SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

474 CHAPTER 9. FIELD EFFECT TRANSISTORS: MOSFET

108

107

106

(^105102 103 104 105 106)
ELECTRIC FIEL D (V /cm)
CARRIER
DR IFT
VELO
CITY
(cm/s) vS ~10^7 cm/s
v = μE
3.0
2.0
1.0
0
Constant-mobility model
VGS =5 V
3 V
3 V
1 V
VDS (volts)
0510
VGS =5 V
V el oci ty - satur ati on model
ID
(mA)
Figure 9.26: (a) Velocity-field relation for the constant-mobility model and saturation-velocity
model. (b)ID−VDSrelations for a MOSFET using the constant-mobility model and the more
accurate saturation-velocity model.
whereID(L=fixed)is the current calculated assuming the channel length is fixed.
To a first approximation we can evaluate the change in effective channel length by assuming
that the excess potentialΔVDSfalls across the regionL.Thisgives

ΔL=

√

2 

eNa

[√

φfb+VDS(sat)+ΔVDS−

√

φfb+VDS(sat)

]

(9.6.4)

where
ΔVDS=VDS−VDS(sat)

This is also referred to asVdpin the Grebene and Ghandhi analysis presented in chapter 8 on
FETs and is only defined forVds>Vds(sat)Following the analysis of chapter 8 the drain
resistance

rd=

ΔVDS

ΔIDS

orrd=

ΔVdp

ΔIDS

is given by

rd=

πVdp

2 ID

(

L

d ̃ox

)

whereVdp=VDS−VDS(SAT),andd ̃oxis/ox·doxthe equivalent oxide thickness. This
emphasizes the need to reduce oxide thickness as we shrink the gate length,L; a high aspect
ratio design.