Chemistry Reference
In-Depth Information
Cut-off wavelength (
m)
µ
4.0
2.0
1.0
0.5
0.28
InSb
AlSb
ZnTe
GaSb
0.26
InAs
lnP
Ge
AlAs
ZnSe
GaAs
0.24
AlP
GaP
Si
0.0
0.5
1.0
1.5
Band gap (eV)
2.0
2.5
Figure 2.16
Plot of the low temperature energy gap (in eV) and the bond length (in Å)
for various group IV, III-V, and II-VI compounds.
As light emission tends to occur due to transitions across the energy gap in
semiconductors, we find that by varying the covalent and ionic contribu-
tions to bonding we can achieve light emission from bulk semiconductors
at wavelengths ranging from the ultra-violet through to about 10
m at the
µ
infra-red end of the spectrum.
References
Harrison, W. A. (1989)
Electronic Structure and the Properties of Solids: The Physics of
the Chemical Bond
, Dover Publications, New York.
Harrison, W. A. (2000)
Applied Quantum Mechanics
, World Scientific Pub Co.,
Singapore.
Problems
2.1
Show that for two quantumwells of depth
V
0
and width
a
separated
by a barrier of width
b
, the energies of states of odd parity are found
as solutions of eq. (2.10):
2
coth
κ
k
2
sin
coth
κ
1
cos
b
2
b
2
κ
−
(
ka
)
+
k
κ
+
(
ka
)
=
0
2.2
Show, by using eqs (1.53) and (1.54) that we can rewrite eq. (2.9) as
2
sin
κ
(
ka
)
+
κ
k
cos
(
ka
)
e
−
κ
b
/
2
k
sin
(
ka
/
2
)
−
κ
cos
(
ka
/
2
)
=
sech
(κ
b
/
2
)
k
cos
(
ka
/
2
)
+
κ
sin
(
ka
/
2
)
(2.38)
