- Open Access
Structure and thermodynamic stability of surfaces
Phys. Rev. B 114, 225410 – Published 14 October, 2026
DOI: https://doi.org/10.1103/ltwn-y8xf
Abstract
We present a comprehensive first-principles investigation of all symmetrically inequivalent low-index surfaces of , examining their structural properties and thermodynamic stability across experimentally relevant growth conditions. Using density-functional theory with both the semi-local functional PBEsol and a modified PBE0 hybrid functional with exact exchange, denoted PBE0(0.26), we calculate surface free energies for the (010), (100), (001), (), (110), (111), and () orientations, including the effects of harmonic vibrational contributions and varying oxygen chemical potentials. We demonstrate that the energetic ordering remains consistent across computational approaches and that the vibrational contributions remain below up to temperatures of . A coordination-based model that correlates surface stability with the density of undercoordinated atoms reveals that undercoordinated oxygen atoms and tetrahedral Ga sites substantially destabilize surfaces, while exposed undercoordinated octahedral Ga atoms serve as indicators of surface stability. Our thermodynamic analysis shows that stoichiometric terminations dominate over nearly the entire range of chemical potentials relevant for stability, while nonstoichiometric terminations emerge only under extreme reducing or oxidizing conditions. Notably, we predict the formation of stable Ga-rich terminations resembling Ga adlayers for the (100) and () surfaces under highly reducing conditions.
Physics Subject Headings (PhySH)
Article Text
References (62)
- A. J. Green, J. Speck, G. Xing, P. Moens, F. Allerstam, K. Gumaelius, T. Neyer, A. Arias-Purdue, V. Mehrotra, A. Kuramata, K. Sasaki, S. Watanabe, K. Koshi, J. Blevins, O. Bierwagen, S. Krishnamoorthy, K. Leedy, A. R. Arehart, A. T. Neal, S. Mou, et al., -gallium oxide power electronics, APL Mater. 10, 029201 (2022).
- M. Higashiwaki and G. H. Jessen, Guest editorial: The dawn of gallium oxide microelectronics, Appl. Phys. Lett. 112, 060401 (2018).
- Gallium Oxide: Materials Properties, Crystal Growth, and Devices, Springer Series in Materials Science, edited by M. Higashiwaki and S. Fujita (Springer International, Cham, Switzerland, 2020), Vol. 293.
- S. J. Pearton, J. Yang, P. H. Cary, F. Ren, J. Kim, M. J. Tadjer, and M. A. Mastro, A review of Ga2O3 materials, processing, and devices, Appl. Phys. Rev. 5, 011301 (2018).
- Z. Galazka, R. Uecker, D. Klimm, K. Irmscher, M. Naumann, M. Pietsch, A. Kwasniewski, R. Bertram, S. Ganschow, and M. Bickermann, Scaling-up of bulk -Ga2O3 single crystals by the czochralski method, ECS J. Solid State Sci. Technol. 6, Q3007 (2017).
- Z. Galazka, -Ga2O3 for wide-band gap electronics and optoelectronics, Semicond. Sci. Technol. 33, 113001 (2018).
- V. Bermudez, The structure of low-index surfaces of -Ga2O3, Chem. Phys. 323, 193 (2006).
- S. Mu, M. Wang, H. Peelaers, and C. G. Van de Walle, First-principles surface energies for monoclinic and and consequences for cracking of (, APL Mater. 8, 091105 (2020).
- Y. Hinuma, T. Gake, and F. Oba, Band alignment at surfaces and heterointerfaces of Al2O3, Ga2O3, In2O3, and related group-III oxide polymorphs: A first-principles study, Phys. Rev. Mater. 3, 084605 (2019).
- Y. Hinuma, T. Kamachi, N. Hamamoto, M. Takao, T. Toyao, and K.-I. Shimizu, Surface oxygen vacancy formation energy calculations in 34 orientations of -Ga2O3 and -Al2O3, J. Phys. Chem. C 124, 10509 (2020).
