a function of the depth of a heavier dopant, Nd

[158] in β-Ga2O3. Nd has Z = 60, which is about twice as heavy as Ga (Z = 31). The overall trends of the intensities in the 20–30 and 30–40 mrad ranges in Figure 38 are different from the trends shown in Figures 33 and 37. In comparison to the vacancy and

Si cases, the first derivative of the graphs shows the opposite sign. This indicates that the de-channeling ripple effect still happens with heavier dopants but in a different way. The result shows that 3D imaging of heavier dopants should also be possible using the selective LAADF angles. However, the HAADF angle, shown in Figure 38(c), shows monotonic increase as a function of the dopant depth, and therefore the HAADF signal alone should be adequate to determine the dopant depth position. The monotonic increase in the intensity shown in Figure 38(c) is consistent to the trend observed in Gd dopant placed in a SrTiO3 host in the previous work [67]. As we have shown in the previous sections, the monotonic increase of HAADF signal as a function of defect depth does not happen in the vacancy and lighter dopant cases. The origin of this difference can be found in the probe channeling oscillation along the depth shown in Figure 38(d). As pointed out by Hwang et al. [67], the HAADF intensity strongly depends on the probe channeling oscillation along the depth. Here, the probe intensity as a function of depth in a perfect column (black) is compared to those containing Nd (light green) and vacancy (light blue).

In the case of a heavier (Nd) point defect, the probe intensity increases at the position of the atom. This means that, while the Nd atom slightly alters the probe channeling profile

109 in the column, the final image intensity will always be an additive sum of the scattering intensities from each atom positions, which result in the monotonic increase of HAADF signals up to the first maximum. However, when a vacancy is placed instead of the heavier dopant, the probe channeling intensity decreases right at the position of the vacancy, and the amount of the decrease is different depending the depth position of the vacancy. This results in a flat or even noisy trend in the final HAADF intensity profile, shown in Figures 31(c) and 33(f), rather than a monotonic change.

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7.4.7 Effect of Local Atomic Distortion

Point defects can also accompany changes in nearby atomic positions, and therefore the effect of local atomic displacements must be understood. We considered the changes in the oxygen positions next to a Ga vacancy. The exact change, or ‘relaxation’, of the oxygen atom positions is, however, difficult to guess, as the positions will be affected by various factors including the charge state of the vacancy and can also be highly anisotropic due to the monoclinic structure. To get the most realistic relaxation model, we performed an ab-initio (VASP) calculation of the structure containing a Ga vacancy with the charge of the vacancy set to the value of –3 which has been previously shown to be stable for the typically n-type Ga2O3 [39]. The computational details are identical to Ref. [39], except that the Perdew-Burke-Ernzerhof (PBE) functional [164] was used instead of HSE06 to decrease computational cost. With that, the optimized unit cell parameters (a = 12.35 Å, b = 3.07 Å, c = 5.86 Å,  = 103.6o) differed from the reported HSE06 results (a = 12.25 Å, b = 3.05 Å, c = 5.84 Å,  = 103.9o) and from experiment (a = 12.23 Å, b = 3.04 Å, c = 5.80 Å,  = 103.7o) by 1.0% or less. Thus, we expect the calculated atomic relaxations to be close to the realistic values.

The relaxed structure shows highly anisotropic displacements of atoms around the vacancy, and the magnitude of the displacement ranges from about 5.1 to 27.5 % of the average bond length, 2.0 Å [Figure 39(a)]. The multislice image simulation shows that, for 20–30 mrad detection angles, the difference between the relaxed and non-relaxed model is very small, falling within the range of the error bar [Figure 39(b)]. The 30–40

111 mrad simulation, however, shows a larger difference at certain vacancy positions. With a vacancy at a depth of 27 Å, for example, the relaxation can make the column intensity higher than the non-relaxation case by about 12% for this very-large relaxation example, which is higher than the allowed experimental error that will be discussed in Section

7.5.2. However, if the exact positions of the displaced atoms are determined from the experimental image or from accompanying DFT relaxations, this information can be included in the simulation, and the resulting uncertainty in the depth position analysis even for an extreme case like this can be reduced to a level that is within the allowed experimental error. Independent of that, the data in Figure 39 demonstrates that our new method is largely robust against the small nearby atomic relaxation around point defects.

