Inserting (4.5) into (4.2) yields

Substituting this into the relation of the electric displacement and the electric field

(4.7) |

results into

The permittivity is considered to be homogenous, therefore the first term in (4.8) is zero due to the definition of (4.5), so the conventional form of the Poisson equation is obtained:

The space charge density can be expressed as the product of the elementary charge and the sum of the electron and hole concentrations and the net concentration of ionized dopants :

Substituting (4.10) into (4.9) gives:

S. Vitanov: Simulation of High Electron Mobility Transistors