Solution of the problem of charge-carrier injection into an insulating layer under self-consistent boundary conditions at contacts

The problem of charge carrier injection into a finite-length insulating layer is analytically solved in the drift-diffusion approximation, taking into account self-consistent boundary conditions. The main assumption is the neglect of intrinsic doping of the i-type layer. The solution allows calculation of the potential, electric field, and current-voltage characteristics of various structures, i.e., metal-i-n ⁺ (or p ⁺)-semiconductor, metal-i-layer-metal, and n ⁺(p ⁺)-i-n ⁺(p ⁺) structures. The solution allows generalization for structures having heterobarriers at semiconductor layer interfaces. The proposed approach considers contact phenomena and volume effects associated with the space-charge-limited current in the i-type layer. The solution is valid in both extreme cases and intermediate conditions.