- E. A. Gonzalez, P. V. Jasen, A. Juan, S. E. Collins, M. A. Baltanás, and A. L. Bonivardi, Hydrogen adsorption on -Ga2O3(100) surface containing oxygen vacancies, Surf. Sci. 575, 171 (2005).
- M. Wang, S. Mu, and C. G. V. de Walle, Surface reconstructions on bare and hydrogenated surfaces: Implications for growth, Phys. Rev. Mater. 7, 064603 (2023).
- R. Anvari, D. Spagnoli, G. Parish, and B. Nener, Density functional theory simulations of water adsorption and activation on the (-201) -Ga2O3 surface, Chem. - Eur. J. 24, 7445 (2018).
- I. Bertoni, A. Ugolotti, E. Scalise, and L. Miglio, Surface and volume energies of -, -, and -Ga2O3 under epitaxial strain induced by a sapphire substrate, J. Mater. Chem. C 12, 1820 (2024).
- K. Lion, P. Mazzolini, K. Egbo, T. Markurt, O. Bierwagen, M. Albrecht, and C. Draxl, -Ga2O3(001) surface reconstructions from first principles and experiment, Phys. Rev. Mater. 10, 043603 (2026).
- S. Bin Anooz, R. Grüneberg, T.-S. Chou, A. Fiedler, K. Irmscher, C. Wouters, R. Schewski, M. Albrecht, Z. Galazka, W. Miller, J. Schwarzkopf, and A. Popp, Impact of chamber pressure and Si-doping on the surface morphology and electrical properties of homoepitaxial (100) -Ga2O3 thin films grown by MOVPE, J. Phys. D: Appl. Phys. 54, 034003 (2021).
- S. Bin Anooz, R. Grüneberg, C. Wouters, R. Schewski, M. Albrecht, A. Fiedler, K. Irmscher, Z. Galazka, W. Miller, G. Wagner, J. Schwarzkopf, and A. Popp, Step flow growth of -Ga2O3 thin films on vicinal (100) -Ga2O3 substrates grown by MOVPE, Appl. Phys. Lett. 116, 182106 (2020).
- R. Schewski, K. Lion, A. Fiedler, C. Wouters, A. Popp, S. V. Levchenko, T. Schulz, M. Schmidbauer, S. Bin Anooz, R. Grüneberg, Z. Galazka, G. Wagner, K. Irmscher, M. Scheffler, C. Draxl, and M. Albrecht, Step-flow growth in homoepitaxy of -Ga2O3(100)—The influence of the miscut direction and faceting, APL Mater. 7, 022515 (2019).
- Z. Cheng, M. Hanke, Z. Galazka, and A. Trampert, Growth mode evolution during (100)-oriented -Ga2O3 homoepitaxy, Nanotechnology 29, 395705 (2018).
- M.-C. Kao, L. P. Schewe, A. Akhtar, A. Vlad, T. F. Keller, K. Henkel, S. B. Anooz, A. Popp, Z. Galazka, J. I. Flege, A. Stierle, and V. Vonk, Surface termination of -Ga2O3(100) as-cleaved single crystals, Appl. Phys. Lett. 128, 071601 (2026).
- T.-S. Chou, P. Seyidov, S. Bin Anooz, R. Grüneberg, T. T. V. Tran, K. Irmscher, M. Albrecht, Z. Galazka, J. Schwarzkopf, and A. Popp, Fast homoepitaxial growth of (100) thin films via MOVPE, AIP Adv. 11, 115323 (2021).
- T.-S. Chou, J. Rehm, S. Bin Anooz, O. Ernst, A. Akhtar, Z. Galazka, W. Miller, M. Albrecht, P. Seyidov, A. Fiedler, and A. Popp, Exploring miscut angle influence on (100) -Ga2O3 homoepitaxial films growth: Comparing MOVPE growth with MBE approaches, J. Appl. Phys. 134, 195301 (2023).
