In order to obtain the continuity equations from the first Maxwell equation (4.1) the current density has to be split in an electron and hole component and . Assuming the net concentration of ionized dopants is time-invariant the following equation is obtained:

(4.12) can be expressed in two different ways with the help of the quantity :

This formulation gives the meaning of the net generation or recombination of electrons and holes. As such, it can be modeled for the respective recombination/generation mechanisms, thereby (4.13) and (4.14) can be considered as two equations.

S. Vitanov: Simulation of High Electron Mobility Transistors