Stress effect on bandgap change of a semiconductor nanocrystal in an elastic matrix

In this work, we study the bandgap change of a spherical semiconductor nanoparticle in an elastic matrix under the framework of linear elasticity. There are two important ratios – one is the ratio of interface energy between the nanoparticle-solution interface and the nanoparticle-matrix interface, and the other is the ratio of elastic modulus between the nanoparticle and the elastic matrix. Without external loading, the bandgap change is dependent on both ratios. Under a hydrostatic strain or a simple shear strain, the bandgap change decreases with increasing the ratio of the elastic modulus of the nanoparticle to that of the elastic matrix. Under simple shear strain, the bandgap change is orientation-dependent.