Environmental Engineering Reference
In-Depth Information
Table 3.2
Energy gaps and other electronic parameters of important semiconductors.
/
Semiconductor Bandgap (eV) Mobility at 300 K
(cm
2
/V s)
Effective mass
m
m
o
Permittivity e
300 K 0 K
Electrons Holes Electrons
Holes
C
5.47
5.51
1800
1600
0.2
0.25
5.5
1900
m
l
¼
1.6
m
lh
¼
0.044
Ge
0.66
0.75
3900
16
m
t
¼
0.082
m
hh
¼
0.28
m
l
¼
0.97
m
lh
¼
0.16
Si
1.12
1.16
1500
600
11.8
m
DOS
¼
0.19
m
hh
¼
0.5
Grey Tin
0.08
AlSb
1.63
1.75
200
420
0.3
0.4
11
GaN
3.4
0.2
0.8
8.9
GaSb
0.67
0.80
4000
1400
0.047
0.5
15
GaAs
1.43
1.52
8500
400
0.068
0.5
10.9
GaP
2.24
2.40
110
75
0.5
0.5
10
InSb
0.16
0.26
78000
750
0.013
0.6
17
InAs
0.33
0.46
33000
460
0.02
0.41
14.5
InP
1.29
1.34
4600
150
0.07
0.4
14
The last topic relates to the origin of resistivity. Conceptually, the electron states
that we have been dealing with are perfectly conducting, in the sense that an electron
in such a state maintains a velocity
v ¼
h
k
/
m
. A perfectly periodic potential gives a
perfect conductor. Indeed, very pure samples of GaAs, especially epitaxial
films,
measured at low temperatures, give mobility values of millions, in units of cm
2
/V s,
and mean free paths many thousands of atomic spacings. The meaning of
t
then in
the expression for the mobility is the lifetime of an electron in a particular
k
state. The
cause of limited state lifetime
t
in pure metals and semiconductors at room
temperature is loss of perfect periodicity as a consequence of thermal vibrations
of the atoms on their lattice positions. Calculations of this effect in metals, for
example, lead to the observed linear dependence of the resistivity
r
on the absolute
temperature
T
, as shown in Fig. 3.2.
3.6.1
Hydrogenic Donors and Excitons in Semiconductors, Direct and Indirect Bandgaps
Pure semiconductors have
filled valence bands and empty conduction bands and
thus have only small thermally activated electrical conductivity, depending on the size
of the energy gap. As mentioned above, larger electrical conductivity is accomplished
by doping; substitution for the 4-valent Si or Ge atoms either acceptor atoms of
valence 3 or donor atoms of valence 5.
In the case of 5-valent
donor
atoms like P, As, or Sb, four electrons are incorporated
into tetrahedral bonding and the extra electron, which cannot be accommodated in
the already
filled valence band, must occupy a state at the bottom of the next empty
band, which can be close to the donor ion, in terms of its position. This free electron is
