Pseudopotential theory of nanometer silicon quantum dots

Abstract

We present a systematic approach to the study of the electronic structure of thousand atom (nanometer scale) quantum structures. This approach uses the empirical pseudopotential method to approximate the Hamiltonian and a plane wave basis to expand the wavefunctions. Two complementary, newly developed methods are used to calculate the electronic structure of the system. The first method solves for the discrete near-edge states (the valence band maximum and the conduction band minimum). Its computational time scales linearly with the size of the system. The second method calculates statistically the electronic density of states and optical absorption spectra. For a given resolution and statistical accuracy, its computational time is independent of the size of the system for systems smaller than ≈10,000 atoms. The combination of these two methods is used to study the electronic and optical properties of up to thousand Si atom quantum dots passivated by hydrogen. The properties studied include: (1) band gap vs size; (2) band gap vs shape; (3) analysis of band edge states in terms of bulk Bloch functions; (4) total electronic density of state and optical absorption spectra; (5) dielectric constant vs size; (6) photoluminescence radiative lifetime vs luminescence photon energy. The results are compared with tight binding and other model calculations. Comparison with experimental data is made whenever possible. Good agreements with experiment are obtained for photoluminescence lifetime and for the ratio between conduction band shift and valence band shift.