Pre-requisites: PHY-102, 203, 301, 304

PART A

1. Crystal Structure

• The Crystalline State of Solids
• Unit Cell
• Bravais Lattice
• Symmetry operations
• Miller Indices
• Simple Crystal Structures
• Packing Factor
• Inter-planar Spacing
• Concept of Reciprocal Lattice
• Bragg Diffraction in Reciprocal Lattice
• Brillouin Zones
• Diffraction of X-rays by crystals
• Laue equations and Bragg law
• Experimental diffraction methods-Laue method:
  • Rotating crystal method and power methods
  • Defects

2. Crystal Bonding

• Interatomic forces and crystal bonding
• Ionic crystals
• Calculation of :
  • electrostatic energy,
  • binding energy,
  • Madelung constant and
  • bulk modulus
• Covalent crystals
• Crystals of inert gases
• Van der Waals and repulsive interactions
• Metal crystals and hydrogen bonded crystals

3. Lattice Vibrations and Thermal Properties

• Vibrations of monoatomic linear lattice
• Vibrations of diatomic linear lattice
• Nonelectronic dynamical properties
• Phonon
• Phonon momentum
• Elastic vibration of a continous medium
• Enumeration of normal modes
• Neutron scattering by a crystal
• Theories of lattice specific heat
  • Einstein model
  • Debye Model
• Lattice thermal resistivity
• Anharmonicity
• Thermal expansion
• Heat conductivity
• Normal and Umklapp processes

4. Multi-electron atoms

• Wave functions of identical particles
• Exchange symmetry
• Pauli exclusion principle
• Helium atom
• Hartree approximation
• X-ray spectra
• Hund’s rules
• Molecular orbital theory applied to covalent bonding
• Hydrogen ion
• Hydrogen molecule

PART B

5. Free Electron Theory of Metals

• Drude phenomenology of electronic properties
  • Fermi gas, Energy levels and density of states in one dimension
• Free electron gas in three dimensions
• Heat capacity of the electron gas
• Effect of temperature on $F-D$ distribution
• Electrical conductivity and Ohm’s law
• Hall effect
• Wiedmann Franz law
• Electrical and thermal conductivity:
  • scattering of electrons from crystal defects and phonons,
  • Pauli paramagnetism,
  • Sommerfeild theory of conduction in metals.

6. Electronic structure of solids

• Wave functions of electrons in a one-dimensional crystal
• Crystal momentum.
• Modification of free-electron dispersion relation
• Energy bands and band gaps
• Classification of solids by their electrical properties at zero temperature: metals and insulators
• Nearly Free electrons model of electronic structure, The tight binding approximation
• Fermi surfaces, Properties of the fermi surface
• Band structures
• Semi-classical dynamics of Bloch electrons
• Concept of hole charge carriers and effective mass, dynamics in presence of magnetic field
• Semiclassical transport
• Optical properties

7. Dielectric Properties

• Macroscopic Electric Field
• Local Electric Field at an atom
• Dielectric Constants and Polarizabilities
• Clausius-Mossotti Relation
• Dielectric Phenomena in an $AC$ Field
• Debye Equations for Dielectric Constant and Dielectric Loss
• Dielectric Response of an Electron Gas
  • Concept of Plasmon and Calculation of Plasma Frequency
• Screened and Unscreened Coulomb Potential
• Motion in Magnetic Fields
• Pyro, piezo and Ferroelectricity
• Light propagation in solids

8. Semiconductors

• General properties and band structures,
  • impurities,
  • intrinsic and doped semiconductors,
  • concept of hole charge carriers and
  • effective mass,
  • Electron statistics
• Carrier concentration and transport
• conductivity
• mobility
• Impurities and defects
• Magnetic field effects: cyclotron resonance and Hall effect
• Optical properties
• absorption
• photoconductivity
• luminescence and excitons
• p-n junctions
• Basic semiconductor devices:
  • light-emitting diodes,
  • photovoltaic cells,
  • transistors,
  • quantum dots:
    • elements of quantum confinement and quantum transport.