SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

370 CHAPTER 8. FIELD EFFECT TRANSISTORS

W(x)

δ

SGD

LI LII

h

EFn (drain)

EFn (source)

(a)

(b)

Semi-insulating substrate

x

Region I Region II

EC

quasi-linear hyperbolic

Figure 8.10: Schematic diagram of FET whenVDS>VDS(sat), drain end of channel is pinched
off. (b) Band diagram across the channel of the device.

where the sine function represents the symmetric boundary conditions in they-direction. This
voltage distribution is caused by the positive charges on the drain electrode. The boundary
conditions that have to be satisfied are

Vhom(x,0) = 0

Vhom(0,y)=0

∂Vhom(x, h)

∂y

=0 (8.3.20)

∂Vhom(0,h)

∂x

= −Ec

The first two conditions are satisfied by the chosen functional form ofVhom. The third condi-
tion requires

αn=βn=

(2n−1)π

2 h

(8.3.21)