- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Materials

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Thermodynamic and electronic properties of rutile Sn1−xGexO2 alloys from first principles

Yann L. Müller1,2,*, Alp Umut Kurbay3,*, Xiao Zhang3, Emmanouil Kioupakis3,†, and Anirudh Raju Natarajan1,2,‡

  • *These authors contributed equally to this work.
  • †Contact author: kioup@umich.edu
  • ‡Contact author: anirudh.natarajan@epfl.ch
PDF

Phys. Rev. Materials 10, 074602 – Published 27 July, 2026

DOI: https://doi.org/10.1103/q3ht-wjty

Abstract

Rutile Sn1−xGexO2 alloys are promising materials for high-power electronic applications due to their dopability and tunable ultrawide band gaps. We use first-principles density functional theory and statistical mechanics to investigate the crystallographic, electronic, and thermodynamic properties of rutile Sn1−xGexO2 alloys. We predict that the lattice parameters follow Vegard's law, while band gaps calculated with the hybrid HSE06 functional exhibit strong bowing, consistent with experiment. We also predict that the disordered phase has a large positive mixing enthalpy and a slight tendency for Ge-Sn clustering, indicated by weakly negative short-range order parameters. This large positive mixing enthalpy produces a miscibility gap with a critical temperature above 2300 K, implying that the high Ge and Sn solubilities observed in thin-film synthesis cannot be explained by the incoherent phase diagram alone. We demonstrate that coherency strain substantially alters phase stability. Calculations of the coherent spinodal show significant suppression of the miscibility gap, reducing the critical temperature to ≈900K. These coherent phase boundaries could account for the experimentally observed high solubilities at typical growth temperatures. Our results indicate that coherency strain stabilizes these metastable alloys and enables band-gap engineering in this ultrawide-band-gap material system.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (64)