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7.4.8 Verification of the Low Angle Ripple Effect and Vacancy Contrast

As previously shown, capturing the signals from the low angle extra ripple effect in the 20–40 mrad angle range can critically assist the 3D imaging of vacancies and lighter atoms. Here we verify the generality of the ripple effect by simulating the CBED patterns using a higher symmetry crystal, SrTiO3, and also showing that the ripple effect is not caused by any simulation artifacts. Figure 40 shows the CBED patterns simulated without TDS for the Sr position in SrTiO3 (thickness = 19.5 Å) with no vacancy [Figure

40(a)] and with a vacancy positioned in the middle of the column [Figure 40(c)]. The low angle de-channeling ripples become stronger in the CBED with a vacancy, which is consistent to the β-Ga2O3 case shown in Figure 32(b). The exact same change in ripples also occurs with a model that is laterally five times larger [Figures 40(b) and 40(d)], indicating that the ripple effect is not an artifact caused by the use of a small real space model. The ripple patterns are also unaffected by the use of a smaller slice thickness in the multislice simulations [Figures 40(e) and 40(f)].

We also tested the effect of the amplitude of thermal vibration to the contrast of the vacancy-containing column in selective LAADF imaging. As shown in Figure 32, the ripple effect is present even when TDS is used, which is why the LAADF can distinguish the columns with bulk vacancies. However, we have to question if the RMS value for

TDS used in the simulation is really an accurate one. The multislice code assumes isotropic thermal vibration in Cartesian coordinates (or just in x and y directions since the vibration along z will be typically smaller than the slice thickness and therefore becomes

113

irrelevant) [60], but this may be erroneous due to the structural anisotropy of β-Ga2O3

[128]. Due to the anisotropic thermal vibration in β-Ga2O3 [128], we estimate that the isotropic RMS value that we used may be off by ~15% depending on the imaging orientation. Therefore, we tested whether the isotropic assumption could cause systematic error in the column intensity by increasing the thermal vibration RMS values by 15%.

The result shows that the absolute column intensity values can decrease by 3-5% [Figures

41(a) and 41(b)] due to the increase in RMS, which indicates that the use of accurate anisotropic TDS parameters will be required for a fully quantitative comparison between

114 experimental and simulated images. Nevertheless, the ratio of the intensities between the columns with and without a vacancy does not change significantly [Figures 41(c) and

41(d)], hence the relative contrast of the vacancy-containing column will not be affected by the potential error.

Figure 41. Column intensity data for the sample with thickness = 33 Å and [010]m orientation with vs. without a vacancy shown in Figure 33 (solid and dotted blue curves, respectively), as compared to the same simulation run with thermal vibration RMS value increased by 15% (solid and dotted red curves) for (a) 20–30 mrad, and (b) 30–40 mrad. 풘풊풕풉 풗풂풄풂풏풄풚 (c) and (d) show the intensity ratio ( ) for the normal RMS (pink) and 풘풊풕풉풐풖풕 풗풂풄풂풏풄풚 RMS+15% (blue) data in (a) and (b), respectively.

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7.5 Discussion

7.5.1 Experimental Realization of Multiple, Narrow ADF Ranges

We demonstrated that, using small detection angle range in LAADF mode, such as 20–30 and 30–40 mrad ranges, can substantially enhance the contrast of the defect- containing column with its dependence on the defect depth information. Our result can therefore create new opportunities for imaging point defects in material with accurate 3D information, if the experiment uses the same detection angles presented in this work.

