Intrinsicn-Type Behavior in Transparent Conducting Oxides: A Comparative Hybrid-Functional Study ofIn2O3,

Abstract

We present a comparative study of oxygen vacancies in In2O3, SnO2, and ZnO based on the hybrid-functional method within the density-functional theory (DFT). For In2O3 and SnO2, our results provide strong evidence of shallow donor states at oxygen vacancies. In comparison with the (semi)local exchange-correlation approximations in DFT, the hybrid-functional method strongly lowers the formation energy of the positive charge state and keeps that of the neutral state nearly intact. The trend is analyzed in terms of changes in lattice relaxation energies and in electron energy levels near the band gap. The existence of shallow donor states at oxygen vacancies and the consequent n-type conductivity are in line with experimental findings. The results invalidate some former theoretical interpretations based on standard DFT calculations.

Deep vs shallow nature of oxygen vacancies and consequentn-type carrier concentrations in transparent conducting oxides

“…We describe the model in full and verify its accuracy through comparison with relevant calculations using more conventional, plane-wave based methods. In all cases we find that the defects are compact donors, but in agreement with Ágoston et al [41], we find that vacancies in the bulk of In 2 O 3 are shallow donors, which can account for a significant proportion of the observed intrinsic n-type conductivity. For SnO 2 and ZnO we determine that the vacancies are deep, and, depending on the hybrid density functional used, determine transition levels either in excellent agreement with previous studies or slightly shallower (our results in these cases agree well with the experimentally determined ionization energies).…”

“…If the ionization energies of these defects are low, the system will tend to be an intrinsic n-type conductor. Some early studies have indicated that vacancies are shallow donors in these oxides [29][30][31][32][33][34][35][36][37][38], but more recent analysis based on plane-wave density functional theory (DFT), first using a Hubbard U parameter then, in later studies, a hybrid functional, tends to place them as deep centers in many TCOs [20,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. Of those that have been shown to form shallow centers [41,[56][57][58][59], it has been argued that their compact wave functions preclude the possibility of them contributing to n-type conductivity [59][60][61].…”

“…A clear increase in conductivity as P O 2 is decreased can be observed when temperature T > 1000 K, indicating the presence of a relatively deep donor [34]. From these data, a donor activation energy of 0.15 eV in the dilute limit has been derived [72][73][74], or possibly at ∼0.3 eV [75], but the majority of computational studies indicates that the most likely donor, the oxygen vacancy, is deeper with the (2+/0) transition occurring at about 1 eV below the conduction band minimum (CBM) [20,41,43].…”

Computationally predicted energies and properties of defects in GaN

“…A variety of approaches have been proposed, 22 including applications of Hubbard-U-like terms (LDA + U or GGA + U) to cation d states 40 or to multiple orbital channels, 41 the Slater-Janak transition model, 42,43 modified pseudopotentials, 44 Becke-Johnson type functionals, 45,46 combining DFT with quasiparticle calculations, 35,36 and hybrid functionals. [47][48][49][50][51][52][53][54][55][56] Hybrid functionals have emerged as the current method of choice, 22 applicable to a wide variety of systems including defects in Si, 47,48 GaAs, 51 diamond, 48 and oxides. 49,50 In the following, unless specified otherwise, we assume that hybrid functional results are obtained with HSE.…”

“…[47][48][49][50][51][52][53][54][55][56] Hybrid functionals have emerged as the current method of choice, 22 applicable to a wide variety of systems including defects in Si, 47,48 GaAs, 51 diamond, 48 and oxides. 49,50 In the following, unless specified otherwise, we assume that hybrid functional results are obtained with HSE. 30,31 Here, we set the fraction of exact exchange to 0.31 so that a band gap of 3.51 eV is obtained, in agrement with the experimental value.…”