Metals - the basics of electronic structure

Question 1

State and describe the de Broglie relationship

Answer 1

If an electron moves then the de Broglie relation tells us that there will be a wavelength associated with that electron

Question 2

Define and describe the wavevector, k

Answer 2

k is a measure of the energy of a particular electron, as it is proportional to momentum.

Question 3

Describe how to calculate the energy of an electron

Answer 3

The Schrödinger equation allows us to calculate the energy of the electron, and we need a wavefunction ψ to define how the electron behaves.

Question 4

Define a band

Answer 4

A band refers to a continuous run of electrons up to a given level. These electrons will have very similar energies

The energy of any electron within the band depends on the square of the wave vector.

Question 5

Define and describe the Fermi level (E_F)

Answer 5

The Fermi level describes the upper limit of a band (at absolute zero).

E_F determines how reducing the metal is.

Question 6

Give and describe the Fermi-Diract distribution

Answer 6

As temperature increases, some of the electrons below EF are excited. Therefore the probability of finding an electron at a particular energy differs with temperature.

Important note: E_F is the energy at which the electron probability is 50%

Question 7

Describe thermionic emission

Answer 7

Thermionic emission describes the effect in which some electrons have so much energy that they exceed the work function and are able to escape from the metal.

Question 8

Define band gaps

Answer 8

Band gaps are breaks in the energy diagram corresponding to certain values of k, as waves behave like waves and there is a Bragg condition for electrons

Question 9

Define an insulator

Answer 9

If you fill a band right up to the top so that every slot is filled and apply a voltage, the electrons cannot move because there is nowhere for them to move to. This is an insulator.

Question 10

Define the conduction band

Answer 10

The conduction band refers to the upper band in a situation where there is a filled band below a band gap below an empty band.

Question 11

Define the valence band

Answer 11

The valence band refers to the lower band in a situation where there is a filled band below a band gap below an empty band.