Electrostatic model of the energy gap between Hubbard bands for boron atoms in silicon

Abstract

Electrostatics is used to model the narrowing of the energy gap ε₂ between Hubbard bands (the A⁰-and A⁺-bands) in a p-doped semiconductor with increasing acceptor concentration N=N₀+N_-1+N₊₁ and with increasing degree of compensation K by donors for N_-1≈KN. The screening of impurity ions by holes hopping from acceptor to acceptor is taken into account. It is shown that this effect leads to a shift of the A⁰-band towards the valence band and the A⁺-band towards the conduction band. The concentration of holes hopping in the A⁺-band N₊₁N₀/N is determined by the energy of their thermal generation ε₂ from the A⁰-band. The values of ε₂ calculated for Si : B are in agreement with experimental data.