First-Principle Analysis of Elastic Constants of $\beta-(\text{Al}_{\mathrm{x}}\text{Ga}_{1-\mathrm{x}})_{2}\mathrm{O}_{3}$ for Heterogeneous Interface Applications

Monoclinic
$\beta-\text{Ga}_{2}\mathrm{O}_{3}$
, with its wide bandgap, shows great potential for high-power electronics, offering high critical electric field strength for FETs and tunability through alloying with Al for enhanced performance. Determining the elastic constants for
$(\text{Al}_{\mathrm{x}}\text{Ga}_{1-\mathrm{x}})_{2}\mathrm{O}_{3}$
is crucial, as it enables the prediction of material properties, including piezoelectricity, thereby broadening the potential for advanced device applications. This study uses first-principle calculations to investigate the piezoelectric properties of
$\beta-(\text{Al}_{\mathrm{x}}\text{Ga}_{1-\mathrm{x}})_{2}\mathrm{O}_{3}$
, focusing on the analysis of elastic constants. Within the field of semiconductor materials science, the structural stability and piezoelectric properties of
$\beta-(\text{Al}_{\mathrm{x}}\text{Ga}_{1-\mathrm{x}})_{2}\mathrm{O}_{3}$
alloys, particularly for compositions where
$\mathrm{x}=0.25$
and
$\mathrm{x}=0.5$
, have been meticulously investigated. This study employs first-principle calculations to identify the most stable configurations by analyzing inter-atomic distances between Aluminum atoms, pinpointing the optimal Aluminum positions within the crystal structure for these compositions. The foundation of understanding the material's structural integrity facilitates an in-depth exploration of its piezoelectric characteristics through the calculation of six essential elastic constants C11,C22, C33, C12, C23, and C13. These calculations reveal the material's mechanical and electrical responses under stress, offering critical insights into the trends and behaviors of these elastic constants. This research thus provides a comprehensive overview of the piezoelectric properties of
$\beta- (\text{Al}_{\mathrm{x}}\text{Ga}_{1-\mathrm{x}}$
)2O
3
alloys, focusing on the intrinsic properties of the materials. The findings of this research promise to enhance our understanding of
$\beta-(\text{Al}_{\mathrm{x}}\text{Ga}_{1-\mathrm{x}})_{2}\mathrm{O}_{3}$
properties, paving the way for advancements in semiconductor technology.