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PHYS3004 Crystalline Solids

PHYS3004 Crystalline Solids. Prof. P.A.J. de Groot. 1. BONDING IN SOLIDS. Born-Oppenheimer Approximation Linear Combination of Atomic Orbitals. 1. BONDING IN SOLIDS. Covalent bonding Ionic bonding Metallic bonding Van der Waals bonding. 1. BONDING IN SOLIDS. Covalent bonding: LCAO

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PHYS3004 Crystalline Solids

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  1. PHYS3004Crystalline 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. R1 2. CRYSTAL LATTICES • Lattice & basis • Wigner-Seitz cell

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

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