EMS 172
Profs. Y. Takamura and A. Moulé, 2009
UNIVERSITY OF CALIFORNIA, DAVIS
Department of Chemical Engineering and Materials Science
EMS 172: Electronic, Magnetic, and Optical Properties of Materials
Homework 4
Due Date: Tuesday, Oct. 27
th
, 2009 in class
Note: You must show all the steps you used to obtain your answer in order to receive full credit.
1. Intrinsic Semiconductors
[16
pts]
[
Computer problem
] The equation for the intrinsic carrier concentration,
N
i
, is given by:
N
i
= (
N
c
N
υ
)
1/2
exp[
E
g
/2
k
B
T
]
[Eqn. 1]
Within this equation, several terms depend on temperature according to the following relationships:
Barber [
Solid State Electronics,
10,
1039 (1967)] showed that the temperature dependence of the effective mass of
the electrons and holes for silicon over the temperature range 200 K< T < 700 K could be approximated by:
(
)
(
)
2
7
4
0
*
10
09
.
3
10
11
.
6
028
.
1
T
T
m
m
e
−
−
×
−
×
+
=
[Eqn. 2]
(
)
(
)
2
7
4
0
*
10
46
.
4
10
83
.
7
61
.
0
T
T
m
m
h
−
−
×
−
×
+
=
[Eqn. 3]
In order to match experimental data, Barber had to include an additional term when computing the band gap
energy, such that
E
g
(T) = E
gT
– E
ex
,
where
D
g
gT
T
T
E
E
θ
ξ
+
−
=
2
0
.
E
ex
is the exciton correction factor,
E
g0
is the
bandgap at 0K
,
ξ
is a coefficient,
θ
D
is the Debye temperature, and
T
is in Kelvin
.
(see Table I).
(a) With this information use your favorite plotting software (Matlab, Mathematica, etc…) to create a plot of log
(
N
i
) [cm
3
] as a function of temperature [K] for silicon from 200 K < T < 700 K.
Note
:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '10
 Takamura
 inp, Profs. Y. Takamura

Click to edit the document details