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3.1.1 The Basic Semiconductor Equations

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

div($\displaystyle \varepsilon$ . grad $\displaystyle \psi$) = q . (n - p - C) (3.2)
div Jn = q . $\displaystyle \left(\vphantom{R+\frac{\partial n}{\partial t}}\right.$R + $\displaystyle {\frac{\partial n}{\partial t}}$ $\displaystyle \left.\vphantom{R+\frac{\partial n}{\partial t}}\right)$ (3.3)
div Jp = - q . $\displaystyle \left(\vphantom{R +\frac{\partial p}{\partial t}}\right.$R + $\displaystyle {\frac{\partial p}{\partial t}}$ $\displaystyle \left.\vphantom{R +\frac{\partial p}{\partial t}}\right)$ (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.

Tibor Grasser