Transient Response of a p-n Junction

Abstract

The authors investigate the transient response of a p‐n junction in a circuit where the applied voltage is suddenly switched from the forward to the reversed direction. The behavior is studied as a function of the circuit resistance. The solution of the appropriate diffusion equation is carried out for a time‐dependent boundary condition, resulting in an integrodifferential equation. Analytical and numerical results for the current and the junction voltage as a function of time are then obtained by suitable approximations for the ``recovery'' and reverse periods. The ``recovery'' or reversal time t_f is the time required for the junction voltage to become negative and is given by $$\mathrm{erf}\sqrt{\frac{t_f}{\tau }}=\frac{1}{{\text{1+(I}}_f{\mathrm{/I}}_r)}$$ , where τ is the lifetime of holes, I_f is the forward current, and I_r the initial reverse current, which is limited by the external resistance.