Experimentally, the best option to achieve such narrow LAADF angle ranges with ~10 mrad width would be using the direct electron detector with ultrafast read-out speed (e.g.,

[165]) or a fast pixelated STEM detector (e.g., [166]) which can acquire CBED patterns

(such as the one shown in Figure 32) for each probe position while scanning the probe across the sample area. From the CBED patterns collected for every probe position, reconstructing the STEM images using the signals in multiple scattering angle ranges, for example, 20–30 and 30–40 mrad, and HAADF angles, should be possible. The experiment should also be possible using conventional STEM ADF detectors. The small

LAADF angle range can be selected, for example, by using a normal ADF detector combined with the use of the shadow of an objective aperture onto the detector. In our

FEI Titan STEM, using a camera length of 230 mm and an objective aperture with 100

μm diameter, the angle range of 20–27 mrad can be selected. In a similar manner, the 30–

40 mrad angle range can be selected as well. Simultaneous acquisition of the two images

116 may be difficult, but they can be acquired consecutively, as we have demonstrated in

Zhang et al [70].

7.5.2 Allowable Experimental Uncertainties

The determination of the depth of point defects will be ultimately limited by the experimental uncertainties in real imaging experiments [67]. Here we have estimated the maximum allowed experimental uncertainty based on the vacancy depth imaging case shown in Figure 33. For 20–30 and 30–40 mrad data, we have calculated the difference ratio (R) between the column intensities with and without a vacancy using

R = I - I / I , where Ivac is the intensity of the vacancy-containing column and I0 is vac 0 0 the intensity of the column without vacancy. The R value changes as a function of the vacancy depth as displayed in Figure 42(a). For example, for the vacancy placed at the 5th position from the top, the R value is 0.174 for the 20–30 mrad range, and 0.071 for the

30–40 mrad range. This means that if the experimental uncertainty is less than 0.071

(~7%), the accurate determination of the vacancy located at the 5th position should be possible. Throughout the whole thickness range, at least one of the 20–30 and 30–40 mrad data points is above the 5% uncertainty line (dashed line), indicating that the exact vacancy depth identification should be possible if the experimental uncertainty (in standard deviation) can be kept less than 5%. 5% is about half the uncertainty we previously reported with HAADF dopant imaging [67]. Since the LAADF detection angles have much higher signal, they should increase the signal-to-noise ratio, and if we

117 assume that the experimental uncertainty only depends on the signal-to-noise ratio in the signal collection, the experimental error should decrease. However, unaccounted large atomic relaxations as discussed in Sec. 7.4.7 and non-ideal sample conditions, such as surface roughness, can also contribute to the experimental uncertainty. This may be especially important because LAADF intensity is known to be more sensitive to surface features, although it is unclear whether this will still be the case when the narrower

LAADF angle ranges are selected. Surface reconstruction may also complicate the image contrast, but no surface reconstruction in β-Ga2O3 has been reported [97, 167].

7.5.3 The Use of Column Averaged Intensity

The change in the contrast as a function of the vacancy depth is also evident in the image intensity line profile across the Ga column containing the vacancy shown in Figure

42(b). However, we do prefer the column average intensity that we used in this work because it tends to suppress the noise and sample drift that may be present in the experimental image [160], and because the use of an area instead of a line profile means using more pixels in the image which allows higher sampling rate. Column averaged intensity is also independent of the shape or dimension of the selected area, as long as the same way of area selection is applied to both experimental and simulated images under comparison.

118

7.6. Conclusion

In summary, we have shown that the 3D characterization of vacancies, lighter and heavier dopants can be determined from quantitative STEM imaging by optimizing the

ADF detection angles. The selection of a small range of LAADF signals can make the contrast of vacancy and lighter dopant-containing atomic columns more depth dependent, while HAADF signals are more sensitive to the depth of heavier dopants. Simulated

CBED patterns revealed the cause of the LAADF’s dependence on the vacancy depth to be a ripple effect, which is the result of de-channeling of the electron due to the existence of the vacancy in the column. Capturing the de-channeling signal with a narrowly selected range of ADF angles critically assists the 3D imaging of vacancies and lighter atoms by enhancing the contrast of the point defect-containing columns. Using this

119 method, we have shown that the probe convergence angle or nearby atomic distortion does not significantly change the overall trend of the profile and that depending on crystal orientation, thicker TEM foils can be used. However, the application of this method to determine the depth of point defects is ultimately limited by the experimental uncertainties in real imaging experiments. With the use of the detection angles presented, new opportunities for imaging point defects in materials with accurate 3D information can be created.

