87
Metal-Oxide-Semiconductor System
function between the two ends of the composite system of materials depends
only on the first and the last materials [7]. Thus, for an MOS system, the work
function difference between the metal and the semiconductor defines the
behavior of the system. The work function difference between two materials
in contact can be visualized as the contact potential between them. For an
MOS capacitor system, the work function difference between the metal and
semiconductor (Φ m –Φ s ) causes distortion in the band structure of the system
as shown in Figure 3.3a. This is because when three materials are in contact, E f
is constant at equilibrium and E 0 is continuous; holes flow from p-type semiconductor to metal and electrons flow from metal to p-type semiconductor on
contact until a potential is built up to counterbalance the difference in work
function. However, the currents through SiO 2 are very small. Thus, there is a
variation in electrostatic potential from one region to another, causing band
TABLE 3.1
Work Function of Different Materials Used as Gate Materials
Material
Work Function (eV)
Al
4.10
Au
5.27
MoSi 2
4.73
TiSi 2
3.95
n-type degenerately doped polysilicon
4.05
p-type degenerately doped polysilicon
5.17
0.4 eV
E c
E c
qΦ ms
E f
E fm
E v
E v
E f
E c
E v
3.15 eV
3.15 eV
3.1 eV
3.1 eV
3.8 eV
Oxide
(a)
(b)
Aluminum
p-Silicon
Oxide
Aluminum
p-Silicon
FIGURE 3.3
MOS capacitor system at applied gate voltage, V g  = 0, showing (a) band bending at the surface
due to Φ ms between aluminum metal and p-type semiconductor and (b) flat band condition for
structure shown in (a); oxide is assumed to be free of any charges.