SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

9.6. IMPORTANT ISSUES IN REAL MOSFETS 477

L

N+ dj N+

dB L

L

L

N+ N+

Figure 9.29: Schematic of the channel of a short-channel MOSFET showing the definitions for
relevant length parameters.

of strong inversion (threshold) is determined by the 1-dimensional potential distribution from
the gate to the substrate. This in effect neglects the effect of the source and drain contacts on the
charge and hence band bending in the channel. Figure 9.28 shows the impact of the contacts on
the band bending in the channel. The depletion due to the source and drain contacts encroaches
substantially under the gate, increasing the band bending and hence decreasing the additional
gate voltage required to create strong inversion compared to the long channel case. This is shown
in figure 9.29 where the source and drain regions are assumed to be cylindrical with radiusdj
and the depletion depth of extentdB. At strong inversion the conduction band at the surface is
close to the source and hence the surface band bending is similar to band bending at then+−p
junctions giving a uniform value ofdBfor small values ofVDS. The amount of charge that
images on the gate electrode is assumed under a trapezoidal approximation to be:

Q′B=−eNAdB

(

L+L′

2

)

In the long channel case:
QB=−eNAdBL

or the charge in the shaded regions image on the gate and not on the contacts. Thus the reduced
bulk charge is the source of the reduced threshold voltage from

VT=2φF+Vfb−

QB

Cox

and

VˆT=2φF+Vfb−Q

′
B
Cox
or

ΔVT=

QB−Q′B

Cox

=

QB

Cox

[

1 −

Q′B

QB

]