CHE-30043
Materials Chemistry & Catalysis :
Solid State Chemistry lecture 3
Rob Jackson
LJ1.16, 01782 733042
r.a.jackson@keele.ac.uk
www.facebook.com/robjteaching
@robajackson
Lecture plan
• Compound semiconductors – III/V and II/VI
compounds
• Band gaps and the appearance of
materials
• Determination of band gaps from
conductivity measurements
• Band structures of d block compounds
che-30043 lecture 3
2
Compound semiconductors
• Compound semiconductors
are compounds that show
semiconductor behaviour (in
contrast to the insulating
compounds
considered
earlier).
• A commercially important
example is GaAs, gallium
arsenide.
• GaAs has a similar structure
to Si (the diamond structure)
with alternating Ga and As
atoms.
http://phycomp.technion.ac.il/~nika/diamond_structure.html
che-30043 lecture 3
3
GaAs
• First, look at the valence electrons:
Ga is 4s24p1, As is 4s24p3
• There will be 2 bands formed, each with 4N
levels (the band structure will be drawn).
• The lower band will have a greater
contribution from As than Ga (nuclear
charge higher in As).
• The 8N valence electrons fill the lower band.
• The band gap is ~ 1.4 eV.
che-30043 lecture 3
4
Other III/V semiconductors
• GaAs is an example of a III/V semiconductor
(a combination of an element from group 3,
with one valence electron less than Si, with
one from group V, with one valence electron
more than Si).
• Other examples are GaSb, InP, InAs and
InSb.
che-30043 lecture 3
5
II/VI semiconductors
•
•
•
•
II/VI semiconductors are typified by CdTe.
Cd has valence electrons in 5s24d10
Te has valence electrons in 5s24d105p4
Band structure is based on 5s and 5p levels
from each element.
• The band structure of CdTe will be drawn as
an example.
• Other examples include ZnTe and ZnS.
che-30043 lecture 3
6
Compound semiconductors: trend in
band gaps
material
Band gap
300K, eV
material
Band gap
300K, eV
GaP
2.25
ZnO*
3.2
GaAs
1.43
ZnS*
3.6
GaSb
0.68
CdSe
1.74
InP
1.27
CdTe
1.44
InAs
0.36
Si
1.11
InSb
0.17
Ge
0.66
* Note wide
band gaps
Kittel, C., Intro. to Solid State Physics, 6th Ed., New York: John Wiley, 1986, p. 185
che-30043 lecture 3
7
Applications of semiconductors:
photocells – (i)
• A good example of the use of
semiconductors is in photocells.
• Photocells work because electricity is
conducted and a circuit completed when
light shines on a semiconducting
material – but thus will only work if the
bandgap is in the visible region.
che-30043 lecture 3
8
Applications of semiconductors:
photocells – (ii)
• What values of bandgaps are useful?
– Use E = hc/
– e.g., for a cell to be useful in the visible
region, the bandgap must be low enough
for the lowest frequency (longest
wavelength) light.
– Red light has =700 nm = 700 x 10-9 m
– Calculate E and convert to eV
che-30043 lecture 3
9
Band gaps and colour/appearance of
materials - 1
• Absorption/reflection of light by metals and
compounds depends on their band
structure/band gap, since the photons that
are absorbed and then re-emitted will have
appropriate frequencies for the band gaps of
the materials in question.
che-30043 lecture 3
10
Band gaps and colour/appearance of
materials - 2
• Metals – transitions between levels in bands
correspond to visible light – shiny
appearance.
• Silicon – band gap in lower end of visible
region – shiny metallic appearance.
• Insulators (e.g. crystalline NaCl, SiO2) –
larger band gaps – higher energy –
corresponding, e.g. to UV region –
colourless – but changed by defects ...
che-30043 lecture 3
11
Decreasing band gap and colour
Germanium – described
as ‘grey-white’
C (diamond) – clear
and transparent
Silicon – showing shiny appearance
(but not transparent)
che-30043 lecture 3
12
Relationship between band structure
and crystal structure in group IV
band gap/eV
C
Si
Ge
Sn
Pb
5.5
1.1
0.7
0.1
0.1
che-30043 lecture 3
13
Crystal structure - 1
• In C, Si and Ge the valence s and p
orbitals can combine – hence the sp3
model is a valid description – and all
valence electrons go into bonding
orbitals and fill the valence band.
