446 CHAPTER 9. FIELD EFFECT TRANSISTORS: MOSFET
Parameter NMOS PMOS
Substrate p-type n-type
φms
Al-gate – –
n+ Si-gate – –
p+ Si-gate + +
φF +–
Qox ++
γ +–
–
Cox ++
Source-to-body voltage VSB +
Table 9.1: Signs for various terms in the threshold voltage equation for a MOSFET.
Example 9.1Assume that the inversion in an MOS capacitor occurs when the surface
potential is twice the value ofeφF. What is the maximum depletion width at room
temperature of a structure where thep-type silicon is doped atNa=10^16 cm−^3
At room temperature, the intrinsic carrier concentration isni=1.5× 1010 cm−^3 for Si.
Thus, we have for the potentialφF,
φF =
kBT
e
ln
Na
ni
=(0.026eV) ln
(
1016
1. 5 × 1010
)
=0.347 V
The corresponding space charge width is
W =
[
4 s|φF|
eNa
] 1 / 2
=
[
4 × 11. 9 ×(8. 85 × 10 −^14 )(0.347)
1. 6 × 10 −^19 × 1016
] 1 / 2
=0. 30 μm
Example 9.2Consider an aluminum-SiO 2 -Si MOS device. The work function of Al is
4.1 eV, the electron affinity for SiO 2 is 0.9 eV, and that of Si is 4.15 eV. Calculate the
potentialVfbif the Si doping isNa=10^14 cm−^3.
