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

Electrostatics is used to model the narrowing of the energy gap ɛ2 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 ɛ2 from the A0-band. The values of ɛ2 calculated for Si: B are in agreement with experimental data.