CHE-30005 Solids, Surfaces and Catalysis : Solid State Chemistry lecture 3

CHE-30005 Solids, Surfaces and Catalysis :Solid State Chemistry lecture 3 Rob Jackson LJ1.16, 01782 733042 r.a.jackson@keele.ac.uk www.facebook.com/robjteaching

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-30005 lecture 3

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-30005 lecture 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-30005 lecture 3

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-30005 lecture 3

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-30005 lecture 3

Compound semiconductors: trend in band gaps * Note wide band gaps Kittel, C., Intro. to Solid State Physics, 6th Ed., New York: John Wiley, 1986, p. 185 che-30005 lecture 3

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-30005 lecture 3

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-30005 lecture 3

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-30005 lecture 3

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-30005 lecture 3

Decreasing band gap and colour Germanium – described as ‘grey-white’ C (diamond) – clear and transparent Silicon – showing shiny appearance (but not transparent) che-30005 lecture 3

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 che-30005 lecture 3

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-30005 lecture 3

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-30005 lecture 3

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-30005 lecture 3

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-30005 lecture 3

Determination of Eg from data T/K 300 350 400 G 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 / 2k A rough plot will be drawn in the lecture. che-30005 lecture 3

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-30005 lecture 3

MO Structure revisited All the MO compounds adopt this structure, but their properties vary widely che-30005 lecture 3

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-30005 lecture 3

Classification of d-orbitals http://chimge.unil.ch/En/lc/1LC20.htm che-30005 lecture 3

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-30005 lecture 3

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-30005 lecture 3

TiO VO MnO FeO CoO NiOmetals  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-30005 lecture 3

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-30005 lecture 3

CHE-30005 Solids, Surfaces and Catalysis : Solid State Chemistry lecture 3