Claridge - electronic properties of solids

Question 1

Requirements for a material to be an ionic conductor?

Answer 1

• some vacancy defects
• some interstitials defects

to allow neighbouring ions to move into empty vacant sites or interstitials

Question 2

Why does the conductivity of NaCl have an exponential temp dependence?

Answer 2

Schottky defect formation is temp dependent so the cations mobility to move into the vacant sites is temp dependent

Question 3

Difference between band gap energy (Eg) and bandwidth?

Answer 3

Eg = energy between different bands

bandwidth = the energy spread of a band

Question 4

What determines the size of the bandwidth?

Answer 4

greater overlap of atomic orbitals leads to a larger bandwidth

Question 5

Conduction band vs valence band?

Answer 5

conduction band = empty states above the Fermi level

valence band = fully occupied states below the Fermi level

Question 6

What is the Fermi level?

Answer 6

the highest occupied level at 0K, with the energy Ef, inbetween the two bands/in the centre of the band gap

Question 7

What happens at T above 0K in the band structure?

Answer 7

electrons can be promoted above the Fermi level, to act as charge carriers (why it’s called the conduction band)

Question 8

How does the colour of a material relate to band gap size?

Answer 8

large band gap = transparent
small band gap = darker in colour

Question 9

Compare insulators and semiconductors to conductors in terms of band gap

Answer 9

insulators & semiconductors: full valence band, conductivity increases with T

conductors: partially filled valence band, no band gap, conductivity decreases with T

Question 10

compare insulators and semiconductors in terms of band gap size

Answer 10

insulators: band gap > 3 eV
semiconductors: band gap 0.5 to 3eV

Question 11

What is the conductivity trend descending group 14? why?

Answer 11

increase in conductivity (decreasing band gap):
- atomic orbitals larger/more diffuse
- larger bandwidth, lower electronegativity

Question 12

Key difference between intrinsic and extrinsic semi conductors?

Answer 12

extrinsic are doped so conductivity depends on mobile charge carriers (as well as band gap size and temp as in intrinsic)

Question 13

n-type doping v p-type?

Answer 13

n-type = added neg charge (e-)
p-type = added pos charge carriers (less e-)

Question 14

what value does the Fermi-Dirac equation give?

Answer 14

the number of mobile charge carriers in an intrinsic semiconductor

Question 15

How can the conductivity of an extrinsic semiconductor be controlled?

Answer 15

controlling the level of doping to lower the band gap energy

Question 16

How is the band diagram affected by extrinsic p-type doping?

Answer 16

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

Question 17

How is the band diagram affected by extrinsic n-type doping?

Answer 17

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

Question 18

parameters required for photoconductivity?

Answer 18

Ehv must be bigger than Eg for the e- to move from the valence to conduction band

Question 19

3-5 semiconductors are isoelectronic to which group?

Answer 19

4

Question 20

Trend in band gap down groups 3 & 5 for 3-5 semi-conductors?

Answer 20

going down both groups the band gap decreases due to larger difference in electronegativity

Question 21

What does f(E) mean for Fermi-Dirac?

Answer 21

the probability of an e- being in a certain state

Question 22

What is Hubbard energy?

Answer 22

(U) = the energy cost for two electrons to be on the same atom during the movement of electrons in conduction

Question 23

How bandwidth energy relates to U?

Answer 23

larger bandwidth E than U = e- delocalise = metal

smaller bandwidth E than U = e- localised = semiconductor or insulator

Question 24

Band theory trend with first row TM

Answer 24

going left to right = smaller d-orbitals, less orbital overlap = narrow bands, localised e-

Question 25

Band theory trend with 2nd and 3rd row TM

Answer 25

going left to right = larger d-orbitals, more orbital overlap = wider bands, delocalised e-

Question 26

What gives good overlap of d-orbitals?

Answer 26

small cation charge, cation early in TM row, cation in 2nd or 3rd row, electropositive anion

Question 27

superconductor properties

Answer 27

conduct electrical current with zero resistance & expel magnetic field from their interior (Meissner effect) below their Tc

Question 28

Describe BCS theory

Answer 28

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

Question 29

How is oxygen deficiency linked to high-Tc superconductivity?

Answer 29

• 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

Question 30

in metals what causes conductivity to decrease with increasing temp?

Answer 30

electron-phonon scattering as mobile conduction electrons collide with phonons, impeding the e- flow
(phonon = lattice vibration)