Strain effects on $n$-type doping in AlN

Controllable doping in AlN and its alloys is essential for deep-ultraviolet light sources. Ionization energies for donors in AlN ($\mathrm{Si_{Al}}$, $\mathrm{S_N}$, $\mathrm{Se_N}$) are high. We report first-principles calculations demonstrating that strain engineering can result in a reduction in ionization energies. The donor levels for $\mathrm{S_N}$ and $\mathrm{Se_N}$ shift closer to the conduction-band minimum (CBM) under in-plane tensile strains, driven by a downward shift of the CBM. The most widely used donor, $\mathrm{Si_{Al}}$, forms a $DX$ center in AlN. We find that a 2.5% in-plane tensile strain (which would be induced by pseudomorphic growth on GaN in experiment) shifts the ($+/-$) transition level from 271 meV to 98 meV below the CBM, which would enhance the electron concentration by three orders of magnitude. These results demonstrate that strain engineering offers an effective route to enhance doping levels in AlN.