Thermally assisted tunneling and the Poole–Frenkel effect in homogenous a-Si

Abstract

Basic ideas for carrier capture and emission are applied to a homogenous a-Si exposed to high electric fields. By adding anisotropic Poole–Frenkel and tunneling transitions to the isotropic pure thermal transitions of free carriers between band states and traps, an analytical model for capture-emission rate of carriers in a-Si is developed. A stream of lateral electron flow in the conduction band incident to the potential barrier is obtained by integrating the contributions of all electrons within a thin electron sheet above the conduction band edge striking the potential barrier. Some of the incident electrons either tunnel through the barrier to the capturing funnel or cross the barrier apex as the Poole–Frenkel contribution to the captured electron flux. The opposite process of electron release from traps is described as an enhanced thermal emission of electrons crossing the barrier or tunneling through it to the conduction band. Equivalent expressions can be obtained for holes communicating between traps and the valence band. The effect of a high electric field is much more intense on carrier emission than on carrier capture. The balance between capture and emission rates in steady-state conditions is maintained at increased free carrier concentrations, resulting in strongly enhanced conductivity.