4.3.4 Channel Region

From the numerical point of view, the simulation of semiconductor devices at 77 K should not be different from the 300 K case, if critical quantities are properly scaled. Slight differences should come from the physical models used for the characteristic parameters. Except for high gate voltages, plots showing the potential, electron concentration, electric field, and electron mobility have a similar shape as their counterpart at 300 K. Having this in mind, only figures with evident differences are presented.

Figure 4.87: Potential in the channel
@(110$\mu$m,77K,Vg=1.0V).

Figure 4.88: Potential in the channel
@(110$\mu$m,77K,Vg=5.0V).

Figure 4.87 and Figure 4.88 show the potential inside the channel at 110 $\mu$m from the source and at 1 nm from the silicon oxide-silicon interface at 77 K for a gate voltage of 1 V and of 5 V, respectively, and different magnetic fields. Although the cuts are made close to the drains, Figure 4.88 is different from its 300 K counterpart, where the potential is stronger influenced by the gate than by the drains.

Figure 4.89: Electron concentration in the channel
@(110$\mu$m,77K,Vg=1.0V).

Figure 4.90: Electron concentration in the channel
@(110$\mu$m,77K,Vg=5.0V).

Figure 4.89 and Figure 4.90 show the electron concentration inside the channel at 110 $\mu$m from the source and at 1 nm from the silicon oxide-silicon interface at 77 K for a gate voltage of 1 V and of 5 V, respectively, and different magnetic fields. Except for the case of a gate voltage of 1 V, the electron concentration behaves differently as compared to the 300 K case (see Figures 4.52 and 4.57). This behavior can be attributed to the cryogenic operation of silicon devices. In this case the charge ionization, the process which electrically turns on the charges for electric conduction, is dominated by the electric field, because the carriers (in this case, electrons) obtain energy from both the lateral and the transversal electric field. The extreme points in the electron concentration in Figure 4.90 are the result of the influence of the lateral electric field.

Figure 4.91: Electric field in the channel
@(110$\mu$m,77K,Vg=1.0V).

Figure 4.92: Electric field in the channel
@(110$\mu$m,77K,Vg=5.0V).

Figure 4.91 and Figure 4.92 show the electric field inside the channel at 110 $\mu$m from the source and at 1 nm from the silicon oxide-silicon interface at 77 K for a gate voltage of 1 V and of 5 V, respectively, and different magnetic fields. Except for the case of a gate voltage of 1 V, the electric field behaves differently from the 300 K case.