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3.2.1 Poisson's Equation

Poisson's equation is a common constituent to all charge transport models for semiconductor devices and serves as the link between the electrostatic potential and the charge distribution within the device. It reads

$\displaystyle \ensuremath{\ensuremath{\ensuremath{\mathitbf{\nabla_{\!r}}}}\ens... ...t( \ensuremath{p}- \ensuremath{n}+ \ensuremath{N_A}- \ensuremath{N_D}\right)\,,$ (3.1)

where $ \ensuremath{\varphi}$ denotes the electrostatic potential, $ \ensuremath{\epsilon}$ the dielectric permittivity, $ \ensuremath{n}$ and $ \ensuremath{p}$ the electron and hole concentration, respectively, and $ \ensuremath{N_A}$ and $ \ensuremath{N_D}$ the concentration of acceptors and donors. Its derivation is straight-forward from Gauss' law and the proper material equation for the quasi stationary case [72]. In order to obtain a complete device description, Poisson's equation has to be solved self-consistently with the transport system in an iterative approach.


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M. Wagner: Simulation of Thermoelectric Devices