Chemistry Reference
In-Depth Information
(a)
(b)
K
z
U
W
K
L
Γ
K
y
X
K
x
Figure 3.13
(a) The unit cell (basic building block) of a FCC lattice: the FCC lattice
can be constructed by filling all space with a set of blocks identical to that
shown. (b) The first Brillouin zone for the reciprocal lattice of an FCC
lattice. Several high symmetry points in this Brillouin zone have been
given specific names, some of which are indicated in the figure. The shape
shown is the unit cell for a BCC lattice, because the reciprocal lattice of
an FCC lattice is a BCC lattice. (From H. P. Myers (1997)
Introductory Solid
State Physics
, 2nd edn.)
bands then form the filled valence (bonding) bands, and are separated
by the energy gap,
E
g
, from the empty conduction bands. It can be seen
that the two calculations are in very good agreement with each other for
the valence bands, confirming the validity of either approach, although
clearly the agreement becomes less good at higher energy, in the conduc-
tion bands. This problem is related to the use of only a small number of
basis states in the TBmodel, and can be overcome, at least in part, by using
more basis states and including extra interactions in the Hamiltonian.
Figure 3.14(c) gives the free-electron band structure for an empty germa-
nium lattice. Each free-electron state has been shifted into the first Brillouin
zone, as was done earlier in fig. 3.2(c). It is clear that there are many
similarities between the true bands of fig. 3.14(b) and the free-electron
bands, further justifying and motivating the use of NFE-type models.