7.7 Acknowledgements

The authors acknowledge the use of the computing facilities at the Ohio

Supercomputer Center, which were used to carry out the STEM image and diffraction simulations. S.I. was supported by the Seed Grant from the Institute for Materials

Research at the Ohio State University and the Center for Emergent Materials, an NSF funded MRSEC under award DMR-1420451. WW acknowledges funding from AFOSR award FA9550-14-1-0322.

120

Chapter 8: Summary and Final Conclusions

The goal of the research presented in this dissertation was to establish the all- important structure-property relationships in the up-and-coming UWBG semiconductor

β-Ga2O3. This study has uncovered critical atomic scale point defect information, the first of its kind, contributing to the characterization efforts needed to achieve a better understanding of the material and ultimately, providing guidance to its synthesis with precisely controlled properties.

Chapters 1 and 2 provided detailed background information, revealing the motivation for this study. The manipulation of important properties through point defect control was shown to be vital to the progression of β-Ga2O3. The critical review of recent theoretical and experimental works exposed the lack of direct atomic scale structural information of point defects that was limiting the characterization of the material, prompting our study utilizing STEM. Chapter 3 described the crystal growth, theoretical, and experimental characterization methods used in the point defect investigation.

In Chapter 4, Sn doped β-Ga2O3 was investigated using STEM, DLOS, and DFT.

STEM results provided the first direct observation of unusual divacancy–cation interstitial complexes, which result from the migration mechanism of a single gallium vacancy. This data confirmed DFT predictions that identified the stable formation of the

121 complexes. DLOS results further validated their formation and verified their compensating acceptor functionality through the detection of an EC – 2.0 eV defect state, which showed a positive correlation with Sn doping. Sn was determined to facilitate the formation of the complex through an increase in Fermi level energy and subsequent increase in vacancy concentration. The direction detection of the divacancy-interstitial complexes provided valuable insight on the material’s unique response to impurity incorporation and demonstrated the capability of collectively applying different techniques for the characterization of point defects in semiconductors.

An extension of the work in Chapter 4, Chapter 5 showed the analysis of STEM data to reveal the structure of new defect complexes that form when two adjacent divacancy–cation interstitial complexes cause an atomistic relaxation of a specific Ga atom. MD simulations were utilized to verify the stable formation of these new structures. The creation of the defect complexes, which are the energetically stable configurations of Ga vacancies, were determined to be facilitated by Sn doping. This formation was determined unlikely to vary the trap state of the divacancy–cation interstitial complexes.

In Chapter 6, a quantitative approach was taken to investigate point defects in β-

(AlxGa1-x)2O3 films. The quantitative STEM analysis of these films revealed an almost equal distribution of substitutional Al between the tetrahedrally coordinated Ga1 and octahedrally coordinated Ga2 sites, conflicting with theoretical predictions for Al site occupancy. This result suggested that a higher energy structure is generated and likely inhibits the ability to grow epitaxial β-(AlxGa1-x)2O3 films at high Al concentrations.

122

Additionally, the aforementioned divacancy–cation interstitial complexes were directly observed in the films and showed an increase in concentration with Al. It was proposed that the high complex concentration may be detrimental to the films properties, due to its compensating acceptor character.

The focus was shifted in Chapter 7 to a simulation study designed to optimize the quantitative STEM method for the three-dimensional characterization of all types of point defects, such as vacancies, lighter, and heavier dopants. Multislice simulations using β-

Ga2O3 revealed that the selection of a small range of LAADF signals enhance the depth dependency of vacancies and lighter dopants in atomic columns, while HAADF signals are more sensitive to the depth of heavier dopants. The change in the LAADF detection angle range was shown to be caused by a ripple effect, resulting from the de-channeling of the electron due to the existence of the defect in the column. Contrast from vacancy and lighter dopant containing columns was enhanced by capturing a narrowly selected range of low ADF angles, allowing for the three-dimensional imaging of the point defects.