- A. Bhattacharyya, P. Ranga, S. Roy, J. Ogle, L. Whittaker-Brooks, and S. Krishnamoorthy, Low temperature homoepitaxy of (010) -Ga2O3 by metalorganic vapor phase epitaxy: Expanding the growth window, Appl. Phys. Lett. 117, 142102 (2020).
- G.-X. Qian, R. M. Martin, and D. J. Chadi, First-principles study of the atomic reconstructions and energies of Ga- and As-stabilized GaAs(100) surfaces, Phys. Rev. B 38, 7649 (1988).
- J. Rogal, K. Reuter, and M. Scheffler, Thermodynamic stability of PdO surfaces, Phys. Rev. B 69, 075421 (2004).
- K. Reuter and M. Scheffler, Composition and structure of the RuO2 (110) surface in an O2 and CO environment: Implications for the catalytic formation of CO2, Phys. Rev. B 68, 045407 (2003).
- K. Reuter and M. Scheffler, Composition, structure, and stability of RuO2 (110) as a function of oxygen pressure, Phys. Rev. B 65, 035406 (2001).
- J. Rogal and K. Reuter, Ab Initio atomistic thermodynamics for surfaces: A primer, in Experiment, Modeling and Simulation of Gas-Surface Interactions for Reactive Flows in Hypersonic Flights, Educational Notes RTO-EN-AVT-142 (NATO Research and Technology Organization, Neuilly-sur-Seine, France, 2007), pp. 2-1–2-18.
- K. K. Irikura, Experimental vibrational zero-point energies: Diatomic molecules, J. Phys. Chem. Ref. Data 36, 389 (2007).
- Y. Zhang and W. Yang, A challenge for density functionals: Self-interaction error increases for systems with a noninteger number of electrons, J. Chem. Phys. 109, 2604 (1998).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- M. Ernzerhof, J. P. Perdew, and K. Burke, Coupling-constant dependence of atomization energies, Int. J. Quantum Chem. 64, 285 (1997).
- D. Feller and K. A. Peterson, Re-examination of atomization energies for the Gaussian-2 set of molecules, J. Chem. Phys. 110, 8384 (1999).
- D. Stull and H. Prophet, JANAF Thermochemical Tables, 2nd ed. (U.S. National Bureau of Standards, Washington, DC, 1971).
- CRC Handbook of Chemistry and Physics, Internet Version, edited by D. R. Lide (CRC Press, Boca Raton, FL, 2005).
- V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, K. Reuter, and M. Scheffler, Ab initio molecular simulations with numeric atom-centered orbitals, Comput. Phys. Commun. 180, 2175 (2009).
- J. W. Abbott, C. Mera Acosta, A. Akkoush, A. Ambrosetti, V. Atalla, A. Bagrets, J. Behler, D. Berger, H. Bertschi, B. Bieniek, J. Björk, V. Blum, S. Bohloul, C. L. Box, N. J. Boyer, D. S. Brambila, G. A. Bramley, K. R. Bryenton, M. Camarasa-Gómez, C. Carbogno, et al., Roadmap on advancements of the FHI-aims software package, Electron. Struct. (2026), doi: 10.1088/2516-1075/ae8067.
- J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
- C. Wouters, C. Sutton, L. M. Ghiringhelli, T. Markurt, R. Schewski, A. Hassa, H. von Wenckstern, M. Grundmann, M. Scheffler, and M. Albrecht, Investigating the ranges of (meta)stable phase formation in : Impact of the cation coordination, Phys. Rev. Mater. 4, 125001 (2020).
- K. Lion, P. Pavone, and C. Draxl, Elastic stability of : Addressing the to phase transition from first principles, Phys. Rev. Mater. 6, 013601 (2022).
- C. Adamo and V. Barone, Toward reliable density functional methods without adjustable parameters: The PBE0 model, J. Chem. Phys. 110, 6158 (1999).
