UNIVERSITY OF CALIFORNIA AT BERKELEY
EECS Department
EECS 40, Fall 2006
Prof. Chang-Hasnain
Homework #10
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Posted: 11/15/06
Due at 5 pm in 240 Cory on Wednesday, 11/22/06
Total Points: 100
Put (1) your name and (2) discussion section number on your homework.
You need to put down all the derivation steps to obtain full credits of the problems.
Numerical answers alone will at best receive low percentage partial credits.
No late submission will be accepted expect those with prior approval from Prof.
Chang-Hasnain.
Wave-Shaping Circuits
1. P10.55 (15pts)
2. P10.59 (15pts)
3. P10.61 (15pts)
4. P10.64 (15pts)
Semiconductor Physics
5. (15 pts)
a. In the lecture notes, it is stated that pure silicon conducts poorly at room
temperature, and conducts weakly at high temperatures. Clearly explain the
reason why conduction is poor in the first case, and strong in the second case
b. Suppose we’d like to use silicon as a resistor with a relatively low resistance.
What would be the effect on the resistance of the silicon if we added Indium?
What would be the effect if we added Bismuth? What if we added an equal
amount of Indium and Bismuth?
c. Suppose a large dose of very intense radiation is applied to a block of silicon.
Qualitatively, what happens to the resistance of the silicon over time,
assuming the radiation was applied at time t=0 seconds?
d. Why does the quasi-neutral p and n regions of the PN Junction have low
resistivity, while the depletion region has high resistivity?
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UNIVERSITY OF CALIFORNIA AT BERKELEY
EECS Department
PN Junction and the Depletion Approximation
6. This problem will explore the relationship between the charge density, electrical
field, and voltage potential in the depletion region. (25pts)
a) What is the approximation in the Depletion Approximation?
b) Give the following PN Junction, sketch the depletion region and label the
charges seen in each region.
c) The charge profile in the PN Junction is shown below.
Given this charge profile, use Gauss Law to find and sketch the Electric Field
within the depletion region as a function of x, where x = 0 represents the origin of
the x-axis. Xn and Xp represent the width of the depletion region in the P and N
regions, respectively. Pn and Pp represents the charge density of the depletion
region in the P and N regions, respectively. Remember that the Electric Field
outside of the depletion region is 0.
Note:
Gauss Law:
dE (x)

, where P(x) is the charge density and ε is 11.7x8.85e-14 F/cm.
dx

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UNIVERSITY OF CALIFORNIA AT BERKELEY
EECS Department
d) Having solved for the electric field E(x), why is the depletion region in the P
region much wider than that in the N region of the PN Junction?
e) Given the Electric Field found above, find the Voltage across the depletion
region in terms of x. Assume Vo @ -150nm = 0V
x
Note: V ( x)  Vo    E ( x)dx
0
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