## MSE242 : Physics of Materials

##### Basic principles of modern physics and quantum mechanics as pertain to solid state physics and the physical behavior of materials on the nanometer scale. Applications to solid state and nano-structured materials will be emphasized including band structure, bonding and magnetic, optical and electronic response.

Prerequisites: Math 216 Phys. 240

Cognizant Faculty: Goldman, Millunchick, Mansfield, Shtein, Yalisove

### Course Topics:

- Failure of classical physics; black-body radiation, Planck Postulate (TR 1, TR 3)
- Early experiments exhibiting quantum effects: photo-electric effect, Davisson-Germer results, Compton shift, x-ray production. (TR 3)
- Early models of the atom: Thompson, Rutherford and Bohr models, their successes and shortcomings. (TR 4)
- Wave-particle duality; de Broglie postulate and Einstein relation. (TR 5)
- Introduction to the wave equation and Fourier series analysis. (TR 5)
- The Heisenberg uncertainty principle. (TR 5)
- Probability density, expectation values, energy and momentum operations. (TR 5, TR 6)
- Schrdinger equation, solutions for step, barrier and well potentials (TR 5, TR 6)
- Scanning Probe Microscopy (TR 6)
- Periodic well potentials: Kronig-Penney model (TR 11.1 + supplements)
- Solution of the Schrdinger equation for the hydrogen atom (TR 7)
- Atomic Physics and the Pauli Exclusion Principle (TR 8)
- Classical and Quantum Statistics: Bose-Einstein and Fermi-Dirac statistics (TR 9)
- Origin of Spectra (TR 10)
- Stimulated Emission and Lasers (TR 10)
- Thermal and Magnetic Properties (TR 10)
- Superconductivity (TR 10)
- Band Theory (TR 11)
- Semiconductor Devices : Diodes, Transistors and Photovoltaics (TR 11 + supplements)

Additional Examples of the application of quantum theory in the context of materials science and engineering. May include: Quantum Devices, Quantum Computing, Magnetic Media, Spintronics

### Course Objectives:

- To teach sophomore engineering students the historical experimental results and theoretical developments which led to the formulation of quantum mechanics and solid state physics.
- To teach students the solutions of the time independent Schroedinger?s equation for various potentials.
- To teach students energy bands in solids and the origin of electronic conduction in metals and semiconductors.
- To teach students crystal structure and the Miller index and reciprocal lattice descriptions of crystallography.
- To teach students Fourier methods and the application to diffraction effects in solids.
- To teach students diffraction methods for crystallographic and defect analysis in pure and alloyed materials.
- To provide students with examples of devices and applications for solid state phenomena and materials.

### Course Outcomes:

- Given the energy (E) of a wave/particle, students will be able to determine the de Broglie wavelength and the Einstein frequence for the wave description of the wave/particle.
- Students will be able to estimate position-momentum and energy-time uncertainties for particles in the quantum size limit.
- Students will be able to solve Schroedinger?s equation for step, barrier and well potentials, and find energy values for the solution eigenfunctions.
- Students will be able to describe and sketch the valence and conduction band structure of monovalent, bivalent and trivalent metals, and describe the relative electrical conduction of each type of metal.
- Students will be able to describe and sketch the band structure of pure and doped semiconductors, and illustrate direct band gap and indirect band gap transitions.
- Students will be able to provide the Miller indices for arbitrary crystallographic planes and directions in cubic and hexagonal crystal systems.
- Students will be able to index the reciprocal space lattices for cubic and hexagonal crystal structures.
- Given a real space lattice students will be able to determine the corresponding Fourier transform reciprocal space latticce.
- Given an unknown single phase solid material, students will be able to describe the characterization methods required in order to determine the identity and crystal structure of the host element, the single- or poly-crystalline nature of the material, the grain size (if applicable, and the relative defect level.
- Students will be able to identify the solid state phenomena which provide the basic functionality in many contemporary microelectronic devices.

### Assessment Tools:

- Class ombudspersons will provide continuing feedback from class to the instructor.
- Weekly homework assignments will test objectives #1-6, results will be discussed in class discussion.
- Two closed-book mid-term exams will test objectives #1-6.
- Course mid-term evaluation by CRLT personnel will allow for active feedback to instructor in order to identify areas for greater emphasis and improvement in course presentation.
- Student reports on microelectronic solid state devices and systems will be presented to entire class (objective #7).