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 epsilon(2) between Hubbard bands (the A(0)- and A(+)-bands) in a p-doped semiconductor with increasing acceptor concentration N = N-0 + N-1 + N+1 and with increa sing degree of compensation K by donors for N-1 approximate to KN. The scre ening 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 A(0)-ban d towards the valence band and the A(+)-band towards the conduction band. T he concentration of holes hopping in the A(+)-band N+1N0/N is determined by the energy of their thermal generation epsilon(2) from the A(0)-band. The values of epsilon(2) calculated for Si : B are in agreement with experiment al data. (C) 1999 American Institute of Physics. [S1063-7826(99)00404-4].