Novel scaling laws for band gaps of quantum dots

We present new scaling laws that govern coupled mechanical deformation and opto-electronic properties (band gap) of quantum dots. Our theoretical work on quantum dots, confirmed via electronic structure calculation based on density functional theory indicates that novel size effects in band gap (above and beyond the well studied quantum confinement, electrostatic interaction and mechanical strain coupling) become operative in the 1-5 nm size range. These new coupled size-effects illustrated for Silicon clusters arise out of the size-dependency of the mechanical strain which has traditionally been ignored and devoid in classical continuum field theories (and what is typically employed by most current studies of strain-quantum dot coupling). The surface energies which induce the aforementioned size-effect are themselves found to be size-dependent for extremely small cluster size and peak within a very narrow cluster size range (0.6-2 nm).