4.5 Cause of the Effect

A characteristic difference between a drift-diffusion and an energy transport simulation is that while the carriers stay at lattice temperature in the former one, they can reach significantly higher temperatures in the latter one. Carrier heating occurs in the pinch-off region near the drain. While the vast majority of electrons from the channel flow into the drain, some of them have enough energy to diffuse into the p-doped body, where a certain percentage recombines with holes. The remaining electrons flow into the source and drain regions, and are of no harm. The problem is, that pair recombination causes a lack of holes and hence a steady decrease of the body potential. The difference between drift-diffusion and energy transport can be seen in Fig. 4.4 and Fig. 4.9, respectively, where the distributed potential is shown at a vertical position of $y = 100 \, \mathrm{nm}$.

Figure 4.9: Distributed potential of the SOI (Device 1) obtained by energy transport simulations at a depth of $y = 100 \hspace {.35ex} \textrm {nm}$. The body potential drops below the equilibrium value of $- 0.46 \hspace {.35ex} \textrm {V}$.

In Fig. 4.9 an anomalous drop of the body potential is observed with increasing drain voltage. Not only is the drain-body junction reverse biased but also the source-body junction. Therefore, leakage currents from both junctions flow into the floating body. Clearly, the dropping body potential has an influence to the drain current via the body effect (Fig. 4.10). The gate overdrive $V_\mathrm{GS} - V_\mathrm{th}$ gets reduced because $V_\mathrm{th}$ increases while $V_\mathrm{GS}$ stays the same yielding to a reduced channel charge and therefore to a smaller drain current.

Figure 4.10: Threshold voltage as a function of the body bias of the SOI with a body contact (Device 2) obtained by drift-diffusion simulations. The threshold voltage was defined as the gate-source voltage at which the drain current equals $0.1 \hspace {.35ex} \textrm {mA}$.

The balance of the drift and diffusion currents is affected by carrier heating as follows.

$$\frac{\vert\ensuremath{\boldsymbol{\mathrm{J}}}_\mathrm{diffusion... ...athrm{L}\textcolor{lightgrey}{....}&\textrm{for {energy transport}} \end{cases}$$ (4.1)

This means that carrier diffusion in the energy transport model is enhanced by a factor $T_n / T_\mathrm{L}$ as compared with the drift-diffusion model.

To the occurrence of the current drop four partial effects contribute:

• In device regions where electrons reach high temperatures, such as the pinch-off region, electrons diffuse farther away from the interface and spread deeper into the p-body. This effect is also known as real space transfer (RST).

• Excess electrons accruing from the pinch-off region recombine with holes in the p-body (Fig. 4.1).

• Removing holes causes the body potential to drop and the source-body junction to become reverse biased. A steady state is reached when the reverse junction leakages of both the source-body and drain-body junctions compensate for the recombining holes.

• Due to the body effect the drain current decreases with decreasing body potential.

The RST of hot electrons from the pinch-off region to the depletion region underneath is at the outset of the effect. With drift-diffusion, the RST does not appear since electrons cannot move from the low quasi FERMI level (QFL) in the pinch-off region to any higher QFL in the depletion region or in the p-body. The difference in the electron concentration between drift-diffusion and energy transport can be seen clearly in Fig. 4.11 and Fig. 4.12. In Fig. 4.12 the spread of electrons into the body is remarkable. This difference has a great impact on the SHOCKLEY-READ-HALL generation/recombination rates depicted in Fig. 4.13 to Fig. 4.16. The critical area is the depletion region underneath the pinch-off region. While the drift-diffusion simulation predicts carrier generation in this area, which is the expected situation in this depletion region, in the energy transport simulation carrier recombination takes place because of the excess electrons. As a consequence of recombination, holes are removed from the p-body. If the body is contacted, the recombining holes are substituted by holes from the body contact, leading to a small substrate current which flows into the body (Fig. 4.7). However, in an SOI MOSFET the situation is different. The holes removed by recombination make the body potential drop. Eventually the reverse bias of the source-body and drain-body junctions becomes large enough such that the junction leakage currents compensate for the recombination current and a steady state is reached. Via the body effect the drop of the body potential causes the drain current to decrease.

Figure 4.11: Electron concentration in the SOI (Device 1) obtained by a drift-diffusion simulation.

Figure 4.12: Electron concentration in the SOI (Device 1) obtained by an energy transport simulation.

Figure 4.13: SRH net-generation in the SOI (Device 1) obtained by a drift-diffusion simulation. Generation occurs only in the drain-body junction.

Figure 4.14: SRH net-generation in the SOI (Device 1) obtained by an energy transport simulation. Generation occurs in both junctions.

Figure 4.15: SRH net-recombination in the SOI (Device 1) obtained by a drift-diffusion simulation. Recombination occurs only in the source-body junction.

Figure 4.16: SRH net-recombination in the SOI (Device 1) obtained by an energy transport simulation. Recombination occurs in the whole p-body.

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