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Next: 3.1.3 Hydrodynamic Model Current Up: 3.1 The Device Simulator Previous: 3.1.1 Basic Semiconductor Equations

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:

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

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