Thermal Conductivity and Temperature-Induced Band Gap Renormalization in Crystalline and Amorphous Ga$_2$O$_3$

Abstract

In the present work, we performed calculations of the lattice thermal conductivity (LTC) and electron-phonon interactions in crystalline and amorphous gallium oxide. The calculations were performed by coupling a machine-learned interatomic potential - the moment tensor potential (MTP) model - to first-principles calculations. Crystalline $β$-Ga$_2$O$_3$ exhibits a pronounced zero-point band gap renormalization (BGR) of $\sim 0.2\,\text{eV}$ and a BGR of $\sim 0.45\,\text{eV}$ at $700\,\text{K}$. The computed temperature dependence of BGR induced by classical nuclear motion in $β$-Ga$_2$O$_3$ is stronger than that in amorphous Ga$_2$O$_3$. Thermal transport calculations reveal that the LTC of amorphous Ga$_2$O$_3$ remains near $0.9\,\text{W}\cdot\text{m}^{-1}\cdot\text{K}^{-1}$ for temperatures between $300\,\text{K}$ and $700\,\text{K}$, which is approximately an order of magnitude lower than that of $β$-Ga$_2$O$_3$. Overall, the presented MTP-based framework provides a computationally tractable and reliable route for predicting properties of semiconductors (both crystalline and amorphous) under operating conditions relevant to microelectronics and optoelectronics.

Figures (9)

• Figure 1: Comparison of the interatomic forces calculated with the MTP and DFT for $\beta$-Ga$_2$O$_3$. The training set (453 samples) is described in the section "Details on MTP training and validation for $\beta$-Ga$_2$O$_3$" in supplementary material. The validation set consists of 500 snapshots from the ab initio molecular dynamics trajectory performed at 1000 K. The black dashed line represents an ideal linear fit $x=y$.
• Figure 2: Comparison of the phonon band structures calculated with the MTP- and DFT-based approaches for $\beta$-Ga$_2$O$_3$.
• Figure 3: Comparison of the interatomic forces calculated with the MTP and DFT for amorphous Ga$_2$O$_3$. The training set (302 samples) was obtained after active learning, as described in the section "Details on MTP training for amorphous Ga$_2$O$_3$" in supplementary material. The validation set consists of 500 snapshots from the trajectory of AIMD simulation performed at 3000 K. The black dashed line represents an ideal linear fit $x=y$.
• Figure 4: Band gap renormalization in $\beta$-Ga$_2$O$_3$ computed using the configurations generated by means of harmonic sampling in the classical (${\rm BGR}^{\rm HS}_{\rm class}(T)$) and quantum (${\rm BGR}^{\rm HS}_{\rm quan}(T)$) cases.
• Figure 5: Band gap renormalization in $\beta$-Ga$_2$O$3$ computed using the configurations generated by means of classical harmonic sampling (${\rm BGR}^{\rm HS}_{\rm class}(T)$) and taking into account the anharmonic effects (${\rm BGR}^{\rm anh}(T)$).