Spontaneous Polarization Calculations in Wurtzite II-Oxides, III-Nitrides, and SiC Polytypes through Net Dipole Moments and the Effects of Nanoscale Layering.

William Troy,Mitra Dutta,Michael Stroscio

doi:10.3390/nano11081956

Abstract

Herein, the spontaneous polarization in crystals with hexagonal symmetry are calculated as a function of the number of monolayers composing a nanostructure by adding the dipole moments for consecutive units of the nanostructure. It is shown that in the limit of a large numbers of monolayers that the spontaneous polarization saturates to the expected bulk value of the spontaneous polarization. These results are relevant to understanding the role of the built-in spontaneous polarizations in a variety of nanostructures since these built-in polarizations are generally quite large, on the order of 1 × 108 to 1 × 1010 V/m. Using these formulations, we come to the prediction that small nanolayered structures are theoretically capable of having larger spontaneous polarizations than their bulk counterparts due to how the dipole moments of the anions and cations within a wurtzite lattice cancel out with one another more in larger structures.

Highlights

Spontaneous polarization, Psp, is a polarization in materials that have asymmetric charge distributions, notably in wurtzite structures, and has been verified by both experiments and in highly complex modeling techniques such as Bloch’s Theorem in DensityFunctional Theory and ab initio Berry-phase calculations for periodic systems [1,2]
With the bulk Psp values of wurtzite IIB -VI, IIB referring to elements in the zinc family while IIA are alkaline earth metals, semiconductors such as CdSe, CdS, and ZnO being accurately calculated as primitive lattice net dipole moments [4]
The underlying causes for Psp to differ for such nanoscale structures and for the bulk2 isofnon10 integer number of elementary lattices within the overall structure and surface/interface charges, an effect which is negligible in bulk values but can have a large effect on the Psp values in small nanoscale lattices [6,7,8]

Summary

Introduction

Spontaneous polarization, Psp , is a polarization in materials that have asymmetric charge distributions, notably in wurtzite structures, and has been verified by both experiments and in highly complex modeling techniques such as Bloch’s Theorem in Density. Functional Theory and ab initio Berry-phase calculations for periodic systems [1,2] These studies of spontaneous polarization are promising for development of multifunctional surfaces, structures, and thin films with superior properties [3]. The underlying causes for Psp to differ for such nanoscale structures and for the bulk isofnon integer number of elementary lattices within the overall structure and surface/interface charges, an effect which is negligible in bulk values but can have a large effect on the Psp values in small nanoscale lattices [6,7,8]. P of=this atom terminate will become clear both in theory and mathematically as we continue

Materials and Methods

Results

Purely Hexagonal Lattice Structures

Depiction layering structure where is the anion and that

Conclusions