The work in this dissertation has demonstrated only the beginning of point defect characterization in β-Ga2O3, which is still in its infancy as a material. As growth methods continue to develop and the current limits of band gap engineering and doping are pushed, the fundamental understanding of property manipulation through point defect control will remain critical and opportunities for advanced characterization will be endless. However, the ultimate vision is that our collective use of characterization techniques, centered around STEM, will be applied to several material systems, with

123 hopes that point defects and their complexes will be discovered and linked to important properties.

124

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135

Appendices

A. “Unusual Formation of Point Defect Complexes in the Ultra-Wide Band Gap

Semiconductor β-Ga2O3”

This is the supplementary material published with the peer reviewed journal article, J. M. Johnson, Z. Chen, J. B. Varley, C. M. Jackson, E. Farzana, A. R. Arehart,

H. Huang, A. Genc, S. A. Ringel, C. G. Van de Walle, D. A. Muller, and J. Hwang,

Unusual Formation of Point Defect Complexes in the Ultra-wide Band Gap

Semiconductor β-Ga2O3, Phys. Rev. X 9, 041027 (2019).

A.1 Methods

The (2̅01) Sn-doped and unintentionally doped (UID) β-Ga2O3 bulk crystals used in this investigation were fabricated by the edge-defined, film-fed growth (EFG) process by the Tamura Corporation. The Sn doped and UID samples have carrier concentrations of 8.2 x 1018 cm-3 and 2.4 x 1017 cm-3, respectively. Crystal orientations such as the

[010]m and [001]m yield advantageous viewing directions for point defect imaging due to the large atomic spacings. Cross-sectional [010]m TEM samples were prepared using

136 focused ion beam (FIB). As atomic resolution imaging of [010]m β-Ga2O3 requires thin, clean samples, we further milled TEM samples using a low-energy (500 eV) ion mill

(Fischione Nanomill). The final thickness of the TEM foils was determined by position averaged convergent beam electron diffraction to be about 25 nm [66, 101], meaning each gallium column contains about 80 atoms along the depth direction. STEM was then performed using aberration-corrected Thermo Fisher Scientific Titan Themis STEM instruments, all operated at 300 kV.

All STEM HAADF image simulations were performed using the multislice algorithm [60]. For each image simulation of randomly distributed defect complexes, ten random arrangements were simulated and then averaged to increase statistical reliability.

Thermal vibrations were ignored as their contribution to column intensity is minimal. The image simulations used aberration parameters of our probe corrected FEI Titan STEM

(Cs3=0.002 mm, Cs5=1.0 mm) with a 20.0 mrad convergence half angle at an acceleration voltage of 300 kV.

The DFT atomistic simulations of the vacancy complex energetics were based on hybrid functional calculations performed using the same methodology as described in

Ref. [41]. Specifically, the vacancy and vacancy complexes were modelled within a 160- atom supercell representation of bulk β-Ga2O3, where corrections to the formation energies of charged defects owing to image-charge interactions were included as detailed in Ref. [41]. Migration barriers were computed between linearly interpolated structures and thus offer upper bounds to the real barriers.

137

DLOS was performed on Ni/Ga2O3 Schottky diodes on four different β-Ga2O3 substrates from Tamura: n~1 x 1017 cm-3 UID (010), n~1.5 x 1018 cm-3 Sn-doped (-201), n~3.5 x 1018 cm-3 Sn-doped (010), n~5 x 1018 cm-3 Sn-doped (010). Carrier concentrations on these samples were confirmed by C-V measurements. DLOS utilizes monochromatic sub-bandgap light to observe optically stimulated photoemission transients as a function of incident light energy. Here, light from a 1000W Xe-lamp was dispersed through a high-resolution monochromator to provide incident light from 1.2 eV to 5.0 eV in 0.02 eV steps, and photoemission transients were measured for 300 seconds.

