SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

9.5. MOSFET OPERATION 457

Ohmic

region

DRAIN

CURRENT

ID

DRAIN TO SOURCE BIASVD

Electron velocity ~ VS= 1.1 X 107 cm/s

VD = VDsat

Gate bias

Figure 9.15: A schematic of the I-V characteristics of a MOSFET. In the ohmic region the current
increases linearly with the drain bias for a fixed gate bias.

Material and Device Parameters

Important material and device parameters can be extracted from the I-V characteristics of the
MOSFET. At low drain bias we can ignore the quadratic term inVDS. The drain current is given
by

ID=

ZμnCox

L

(VGS−VT)VDS (9.5.11)

so that the extrapolation of the low drain bias current points gives the threshold voltageVT.This
is shown schematically in figure 9.16. Also, if the drain current is measured at two different
values ofVGSwhile keepingVDSfixed, the mobility in the channel can be determined, since

ID 2 −ID 1 =

ZμnCox

L

(VGS 2 −VGS 1 )VDS (9.5.12)

whereID 1 andID 2 are the currents at gate biases ofVGS 1 andVGS 2 .SinceZ, LandCoxare
known, the inversion channel mobility can be obtained.Itisworthnotingthatthemobilityina
MOSFETchannelisusuallymuchsmallerthanthemobilityinbulksilicon.Thisisbecauseof
thestrongscatteringthatoccursduetotheroughnessoftheSi-SiO 2 interface.TypicalMOSFET
electronmobilitiesare∼ 600 cm^2 /V·swhiletypicalelectronmobilitiesinbulksiliconare∼
1300 cm^2 /V·s.
The performance of the MOSFET as a device is defined via two important parameters, the
drain conductance (output conductance) and the transconductance.
The drain conductance is defined as

gD=

∂ID

∂VDS

∣∣

∣∣

VGS=constant

(9.5.13)