Environmental Engineering Reference
In-Depth Information
(a)
(b)
Figure 3.15 Energy band structures for silicon
(a) and GaAs (b). Energy is shown vertically,
measured from the top of the valence band, and
k horizontally. The horizontal line marks the top
of the filled
valence
bands; in pure samples,
the upper bands are empty except for thermal
excitations (indicated by þþ and symbols.)
The zero of momentum is indicated as
separate sketches are given for E versus k in (111)
left and (100) right directions. GaAs (b) has a
direct bandgap
because the minimum in the
conduction band and the maximum in the valence
band occur at the same value of wavevector k.This
makes it easier for electrons and holes to
recombine to produce light. The number of
equivalent conduction bandminima in Silicon is 6.
C
, and
m
¼
h
2
2
E
k
2
=ð
q
=
q
Þ:
ð
3
:
47
Þ
While looking at the energy bands for Si and GaAs in Figure 3.15,
rst, one can see
that generally the curvature is higher in the conduction band than in the valence
band, meaning that the effective mass is smaller and the mobility, therefore, higher
for electrons than for holes. Second, comparing Si and GaAs, the curvature in the
conduction band minimum is higher in the latter case, leading to a higher mobility
for electrons in GaAs than in Si. Another aspect is that the conduction band
minima in Si are shifted from
k¼
0, which has important effects especially on the
absorption of photons by Si, and similar semiconductors having an indirect
bandgap. Parameters describing several important semiconductors are collected in
Table 3.2.
The energy gaps of semiconductors range from about 0.2 eV to about 3.5 eV, as
indicated in Table 3.2. Carbon in diamond form, listed at 5.5 eV, is normally
considered an insulator. For devices that operate at room temperature, a gap of at
least 1 eV is needed to keep the number of thermally excited carriers suf
ciently low.
GaN, with bandgap 3.4 eV, from a transport point of view is an insulator but from the
point of view of making an injection laser is more reasonably regarded as a
semiconductor. For Si with six ellipsoidal electron energy surfaces, the density of
states mass is
m
DOS
¼
(
m
l
m
t
m
t
)
1/3
¼
0.187.
