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Calculations of AC conductivity and DC hall mobility for hopping carriers

1980; Elsevier BV; Volume: 35-36; Linguagem: Inglês

10.1016/0022-3093(80)90577-3

1873-4812

P N Butcher, J. David Clark, Anjani Kumar, J A McInnes,

Theoretical and Computational Physics

The first direct computer calculations of ac conductivity are presented for 3-dimensional r-percolation hopping systems. Kirchhoff's equations are solved for 1600 randomly distributed sites using constant capacitances and conductances in which the dependence on the intersite separation r has the form r32exp (−2αr). The computer data are compared with the predictions of the pair approximation, corrected by the addition of the known dc limit 〈σ(O)〉 and with the predictions of the continuous-time random-walk theory. A simple general formula for the Hall mobility μH is derived. It involves the contribution to the equilibrium hopping rates from Holstein's three-sited process and the product of potential differences in the Miller-Abrahams network in zero magnetic field calculated with an electric field oriented in two orthogonal directions. We find that μH is proportional to site density in the r-percolation régime. For P-doped c-Si at 4K μH is in the order of 10−1 – 10−2 cm2V−1s−1 and is considerably larger than the drift mobility.