3.5.5.1 Carrier Balance Equation

The derivation of the continuity equation is trivial starting from equation (3.29). Inserting the weight $\ensuremath{X}=1$ results in a vanishing Poisson bracket because of (A.9) as well as a vanishing field term. Thus, the continuity equation for carriers reads

$$\ensuremath{\ensuremath{\partial_{t} \ensuremath{\nu}}} + \ensure... ...suremath{\cdot}}\ensuremath{\ensuremath{\mathitbf{j}}_\nu}= - \ensuremath{R}\,.$$ (3.37)

The systematically derived equation is what can also be expected from a phenomenological point of view: The increase of carriers within a certain volume has to be equal to the influx minus the net recombination rate within this volume.

M. Wagner: Simulation of Thermoelectric Devices