The high K anomaly in ScAlN explained

Abstract

The integration of scandium aluminum nitride (ScAlN) into functional heterostructures has pushed semiconductor device physics into an extreme piezoelectric regime. Accurately determining the fundamental clamped dielectric permittivity (ε_33^S) of these alloys remains a major challenge, as standard density functional theory systematically overestimates this specific parameter due to well-known bandgap-underestimation limits. Furthermore, electrical capacitance-voltage (C-V) measurements of real-world devices do not yield this clamped baseline; instead, they capture an effective permittivity inflated by linear electromechanical coupling. Because epitaxial thin films are unconstrained in the out-of-plane direction, small-signal electrical measurements dynamically induce macroscopic lattice strain via the inverse piezoelectric effect. By applying these specific mechanical boundary conditions to the coupled equations of state, we utilize the analytical relation for operational permittivity: ε_eff=ε_33^S+e_33^2/C_33. Leveraging highly accurate first-principles predictions for the structural and piezoelectric tensors, we invert this model to extract the true, uninflated clamped dielectric baseline directly from experimental thin-film data. This approach circumvents the conventional limitations of pure first-principles dielectric calculations, flawlessly resolving the theoretical-experimental discrepancy and providing a critical framework for accurate device simulation in highly polar nitrides.