Analytic Calculation About the Strain Distribution of Any-Shaped Self-Organized Quantum Dot

The strain distribution of quantum dots is analytically calculated using the Green’s function technique; the general expressions for any shaped quantum dot are derived. As examples, this method is applied to cube, pyramid column, and taper-shaped quantum dot. Our expressions are correct comparing with the calculated results by finite element method and finite difference. This approach is very powerful and can be applied to any-shaped quantum dot, especially this method can directly used in the calculation of electronic structure of quantum dot by the envelop function approximation or plane wave expansion methods, because the analytic expression can exactly calculate the strain at any position. In the paper, we give the strain distribution of four types of shaped quantum dot, and some comparisons are given with the results calculated by the finite element method.