  1. M. H. Wong, O. Bierwagen, R. J. Kaplar, and H. Umezawa, Ultrawide-band gap semiconductors: An overview, J. Mater. Res. 36, 4601 (2021).
  2. J. L. Lyons and A. Janotti, A p-type dopable ultrawide-band gap oxide, J. Phys.: Condens. Matter 36, 085501 (2024).
  3. S. Chae, N. Sanders, K. A. Mengle, A. Wang, X. Zhang, J. L. Bartolome, K. Luo, Y.-C. Huang, F. Giustino, J. T. Heron, and E. Kioupakis, Extreme-band-gap semiconductors with shallow dopants and mobile carriers, npj Comput Mater (2026)10.1038/s41524-026-02173-z.
  4. K. A. Mengle, S. Chae, and E. Kioupakis, Quasiparticle band structure and optical properties of rutile GeO2, an ultrawide-band-gap semiconductor, J. Appl. Phys. 126, 085703 (2019).
  5. S. Chae, J. Lee, K. A. Mengle, J. T. Heron, and E. Kioupakis, Rutile GeO2: An ultrawide-band-gap semiconductor with ambipolar doping, Appl. Phys. Lett. 114, 102104 (2019).
  6. K. Bushick, K. A. Mengle, S. Chae, and E. Kioupakis, Electron and hole mobility of rutile GeO2 from first principles: An ultrawide-band gap semiconductor for power electronics, Appl. Phys. Lett. 117, 182104 (2020).
  7. S. Chae, K. A. Mengle, R. Lu, A. Olvera, N. Sanders, J. Lee, P. F. P. Poudeu, J. T. Heron, and E. Kioupakis, Thermal conductivity of rutile germanium dioxide, Appl. Phys. Lett. 117, 102106 (2020).
  8. S. Chae, K. Mengle, K. Bushick, J. Lee, N. Sanders, Z. Deng, Z. Mi, P. F. P. Poudeu, H. Paik, J. T. Heron, and E. Kioupakis, Toward the predictive discovery of ambipolarly dopable ultrawide-band-gap semiconductors: The case of rutile GeO2, Appl. Phys. Lett. 118, 260501 (2021).
  9. Z. Galazka, R. Blukis, A. Fiedler, S. B. Anooz, J. Zhang, M. Albrecht, T. Remmele, T. Schulz, D. Klimm, M. Pietsch, A. Kwasniewski, A. Dittmar, S. Ganschow, U. Juda, K. Stolze, M. Suendermann, T. Schroeder, and M. Bickermann, Bulk single crystals and physical properties of rutile GeO2 for high‐power electronics and deep‐ultraviolet optoelectronics, Physica Status Solidi (B) 262, 2400326 (2025).
  10. K. Shimazoe, I. Seike, K. Kanegae, and H. Nishinaka, Enhanced growth temperature window and Sb doping of rutile GeO2 enabled by graded buffer layers, Jpn. J. Appl. Phys. 64, 50903 (2025).
  11. K. Tetzner, Z. Galazka, A. Thies, A. Külberg, and O. Hilt, Lateral rutile GeO2 MOSFET devices on single-crystal r-GeO2 substrates, IEEE Electron Device Lett. 47, 566 (2025).
  12. K. Kanegae, K. Shimazoe, I. Seike, and H. Nishinaka, Ni/rutile GeO2 vertical Schottky barrier diode on Nb-doped TiO2 substrate using Sb-doped graded Geysn1−yo2 buffer layers, Appl. Phys. Express 18, 041001 (2025).
  13. Y. Nagashima, M. Fukumoto, M. Tsuchii, Y. Sugisawa, D. Sekiba, T. Hasegawa, and Y. Hirose, Deep ultraviolet transparent electrode: Ta-doped rutile Sn1−xGexO2, Chem. Mater. 34, 10842 (2022).
  14. E. Kluth, Y. Nagashima, S. Osawa, Y. Hirose, J. Blasing, A. Strittmatter, R. Goldhahn, and M. Feneberg, Blue shift of the absorption onset and band gap bowing in rutile GexSn1−xO2, Appl. Phys. Lett. 125, 122102 (2024).
  15. H. Takane, Y. Ota, T. Wakamatsu, T. Araki, K. Tanaka, and K. Kaneko, Band-gap engineering of rutile-structured SnO2−GeO2−SiO2 alloy system, Phys. Rev. Mater. 6, 084604 (2022).
  16. A. M. Abed and R. L. Peterson, Effect of post-deposition annealing on crystal structure of RF magnetron sputtered germanium dioxide thin films, J. Vac. Sci. Technol. A 42, 063403 (2024).
  17. A. M. Abed and R. L. Peterson, Growth and characterization of rutile-type GexSn1−xO2 alloy thin films via RF magnetron sputtering, APL Mater. 13, 111115 (2025).
  18. S. Chae, H. Paik, N. M. Vu, E. Kioupakis, and J. T. Heron, Epitaxial stabilization of rutile germanium oxide thin film by molecular beam epitaxy, Appl. Phys. Lett. 117, 072105 (2020).
