Chapter 7
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7.16
(a)
V
(b)
(i) For ,
cm
or m
(ii) For V,
cm
or m
(c)
(i)For ,
V/cm
(ii)For V,
V/cm
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7.17
(a)
V
(b)
cm
or m
cm
or m
cm
or m
Also m
(c)
V/cm
(d)
F
or pF
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7.18
(a)
We find
cm
cm
(b)
cm
or m
cm
or m
(c)
V/cm
(d)
F/cm
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7.19
(a)
V
(b)
So
(c) For a larger doping, the space charge width narrows which
results in a larger capacitance.
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7.20
(a)
or
V
Now
or
or
so that
V
which yields
V
(b)
or
V
We have
so that
V
which yields
V
(c)
or
V
We have
so that
V
which yields
V
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7.21
(a)
or
We find
V
V
We find
or
(b)
or
(c)
or
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7.22
(a) We have
or
For V, we find
or
V
(b)
Then
Now
so
We can then write
which yields
cm
and
cm
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7.23
V
So
which yields V
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7.24
(a)
V
(i) For ,
pF
(ii) For V,
pF
(b)
V
(i) For ,
pF
(ii) For V,
pF
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7.25
V
(a)
F
HmH
(b)
(i) For V, pF
HzMHz
(ii) For V, pF
HzMHz
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7.26
Let V
(a)
cm
(b)
cm
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7.27
(a)
By trial and error,
cm,
cm,
V
(b) From part (a),
By trial and error,
cm,
cm,
V
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7.28
(a)
or
V
(b)
or
cm
Also
or
cm
(c) For m, we have
which becomes
We find
V
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7.29
An junction with cm,
(a) A one-sided junction and assume
. Then
or
which yields
V
(b)
so
cmm
(c)
or
V/cm
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7.30
(a)
V
(b)
EMBED Equation.3
(i) For V, F
(ii) For V, F
(iii) For V, F
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7.31
(a)
EMBED Equation.3
cm
(b)
cm
(c)
V
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7.33
(a)
(c) p-region
Or
We have
at
Then for
n-region,
or
n-region,
or
We have at
so that for , we have
We also have at
Then
which gives
Then for we have
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7.34
(a)
For m,
So
At m,
So
Then
At , , so
or
V/cm
(c) Magnitude of potential difference is
EMBED Equation.3
Let at , then
Then we can write
At m
or
V
Potential difference across the intrinsic region
or
V
By symmetry, the potential difference across
the p-region space-charge region is also
3.863 V. The total reverse-bias voltage is
then
V
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7.35
(a)
or
Then cm
(b)
Or cm
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7.36
cm
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7.37
(a) For cm, from Figure 7.15,
V
(b) For cm,
V
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7.38
(a) From Equation (7.36),
Set and
V Then
V
So V
(b)
V
Then
So V
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7.39
For a silicon junction with
cm and V, then,
neglecting we have
or
cmm
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7.40
We find
V
Now
so
which yields
cm
Now
Then
which yields
V
or
V
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7.41
Assume silicon: For an junction
Assume
(a) For m
which yields
V
(b) For m
which yields
V
Note: From Figure 7.15, the breakdown
voltage is approximately 300 V. So, in each
case, breakdown is reached first.
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7.42
Impurity gradien
cm
From Figure 7.15, V
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7.43
(a) For the linearly graded junction
Then
Now
At and ,
So
Then
(b)
Set at , then
Then
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7.44
We have that
Then
which yields
cm
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7.45
(a)
Let cm
