1. PHYS3004 Crystalline Solids
Prof. P.A.J. de Groot

2. 1. BONDING IN SOLIDS Born-Oppenheimer Approximation
Linear Combination of Atomic Orbitals

3. 1. BONDING IN SOLIDS Covalent bonding Ionic bonding Metallic bonding
Van der Waals bonding

4. 1. BONDING IN SOLIDS Covalent bonding: LCAO
Bonding and anti-bonding states

5. 2. CRYSTAL LATTICES
Lattice & basis
Wigner-Seitz cell R1

6. 3. RECIPROCAL LATTICE
Diffraction of waves (x-rays)
Reciprocal lattice

7. 3. RECIPROCAL LATTICE
First Brillouin zone
Bloch theorem:

8. 4. FREE ELECTRON MODEL – JELLIUM
Electrons in a box
Time independent Schrödinger eq.
Plane wave solutions
Boundary conditions (box is finite)

9. 4. FREE ELECTRON MODEL – JELLIUM
Density of states
Fermi energy

10. 4. FREE ELECTRON MODEL – JELLIUM
Charge oscillations – plasmons
Electrical transport (relaxation time)
Quantum Jellium
Hall effect
Breakdown of Jellium Model

11. 5. NEARLY-FREE ELECTRON MODEL
Perturbation theory – only significant changes in E(k) near degenerate points

12. 5. NEARLY-FREE ELECTRON MODEL
Effective mass
Electrons and holes

13. 6. TIGHT BINDING
jellium  nearly-free electrons  tight binding  atoms

14. 6. TIGHT BINDING
LCAO
Bloch theorem
Crystal momentum

15. 7. MAGNETIC PROPERTIES OF CRYSTALS
Paramagnetism – partly filled shells
Curie’s law

16. 7. MAGNETIC PROPERTIES OF CRYSTALS
Pauli paramagnetism
Ferromagnetism & mean field theory

17. 7. MAGNETIC PROPERTIES OF CRYSTALS

18. 8. SEMICONDUCTORS Intrinsic Doping (donors/acceptors) Valence band
Conduction band

19. 8. SEMICONDUCTORS
Transport (electrons/holes)
Einstein relation

20. 8. SEMICONDUCTORS MOSFET Depletion width
Gate-controlled conduction channel
2D electron gas – quantum Hall effect Vs
metal
SiO2 x
p-Si