Materials Physics I

Abstract

This course introduces classical and quantum mechanical concepts for the understanding of material properties from a microscopic point of view. The lectures focus on the static and dynamic properties of crystals, the formation of chemical bonds and electronic bands in metals, and semiconductors, and on the thermal and electrical properties that emerge from this analysis.

Objective

Providing physical concepts for the understanding of material properties: Understanding the electronic properties of solids is at the heart of modern society and technology. The aim of this course is to provide fundamental concepts that allow the student to relate the microscopic structure of matter and the quantum mechanical behavior of electrons to the macroscopic properties of materials. Beyond fundamental curiosity, such level of understanding is required in order to develop and appropriately describe new classes of materials for future technology applications. By the end of the course the student should have developed a semi-quantitative understanding of basic concepts in solid state physics and be able to appreciate the pertinence of different models to the description of specific material properties.

Content

PART I: Structure of solid matter, real and reciprocal space The crystal lattice, Bravais lattices, primitive cells and unit cells, Wigner-Seitz cell, primitive lattice vectors, lattice with a basis, examples of 3D and 2D lattices. Fourier transforms and reciprocal space, reciprocal lattice vectors, Brillouin zones Elastic and inelastic scattering of elementary particles with matter (x-rays, neutrons, electrons). Interaction of x-rays with matter. X-ray diffraction, Bragg condition, atomic scattering factors, scattering length, absorption and refraction. PART II: Dynamics of atoms in crystals Lattice vibrations and phonons in 1D, phonons in 1D chains with monoatomic basis, phonon in 1D chains with a diatomic basis, optical and acoustic modes, phase and group velocities, phonon dispersion and eigenvectors. Phonons in 2D and 3D. Quantum mechanical description of lattice waves in solids, the harmonic oscillator, the concept of phonon, phonon statistics, Bose-Einstein distribution, phonon density of states, Debye and Einstein models, thermal energy, heat capacity of solids. PART III: Electron states and energy bands in crystalline solids Electronic properties of materials, classical concepts: electrical conductivity, Hall effect, thermoelectric effects. Drude model. Transition to quantum models and review of quantum mechanical concepts. The formation of electronic bands: from molecules to periodic crystal structures. The free electron gas: Fermi statistics, Fermi energy and Fermi surface, density of states in k-space and as a function of energy. Inadequacy of the free electron model. Electrons in a periodic potential, Bloch's theorem and Bloch functions, electron Bragg scattering, nearly free electron model, physical origin of bandgaps, band filling. Energy bands of different types of solids: metals, insulators, and semiconductors. Fermi surfaces. Examples. PART IV: Electrical and heat conduction Dynamics of electrons in energy bands, phase and group velocity, crystal momentum, the effective mass concept, scattering phenomena. Electrical and thermal conductivities revisited. Electron transport due to electric fields (drift) and concentration gradients (diffusion). Einstein's relations. Transport of heat by electrons, Seebeck effect and thermopower, Peltier effect, thermoelectric cooling, thermoelectric energy conversion. PART V: Semiconductors: concepts and devices Band structure: valence and conduction states. Intrinsic and extrinsic charge carrier density. Electrical conductivity. p-n junctions. Metal-semiconductor contacts. FET transistors. Transistors as switches and amplifiers.

Resources