Electronic structure calculations of ultrasmall Si quantum boxes: Characteristics of band-edge states

Abstract

The electronic structure of ultrasmall Si quantum boxes (QB's) (in the range from tens to hundreds of Si atoms) saturated by hydrogen are calculated using the extended H\"uckel-type nonorthogonal tight-binding method. Special attention is given to electronic and optical characteristics of the valence-band (VB) and conduction-band (CB) edges (band gaps, oscillator strengths, and radiative lifetimes), which are closely associated with light-emission properties of a Si QB. Four atom configurations (types I--IV) of QB's with (100), (010), and (001) planes on the surface are studied, and calculated results are compared to ones calculated for QB's with (110), (11\ifmmode\bar\else\textasciimacron\fi{}0), and (001) planes. It is found that the Si(100)\ifmmode\times\else\texttimes\fi{}(010)\ifmmode\times\else\texttimes\fi{}(001) QB's can present both bulklike and surfacelike states at the CB edge and resulting oscillatory behavior in the band gap, depending on the atom configuration of the QB studied, whereas the (110)\ifmmode\times\else\texttimes\fi{}(11\ifmmode\bar\else\textasciimacron\fi{}0)\ifmmode\times\else\texttimes\fi{}(001) QB's show neither oscillatory behavior in the band gap nor surfacelike states at the CB edge. Analysis shows that the occurrence of the surfacelike CB-edge states in the ultrasmall Si(100)\ifmmode\times\else\texttimes\fi{}(010)\ifmmode\times\else\texttimes\fi{}(001) QB's, which is responsible for the enhanced oscillator strengths in optical transitions between the VB- and CB-edge states, is ascribed to interhydride interactions between trihydride units on the hydrogenated QB surface.