8.3. CURRENT-VOLTAGE CHARACTERISTICS 371
LII
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E
Figure 8.11: Schematic diagram of (a) the charge distribution and (b) thex-component of the
electric field in the pinched-off region. The exact form of the electric field distribution is found
by solving Laplace’s equation.
The fourth condition, which reflects the assumption that pinch-off and velocity saturation occur
simultaneously, leads to
∑∞
n=1An(2n−1) =2 hEc
π(8.3.22)
For a physically meaningful solution,Anmust rapidly tend to zero for increasing values of
n. Otherwise, the sinh function will lead to extremely high fields near the drain which are larger
than the breakdown field of the semiconductor. We therefore retain only the first term in the
series, which leads to
Vhom(x, y)∼=2 hEc
πsin(πy
2 h)
sinh(πx
2 h)
(8.3.23)
Theparticularsolution,whichisdependentonthegatingstructureandhencethetypeofFET