SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

456 CHAPTER 9. FIELD EFFECT TRANSISTORS: MOSFET

value ofQsgives (Vc(L)=VDS)

ID=

μnZCox

L

[{

VGS−VT−

VDS

2

}]

VDS (9.5.5)

Let us define parameterskandk′to define the prefactor in the equation above:

k=

μZCox

L

=

k′Z

L

(9.5.6)

From equation 9.5.1 we see that for a sufficiently high drain bias, the channel mobile charge be-
comes zero (the channel is said to havepinchedoff) at the drain side. This defines the saturation
drain voltageVDS(sat), i.e.,

Qs(VDS)=Qs(VDS(sat)) = 0

The pinch-off occurs at the drain end of the channel.

VDS(Qs(x=L)=0)=VDS(sat)=VGS−VT (9.5.7)

Our derivation of the current is valid only up to pinch-off. Beyond pinch-off as discussed in
chapter 7 the current essentially remains constant except for a small increase related to a decrease
in effective channel length. Other factors that cause increase in drain current beyond pinch-off
such as lowering of the threshold voltage and substrate injection are considered later.

Linear or Ohmic Region

In the case where the drain biasVDSis less thanVDS(sat)

VDS<VDS(sat)=VGS−VT (9.5.8)

For very small drain bias values, the current increases linearly with the drain bias, since the
quadratic term inVDSin equation 9.5.6 can be ignored. The current in this linear regime is

ID=k[(VGS−VT)VDS] (9.5.9)

whereVTis the gate voltage required to “turn on” the transistor by creating strong inversion.

Saturation Region

The analysis discussed above is valid up to the point where the drain bias causes the channel to
pinch off at the drain end. The saturation current now becomes, after substituting forVDS(sat)
in equation 9.5.5,

ID(sat)=k

{

(VGS−VT)^2 −(VGS−VT)

2

2

}

= k 2 (VGS−VT)^2

(9.5.10)

Thusoncesaturationstarts,thedraincurrenthasasquare-lawdependenceuponthegatebias
similartoallFETs.