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ECE G201 H.W. #6, Due March 17, 2009
1. A planar silicon diode is designed as follows: p+  n junction, with junction depth of 0.5µm from the
surface of the wafer, fabricated in an 21micron thick layer of lightly doped silicon (this layer ends 21
microns from the surface) over a very heavily doped silicon substrate (this is the thick silicon substrate).
Doping: p+  10
18
n  10
15
n+ substrate  large, you can assume 10
18
but it doesn't matter.
Lifetimes: t
p
= t
n
= 10
7
sec
T = 300K
a. What is the breakdown voltage of the diode, ignoring 3dimensional effects? (refer to figures in Sze
Ch. 2, figures 26, 29, 35. (on web site))
b. What is the breakdown voltage of a square diode of the same doping, (shape as viewed from above) 0.1
cm x 0.1 cm in dimension? (Refer to Fig. 9, Ch. 2, Sze. (on web site))
c. What is the breakdown voltage of a circular diode, again of the same doping, 0.1 cm in diameter?
2. a. Considering only onedimensional effects, does the onset of series resistance effects, or high
injection effects, occur first in this diode? (diode from previous problem, onedimensional analysis)
Estimate the onset of high injection effects as the voltage at which p
n
at x
n
= n
no
. Estimate the onset of
series resistance effects by computing the resistivity of the bulk semiconductor, and determining the
voltage at which the current is half of that predicted by the ideal diode equation. Examine each effect
separately, assuming no other nonideal effects. T = 300K.
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