A.2 Statistical Analysis of Column Intensities for Ga1 vs Ga2 with Cation Interstitials

Confirming the existence of vacancies in Ga1 sites requires identifying the intensity decrease of Ga1 columns in the presence of interstitials while Ga2 columns remain unaffected. Table 2 shows the reduced intensity of Ga1 columns adjacent to interstitials was substantially more significant than the overall intensity decrease in the area (Ga1 vs Ga2 with interstitials). As Ga2 columns are not expected to be involved in the

1 formation of 2VGa - Gai complexes, this areal decrease in intensity is likely due to strain near interstitials. Despite this loss in intensity, the decrease in Ga1 intensity indicates the

1 presence of vacancies within the columns and the formation of 2VGa - Gai complexes.

138

Neighboring Ga column Type Avg. Intensity

Ga1 when there is no interstitial 30,164 ± 4.7%

Ga2 when there is no interstitial 31,051 ± 9.2%

Ga1 with an interstitial in the ib site 23,577 ± 11.5%

Ga2 with an interstitial in the ib site 26,953 ± 14.6%

Ga1 with an interstitial in the ic site 22,782 ± 12.5%

Ga2 with an interstitial in the ic site 25,893 ± 14.0%

A.3 Multislice Image Simulation

Determining the total number of defect complexes located along the depth direction of the TEM sample and identifying the chemical species of the interstitial atoms must involve quantitatively relating the change in intensities to the exact number and location of defect complexes through image simulation. Using the multislice method

[60], we have simulated arrangements of defect complexes with both Ga and Sn interstitials (Figure 43). Trends found in Figures 43(i) and A1(j) confirm that intensity increases due to interstitials and decreases due to vacancies. By simulating top-surface- clustered and randomly distributed defect complexes, we have obtained the upper and lower limits of possible intensity variation from the defect complexes (due to probe

139 channeling and oscillation [31]). The analysis indicates that there is a wide range of possible intensity changes due to the immense dependence on location and chemical species of the defect complexes (the details on determining the exact number of the defect complexes are provided in the next section). Some important insights can be gained from the data. Random distributions of defect complexes along the column display minuscule changes in interstitial intensity (~ 2% for 10 Ga interstitial atoms), which is substantially smaller than the intensity change that observed in the experimental data. This means that a random distribution would require the defect segregation involve many atoms, extending beyond a few nanometers, which would be inconsistent to observed clustering along the lateral direction shown in Figure 19(g). This weighs more on the scenario that the cations are in fact clustered within the column, which would not be surprising, given that the clustering is already observed along the lateral direction.

Based on the low magnification image in Figure 19(g) and assuming Ga as the interstitial along with top-surface-clustering, the concentration of the defect complexes within the region is ~ 2 x 1020 cm-3. Greatly exceeding the measured carrier concentration, this number is an overestimation of the total concentration within the bulk because of the especially small sampling. The small sampling is caused by both the nature of STEM imaging and the chosen specific regions of interest containing visible defects. However, we also acknowledge that from the image simulation, the regions with apparently no detectable interstitials may still contain some number of interstitial atoms (and therefore potentially the complexes as well). But their contrast may be too low to be identified possibly because they are either too small in number (< 3 along the column) or not

140 clustered. In this case, our chosen images mostly contain visible defect complexes, thus overestimating the total concentration within the bulk.

