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ECE 340
Homework III
Spring 2004
Due: Wednesday, February 04, 2004
1.
(a) It was mentioned in Section 3.2 that the covalent bonding model gives false impression of
the localization of carriers. As an illustration, calculate the radius of the electron orbit around
the donor in Fig. 312c, assuming a ground state hydrogenlike orbit in Si. Compare with the
Si lattice constant. Use m
n
*
= 0.26 m
o
for Si.
(b) Repeat part (a) for the radius of an electron orbiting around the donor in GaAs, assuming
m
n
*
= 0.067 m
o
for GaAs. Compare the radius with the GaAs lattice constant.
(c) Refer to part (a) and estimate the donor binding energy for Si. Compare your results to
the donor levels of simple donors such as P, As and Sb as shown in Fig. 49 (page 119).
Solutions:
(a), Use equation (210) from the book, radius of electron orbit can be calculated by:
22
2
n
Kn
r
mq
=
=
,
0
4
r
K
πεε
=
, For Si,
ε
r
= 11.8,
m: use effective mass m
n
*
Because we assume ground state hydrogenlike orbit, n = 1:
2
34
12
2
9
1
31
19 2
6.63 10
4 8
.
8
51
0
1
1
.
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