Electron effective mass in Sn-doped monoclinic single crystal $\beta$-gallium oxide determined by mid-infrared optical Hall effect

TL;DR

This study experimentally measures the isotropic average electron effective mass in Sn-doped monoclinic $eta$-Ga$_2$O$_3$ using mid-infrared optical Hall effect, confirming theoretical predictions and finding no significant anisotropy.

Contribution

First experimental determination of the isotropic electron effective mass in Sn-doped monoclinic $eta$-Ga$_2$O$_3$ using optical Hall effect, aligning with recent theoretical calculations.

Findings

Effective mass is approximately 0.284m₀.

No detectable anisotropy within experimental uncertainty.

Results agree with density functional theory predictions.

Abstract

The isotropic average conduction band minimum electron effective mass in Sn-doped monoclinic single crystal $\beta$-Ga$_2$O$_3$ is experimentally determined by mid-infrared optical Hall effect to be $(0.284\pm0.013)m_{0}$ combining investigations on ($010$) and ($\bar{2}01$) surface cuts. This result falls within the broad range of values predicted by theoretical calculations for undoped $\beta$-Ga$_2$O$_3$. The result is also comparable to recent density functional calculations using the Gaussian-attenuation-Perdue-Burke-Ernzerhof hybrid density functional, which predict an average effective mass of $0.267m_{0}$ (arXiv:1704.06711 [cond-mat.mtrl-sci]). Within our uncertainty limits we detect no anisotropy for the electron effective mass, which is consistent with most previous theoretical calculations. We discuss upper limits for possible anisotropy of the electron effective mass parameter from our experimental uncertainty limits, and we compare our findings with recent theoretical results.