Claridge - electronic properties of solids Flashcards
Requirements for a material to be an ionic conductor?
- some vacancy defects
- some interstitials defects
to allow neighbouring ions to move into empty vacant sites or interstitials
Why does the conductivity of NaCl have an exponential temp dependence?
Schottky defect formation is temp dependent so the cations mobility to move into the vacant sites is temp dependent
Difference between band gap energy (Eg) and bandwidth?
Eg = energy between different bands
bandwidth = the energy spread of a band
What determines the size of the bandwidth?
greater overlap of atomic orbitals leads to a larger bandwidth
Conduction band vs valence band?
conduction band = empty states above the Fermi level
valence band = fully occupied states below the Fermi level
What is the Fermi level?
the highest occupied level at 0K, with the energy Ef, inbetween the two bands/in the centre of the band gap
What happens at T above 0K in the band structure?
electrons can be promoted above the Fermi level, to act as charge carriers (why it’s called the conduction band)
How does the colour of a material relate to band gap size?
large band gap = transparent
small band gap = darker in colour
Compare insulators and semiconductors to conductors in terms of band gap
insulators & semiconductors: full valence band, conductivity increases with T
conductors: partially filled valence band, no band gap, conductivity decreases with T
compare insulators and semiconductors in terms of band gap size
insulators: band gap > 3 eV
semiconductors: band gap 0.5 to 3eV
What is the conductivity trend descending group 14? why?
increase in conductivity (decreasing band gap):
- atomic orbitals larger/more diffuse
- larger bandwidth, lower electronegativity
Key difference between intrinsic and extrinsic semi conductors?
extrinsic are doped so conductivity depends on mobile charge carriers (as well as band gap size and temp as in intrinsic)
n-type doping v p-type?
n-type = added neg charge (e-)
p-type = added pos charge carriers (less e-)
what value does the Fermi-Dirac equation give?
the number of mobile charge carriers in an intrinsic semiconductor
How can the conductivity of an extrinsic semiconductor be controlled?
controlling the level of doping to lower the band gap energy
How is the band diagram affected by extrinsic p-type doping?
additional EMPTY (as 1 fewer e- in structure) acceptor level band added above valence band
Fermi level and band gap inbetween this and the valence band
the empty acceptor level gives a smaller band gap for e- promotion so increases conductivity
How is the band diagram affected by extrinsic n-type doping?
additional FULL (as 1 extra e- in structure) acceptor level band added just below conduction band
Fermi level and band gap inbetween this and the conduction band
the full donor level gives a smaller band gap so increases conductivity
parameters required for photoconductivity?
Ehv must be bigger than Eg for the e- to move from the valence to conduction band
3-5 semiconductors are isoelectronic to which group?
4
Trend in band gap down groups 3 & 5 for 3-5 semi-conductors?
going down both groups the band gap decreases due to larger difference in electronegativity
What does f(E) mean for Fermi-Dirac?
the probability of an e- being in a certain state
What is Hubbard energy?
(U) = the energy cost for two electrons to be on the same atom during the movement of electrons in conduction
How bandwidth energy relates to U?
larger bandwidth E than U = e- delocalise = metal
smaller bandwidth E than U = e- localised = semiconductor or insulator
Band theory trend with first row TM
going left to right = smaller d-orbitals, less orbital overlap = narrow bands, localised e-
Band theory trend with 2nd and 3rd row TM
going left to right = larger d-orbitals, more orbital overlap = wider bands, delocalised e-
What gives good overlap of d-orbitals?
small cation charge, cation early in TM row, cation in 2nd or 3rd row, electropositive anion
superconductor properties
conduct electrical current with zero resistance & expel magnetic field from their interior (Meissner effect) below their Tc
Describe BCS theory
A conduction electron distorts the superconductor lattice as it passes through, forming an area of positive charge density in the lattice
The next conduction electron is attracted to the pos charge, so passes through the lattice easily,
process repeats, this is phonon-mediated attraction and the two e- form a Cooper pair
How is oxygen deficiency linked to high-Tc superconductivity?
- layered perovskite structure of YBCO superconductors can permit oxygen deficiency which controls the oxidation state of the Cu
- oxygen vacancies create sheets and chains of Cu and O and positive holes
- most conductive parallel to copper oxygen planes
in metals what causes conductivity to decrease with increasing temp?
electron-phonon scattering as mobile conduction electrons collide with phonons, impeding the e- flow
(phonon = lattice vibration)
