SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

368 CHAPTER 8. FIELD EFFECT TRANSISTORS

Saturation

region

Locus for VDS(sat)

Linear

region

VB

VDS

0

VGS = 0

VGS> 0

VGS< 0

DRAIN VOLTAGE

DRAIN CURRENT

ID

Breakdown

region

Figure 8.9: Typical I-V characteristics of ann-MESFET. In the Shockley model discussed in the
text, it is assumed that once pinch-off of the channel occurs, the current saturates. In the figure,
VBis the breakdown voltage.

8.3.2 A Nearly Universal Model for FET Behavior : The Saturation Regime

The Shockley model is only valid for drain voltages smaller thanVDS(sat). Consider again
what happens when the gate voltage is held fixed and the drain voltage is increased toward
positive values. As the drain voltage approachesVDS(sat), the drain end of the channel becomes
very narrow, so the electric field in the direction of current flow must become large in this region
in order for current continuity to be maintained. This clearly violates the assumption of a gradual
channel that was used in the Shockley analysis. The current characteristics beyond pinch-off can
be explained as follows.
Consider the two generic materials Si and GaAs. In materials like silicon the velocity-field
relations are such that the velocity increases monotonically with the applied field and eventually
saturates. In GaAs, the velocity peaks at a fieldEp(∼ 3 kV/cm) and then decreases and gradually
saturates. Therefore, it is reasonable to assume that in a FET, once the drain voltage is very close
toVDS(sat), the velocity of the electrons at the drain side of the channel saturates, as the channel
on the drain side narrows approaching pinch-off; we denote the channel width on the drain side
at pinch-off by the symbolδ.

δ=

ID(sat)

eNdvsatZ

(8.3.16)

wherevsatis the electron saturation velocity in the material.