5.3 Combining the Modifications

By combining the modifications for an anisotropic carrier temperature and a non-MAXWELLian closure relation the modified energy transport model becomes

$$\ensuremath{\ensuremath{\ensuremath{\boldsymbol{\mathrm{\nabla}}}}\ensuremath{\cdot}\ensuremath{\boldsymbol{\mathrm{J}}}_n} = \mathrm{q}\, (R + \ensuremath{\partial_{t} \, n}) \ ,$$ (5.37)

$$\ensuremath{\boldsymbol{\mathrm{J}}}_n = \mu_n \, \mathrm{k}_\mathrm{B}\, \Bigl( \ensuremath{\ensuremath... ...}{\mathrm{k}_\mathrm{B}} \, \ensuremath{\boldsymbol{\mathrm{E}}}\, n \Bigr) \ ,$$ (5.38)

$$\ensuremath{\ensuremath{\ensuremath{\boldsymbol{\mathrm{\nabla}}}}\ensuremath{\cdot}\ensuremath{\boldsymbol{\mathrm{S}}}_n} = - \frac{3}{2} \, \mathrm{k}_\mathrm{B}\, \ensuremath{\partial_{... ...B}\, n \, \frac{T_n - T_\mathrm{L}}{\tau_\mathcal{E}} + G_{\mathcal{E}\, n} \ ,$$ (5.39)

$$\ensuremath{\boldsymbol{\mathrm{S}}}_n = - \frac{5}{2} \, \frac{\mathrm{k}_\mathrm{B}^2}{\mathrm{q}} \, ... ...\ensuremath{\widetilde{\delta}}+ 2 \, \ensuremath{\widetilde{T}}}{5} \Bigr) \ .$$ (5.40)

Only the flux equations (5.38) and (5.40) are changed whereas the balance equations (5.37) and (5.39) remain unchanged.

M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF