SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

454 CHAPTER 9. FIELD EFFECT TRANSISTORS: MOSFET

The maximum depletion width (assumingVs=− 2 φF)is

Wmax=

(

4 |φF|

eNa

) 1 / 2

=

{

4(11. 9 × 8. 85 × 10 −^14 )(0.347)

1. 6 × 10 −^19 × 1016

}

=0. 3 × 10 −^4 cm

The minimum capacitance is now

Cmin =

CoxCs

Cox+Cs

=

(

ox

dox+oxsWmax

)

=2. 3 × 10 −^8 F/cm^2

The capacitance under flat band conditions is

Cfb =

ox

dox+oxs

√(

kBT

e

)(s

eNa

)

=

3. 9 ×(8. 85 × 10 −^14 )

(500× 10 −^8 )+ 113.^9. 9

√

0. 026 × 11. 7 × 8. 85 × 10 −^14

1. 6 × 10 −^19 × 1016

=5. 42 × 10 −^8 F/cm^2

It is interesting to note thatCfbis∼80% ofCoxandCminis∼33% ofCox.

9.5 MOSFETOPERATION ..............................

With some important differences the MOSFET behaves in a manner similar to the MESFETs
and HFETs discussed in chapter 8. A key difference is of course the electron density created by
inversion. In figure 9.14 we show the basic NMOSFET structure.

9.5.1 Current-VoltageCharacteristics ......................

The full three-dimensional analysis of the MOSFET requires complex numerical techniques.
However, we will present a simplified approach that gives a good semi-quantitative understand-
ing of the current-voltage characteristics of the device.
Qualitatively, we can see how the MOSFET I-V characteristics behave. When a bias is applied
between the source and the drain, current flows in the channel near the Si-SiO 2 interface if a
channel exists. The charge density in the channel is controlled by the gate bias as well as the
source-drain bias. The gate bias can thus modulate the current flow in the channel, as discussed
for the MESFET or JFET case. For a simple model we assume that the mobility is constant.
We also use the gradual channel approximation.Intheanalysisdiscussedherewewillassume
thatthesourceisgroundedandallvoltagesarereferredtothesource. Using the gradual channel
approximation for the induced charge in the channel, we can treat the charge-voltage problem