SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

468 CHAPTER 9. FIELD EFFECT TRANSISTORS: MOSFET

S D

N+ N+

A

A'

B

B'

ox

φ F

C

V

iB φ F

C

V

iB

c(x)

φ B

Fnc= FNsource+ c(x)

FNc= FNsource= FB

φs=2φ F φ s=2φ F + ch(x)

~~~~

g

FB

SourceFn

DrainFn

q Vc(x)

e

e e

E

E

E

E E E

E E

E

E

E

E

E

E

eV

eV

eV

eV

eV

Figure 9.21: Band diagrams taken at the source side (AA’) and the drain side (BB’) of the gate

charge decrease faster than the increase in the depletion charge. This is not possible since the
device is in weak inversion and the inversion charge is very small. Hence the change in band
bending in the semiconductor and the oxide is minimal as one approaches the drain which is
equivalent to saying that the lateral field in the channel is small. The very maximum voltage
drop in the channel isφFto keep the channel in weak inversion throughout the channel but even
this is not achievable when we consider the arguments based on the boundary condition placed
by the gate as described above. The combination of very small voltage drop in the channel
coupled with the small charge in the weak inversion layer makes drift currents minimal in the
channel. Another way to physically understand the picture is to recognize that in the weak inver-
sion regime the junction between the drain and the channel is closer to a reverse biased junction
and hence absorbs most of the applied voltage as is shown in figure 9.24.
In this instance, the inversion charge in the channel in the absence of generation and recombi-
nation is obtained as the solution of the diffusion equation

nch(x)=nsource

(

1 −

x

Lch

)