SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

9.6. IMPORTANT ISSUES IN REAL MOSFETS 469

S D

N+

A

A'

B B '

nweak inversion

EFN source EFN(x) EFN drain

EC

EC

EFB

EiB

eVG

Along AA'

Along BB'

N+

nsource=NCexp (eφBS)/kBT

eφBS

eφBS eφF

Figure 9.22: Band diagram as viewed along the gate-substrate axis, and along the source-drain
axis withEFsource=EF channel.

much like the electron profile in a narrow base bipolar transistor

∴IDS=eDn

nsource

Lchannel

the magnitude ofnsourceis limited by the barrier at the source end of the channel

nsource=NCexp (−eφBS/kBT)

or

IDS=q

Dn

Ln

NCexp (−eφBS/kBT)

to getIvs.(Vg−Vth)we need to relateφBSto(Vg−Vth)which is readily done by analyzing
the band diagram alongAA′.

Vg−Vfb=ψs+

1

Cox

√

2 seNAψs