Excited-state relaxations and Franck-Condon shift in Si quantum dots

Excited-state relaxations in molecules are responsible for a redshift of the absorption peak with respect to the emission peak (Franck-Condon shift). The magnitude of this shift in semiconductor quantum dots is still unknown. Here we report first-principle calculations of excited-state relaxations in small (diameter $<~2.2\mathrm{nm})$ Si nanocrystals, showing that the Franck-Condon shift is surprisingly large $(\sim 60\mathrm{meV}$ for a 2.2-nm-diameter nanocrystal). The physical mechanism responsible for the Stokes shift changes abruptly around $\sim 1$ nanometer in size, providing a clear demarcation between “molecules” and “nanocrystals.”