An Approach for Calculating Strain Distributions in Arbitrarily Shaped Quantum Dots

We study strain distribution inside and outside an arbitrarily-shaped quantum dot (QD) buried in an infinite isotropic medium. By defining a very simple vector, we derive a compact formula for stress fields expressed by an integral over the interface between the QD and its surrounding material. Using this method, the analytical solution for a cuboidal QD is obtained, which is different from the previous result. It is shown that our solution satisfies the traction continuity condition on the interface. Based on this solution, it is found that the strain field in the cuboidal QD in the semiconductor heterostructure is sensitive to its height. In addition, the strain distribution around a hemispherical QD is also calculated and demonstrated.