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ECE 440
Homework IV Solutions
Spring 2006
Due: Wednesday, February 08, 2006
1. In practice we assume that the intrinsic Fermi level, E
i
,
coincides with the center of the band
gap. In reality it is not true. Derive an expression relating the intrinsic level E
i
to the center of
the band gap. Find the displacement of E
i
from the center of the band gap for both silicon
and germanium at room temperature. The effective mass values are m
n
* = 0.55 m
o
for Ge
and 1.1 m
o
for Si, m
p
* = 0.37 m
o
for Ge and 0.56m
o
for Si where m
o
is the free electron
mass.
We know that at thermal equilibrium, the intrinsic carrier concentrations for electrons and
holes are equal. By setting equations 315 & 319 equal to one another, a relationship
between the intrinsic Fermi Level and temperature can be found.
At this stage, it is a good idea to draw an energy band diagram to visualize what these
quantities physically mean.
What we are saying here is that our intrinsic Fermi Level is simply half the energy band gap
plus some offset term. You could have also defined the intrinsic Fermi Level as half the band
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 Spring '11
 Leburton

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