Size effect on the bandgap change of quantum dots: Thermomechanical deformation

The size effect on the optoelectronic behavior of semiconductor crystals has attracted great interest for the applications of semiconductor nanocrystals in photonics, bioimaging, energy harvesting etc. In this work, we study the size effect on the bandgap change of spherical semiconductor nanocrystals under concurrent action of mechanical pressure and uniform temperature change and incorporate the theory of surface elasticity in the analysis. Using Taylor series expansion to the first order of approximation, we obtain an analytical relationship between the bandgap change of the spherical semiconductor nanocrystal, the volumetric strain, the maximum shear strain and the temperature change. The thermal expansion due to the temperature increase causes the decrease of bandgap. The effect of surface energy/elasticity on the bandgap change exhibits similar size dependence to the effect of the Coulomb interaction, and the effect of the volumetric strain on the bandgap change is equivalent to the pressure (hydrostatic stress) effect.