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

中文翻译：

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Al1−xScxN 中的压电效应和极化切换

氮化铝是压电性的，沿线呈现自发极化 $C$轴，但不能通过施加电场来切换极化。在 AlN 中添加 Sc 可以增强压电性能，并使合金具有铁电性。我们对自发极化和压电极化进行了详细的第一性原理分析。显式超胞计算之间的比较表明，虚拟晶体近似产生了准确的极化结果，但在描述合金的相稳定性方面存在不足。我们将压电常数的行为联系起来${\mathrm{电子}}_{33}$ 内部位移参数的微观行为 $你$，发现内部应变贡献在 Sc 诱导的增强中占主导地位。的价值$你$随着钪浓度的增加，使合金局部更接近层状六边形结构。我们的方法使我们能够计算铁电开关势垒，我们根据 Ginzburg-Landau 理论将其分析为 Sc 浓度和温度的函数。