Statistical Mechanics of Charged Traps in an Amorphous Semiconductor

The effect of a Coulomb interaction between charged traps in an amorphous semiconductor is investigated within the premises of the Mott-Cohen-Fritzsche-Ovshinsky model. The grand partition function is expressed as a functional integral over a set of Gaussian random fields. The free energy is expressed as a sum of the mean-field result plus fluctuations about the mean field. It is shown that for the system under consideration, the mean field is just the Hartree self-consistent field and that at $T=0\mathrm{}$ °K it represents the exact ground state. It is shown that the fluctuations about the mean field represent correlations in the system. Approximate expressions for the mean occupation number and the renormalized energies of the charges are obtained as well as the renormalized single-particle density of states. The excitation spectrum of single quasiparticles, within any given band, is shown to have a quasigap. It is shown that the effect of a Coulomb interaction between the charged traps is to reduce the density of states at the Fermi energy by a factor of 2 below its value in the absence of interactions.