# MATSE 413 - Solid-State Materials

**This is a sample syllabus. **

This *sample syllabus* is a *representative* example of the information
and materials included in this course. Information about course
assignments, materials, and dates listed here is subject to change
at any time. Definitive course details and materials will be available
in the official course syllabus, in Canvas, when the course begins.

### Overview

The main course objective is to provide sufficient background for the understanding of fundamental phenomena in solid state materials that are based on the atomic level. First, a semi-quantitative description of the driving forces behind bond formation are discussed, followed by a mathematically rigorous description of periodic arrays and the introduction of the concept of reciprocal space. Lattice vibrations occurring in solid state materials are discussed and an introduction into quantum mechanics is given. The solution of the time-independent Schrödinger Equation for various problems relevant in nanostructured materials is presented and the motion of charged carriers in solid state materials is discussed. A semi-quantitative approach is taken how the electronic structure of isolated atoms is changed as they bond to form molecules and solids and emphasis is placed on how such bonding affects whether the resulting material will be a metal, an insulator, or a semiconductor. The goal of this course is to introduce and master the modern framework of solid state materials that describes materials phenomena at an atomic level, such as electronic band structure and electronic transport, the vibrational properties of solid state materials, and to prepare the audience for higher level quantum mechanical problems relevant to a more comprehensive understanding of the solid state.

### Objectives

When you successfully complete this course, you will be prepared to:

- Classify bond types, interpret bond strengths from interatomic potentials, and relate macroscopic properties to their microscopic origin.
- Identify Bravais lattice types and recall their symmetries, relate lattices to crystal structures, and construct reciprocal lattices for given Bravais lattices
- Understand wave phenomena in solid state materials, explain fundamental vibration modes of crystals and interpret the dispersion relation of lattice vibrations in real crystals.
- Understand the physical basics of quantized phenomena in solid state materials.
- Predict outcomes of the photoelectric effect and blackbody radiation experiments and describe their application potential in Materials Science and their role in our daily life.
- Identify the Schrödinger equation, recall the Postulates of Quantum Mechanics, recall the approach to solve quantum mechanical problems and the interpretation of their results for the standard quantum mechanical problems: the infinite quantum well, the finite quantum well, the tunnel effect.
- Describe and analyze experiments to determine the electrical conductivity of metals and semiconductors

### Required Materials

The materials listed here represent those that may be included in this course. Students will find a definitive list in the course syllabus, in Canvas, when the course begins.

#### Required textbook

There is no required textbook for this course

#### Recommended textbooks

Safa O. Kasap: Principles of Electronic Materials and Devices, Mc Graw Hill Education 2018, ISBN 978-0-07-802818-2

John Sydney Blakesmore: Solid State Physics, Cambridge University Press 2004, ISBN 978-0521313919 (paperback)

Rolf E. Hummel: Electronic Properties of Materials(link is external), Springer 2011, ISBN: 978-1-441-98163-9

P. Hofman: Solid State Physics: An Introduction(link is external), Viley-VCH 2008, ISBN: 978-3-527-40861-0

C. Kittel: Introduction to Solid State Physics, John Wiley & Sons 2005, ISBN 0-471-41526-X

James D. Livingston: Electronic Properties of Engineering Materials, Wiley-VCH 1999, ISBN 0-471-31627-X

### Prerequisites

MATSE 201, MATH 220, MATH 230/231

### Expectations

We have worked hard to make this the most effective and convenient educational experience possible. How much and how well you learn is dependent on your attitude, diligence, and willingness to ask for clarifications or help when you need them. We are here to help you succeed. Please keep up with the class schedule and take advantage of opportunities to communicate with us and with your fellow students. You can expect to spend an average of 8 - 10 hours per week on class work.

### Major Assignments

#### Participation (10% of total course grade)

A portion of the final grade results from attendance of a first mandatory office hour as well as the submission of 8 "Muddiest Points" throughout the class. These two activities are designed to provide accessible points as well as for the instructor to ensure that students are not quietly struggling with the course material.

#### Homework (20% of total course grade)

There are 12 homework assignments, which will be available when you are working through the week's reading and activity assignments.

#### Quizzes (50% of total course grade)

There will be 5 quizzes held throughout the summer to test your learning progress.

#### Final Exam (20% of total course grade)

There will be a cumulative final exam at the end of the course.

### Course Schedule

Module | Week | Topic | Assignment |
---|---|---|---|

Module 1: Bonding in Solids | 1 | Solid state materials The origin of attractive interaction Macroscopic properties | Homework 1 |

Module 1: Bonding in Solids | 2 | The covalent bond The metallic bond The ionic bond | Homework 2 |

Module 2: Atoms in Periodic Arrays | 3 | The atomic lattice Symmetries in lattices and the atomic basis Lattice planes and X-ray diffraction | Homework 3 Quiz 1 |

Module 2: Atoms in Periodic Arrays | 4 | The reciprocal lattice From the direct to the reciprocal lattice From Bragg's Law to the von Laue condition | Homework 4 |

Module 3: Lattice Vibrations | 5 | Oscillations and waves in crystals Lattice vibrations The monatomic chain | Homework 5 Quiz 2 |

Module 3: Lattice Vibrations | 6 | Lattice vibrations in real solids The diatomic chain Generalization to 3D solids | Homework 6 |

Module 4: Introduction to Quantum Mechanics | 7 | The need for a new theory: quantum mechanics When waves behave like particles When particles behave like waves The quantum nature of matter | Homework 7 Quiz 3 |

Module 5: Quantum Mechanics in Materials | 8 | A way out of the dilemma: The Schrodinger equation The postulates of quantum mechanics The infinite quantum well | Homework 8 |

Module 5: Quantum Mechanics in Materials | 9 | Scattering at a potential steps The tunneling effect | Homework 9 Quiz 4 |

Module 6: Electrons in Solid State Materials | 10 | The finite quantum well Sketching wave functions | Homework 10 |

Module 6: Electrons in Solid State Materials | 11 | Electrical conduction The classical Drude model The Hall effect | Homework 11 |

Module 6: Electrons in Solid State Materials | 12 | The Sommerfield model Electrical conduction: a semiclassical picture The Kronig Penney Model | Homework 12 Quiz 5 |

Final Exam |