Structural, Electronic Properties, and Relative Stability Studies of Low-Energy Indium Oxide Polytypes Using First-Principles Calculations

Abstract

Materials made of indium oxide (In₂O₃) are now being used as a potential component of the next generation of computers and communication devices. Density functional theory is used to analyze the physical, electrical, and thermodynamical features of 12 low-energy bulk In₂O₃ polytypes. The cubic structure In₂O₃ is majorly used for many of the In₂O₃-based transparent conducting oxides. The objective of this study is to explore other new stable In₂O₃ polytypes that may exist. The structural properties and stability studies are performed using the Vienna ab initio simulation package code. All the In₂O₃ polytypes have semiconductive properties, according to electronic band structure investigations. The full elastic tensors and elastic moduli of all polytypes at 0 K are computed. Poisson's and Pugh's ratio confirms that all stable polytypes are ductile. The phonon and thermal properties including heat capacity are obtained for mechanically stable polytypes. For the first time, we report the Raman and infrared active modes of stable polytypes.

Figure 1

Optimized crystal structure of In₂O₃ polytypes: (a) In₂O₃-H, (b) In₂O₃-C, (c) In₂O₃-T1, (d) In₂O₃-T2, (e) In₂O₃-M1, (f) In₂O₃-M2, (g) In₂O₃-M3, (h) In₂O₃-M4, (i) In₂O₃-O1, (j) In₂O₃-O2, (k) In₂O₃-O3, and (l) In₂O₃-O4.

Figure 2

Calculated total energy as a function of the volume for 12 low-energy In₂O₃ polytypes. All the energy volumes are standardized to one formula unit (f.u.).

Figure 3

Calculated pressure versus Gibbs free energy plot for selected In₂O₃ polytypes. In₂O₃-C is the reference structure. Pressure involved in the phase transition from In₂O₃-C to In₂O₃-O4 is 10.1 GPa (at point a), from In₂O₃-O4 to In₂O₃-O2 is 12.9 GPa (at point b), and from In₂O₃-O2 to In₂O₃-O3 is 41.7 GPa (at point c).

Figure 4

Computed band structures with the direct band gap of polytypes (a) In₂O₃-H, (b) In₂O₃-C (calculated using GGA approximation), (c) In₂O₃-T1, (d) In₂O₃-T2, (e) In₂O₃-M1, (f) In₂O₃-M2, (g) In₂O₃-M3, (j) In₂O₃-O2, (k) In₂O₃-O3, and (l) In₂O₃-O4 and with the indirect band gap of polytypes (h) In₂O₃-M4 and (i) In₂O₃-O1 calculated using hybrid DFT (HSE-06 level).

Figure 5

Spatial dependence of the (a) Young’s modulus, (b) shear modulus, and (c) Poisson’s ratio of the In₂O₃-M4 polytype. Directions x, y, and z represent the increments along the a, b, and c directions of the primitive cell shown in Figure 1

Figure 6

Computed phonon dispersion curve with PhDOS of mechanically stable In₂O₃ polytypes: (a) In₂O₃-C, (b) In₂O₃-M3, (c) In₂O₃-M4, (d) In₂O₃-O1, and (e) In₂O₃-O3 display positive modes.

Figure 7

Thermal parameters, (a) internal energy, (b) free energy, (c) entropy, and (d) heat capacity as a function of temperature (K) for all mechanically and dynamically stable In₂O₃ polytypes.

Figure 8

Calculated Raman (a) and IR (b) spectra for all mechanically and dynamically stable In₂O₃ polytypes.

Figure 9

(a) Phonon dispersion curve of In₂O₃-M3 with (b) atomic displacements for the strongest Raman peak A_g (at 581 cm^–1) and (c) for the strongest IR peak A_u (at 487 cm^–1) vibration modes.

Figure 10

(a) Phonon dispersion curve of In₂O₃-O1 with (b) atomic displacements for the strongest Raman peak A_g (at 496 cm^–1) and (c) for the strongest IR peak B_2u (at 435 cm^–1) vibration modes.