Piezoelectric effect and polarization switching in Al_1−<i>x</i>Sc_<i>x</i>N

Aluminum nitride is piezoelectric and exhibits spontaneous polarization along the $c$-axis, but cannot be switched by applying an electric field. Adding Sc to AlN enhances properties, can make alloy ferroelectric. We perform a detailed first-principles analysis of polarization. Comparisons between explicit supercell calculations show that virtual crystal approximation produces accurate results for polarization, falls short in describing phase stability alloy. relate behavior constant $e_{33}$ microscopic internal displacement parameter $u$, finding strain contribution dominates Sc-induced enhancement. The value $u$ increases with scandium concentration, bringing locally closer layered hexagonal structure. Our approach allows us calculate ferroelectric switching barrier, which we analyze as function concentration temperature based on Ginzburg-Landau theory.