141

1 1 Figure 43. HAADF multislice image simulations and analysis for 2VGa – Gai and 2VGa – Sni complexes. (a) Schematic examples of β-Ga2O3 used in the simulations along the [010]m beam direction of (a-left) a defect free cell, (a-middle) a cell containing four 1 randomly distributed 2VGa – Gai complexes (positions 2,5,6,10), and (a-right) a cell 1 containing four clustered 2VGa – Sni complexes (positions 1,2,3,4). (b) Schematic of the 1 c 2VGa – Gai defect complex. (e) Line profiles from a defect free (c, green-dashed) and a 1 c 2VGa – Gai defect complex containing (d, red-dashed) simulated HAADF image showing the decrease in Ga1 intensity (blue arrows) from the incorporated vacancies and increase 1 b in interstitial site intensity (red triangle). (f) Schematic of the 2VGa – Gai defect complex. 1 b (i) Similarly, line profiles from a defect free (g, green-dashed) and a 2VGa – Gai defect complex containing (h, aqua-dashed) simulated HAADF image show similar intensity 1 changes. Plots (j) and (k) show the multislice image simulation analysis for (j) 2VGa – Gai 1 and (k) 2VGa – Sni complexes in a 25 nm (82 atom) thick crystal. Displayed is the fraction of intensity with respect to a defect free Ga1 column versus the number of complexes inserted along the depth direction. Each plot shows a random arrangement of defect complexes and defect complexes clustered at the surface of the crystal. 142

A.4 Estimating the Number of Defect Complexes in the Atomic Column

For the STEM simulations shown in Figures 43(j) and A1(k), we have considered the two cases that give the high- and low-end limits of the column intensity, (i) the case where the complexes are clustered near the top surface of the TEM specimen

(corresponding to high column intensity [31]), and (ii) the case where the complexes are randomly (i.e. homogeneously) distributed throughout the column (corresponding to low column intensity). The clustering can happen at any position along the specimen thickness direction. However, the analyzed region, where the interstitial column intensities are the highest, show a decrease in Ga1 site intensities due to vacancies, corresponding to complexes that are clustered near the top surface within those regions.

Such scenario corresponds to the data points presented with gray and orange colors

(vacancy- and interstitial-containing columns, respectively) in both Figures 43(j) and

A1(k). Another assumption is that it is more likely that the majority of the interstitial atoms are Ga atoms, based on the comparison of the STEM data to the DLOS data, as described in the manuscript. The experimental data in Figures 20(d) and 20(h) showed that the ratio of the intensity of the columns containing interstitial atoms to that of the defect-free columns (which is also the quantity displayed in the y-axis of both Figures

43(j) and A1(k)) is about 0.3. The same ratio for the vacancy containing column is about

0.7. Therefore, assuming that the interstitial atoms are Ga, the interpolated value for the intensity of the interstitial-containing columns for the case of the clustering at the top surface (orange data points) is ~ 0.3 when the number of defect complexes is ~ 12. The

143 same number of defect complexes would yield an intensity of ~ 0.7 for the vacancy- containing columns in the case of clustering at the top surface (gray data points), which matches the experimental observation. However, if the interstitial atom is Sn, which may still be possible, the same analysis would yield the number of complexes to be ~ 7, according to the data in Figure 43(k). Considering these two cases (i.e. Ga vs. Sn), we estimate number of complexes in these columns to be ~ 10.

144

1 A.5 Formation Energies for 2푉퐺푎 – Sni Complexes

1 DFT calculations show 2VGa – Sni acceptor complexes can readily form when VGa

1 are nearby (calculated barriers < 0.3 eV for a SnGa to displace to octahedrally- coordinated interstitials adjacent to VGa1) and are quite stable with calculated binding energies of at least 1.4 eV relative to isolated VGa and SnGa species. As Sn atom is expected to incorporate as substitutional dopants on the octahedrally coordinated Ga2 site becoming unavailable for migration from the Ga1 site, these complexes would need to form during growth.

2 1 Figure 44. Formation energies for SnGa and 2VGa – Sni complexes vacancies in β-Ga2O3, shown in the limit of (a) Ga-rich and (b) O-rich conditions.

145

B. “Al Distribution and Point Defect Complexes in β-(AlxGa1-x)2O3 Films”

This is the supplementary material for Chapter 6 presented as J. M. Johnson, H.

Huang, A. F. M. A. U. Bhuiyan, Z. Feng, N. K. Kalarickal, S. Rajan, H. Zhao, and J.

Hwang, Al Distribution and Point Defect Complexes in β-(AlxGa1-x)2O3 Films.

