3.1.2 Drift-Diffusion Current Relations

The current densities $J_\nu$ for the carrier $\nu$ are derived from the momentum balance of the carrier system. The approximation for the drift-diffusion (DD) approach reads for electrons:

$${\bf {J}}_n = q \cdot \mu_n \cdot n \cdot \bigg( \bigg(\frac{E_C}{q}-\psi \bigg) +\frac{{\it k}_{\mathrm{B}}}{q} \cdot \frac{N_{C,0}}{n} \cdot \bigg( \frac{n \cdot {\it T}_\mathrm{L}}{N_{C,0}}\bigg )\bigg)$$ (3.4)

and for holes:

$${\bf {J}}_p = q \cdot \mu_p \cdot p \cdot \bigg( \bigg(\frac{E_V}{q}-\psi \bigg) -\frac{{\it k}_{\mathrm{B}}}{q} \... ...t {\text{grad}} \bigg( \frac{p \cdot {\it T}_\mathrm{L} }{N_{V,0}}\bigg )\bigg)$$ (3.5)

The quantities used in these equations are the conduction and valence band edges $E_C$ and $E_V$, the carrier mobilities $\mu_n$ and $\mu_p$, and the effective carrier densities of states $N_{C,0}$ and $N_{V,0}$.