ECE 340
Homework VIII
Fall 2003
Due: Friday, October 10, 2003
1.
An abrupt Si pn junction has N
a
= 7x10
16
/cm
3
on the pside and N
d
= 2x10
17
/cm
3
on the nside.
(a)
Calculate the Fermi level positions at 300 K in the p and n regions.
(b)
Draw an equilibrium band diagram for the junction and determine the contact potential V
o
from
the diagram.
(c)
Compare the results of part (b) with V
o
as calculated from Eq. (58).
(d)
Using Eq. (58), calculate and plot V
o
versus temperature ranging from 300 K to 500 K.
Solutions:
(a), At p side
16
10
71
0
ln
0.0259ln
0.398
1.5 10
iF
i
kT
p
E
Ee
V
qn
×
−=
=
=
×
At nside:
17
10
21
0
ln
0.0259ln
0.425
1.5 10
Fi
i
kT
n
E
V
×
=
=
×
(b),
I found the easy way to draw this kind of energy band diagram is to draw the Fermi level first, then
add the conduction band and valence band on p and n side according to the calculations, then connecting
the two sides by curves.
Therefore,
0
0.823
VV
=
(c), V
0
calculated from Eq. (58) is:
16
17
0
0
2
0 21
0
ln
0.0259ln
0.823
(1.5 10 )
ad
i
NN
kT
××
×
==
=
×
Same as part (b)
(d), Notice that the n
i
is also related to temperature through Eq. 326
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 Fall '03
 Lebutron
 Trigraph, Condensed matter physics

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