9.3. METAL-OXIDE-SEMICONDUCTOR CAPACITOR 439
1.0
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1.0
1014 1015 1016 1017 1018
p+ poly (n-Si)p+poly (p-Si)n+ poly (n-Si)Al(p-Si)Al(n-Si)n+ poly (p-Si)DOPING DENSITY (cm–3)φms(volts)Figure 9.7: Metal-semiconductor work function difference for some important gate metals used
in MOS devices. Note the signs ofφmsfor three different gate types for NMOS and PMOS.
In figure 9.7 we show the values ofφmsfor several different metals as a function of doping
density. Starting from the flat band position, there are three important regimes of biasing in the
MOS capacitor, as shown in figure 9.8.
(i)HoleAccumulation: If a negative bias is applied between the metal and the semiconductor,
the valence bands are bent to come closer to the Fermi level, causing an accumulation of holes
at the interface as shown in figure 9.8a. The difference between the Fermi level in the metal and
the semiconductor is the applied bias.
(ii)Depletion: If a positive bias is applied to the metal with respect to the semiconductor, the
Fermi level in the metal is lowered by an amounteVwith respect to the semiconductor, causing
the valence band to move away from the semiconductor Fermi level near the interface. As a
result the hole density near the interface falls below the bulk value in thep-type semiconductor
as shown in figure 9.8b. So,n∼p∼ 0.
(iii)Inversion: If the positive bias on the metal side is increased further, the conduction band
at the oxide-semiconductor region comes close to the Fermi level in the semiconductor. This
reverses the mobile charges from holes to electrons at the interface and theelectron density at
the interface starts to increase. If the positive bias is increased untilEccomes quite close to
the electron quasi Fermi level near the interface, the electron density becomes very high and the