Elastic and piezoelectric fields in substrates GaAs (001) and GaAs (111) due to a buried quantum dot

Abstract

In this article we present a rigorous study on the elastic and piezoelectric fields in substrates GaAs (001) and GaAs (111) due to a buried quantum dot (QD) using an efficient and accurate continuum mechanics model. It is based on a Green’s function solution in anisotropic and linearly piezoelectric half space combined with the generalized Betti reciprocal theorem. To address the effect of material anisotropy, two other substrates, Iso (001) and Iso (111), are also examined and they are assumed to be elastically isotropic. For a point QD with hydrostatic misfit strain γ*=0.07 in volume va=4πa3/3 where a=3 nm, and at depth h=10 nm below the surface, we have observed the following features. (1) The simplified elastically isotropic model should, in general, not be used for predicting elastic and piezoelectric fields in the semiconductor GaAs. (2) The magnitude of the QD-induced piezoelectric potential on the surface of GaAs (111) or GaAs (001) is comparable to, or even larger than, the direct potential. (3) Large horizontal and vertical electric fields, on the order of 106 V/m, can be induced on the surface of GaAs (001) and GaAs (111). (4) The elastic field induced on the surface of GaAs (001) has rotational symmetry of order C4 (i.e., the elastic field remains the same after rotation of 2π/4 around the [001] axis), while the corresponding piezoelectric field has rotational symmetry of order C2. On the other hand, both the elastic and piezoelectric fields on the surface of GaAs (111) have rotational symmetry of C3 around the [111] axis. (5) The magnitude of the elastic and piezoelectric quantities on the surface of GaAs (111) is, in general, larger than that of the corresponding quantities on the surface of GaAs (001). (6) Under different electric surface conditions (insulating or conducting), the surface piezoelectric fields induced are quite different.