Symmetry-adapted calculations of strain and polarization fields in (111)-oriented zinc-blende quantum dots

We present expressions for the elastic and first-order piezoelectric tensor in (111)-oriented III-V zinc-blende semiconductors. Moreover, an equation for the second-order piezoelectric polarization vector in these systems is derived. Together these expressions provide an efficient route to calculate built-in potentials and strain fields in (111)-oriented zinc-blende nanostructures. Our detailed analysis provides insight into the key parameters that modify strain and built-in fields in a (111)-oriented zinc-blende system compared to a conventional (001) structure. We show that the calculated strain field in a (111)-oriented quantum dot displays the correct C_3v symmetry of the underlying crystal structure, even though we use a continuum-based approach and the quantum dot geometry is higher in symmetry than C_3v, e.g., C _v. This behavior originates from an in-plane angle dependence of certain elastic tensor components in the (111)-zinc-blende system. In addition, we compare the elastic and the first-order piezoelectric tensor of the (111)-zinc-blende systems with the corresponding quantities in a wurtzite structure and point out similarities and differences. This comparison provides, for example, insight into the sign of the shear piezoelectric coefficient e ₁₅ in the wurtzite system, which is still under debate in the literature. Our analysis indicates e₁₅<0, in accordance with recent experimental and theoretical results.