SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

458 CHAPTER 9. FIELD EFFECT TRANSISTORS: MOSFET

I-V curve in the ohmic region

Intercept is turn-on voltage VT

VG

VT

ID

0

μn Cox Z VD

L

Slope =

Figure 9.16: A schematic showing how the basic parametersVTand mobility can be obtained
from theID−VGScurves in the ohmic region of the MOSFET.

At low drain biases we get from equation 9.5.9 for the ohmic region

gD=

ZμnCox

L

(VGS−VT) (9.5.14)

In the saturation region in our simple model, the drain conductance is zero. In real devicesgD
is not zero at saturation, as discussed in section 9.6.2. The transconductance of the MOSFET is
closely linked to the speed of the device and is given by

gm=

∂ID

∂VGS

∣∣

∣∣

VDS=constant

(9.5.15)

In saturation we have

gm=

ZμnCox

L

(VGS−VT) (9.5.16)

A high-transconductance device is produced if the channel length is small and channel mobility
is high. The transconductance represents the control of the gate on the channel current and is
usually quoted in millisiemens per millimeter (mS/mm) to remove the dependence on the gate
widthZ.

9.5.2 Substrate Bias Effects

In the analysis above we have assumed that the substrate bias is the same as the source bias. In
MOSFET circuits, the source-to-substrate (or body) biasVSBis an additional variable that can