SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

470 CHAPTER 9. FIELD EFFECT TRANSISTORS: MOSFET

Vox

EC

EV

EiB

qVch(x) EFn

ch(x)

~~~~

qVg

EFB

S D

N+ N+

S D

N+ N+

EFN source

EFN drain

φBS

EFN (c h)

EC (x)

Vch(x)

EC

EV

EiB

φBS

EFsource=EFB

q Vg

EFB

VG

e

e

e

Figure 9.23: Band diagrams for anMOSFET at the source, drain, and along the direction of
transport for a device in the drift regime (for illustrative purposes only).

at threshold

Vth−Vfb=2φF+

1

Cox

√

2 seNA(2φF)

below threshold,

Vg−Vfb=ψS (φF<ψS< 2 φF)+

1

Cox

√

2 seNAψs

∴(Vg−Vth)=ψs− 2 φF

−φBS

where we have neglected the terms in the square root

∴IDS=

eDnNC

LCh

exp

(

VG−Vth

kBT

)