ECE 440
Homework V
Fall 2009
Due: Friday, October 09, 2009
Please write your name and net ID on your homework. Show all work leading to your
answer.
1.
The acceptor profile of a silicon sample is shown below. Assume that the majority carrier
mobility can be obtained from Fig. 323 (or the enlarged graph posted in the 440 website),
and the sample is at thermal equilibrium at 300 K.
(a) Determine the diffusion coefficients for majority carriers at points A, B and C,
respectively.
(b) Find the majority carrier diffusion current densities along the cross sections at points A,
B and C, respectively. Indicate not only the magnitude but also the direction.
(c)
Find an expression for the builtin electric field
E
(x) at equilibrium over the range from
x= 1µm to x=3 µm.
(d)
Sketch a band diagram such as in Fig. 415 over the range from x= 1µm to x=3 µm and
indicate the direction of
E
.
X (μm)
0
10
16
/cm
3
N
A
10
15
/cm
3
1
2
3
4
5
6
7
8
A
B
C
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View Full DocumentTo find the diffusion coefficients, we have to first find the doping concentrations at those
points. After we find those values, we can use the Einstein Relationship (429) to figure
out the diffusion coefficients:
(b) Find the majority carrier diffusion current densities along the cross sections at points A, B
and C, respectively. Indicate not only the magnitude but also the direction.
Before we can calculate the diffusion current densities, we need to find the equation for
the majority carriers N
A
(x) = p(x).
diff
p
p
p
J
qD
x
∂
= 
∂
Remember that the plot shown in the HW is a semilog plot. Therefore, we need to
formally calculate the carrier concentration as a position of x, because the slope is
different at every point! Luckily, with a mathematical trick and 2 points, we can easily
find the equations we need. For the range 1μ
m
≤
x
3μ
≤
m
, the general form of the solution
and our boundary conditions are (note the solution here assumes the general solution is an
exponential in order to be consistent with the
results obtained in the book,
however,
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 Fall '09
 Lie
 band diagram, Streetman

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