5.1 Monte Carlo Simulations

The Monte Carlo code described in [62] has been used to generate reference data for comparison. Such comparison shows that the energy transport model significantly overestimates the electron diffusion into the substrate, (Fig. 5.1) whereas the drift-diffusion model underestimates it (Fig. 5.2).

Figure 5.1: Electron concentration in a MOSFET (Device 3) obtained by energy transport and Monte Carlo simulations.

Figure 5.2: Electron concentration in a MOSFET (Device 3) obtained by drift-diffusion and Monte Carlo simulations.

In Monte Carlo simulations the spreading of hot carriers away from the interface is much less pronounced than in energy transport simulations (Fig. 5.3). Another Monte Carlo/energy transport comparison is reported in [63]. The authors state that the electron concentration resulting from the energy transport model are several orders too high in the substrate region of a MOSFET, and propose a reduction of the heat flow by multiplying it with a constant $0.2$ to get better agreement between energy transport and Monte Carlo results. However, even with this crude measure the electrons under the pinch off region still spread deeply in the substrate [63, Fig.5].

Figure 5.3: Comparison of the electron concentration in a MOSFET (Device 3) at a vertical cut located in the middle between source and drain obtained by drift-diffusion, energy transport, and Monte Carlo simulations.

Subsections

• 5.1.1 Anisotropic Distribution Function
• 5.1.2 Non-MAXWELLian Closure

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