Polarization spontaneous and piezo: fundamentals and their implementation in ab initio calculations

TL;DR

This paper reformulates and critically reviews the fundamental properties of spontaneous and piezoelectric polarization, introduces a local model for calculations, and validates it through ab initio methods for nitride semiconductors.

Contribution

A new local model for spontaneous polarization is proposed and validated against ab initio calculations, improving understanding of polarization in nitride semiconductors.

Findings

The local model accurately predicts c-axis spontaneous polarization in nitride wurtzite semiconductors.

The model's polarization predictions align with Berry phase calculations and symmetry requirements.

Ab initio calculations of superlattices confirm the model's predictions and determine piezoelectric parameters.

Abstract

Fundamental properties of spontaneous and piezo polarization are reformulated and critically reviewed. It was demonstrated that Landau definition of polarization as a dipole density could be used to the infinite systems. The difference between the bulk polarization and surface polarity are distinguished thus creating clear identification of both components. The local model of spontaneous polarization was created and used to calculate spontaneous polarization as the electric dipole density. It was shown that the proposed local model correctly predicts c-axis spontaneous polarization values of the nitride wurtzite semiconductors. It was also shown that the proposed model predicts zero polarization in the plane perpendicular to the c-axis, in accordance with symmetry requirements. In addition, the model results are in accordance with polarization equal to zero for zinc blende lattice. These data confirm the basic correctness of the proposed model. The spontaneous polarization values obtained for all wurtzite III nitrides (BN, AlN, GaN and InN) are in basic agreement with the earlier calculations using Berry phase and slab models of Bernardini et al. {Bernardini et al. Phys Rev B 56 (2001) R10024 & 63 (2001) 193201} but not with Dreyer et al. {Dreyer et al. Phys. Rev X 6 (2016) 021038}. Wurtzite nitride superlattices ab initio calculations were performed to derive polarization-induced fields in the coherently strained lattices showing good agreement with the polarization values. The strained superlattice data were used to determine the piezoelectric parameters of wurtzite nitrides obtaining the values that were in basic agreement with the earlier data. Zinc blende superlattices were also modeled using ab initio calculations showing results that are in agreement with the absence of polarization of all nitrides in zinc blende symmetry.