  19. F. Liu, N. J. Szymanski, K. Noordhoek, H.-s. Shin, D. Kim, C. J. Bartel, and B. Jalan, Unraveling the growth dynamics of rutile Sn1–xGexO2 using theory and experiment, Nano Lett. 25, 299 (2025).
  20. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  21. J. W. Furness, A. D. Kaplan, J. Ning, J. P. Perdew, and J. Sun, Accurate and numerically efficient rSCAN2 meta-generalized gradient approximation, J. Phys. Chem. Lett. 1, 8208 (2020).
  22. J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118, 8207 (2003).
  23. G. Kresse and J. Furthmuller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  24. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  25. A. Zunger, S.-H. Wei, L. G. Ferreira, and J. E. Bernard, Special quasirandom structures, Phys. Rev. Lett. 65, 353 (1990).
  26. M. Feneberg, C. Lidig, K. Lange, R. Goldhahn, M. D. Neumann, N. Esser, O. Bierwagen, M. E. White, M. Y. Tsai, and J. S. Speck, Ordinary and extraordinary dielectric functions of rutile SnO2 up to 20 eV, Appl. Phys. Lett. 104, 231106 (2014).
  27. M. Stapelbroek and B. D. Evans, Exciton structure in the U.V. absorption edge of tetragonal GeO2, Solid State Commun. 25, 959 (1978).
  28. D. O. Scanlon and G. W. Watson, On the possibility of p-type SnO2, J. Mater. Chem. 22, 25236 (2012).
  29. J. M. Sanchez, F. Ducastelle, and D. Gratias, Generalized cluster description of multicomponent systems, Physica A 128, 334 (1984).
  30. D. D. Fontaine, Cluster approach to order-disorder transformations in alloys, in Solid State Physics, edited by H. Ehrenreich and D. Turnbull (Academic Press, New York, 1994), Vol. 47, pp. 33–176.
  31. D. K. Lee, Y. L. Müller, and A. R. Natarajan, Modeling the equilibrium vacancy concentration in multi-principal element alloys from first-principles, Acta Mater. 304, 121752 (2026).
  32. Y. L. Müller and A. R. Natarajan, First-principles thermodynamics of precipitation in aluminum-containing refractory alloys, Acta Mater. 274, 119995 (2024).
  33. Y. L. Müller and A. R. Natarajan, Constructing multicomponent cluster expansions with machine-learning and chemical embedding, npj Comput. Mater. 11, 60 (2025).
  34. A. R. Natarajan and A. Van der Ven, First-principles investigation of phase stability in the Mg-Sc binary alloy, Phys. Rev. B 95, 214107 (2017).
  35. A. R. Natarajan and A. Van der Ven, Machine-learning the configurational energy of multicomponent crystalline solids, npj Comput. Mater. 4, 56 (2018).
  36. C. A. Paetsch and A. R. Natarajan, First-principles thermodynamics of hydrogen absorption in binary C15 Laves phases, Chem. Mater. 38, 683 (2026).
  37. M. Ångqvist, D. O. Lindroth, and P. Erhart, Optimization of the thermoelectric power factor: Coupling between chemical order and transport properties, Chem. Mater. 28, 6877 (2016).
  38. M. Ångqvist and P. Erhart, Understanding chemical ordering in intermetallic clathrates from atomic scale simulations, Chem. Mater. 29, 7554 (2017).
  39. J. Brorsson, A. E. C. Palmqvist, and P. Erhart, First-principles study of order–disorder transitions in pseudobinary clathrates, J. Phys. Chem. C 125, 22817 (2021).
  40. D. K. J. Lee, Z. Deng, G. Sai Gautam, and P. Canepa, Thermodynamics of sodium–lead alloys for negative electrodes from first-principles, Chem. Mater. 36, 6831 (2024).
  41. Z. Wang, T. P. Mishra, W. Xie, Z. Deng, G. S. Gautam, A. K. Cheetham, and P. Canepa, Kinetic Monte Carlo simulations of sodium ion transport in NaSICON electrodes, ACS Mater. Lett. 5, 2499 (2023).
  42. S. Schulz, M. A. Caro, C. Coughlan, and E. P. O'Reilly, Composition dependent band gap and band edge bowing in AlInN: A combined theoretical and experimental study, Appl. Phys. Lett. 103, 242102 (2013).
