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ECE 440
Homework V Solutions
Spring 2008
1.
(a) A Si bar 0.1 cm long and 100 µm
2
in crosssectional area is doped with 5x10
16
/cm
3
arsenic atoms. Find the current at 300 K with 10 V applied across the length.
To find current, use Ohm’s law:
Since we already know the bias, all we need to do is find is the resistance (R) in order to
solve for the current. Equation (344) gives resistance in terms of area, charge carriers, and
mobilities.
If we substitute (344) into Ohm’s Law, we get the following expression for current.
Notice that this is the formula for the drift current which was derived in the text. Keep in
mind that this expression is only valid if the drift velocity of the carriers is smaller than the
saturation velocity. The saturation velocity is fixed for a particular material system. For
Silicon, the saturation velocity is approximately 10
7
cm/s.
First, we need to check that we are not in the saturation condition.
For an electron concentration of 5x10
16
cm
3
, we can find an electron mobility of 825 cm
2
/V
s. Plugging into the equation we find
Since we are not in the saturation condition we can use (*) to solve for the current.
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View Full Document(b) Repeat for a similar Si bar 1 µm long.
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 Spring '09
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