Solutions Manual
SILICON VLSI TECHNOLOGY 3 © 2000 by Prentice Hall
Fundamentals, Practice and Modeling Upper Saddle River, NJ.
By Plummer, Deal and Griffin
c) x = 5x10
20
cm
−3
()
−1/ 3
=1.3x10
−7
cm = 0.0013μm = 1.3nm
1.3. Consider a piece of pure silicon 100 µm long with a cross-sectional area of 1
µm
2
. How much current would flow through this “resistor” at room
temperature in response to an applied voltage of 1 volt?
Answer:
If the silicon is pure, then the carrier concentration will be simply n
i
. At room
temperature, n
i
≈ 1.45 x 10
10
cm
-3
. Under an applied field, the current will be due to
drift and hence,
I = I
n
+ I
p
= qAn
i
μ
n
+μ
p
)
ε
= 1.6x10
−19
coul
()
10
−8
cm
2
()
1.45x10
10
carrierscm
−3
()
2000cm
2
volt
−1
sec
−1
()
1volt
10
−2
cm
⎛
⎝
= 4.64x10
−12
amps or 4.64pA
1.4. Estimate the resistivity of pure silicon in
ohm cm at a) room temperature, b)
77K, and c) 1000 ˚C. You may neglect the temperature dependence of the
carrier mobility in making this estimate.
Answer:
The resistivity of pure silicon is given by Eqn. 1.1 as
ρ=
1
q μ
n
n +μ
p
p
()
=
1
qn
i
μ
n
+μ
p
(
Thus the temperature dependence arises because of the change in n
i
with T. Using
Eqn. 1.4 in the text, we can calculate values for n
i
at each of the temperatires of
interest. Thus
n
i
= 3.1x10
16
T
3/ 2
exp −
0.603eV
kT
⎝
which gives values of ≈ 1.45 x 10
10
cm
-3
at room T, 7.34 x 10
-21
cm
-3
at 77K and 5.8
x 10
18
cm
-3
at 1000 ˚C. Taking room temperature values for the mobilities , µ
n
=
1500 cm
2
volt
-1
sec
-1
and , µ
p
= 500 cm
2
volt
-1
sec
-1
, we have,
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