Elastic and piezoelectric fields around a buried quantum dot: A simple picture

The elastic field around a buried, strained quantum dot is solved with a scalar potential that obeys Poisson’s equation. Standard methods from electrostatics can therefore be used. The lattice mismatch and displacement are analogous to the charge density and electric field. The dilation is proportional to the local lattice mismatch and therefore vanishes outside a dot. Expressions are also given for the piezoelectric potential. The results agree remarkably well with previous numerical calculations for a pyramidal dot. Thermoelasticity provides another analogy with many useful solutions available. These results are for an isotropic medium but cubic symmetry is considered briefly.