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3.2.5 Low-Field Mobility Reconsidered

Another important issue when comparing DD and HD simulations is caused by the fact that in conventional mobility models the same low-field $ \mu^{\mathrm{LIS}}_{\nu}$ mobility is used for both transport models. This is problematic for position-dependent local models as is the case with the MINIMOS mobility model. Comparing the diffusion component of the DD and HD current (assuming constant density of states)

Jdiff, DD$\scriptstyle \nu$ = - s$\scriptstyle \nu$ . $\displaystyle \mu_{\nu}^{}$ . kB . TL . grad$\displaystyle \nu$ (3.63)
Jdiff, HD$\scriptstyle \nu$ = - s$\scriptstyle \nu$ . $\displaystyle \mu_{\nu}^{}$ . kB . grad$\displaystyle \left(\vphantom{
\nu \cdot T_{\nu}}\right.$$\displaystyle \nu$ . T$\scriptstyle \nu$$\displaystyle \left.\vphantom{
\nu \cdot T_{\nu}}\right)$ (3.64)
  = $\displaystyle {\frac{T_{\nu}}{T_{L}}}$ . Jdiff, DD$\scriptstyle \nu$ - s$\scriptstyle \nu$ . $\displaystyle \mu_{\nu}^{}$ . kB . gradT$\scriptstyle \nu$ (3.65)

it becomes obvious that the gradient of the carrier temperature causes another component of the diffusion current. Furthermore, the diffusion current due to the carrier gradient is enhanced by a factor T$\scriptstyle \nu$/TL. Both effects tend to broaden the carrier distributions in space. This effect is best illustrated in the channel of an NMOS transistor. The carrier distributions before and at the pinch-off point are shown in Fig. 3.13 and Fig. 3.14, respectively.

Since there are less carriers at the surface, the surface mobility model has a different impact on the resulting current which will be larger in the HD case. To account for the different carrier distributions the reference distance yref in (3.28) is modified to

yref, HD = yref, DD . $ \left(\vphantom{\frac{T_{\nu}}{T_{L}} }\right.$$ {\frac{T_{\nu}}{T_{L}}}$ $ \left.\vphantom{\frac{T_{\nu}}{T_{L}} }\right)^{\eta}_{}$ (3.66)

These broadened carrier distributions are the reason why the DD model tends to overestimate the electric field as the carrier concentration increases the space charge density in the channel.


next up previous contents
Next: 3.3 Examples Up: 3.2 Physical Parameters Previous: 3.2.4 Velocity Overshoot
Tibor Grasser
1999-05-31