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

6.2 Cassi Model

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Figure 6.2: Same as Figure 6.1 but for the Cassi model.

Cassi and Riccó proposed an expression to account for the non-Maxwellian shape of the DFs observed in MOSFETs, especially in the drift and the drain regions. Their model for the DF is given by [33]:

(6.2) \begin{equation} f(\varepsilon )=A\exp \left (-\chi \varepsilon ^{3}/E^{1.5}\right ),\label {eq:Cassi} \end{equation}

where \( \varepsilon \) is the carrier energy, \( \chi =0.1 \) a fitting parameter and \( E \) the local electric field. The Cassi model results in DFs which are substantially non-equilibrium in the bird’s beak region, as shown in Figure 6.2. Due to the fixed curvature, the shape of the DF is similar in the channel and in the drain region. Hence, the carrier energies obtained from the Cassi model for these device sections are significantly lower compared to the bird’s beak region.