Sinclair- Band Theory for Metals, Semiconductors and Insulators Flashcards
Why does atomic configuration alone not determine what is a conductor, semiconductor or insulator?
C (diamond), Si, Pb are all group IV and have partly filled valence-shells but diamond is insulator, Si semiconductor and Pb metal (conductor).
What are the other important factors for determining conductivity of an element?
Crystal structure and chemical binding (orbital hybridisation and orbital overlap)
What does element conductivity fundamentally depend on?
How the various atomic orbitals (AO) which contain the electrons overlap and whether there is any for the electrons to be delocalised, such as in a metal, or whether the bonding is more covalent, such as in diamond, when the electrons are then localised in particular orbitals
What does molecular orbital theory (MOT) treat a solid as?
A giant molecule
Rules for MOT
n AO produce n MO
Need only consider valence AOs
Need to consider the relative energy of the valence AOs on the atoms
Need to consider the symmetry and overlap of AOs (crystal structure and ionic radii in solids)
The orbitals that extend throughout the molecule or solid can be called crystal orbitals and are the property of the molecule/solid and not individual atoms/ions. They form bands over certain energy levels.
Other features of MOT
In polyatomic molecules a greater variety of MOs can be formed.
As the molecules become larger, their MOs become more numerous and more closely spaced in energy.
MOT emphasises the delocalised nature of the electron distribution so that MOs are generally extended over all the constituent atoms.
How do bands form in a solid?
It is a large molecule of n atoms. Each forms a bonding and anti-bonding MO. The bonding orbitals have lower energy and are spread over a valence band. The anti-bonding orbitals have higher energy and are spread over a conduction band. Between them is an energy gap Eg
Density of states in a band
N(E). Within the allowed bands, more orbitals are concentrated together at some energies compared to others. Equals 0 in band gap. N(E) vs E forms curved shapes over the CB and VB and are 0 at the edges of the bands
What does the width of a particular band depend on?
The interatomic separation and hence on the degree of overlap between orbitals on adjacent atoms. Strong overlap gives wide bands whereas small overlap gives narrow bands. s and p-block metals are wide band solids
Why does electron delocalisation occur in metals?
Valence s and p orbitals overlap strongly to give bands of many eV (6-8) in width. Contracted core orbitals give very narrow bands (<0.1) and retain their atomic identity and don’t contribute to bonding. If the bands are partially filled by valence electrons then electron delocalisation throughout the solid can occur and result in metallic conductivity
Example of Mg
Has a full 3s orbital and empty 3p orbital. So can hold 8 e- per atom. The smearing out of AO energy levels when forming the solid produces a wide energy band of available electron energies (continuum of about 6-8eV). This band is property of the solid. The 2 e- in 3s orbital means band is 1/4 full.
Where is Ef for a metal?
Fermi level is energy where the probability of electron occupation is 1/2. So half of the energy levels with this energy are empty
Band structure of Cu metal
It is [Ar]3d10 4s1. 3d electrons are effectively part of the core but do form a narrow 3d band. The 4s orbitals overlap to give a half full 4s band. So there is a a narrow, half full 4s band.
Two types of band structures in metals
Partly full bands like in Cu
Overlapping bands where both are partly occupied like Mg where 3s and 3p overlap
Why is CaO an insulator?
The 4s2 electrons from Ca transfer to O atom leaving an Ar core for Ça and a Ne core for O. The CB is formed by the 4p and 4s orbitals of the Ca atoms but these are now empty. The electrons are localised on the O where there is a full VB. the band gap is large (5-7eV)
