Week 7 Nearly Free Electron Model & Tight-Binding Model

Question 1

what does electron interaction with lattice potential lead to

Answer 1

energy bands with gaps which allow for classification of solids

Question 2

what are the 4 classifications of solids

Answer 2

insulator, metal, semi-metal, semi-conductor

Question 3

what does the interaction/potential energy depend upon

Answer 3

wavelength

Question 4

what occurs at long wavelengths

Answer 4

bragg diffraction

Question 5

how can probability densities be found

Answer 5

examining the wavefunction at the BZ boundary to get two stationary waves

Question 6

what leads to energy gaps appearing

Answer 6

the two allowed energy BZ boundaries

Question 7

what is the conclusion of the energy band electron relation

Answer 7

each energy band csn accommodate 2N electrons

Question 8

what gives the electrical properties of a solid

Answer 8

electrical properties have a dependence on filling of energy bands by valence electrons

Question 9

what is the main idea behind the Tight-Bonding model

Answer 9

valence electrons are tightly bound to individual cores

Question 10

what is the crystal orbital equation

Answer 10

ψ = Σ (cφ)

Question 11

what are the two key approximations for the Tight-Bonding model

Answer 11

ignore overlap in normalisation

ignore interactions beyond nearest neighbours