3.1.1 The Basic Semiconductor Equations

The basic equations are the Poisson equation and continuity equations for electrons and holes.

$$\varepsilon \psi$$ = q ^. (n - p - C) (3.2)

$$\left(\vphantom{R+\frac{\partial n}{\partial t}}\right. {\frac{\partial n}{\partial t}} \left.\vphantom{R+\frac{\partial n}{\partial t}}\right)$$ div J_n (3.3)

$$\left(\vphantom{R +\frac{\partial p}{\partial t}}\right. {\frac{\partial p}{\partial t}} \left.\vphantom{R +\frac{\partial p}{\partial t}}\right)$$ div J_p (3.4)

The unknown quantities of this equation system are the electrostatic potential $\psi$ and the electron and hole concentrations n and p, respectively. C denotes the net concentration of the ionized impurities, $\epsilon$ is the dielectric permittivity of the semiconductor, and R is the net recombination rate which has to be modeled properly.