Modeling boundary conditions for computation of piezoelectric fields in quantum dots with image charge analogy

Abstract

We present a simple approach for calculating the piezoelectric fields exerted by a stressor quantum dot buried in a semi-infinite piezoelectric matrix with a weak electromechanical coupling factor. It aims to take into account the electrical boundary conditions by introducing an image quantum dot mirrored the original dot with respect to the matrix surface. The technique is applied to a spherical InAs dot embedded in the GaAs semi-infinite matrix and the computation results exhibit an excellent agreement with more rigorous calculations reported by Pan [E. Pan, J. Appl. Phys. 91, 3785 (2002)]. We demonstrate that the approach can also be used in computing the piezoelectric fields for a square pyramid embedded in a semi-infinite matrix. It is furthermore anticipated that application of the method can remarkably simplify calculations of piezoelectric fields generated by arrays of the quantum dots of various shapes grown in a matrix material. These fields are known to be of considerable importance in quantum dot devices.