Approximate analytical solutions of the electrostatic potential inside semiconductor caused by radiation-induced net positive oxide charge

This paper presents the analytical relation between the electrostatic potential inside the semiconductor and the positive oxide trapped charge at the interface. The expressions for N/P type materials are deduced after the accumulation/depletion approximation to Poisson equation and the truncation approximation to its boundary conditions. The solutions are self-consistent and complete. The exact numerical solutions are also given in this paper. The comparisons between the approximate analytical relations and the numerical solutions show that the analytical relations are good approximations except the case where strong inversion due to net positive oxide charge has occurred on the surface of P type material. Based on the criterion of the occurring of the strong inversion, the requirement for the surface density of positive trapped oxide charge to guarantee the visibility of depletion approximation is given. This work can be helpful in correctly analyzing mechanisms and magnitudes of the damage in the environment involving ionizing radiation in bipolar devices.