Lattice Thermal Conductivity in $\varepsilon$-Ga$_2$O$_3$

$\beta$-Ga$_2$O$_3$ has seen increased popularity as a substrate and device material because of its large band gap and theoretical breakdown field, but it suffers from low thermal conductivity ($\kappa$). The question arises whether other polytypes of Ga$_2$O$_3$ might have higher thermal conductivity along with an ultra-wide band gap. One potential phase is is $\varepsilon$-Ga$_2$O$_3$, which has a large band gap (4.9 eV) and a wurtzite-like crystal structure. Unfortunately, the $\varepsilon$ phase is difficult to model from first principles, as several of the Ga Wyckoff positions are only partially occupied. In this talk we examine several structures which approximate $\varepsilon$-Ga$_2$O$_3$. For these structures we then calculate the lattice contribution to the bulk thermal conductivity tensor $\kappa$ by computing second- and third-order force constants. We compare our results with experimental and theoretical data for $\beta$-Ga$_2$O$_3$.