Chemistry Reference
In-Depth Information
5.0
4.0
3.0
2.0
1.0
1.0
2.0 3.0
Barrier height (eV)
4.0
Figure 3.18
Energy of the third state in the K-P potential where
a
=
b
=
6Å,
calculated as a function of the barrier height
V
0
. Solid line: exact energy;
dashed line: energy estimated using the pseudopotential method.
We have only scratched the surface here in describing some of the differ-
ent general methods used to determine the electronic properties of solids.
We develop some of these ideas further in the next chapter, and then use
them to investigate some of the key features of semiconductors, magnetism
and superconductivity in the remainder of the topic.
References
Ashcroft, N. W. and N. D. Mermin (1976)
Solid State Physics
, Holt, Rinehart and
Winston, New York.
Harrison, W. A. (1989)
Electronic Structure and the Properties of Solids: The Physics of
the Chemical Bond
, Dover Publications, New York.
Ibach, H. and H. Lüth (1995)
Solid State Physics
, Springer-Verlag, New York.
Pettifor, D.M. (1995)
Bonding and Structure ofMolecules and Solids
, OxfordUniversity
Press.
Weaire, D. and J. P. Kermode (1985)
phys. stat. sol. (b)
127
, K143.
Problems
3.1
Consider a linear chain of atoms, distance
L
apart, for which the
band structure is given by
E
sq
(3.50)
where
E
s
is the self-energy of the single orbital on an isolated atom,
and
V
is the nearest neighbour interaction in the chain. Suppose
that each orbital can accommodate two electrons. Calculate from
eq. (3.50) the average band-structure energy gained per atom if there
are
y
electrons per atom on the linear chain.
=
E
s
+
2
V
cos
(
qL
)
