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)

$$\nu \nu \mu_{\nu}^{} \nu$$ = (3.63)

$$\nu \nu \mu_{\nu}^{} \left(\vphantom{ \nu \cdot T_{\nu}}\right. \nu \nu \left.\vphantom{ \nu \cdot T_{\nu}}\right)$$ = (3.64)

$${\frac{T_{\nu}}{T_{L}}} \nu \nu \mu_{\nu}^{} \nu$$ = (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_$\nu$/T_L. 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 y^ref in (3.28) is modified to

$$\left(\vphantom{\frac{T_{\nu}}{T_{L}} }\right. {\frac{T_{\nu}}{T_{L}}} \left.\vphantom{\frac{T_{\nu}}{T_{L}} }\right)^{\eta}_{}$$ (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.