  43. A. Samanta, M. Jain, and A. K. Singh, Ultra-sensitive pressure dependence of band gap of rutile-GeO2 revealed by many body perturbation theory, J. Chem. Phys. 143, 064703 (2015).
  44. P. Borlido, J. Schmidt, H.-C. Wang, S. Botti, and M. A. L. Marques, Computational screening of materials with extreme gap deformation potentials, npj Comput. Mater. 8, 156 (2022).
  45. B. Puchala, J. C. Thomas, A. R. Natarajan, J. G. Goiri, S. S. Behara, J. L. Kaufman, and A. Van der Ven, CASM — A software package for first-principles based study of multicomponent crystalline solids, Comput. Mater. Sci. 217, 111897 (2023).
  46. A. Van der Ven, J. Thomas, B. Puchala, and A. Natarajan, First-principles statistical mechanics of multicomponent crystals, Annu. Rev. Mater. Res. 48, 27 (2018).
  47. B. Puchala and A. Van der Ven, Thermodynamics of the Zr-O system from first-principles calculations, Phys. Rev. B 88, 094108 (2013).
  48. R. Tibshirani, Regression shrinkage and selection via the Lasso, J. Roy. Stat. Soc. B 58, 267 (1996).
  49. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, and D. Cournapeau, Scikit-learn: Machine learning in Python, Journal of Machine Learning Research 12, 2825 2011.
  50. A. Watanabe, T. Kikuchi, M. Tsutsumi, S. Takenouchi, and K. Uchida, Solid solubility of GeO2 in SnO2, J. Am. Ceram. Soc. 66, c104 (1983).
  51. A. R. Natarajan, E. L. Solomon, B. Puchala, E. A. Marquis, and A. Van der Ven, On the early stages of precipitation in dilute Mg–Nd alloys, Acta Mater. 108, 367 (2016).
  52. J. W. Doak and C. Wolverton, Coherent and incoherent phase stabilities of thermoelectric rocksalt IV-VI semiconductor alloys, Phys. Rev. B 86, 144202 (2012).
  53. R. Malik, A. Abdellahi, and G. Ceder, A critical review of the Li insertion mechanisms in LiFePO4 electrodes, J. Electrochem. Soc. 160, A3179 (2013).
  54. J. W. Cahn, On spinodal decomposition, Acta Metall. 9, 795 (1961).
  55. S. S. Behara, J. C. Thomas, B. Puchala, and A. Van der Ven, Chemomechanics in alloy phase stability, Phys. Rev. Mater. 8, 033801 (2024).
  56. F. Léonard and R. C. Desai, Spinodal decomposition and dislocation lines in thin films and bulk materials, Phys. Rev. B 58, 8277 (1998).
  57. S. Hu and L. Chen, Solute segregation and coherent nucleation and growth near a dislocation—a phase-field model integrating defect and phase microstructures, Acta Mater. 49, 463 (2001).
  58. S. Hu and L. Chen, Diffuse-interface modeling of composition evolution in the presence of structural defects, Comput. Mater. Sci. 23, 270 (2002).
  59. MaterialsCloud repository, https://doi.org/10.24435/materialscloud:e2-xp.
  60. A. Wang, K. Bushick, N. Pant, W. Lee, X. Zhang, J. Leveillee, F. Giustino, S. Poncé, and E. Kioupakis, Electron mobility of SnO2 from first principles, Appl. Phys. Lett. 124, 172103 (2024).
  61. V. Wang, N. Xu, J.-C. Liu, G. Tang, and W.-T. Geng, Vaspkit: A user-friendly interface facilitating high-throughput computing and analysis using VASP code, Comput. Phys. Commun. 267, 108033 (2021).
  62. A. Schleife, J. B. Varley, F. Fuchs, C. Rödl, F. Bechstedt, P. Rinke, A. Janotti, and C. G. Van de Walle, Tin dioxide from first principles: Quasiparticle electronic states and optical properties, Phys. Rev. B 83, 035116 (2011).
  63. J. B. Varley, A. Janotti, and C. G. Van de Walle, Group-V impurities in SnO2 from first-principles calculations, Phys. Rev. B 81, 245216 (2010).
  64. K. J. Button, C. G. Fonstad, and W. Dreybrodt, Determination of the electron masses in stannic oxide by submillimeter cyclotron resonance, Phys. Rev. B 4, 4539 (1971).

Outline

Information

Phys. Rev. Materials 10, 074602– Published 27 July, 2026
  • Received 27 January 2026
  • Accepted 17 June 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation