Question 1.
Consider a silicon wafer, which is doped uniformly with 10
17
cm
3
phosphorous atoms and 5 x
10
16
cm
3
boron atoms. Calculate the following using numerical techniques:
1.
The electron density versus temperature
2.
The Fermi energy versus temperature
3.
The resistivity versus temperature
Plot all variables on a linear scale versus the inverse of the temperature (1000/
T
). Vary the
temperature from 75 K to 1000 K and make sure you include enough points on each plot to
obtain a smooth continuous curve.
Make sure you include the impurity distribution functions (see section 2.5.3) when calculating
the carrier densities. The ionized donor density equals the donor density times the probability
that the donor level is not occupied or
N
d
+
=
N
d
[1 
f
donor
(
E
d
)].
Start from charge neutrality and specify each term as a function of the Fermi energy. This gives
you a single transcendental equation, which needs to be solved numerically.
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 '08
 staff
 Electron, Fermi, ni exp, Na

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