Thomas-Fermi model of electronic screening in semiconductor nanocrystals

Using first-principle density-functional theory in the GGA approximation we have studied the electronic screening in semiconductor nanocrystals. Combining simple electrostatics and the Thomas-Fermi theory it is shown that an analytical and general form of a model position-dependent screening function can be obtained. Taking as a case study silicon nanocrystals, the relative weights of the nanocrystal core and surface polarization contribution to the screening are thoroughly discussed. The connection between the screening at the nanoscale and in the bulk is clarified.