Structural, electronic, elastic, power, and transport properties of $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ from first principles

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Structural, electronic, elastic, power, and transport properties of $β − {Ga}_{2} O_{3}$ from first principles

Samuel Poncé and Feliciano Giustino

Phys. Rev. Research 2, 033102 – Published 20 July 2020

Abstract

We investigate the structural, electronic, vibrational, power, and transport properties of the $β$ allotrope of ${Ga}_{2} O_{3}$ from first principles. We find phonon frequencies and elastic constants that reproduce the correct band ordering, in agreement with experiment. We use the Boltzmann transport equation to compute the intrinsic electron and hole drift mobility and obtain room-temperature values of 258 and 1.2 ${cm}^{2}$ /Vs, respectively, as well as 6300 and 13 ${cm}^{2}$ /Vs at 100 K. Through a spectral decomposition of the scattering contribution to the inverse mobility, we find that multiple longitudinal-optical modes of $B_{u}$ symmetry are responsible for the electron mobility of $β − {Ga}_{2} O_{3}$ but that many acoustic modes also contribute, making it essential to include all scattering processes in the calculations. Using the von Hippel low-energy criterion, we computed the breakdown field to be 5.8 MV/cm at room temperature, yielding a Baliga figure of merit of 1250 with respect to silicon, ideal for high-power electronics. This work presents a general framework to predictively investigate novel high-power electronic materials.

Received 5 May 2020
Accepted 24 June 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033102

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

Physics Subject Headings (PhySH)

Elastic modulus Electron relaxation Electron-phonon coupling Transport phenomena

Oxides

Boltzmann theory First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Samuel Poncé ^1,2,* and Feliciano Giustino^3,4,2,†

¹Theory and Simulation of Materials (THEOS), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
²Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
³Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
⁴Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA

^*samuel.ponce@epfl.ch
^†fgiustino@oden.utexas.edu

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Vol. 2, Iss. 3 — July - September 2020

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Figure 1
Relaxed crystal structure of the primitive cell of $β − {Ga}_{2} O_{3}$ where the large atoms are gallium and the small red atoms are oxygen. Rendered using vesta [36].
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Figure 2
Electronic (a) and phonon (b) band structure of $β − {Ga}_{2} O_{3}$ along high-symmetry lines of the monoclinic Brillouin zone. For the phonons, the gray lines denote bands with the identity point group while the red lines have a $π$ rotation around the [0,1,0] Cartesian axis ( $C_{2}$ point group), and the blue line are lines with inversion symmetry [ $C_{s} (m)$ point group].
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Figure 3
Spatial dependence of the (a) Young modulus, (b) shear modulus, and (c) Poisson's ratio of $β − {Ga}_{2} O_{3}$ using the elate software [59] for visualization of second-order elastic constants. In (b), (c) the blue and green surfaces represent the maximum and minimum of the third-angle parametrization, see text. The directions $x$ , $y$ , and $z$ represent the increments along the $a$ , $b$ , and $c$ directions of the primitive cell shown in Fig. 1.
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Figure 4
(a) Electron and (b) hole drift mobility of $β − {Ga}_{2} O_{3}$ using the Boltzmann transport equation along the three principal directions where the dashed line indicates the direction-averaged drift mobility, including the effect of $10^{15} {cm}^{- 3}$ ionized impurity scattering. The experimental data of Oishi et al. [70], Irmscher et al. [12], and Chikoidze et al. [71] are Hall measurements of the mobility.
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Figure 5
Direction-averaged momentum and mode-resolved contribution to the inverse electron mobility $T_{q ν}$ at room temperature (left) as well as spectral decomposition of the inverse mobility (right). The dashed red line represent the cumulative integral of each spectrum $\partial μ^{- 1} / \partial ℏ ω$ and adds up to the inverse electron mobility in the self-energy relaxation time approximation.
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Figure 6
(a) Average energy-gain rate $A (ɛ)$ from an applied external field and average energy loss to the lattice $B (ɛ)$ . Both quantities are for 300 K. The intrinsic breakdown occurs when the applied electric field is such that the gain rate is larger than the loss rate for all energies between the conduction-band minimum (CBM) and the CBM plus the energy of the band gap (4.5 eV). (b) Variation of computed breakdown field with temperature. (c) Experimental variation of dielectric function with direction and temperature of $β − {Ga}_{2} O_{3}$ from Ref. [81]. (d) Baliga's figure of merit (BFOM) with respect to the BFOM of silicon. The BFOM of Si was obtained using dielectric constants from Ref. [82] and a breakdown field of 0.3 MV/cm, as well as the experimental electron mobility from Norton et al. [83].
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Physical Review Research

Structural, electronic, elastic, power, and transport properties of β−Ga2O3 from first principles

Samuel Poncé and Feliciano Giustino

Phys. Rev. Research 2, 033102 – Published 20 July 2020

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Structural, electronic, elastic, power, and transport properties of $β − {Ga}_{2} O_{3}$ from first principles