• In Sn and Pb there is less overlap of the
s and p orbitals so separate bonding
and antibonding orbitals are not formed.
che-30043 lecture 3
14
Crystal structure - 2
• Instead the orbitals form a continuous
band, with a very small band gap, as in
metallic structures.
• In general, the structure that is formed
is the one which involves the electrons
most in bonding, and this is achieved
differently in metals, through having
delocalised valence electrons.
che-30043 lecture 3
15
Why the band gap decreases going
down the ‘C’ group
• The degree of s, p overlap decreases as
nuclear charge increases (going down the
group).
• At Sn there is virtually no overlap, and a
continuous band is formed from the s and p
orbitals.
• As the degree of overlap decreases, both the
bond strength, and the difference between
bonding and antibonding orbitals decreases.
che-30043 lecture 3
16
Determination of band gaps from
conductivity measurements
• An insulator or semiconductor will show an
increase in conductance (the inverse of
resistance) with temperature.
• Conductance G is related to temperature T
by the expression:
G = G0 exp (-Eg / 2kT)
where Eg is the band gap of the material.
che-30043 lecture 3
17
Determination of Eg from data
T/K
G
300
0.1
350
0.5
400
3.0
Procedure is to take the expression and
take logs of both sides:
ln G = ln G0 – Eg / 2kT
Plot ln G against 1/T, gradient = - Eg / 2k
A rough plot will be drawn in the lecture.
che-30043 lecture 3
18
Band structures of d block
compounds
• We consider the first row transition metal
monoxides:
MO, where M = Ti, V, Mn, Fe, Co and Ni
• Structures are based on the rock salt
structure, but their properties differ widely
because of the behaviour of the d-orbitals,
which control their properties.
che-30043 lecture 3
19
MO Structure revisited
All the MO compounds adopt this structure, but their properties vary widely
che-30043 lecture 3
20
Classification of d-orbitals
• The metal d-orbitals are divided into two sets, one
pointing towards the oxide ions and one between
them.
• The two sets of orbitals will be drawn, and are also
shown on the next slide
(or see Dann pp 111-3)
The t2g orbitals on each metal atom (dxy, dyz, dzx)
point towards other metal atoms, and the other d
orbitals overlap with orbitals from the oxygen
atoms.
che-30043 lecture 3
21
Classification of d-orbitals
http://chimge.unil.ch/En/lc/1LC20.htm
che-30043 lecture 3
22
Can bands form?
• If the metal t2g d-orbitals can overlap, then
bands can form. Also, these bands will not
be fully occupied because the d-orbitals are
themselves not filled.
• So, if bands can form, the oxides will have
metallic properties and be conductors.
• This applies to TiO and VO.
che-30043 lecture 3
23
Trends in properties along the group
• With TiO and VO there is good overlap of the
d orbitals, so they have metallic properties
and conduct electricity.
• As we move along the group, the d-orbital
electrons become more tightly bound (with
increasing nuclear charge) and this inhibits
band formation.
• The oxides show semiconductor and then
insulator properties.
che-30043 lecture 3
24
TiO VO MnO FeO CoO NiO
metals 
semiconductors  insulators
• Colour of the compounds can also be a
useful indication of their conductivity. Nickel
oxide is green, as is a nickel complex in
solution, suggesting discrete nickel ions
with well-spaced energy levels.
• Vanadium oxide is black – light is absorbed
over the full spectral range, corresponding
to many closely spaced energy levels.
che-30043 lecture 3
25
Summary
• Compound semiconductors have been
described
• The influence of band gaps on the
appearance of materials has been considered
• The determination of band gaps from
conductivity
measurements
has
been
described
• The band structures of d block compounds
has been described
che-30043 lecture 3
26