CHE-30043 Materials Chemistry & Catalysis : Solid State Chemistry lecture 3 Rob Jackson LJ1.16, 01782 733042 [email protected]

CHE-30043 Materials Chemistry & Catalysis :Solid State Chemistry lecture 3

Rob JacksonLJ1.16, 01782 733042

[email protected]/robjteaching

@robajackson

che-30043 lecture 3 2

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


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


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.


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.


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.


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

Kittel, C., Intro. to Solid State Physics, 6th Ed., New York: John Wiley, 1986, p. 185

* Note wide band gaps


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.


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


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.


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 ...


Decreasing band gap and colour

Silicon – showing shiny appearance (but not transparent)

C (diamond) – clear and transparent

Germanium – described as ‘grey-white’


Relationship between band structure and crystal structure in group IV

band gap/eV

C 5.5

Si 1.1

Ge 0.7

Sn 0.1

Pb 0.1


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.


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.


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.


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.


Determination of Eg from data

T/K 300 350 400G 0.1 0.5 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 / 2kA rough plot will be drawn in the lecture.


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.


MO Structure revisited

All the MO compounds adopt this structure, but their properties vary widely


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.


Classification of d-orbitals

http://chimge.unil.ch/En/lc/1LC20.htm


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.


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.


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.


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

Documents

CHE-30043 Materials Chemistry & Catalysis : Solid State Chemistry lecture 3 Rob Jackson LJ1.16, 01782 733042 [email protected]