SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

8.3. CURRENT-VOLTAGE CHARACTERISTICS 373

VD

ID

Vdp

VDS(sat)

slope = gd

Figure 8.12:IDvs.VDfor constantVG.

VD(or a large output conductancegd) implies a large increase inEs, whereas insensitivity ofID
with respect toVD(or a smallgd) implies a small increase inEs.
The first is the case before saturation where

Es

VD

L

Escontinues to increase untilVD=VDS(sat)and at a corresponding current

ID(sat)=σs

VDS(sat)

L

In general

ID(sat)=σs

VDS(sat)

LI

whereLIis the length of Region I. Prior to saturation,L=LI.
OnceVD>VDS(sat), the total channel voltage is split between Region I and Region II.
The voltage drop across Region I remains close toVDS(sat), while the remaining voltageVdp=
VD−VDS(sat)is dropped across Region II. In Region II, the hyperbolic relation ofVto distance
allows for large changes inVto be absorbed with only a small change inLII. Hence the
gradual channel lengthLI=L−LIIchanges very slowly with drain bias, leading to a very
small increase inIDS(sat)forVD>VDS(sat), or a small output conductance in the saturation
regime. This is critical to good device operation.
This analysis can also give a clear understanding of the square law behavior ofIDS(sat)=
K(VG−VT)^2. The channel conductivity at the sourceσscan be written as

σs=eμnns=eμnCG(VG−VT) (8.3.28)