First-principles band alignment engineering in polar and nonpolar orientations for wurtzite AlN, GaN, and B$_x$Al$_{1-x}$N alloys

Boron aluminum nitride (B$_x$Al$_{1-x}$N) is a promising material for next-generation electronic and optoelectronic devices due to its ultra-wide bandgap, high thermal stability, and compatibility with other III-nitride semiconductors. Despite its potential, the band alignments of B$_x$Al$_{1-x}$N remain largely unexplored, although this information is essential for device design. In this study, we compute the valence and conduction band alignments of nonpolar ($a$-plane) and polar ($c$-plane) B$_x$Al$_{1-x}$N, and compare them with those of AlN and GaN. Using density functional theory, many-body perturbation theory, $GW_0$ method, and a novel passivation scheme, we find that they have near-zero valence band alignments for low-$x$ B$_x$Al$_{1-x}$N/AlN, while higher compositions ($x > $0.333) exhibit type I or II band alignments. The band alignments also show a notable dependence on surface polarity and the tetrahedral distortion of the B$_x$Al$_{1-x}$N structures. Our computed offsets are in good agreement with available experimental data. Due to their low valence band alignments and higher conduction band alignments, the B$_x$Al$_{1-x}$N/AlN heterostructures could be well suited for high-electron-mobility transistors and ultraviolet light-emitting diodes. The band alignments of B$_x$Al$_{1-x}$N determined in this study provide essential design guidelines for integrating these ultra-wide bandgap alloys into advanced semiconductor technologies.