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.

对于半导体纳米晶体在光子学，生物成像，能量收集等方面的应用，尺寸大小对半导体晶体光电性能的影响引起了极大的兴趣。在这项工作中，我们研究了在纳米粒子同时作用下球形半导体纳米晶体的带隙变化的尺寸影响。机械压力和均匀温度变化，并在分析中纳入了表面弹性理论。使用泰勒级数展开到近似一阶，我们得到球形半导体纳米晶体的带隙变化，体积应变，最大剪切应变和温度变化之间的解析关系。由于温度升高而引起的热膨胀引起带隙的减小。