The high K anomaly in ScAlN explained

TL;DR

This paper explains the high dielectric constant in ScAlN as an electromechanical effect caused by internal electric fields inducing lattice strain, reconciling theory and experiment.

Contribution

It introduces an analytical model linking permittivity to electromechanical coupling, explaining the high K behavior in polar semiconductors like ScAlN.

Findings

The model accurately predicts experimental permittivity values across ScAlN alloys.

Electromechanical inflation accounts for the discrepancy between rigid-lattice calculations and experiments.

Defines the fundamental limit of the rigid-lattice approximation in highly polar materials.

Abstract

We resolve the long-standing discrepancy between theoretical material constants and experimental observations of the dielectric response in scandium aluminum nitride (ScAlN). While first-principles calculations of the rigid lattice predict a permittivity of about 11.7, experiments consistently report values near 15. We demonstrate that this "high K" behavior is a manifestation of electromechanical inflation, where the enormous internal electric fields of polar heterostructures induce macroscopic lattice strain via the inverse piezoelectric effect. By applying stress-free mechanical boundary conditions to the coupled equations of state, we derive an analytical relation for the effective permittivity: epsilon_eff=epsilon_33^S + e_33^2/C_33. This model quantitatively accounts for experimental observations across the ScAlN alloy range and defines the fundamental limit of the rigid-lattice approximation in highly polar semiconductors.