Predictive and Efficient Modeling of Hot Carrier Degradation with Drift-Diffusion Based Carrier Transport Models

6.4 Reggiani Model

Reggiani et al. have recently developed an analytical model for the DFs which is focused on modeling of HCD in LDMOS devices [35, 36]. The DF is expressed as:

$(6.4) \begin{equation} f(\varepsilon )=A\exp \left [-\alpha \varepsilon (1+\delta \varepsilon )/(k_{\mathrm {B}}T_{n}(1+\beta \varepsilon ))\right ].\label {eq:DF-Reggiani} \end{equation}$

Here $\delta$ and $\beta$ are fitting parameters, while $A$ and $\alpha$ are evaluated using the carrier concentration $n$ and carrier temperature $T_{n}$ computed using the DD scheme. In long channel devices the moment $n$ can be obtained directly from DD simulations while $T_{n}$ is evaluated using the local energy balance equation [177]. The Reggiani model produces non-equilibrium DFs for the bird’s beak and drain regions as shown in Figure 6.4. As for the channel region, the corresponding DFs are close to the equilibrium ones.

The DFs obtained by the approach proposed in this work, Section 4.3, are shown in the Figures 6.1, 6.2, 6.3, and 6.4 as gray curves. One can see that this DD-based scheme for the carrier distribution function can adequately represent the DFs.