- M. Ernzerhof and G. E. Scuseria, Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional, J. Chem. Phys. 110, 5029 (1999).
- P. Deák, M. Lorke, B. Aradi, and T. Frauenheim, Optimized hybrid functionals for defect calculations in semiconductors, J. Appl. Phys. 126, 130901 (2019).
- M. Orita, H. Ohta, M. Hirano, and H. Hosono, Deep-ultraviolet transparent conductive -Ga2O3 thin films, Appl. Phys. Lett. 77, 4166 (2000).
- J. Åhman, G. Svensson, and J. Albertsson, A reinvestigation of -gallium oxide, Acta Crystallogr. C Cryst. Struct. Commun. 52, 1336 (1996).
- S. P. Ong, W. D. Richards, A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V. L. Chevrier, K. A. Persson, and G. Ceder, Python materials genomics (pymatgen): A robust, open-source python library for materials analysis, Comput. Mater. Sci. 68, 314 (2013).
- W. Sun and G. Ceder, Efficient creation and convergence of surface slabs, Surf. Sci. 617, 53 (2013).
- A. Togo, First-principles phonon calculations with Phonopy and Phono3py, J. Phys. Soc. Jpn. 92, 012001 (2023).
- A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Implementation strategies in phonopy and phono3py, J. Phys.: Condens. Matter 35, 353001 (2023).
- P. Deák, Q. Duy Ho, F. Seemann, B. Aradi, M. Lorke, and T. Frauenheim, Choosing the correct hybrid for defect calculations: A case study on intrinsic carrier trapping in -Ga2O3, Phys. Rev. B 95, 075208 (2017).
- P. W. Tasker, The stability of ionic crystal surfaces, J. Phys. C: Solid State Phys. 12, 4977 (1979).
- L. Wang, F. Zhou, Y. S. Meng, and G. Ceder, First-principles study of surface properties of LiFePO4 : Surface energy, structure, Wulff shape, and surface redox potential, Phys. Rev. B 76, 165435 (2007).
- M. Sterrer and H.-J. Freund, Properties of oxide surfaces, in Surface and Interface Science, edited by K. Wandelt (Wiley, New York, 2013), 1st ed., pp. 229–278.
- G. Wulff, XXV. Zur Frage der Geschwindigkeit des Wachsthums und der Auflösung der Krystallflächen, Z. Für Krist. - Cryst. Mater. 34, 449 (1901).
- J. M. Rahm and P. Erhart, wulffpack: A python package for Wulff constructions, J. Open Source Softw. 5, 1944 (2020).
- C. Draxl and M. Scheffler, NOMAD: The FAIR concept for big data-driven materials science, MRS Bull. 43, 676 (2018).
- C. Draxl and M. Scheffler, The NOMAD laboratory: From data sharing to artificial intelligence, J. Phys. Mater. 2, 036001 (2019).
- M. Scheidgen, L. Himanen, A. N. Ladines, D. Sikter, M. Nakhaee, Á. Fekete, T. Chang, A. Golparvar, J. A. Márquez, S. Brockhauser, S. Brückner, L. M. Ghiringhelli, F. Dietrich, D. Lehmberg, T. Denell, A. Albino, H. Näsström, S. Shabih, F. Dobener, M. Kühbach, et al., NOMAD: A distributed web-based platform for managing materials science research data, J. Open Source Softw. 8, 5388 (2023).
- http://doi.org/10.17172/NOMAD/2026.04.15-1.
- M. D. Pashley, Electron counting model and its application to island structures on molecular-beam epitaxy grown GaAs(001) and ZnSe(001), Phys. Rev. B 40, 10481 (1989).
- M. Wang, S. Mu, and C. G. Van de Walle, Role of Ga and In adatoms in the epitaxial growth of -Ga2O3, Phys. Rev. B 102, 035303 (2020).
- C. Noguera, Physics and Chemistry at Oxide Surfaces, 1st ed. (Cambridge University Press, Cambridge, England, 1996).