Electrical- Conductivity and Resistance of Metals Flashcards
What is resistivity a function of?
Temperature, impurity concentration, defect concentration
The resistivity due to each add together to get the total
Describe current flow and resistance in conventional metals
Current is result of movement of electrons under influence of applied electric field. Their flow is impeded by resistance which results from the scattering of electrons. Resistance can also be caused by defects in the metal such as impurities and grain boundaries. Scattering from such defects results in extrinsic resistance
What are phonons?
Interactions of electrons with atoms or defects
How does resistivity change with temperature?
Increases with temperature because atomic vibrations increase with temperature hence more electron-phonon interactions.
ρT=ρ25(1+αΔT)
α is associated with thermal vibrations of atoms and also thermally generated defects
T and 25 subscript
Resistivity due to impurities formula
In simple homogeneous alloy system where impurities present at low concentrations c:
ρ impurities =Ac(1-c)
A depends on host metal and impurity
Independent of temperature
ρ vs c plot a dome
If heterogeneous solution then overall resistivity sum of two fractional components
ρ=ρaVa+ρbVb
How does resistivity due to deformation compare with that due to temperature and impurities?
It’s effect is smaller than them
What do metals nee for high conductivity σ?
They need to be pure and O2 free
Ways to improve the problem of pure metals being soft and prone to deformation
Use solid solution alloy. Use dispersed second phase (little effect). Use cold working (can reduce σ)
What is the mean free path λ of conduction electrons?
The average distance between collisions with atoms
What does more frequent collisions of conduction electrons mean?
Shorter λ
Lower electron mobility
Difference between ideal metal and in practice when T=0K
Ideal λ tends to infinity
In practice: atoms vibrate about equilibrium position, impurities may be present, crystal lattice may contain lattice imperfections
Typical λ in good metal
5-20nm
What happens if λ is extremely long with only a few collisions?
Ohm’s law breaks down
New equation is I=rt(V)
How does conductivity and λ change for homogeneous metal alloys, age hardened or dispersion strengthened alloys and work hardened metals compared to the pure metal?
In homogeneous metal alloys, λ is very short as the scattering centres are relatively close together. The σ is much less than pure.
In age hardened or dispersion strengthened alloys, λ is longer than above as the second phase is concentrated in discrete positions rather than being randomly distributed. σ is only reduced a small amount from pure.
In work hardened metals, λ even longer than above as dislocations are well separated as their stress field act to repel each other. σ almost the same as pure.
Which electrons do what in a metal?
The inner orbitals are discrete and localised so don’t take part in conductivity. These are the core electrons. Only the outer (valence) electrons which overlap orbitals to form bands of energy levels do.
The two types of band structures in metals
Partly full bands such as Cu
Overlapping bands where both are partly occupied, e.g Mg where 3s and 3p overlap
Bad theory with metallic bonding
Above the highest occupied levels, there are empty levels of only slightly higher energy so electrons can hop from one to the other. There is a partly filled valence band.
Band theory for insulators
There is a large forbidden energy gap between the highest occupied levels and the next lowest unoccupied level. The band gap is high (>3eV). There is a filled valence band and empty conduction band
Band theory for semiconductors
The band gap is small (<3eV). Electrons can be promoted across the gap either through intrinsic conduction (usually thermally) or by adding dopants that have energy states within the band gap (extrinsic conduction)
Where is the Fermi energy level Ef?
At approximately half the band gap Eg
General points about band theory
The VB is the series of electron energy levels at which all valence electrons normally reside. Unless there are fancies the electrons will not move. The CB is the band level at which electrons are free to move. Theory ignores e-e repulsion effects within the bands (works well for wide bands not for narrow). Width of band related to relative energy of orbitals involved and on degree of overlap between orbitals. Actual position if Ef in intrinsic semi and insulators depends on relative density of states in VB and CB but roughly 0.5Eg
Why is Al a metal?
Due to its structure and bonding. It is hcp so has 12 close neighbours but only 3 valence electrons so not enough electrons to form covalent bonds. Means metallic bonding with the valence electrons delocalised in 3s and 3p.
Why isn’t Si a metal?
Forms solid where all atoms linked by covalent bonds. Structure of solid shows coordination number and geometry similar to that found in molecules where the atom exhibits its normal valency. Group IV solids are tetrahedrally bonded. Covalent bonds in the solid are similar to those in small molecules.
How does sp3 hybridisation work?
Mixing of 3s and 3p atomic orbitals on the same atom to produce 4 sp3 hybridised orbitals that have a definite direction in space. Happens in Si. One electron in 3s and one in each of 3p orbitals goes to one in each of 4sp3 hybridised orbitals. Has tetrahedral geometry.
Band picture in Si solid
Two sp3 orbitals are the AOs. Makes σ and σ* with the 2 electrons in the σ. Band gap about 1.1eV. This is one Si-Si bond.
In pure Si a small number of electrons have sufficient thermal energy to be promoted to CB. This number increases with temperature
