Properties of a solid state device with mobile dopants: Analytic analysis for the thin film device

Current-voltage relations electric field and charge distribution profiles are calculated for a device in which the dopants are mobile. The thin film limit is discussed. The model solved is restricted to: (a) mobile holes and acceptors (b) steady state and (c) metal electrodes which block the ionic current. The solution is expressed as a series expansion in the small parameter delta=L/lambda(D) where L is the sample thickness and lambda(D) is a Debye length. The second order of the series expansion is found to vanish thus the corrections to the leading order appear only in the third term. The approximated analytic solution agrees with numerical results from a previous publication up to the quite high value of delta=1. The leading order in the I-V relations and in the hole distribution is independent of the acceptor motion. This implies that for thin devices of this form any motion of the dopants may be neglected and that dopants need not be limited only to those which exhibit low diffusion constants. Rectification is observed as long as asymmetry is introduced by two different contact potentials. This holds whether the contacts lead to depletion or accumulation. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2993618]