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Gummel-Petit Junction Equation

The fundamental equation governing the current (II) through a p-n junction, derived from the recombination and diffusion of carriers, forming the basis for diode modeling.
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The statement of the theorem

The fundamental current II through a p-n junction, derived from the recombination and diffusion of excess minority carriers, is governed by the Gummel-Petit junction equation. This equation relates the current to the built-in potential VbiV_{bi} and the applied voltage VV: \nI=qA(Dpp0LpWWpeqV/kBT+Dnn0LnWWne−qV/kBT−p0−n0NA+PD)I = q A \left( \frac{D_p p_0}{L_p} \frac{W}{W_p} e^{qV/k_B T} + \frac{D_n n_0}{L_n} \frac{W}{W_n} e^{-qV/k_B T} - \frac{p_0 - n_0}{N_A + P_D} \right) \nWhere DD and LL are the diffusion coefficients and lengths, and qq is the elementary charge.
Source: Wikipedia