B.1 Statistical Analysis of Column Intensities for Ga1 vs Ga2 with Cation Interstitials

Affirming the Al concentration and substitutional site occupancy in β-(AlxGa1- x)2O3 films requires quantitatively identifying the decrease in Ga1 and Ga2 column intensity as compared to a β-Ga2O3 substrate. Table 3 shows the reduced column intensities of the Ga1 and Ga2 sites in the films. A larger decrease in average column intensity is observed in the β-(Al0.4Ga0.6)2O3 film, as compared to the β-(Al0.22Ga0.78)2O3, representing the higher Al concentration. Despite the difference in concentration, an identical decrease of Ga1 and Ga2 column intensities relative to each other occurs in both

β-(Al0.22Ga0.78)2O3 and β-(Al0.4Ga0.6)2O3 films. As shown in Figure 27(d), this result indicates that 54% of the incorporated Al occupies the Ga2 site, regardless of Al concentration or growth technique. Note that error bars in Table 3 represent the variation in intensity from the different columns measured. This means that the error bars for the column measurements in the films are a consequence of the number and positions along the depth direction of Al in the column.

146

Ga column Type Avg. Intensity

MOCVD β-(Al0.4Ga0.6)2O3

Ga atoms in the Ga1 site 1,731 ± 2.56%

Ga atoms in the Ga2 site 1,784 ± 2.40%

Al atoms in the Ga1 site 1,283 ± 4.86%

Al atoms in the Ga2 site 1,214 ± 6.49%

MBE β-(Al0.22Ga0.78)2O3

Ga atoms in the Ga1 site 1,722 ± 3.63%

Ga atoms in the Ga2 site 1,725 ± 3.37%

Al atoms in the Ga1 site 1,432 ± 6.45%

Al atoms in the Ga2 site 1,394 ± 6.15%

B.2 Quantitative STEM Al Composition Analysis

Confirming the exact Al composition requires quantitatively comparing experimental column intensities to image simulations. For this task, we employ the quantitative STEM technique as described in Ref. [59]. Using the multislice method [60], we simulated 16.8 and 18.5 nm crystals with random arrangements of substitutional Al in

Ga1 and Ga2 sites, while varying concentration. Thickness was determined by PACBED

147 comparison, as shown in [Figures 27(b) and 27(c)]. For each image simulation, ten random depth arrangements of Al were simulated and averaged to increase statistical reliability. Thermal vibrations were also considered with Debye-Waller factors obtained from Ref. [168]. For each depth arrangement, ten thermal vibration conditions were applied, resulting in 100 total image simulations. Image simulations used aberration parameters of the probe corrected FEI Titan STEM (Cs3=0.002 mm, Cs5=1.0 mm) with a

28.9 mrad convergence half angle and 51–350 mrad detector semiangles at an accelerating voltage of 300 kV. The simulated HAADF images were modeled by convolving a Gaussian envelope function [169, 170] to reduce contrast and achieve spatial incoherence. A Gaussian with FWHM of 0.025 nm provided excellent agreement with the experimental results. The simulation results, shown in Figure 45(a), confirm a decrease in intensity with increasing Al concentration.

Experimental data from Table 3 was normalized to the incident beam intensity for a direct comparison to simulation. This data, displayed in Table 4, was compared to its respective simulated plots in Figure 45 to determine the average column Al composition.

Comparison for the 18.5 nm thick β-(Al0.4Ga0.6)2O3 film revealed Ga1 and Ga2 sites contained 38.0% and 44.5% Al, respectively with an overall concentration of x = 0.41.

The same comparison for the 16.8 nm thick β-(Al0.22Ga0.78)2O3 film showed Ga1 and Ga2 sites contained 20.5% and 24.0% Al, respectively with an overall concentration of x =

0.22. These results, plotted in Figure 45 and shown in Table 4, are in agreement with the

XRD measurements for concentration. Moreover, both analyses reveal a near equal

148 distribution of Al in the Ga1 and Ga2 sites, indicating the instability of high Al composition β-(AlxGa1-x)2O3 films.

149 differences in column measurements corresponding to the column by column Al composition fluctuation and their random distributions.

150