ECE 340
Homework XV
Fall 2003
Due: Monday, November 17, 2003
1.
Other than aluminum, polysilicon is another common gate metal for the MOS structure in silicon. By
incorporating heavy doping during chemical vapor deposition of polysilicon one can greatly increase the
conductivity of the polysilicon “metal”.
Accidentally our engineer has made a mistake and heavily doped
the polysilicon to be ptype. Reconstruct a diagram similar to Figure 617 showing the variation of the
metalsemiconductor work function potential difference
Φ
ms
with substrate doping concentration for p
+
polySi. Assume that the Fermi level of p
+
polysilicon is at the edge of valence band. Show your work and
draw to scale with accuracy.
Solutions:
Fermi level of p
+
polysilicon is at the edge of valence band, Fermi level of n
+
polysilicon is at the edge of
conduction band, therefore, the new graph is just fig 617 shifted up by E
g
.
For ntype silicon:
1.1
ln
0.0259ln
0.55 0.0259ln
22
g
dd
ms
poly
s
ii
i
E
NN
kT
n
qn
n
n
Φ=
Φ −
Φ= +
= +
=
+
For ptype silicon:
1.1
ln
0.0259ln
0.55 0.0259ln
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 Fall '03
 Lebutron
 Gate, Electric charge, Fermi level, Vfb

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