9.5. MOSFET OPERATION 459
be exploited. In figure 9.17 we show ann-channel MOSFET showing the source-to-body bias,
which is chosen to be zero or positive to reverse bias the source-to-substrate junction.
In the absence ofVSB, the inversion condition occurs whenVs, the surface potential, is equal
to− 2 φFas shown in figure 9.17b. In caseVSBis positive, the surface voltage required for
inversion is increased as shown in figure 9.17c by an amountVSB, since the body is at a higher
energy level.
WhenVSB> 0 , the depletion width is no longerWmaxbut is increased to absorb the added
potentialVSB. As noted previously the body bias alters the threshold voltage. The change in
the threshold voltage is given by
ΔVT=
√
2 esNa
Cox[√
| 2 φF+VSB|−√
| 2 φF|]
(9.5.17)
To ensure a positive shift in the threshold voltage,VSBmust be positive for the NMOS.
The threshold voltage of a MOSFET can also be modified by altering the doping density in the
silicon region as well. This can be done by ion implantation so that an added dose of acceptors
(or donors) is introduced. This changes the value of the depletion charge and consequently the
threshold voltage is altered.
Example 9.7Consider an-channel MOSFET at 300 K with the following parameters:Channel length, L =1. 5 μm
Channel width, Z =25. 0 μm
Channel mobility, μn = 600 cm^2 /V·s
Channel doping, Na =1× 1016 cm−^3
Oxide thickness, dox = 500A ̊
Oxide charge, Qss =10^11 cm−^2
Metal-semiconductor work function difference, φms = − 1 .13 VCalculate the saturation current of the device at a gate bias of 5 V.
The Fermi level position for the device is given byφF=0.026 ln(
1 × 1016
1. 5 × 1010
)
=0.348 V
The flat band voltage isVfb=φms−Qss
Cox=− 1. 13 − 0 .23 =− 1 .35 V
The threshold voltage is given by equation 9.3.12 asVT = − 1 .35 + 0. 696+