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.
Prerequisites
Enrollment in this course requires completion of MATSE 201, MATH 220, and 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
This course will rely on a variety of methods to assess and evaluate student learning, including:
Participation (10% of total 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 grade)
There are 12 homework assignments, which will be available when you are working through the week's reading and activity assignments. Your handwritten homework solutions have to be scanned and uploaded to CANVAS as a single .pdf file. Homeworks will be due on Fridays at 11:59 PM and the solution keys will be posted on Mondays at 9:00 AM. Homeworks may be submitted late with a deduction of 10% per 24 h past the deadline; however, the assignment will be given a zero if submitted after the solution key is posted on Monday. Students are encouraged to look over homeworks earlier so that they may ask questions in office hours as last-minute e-mails have no guarantee of being seen or answered in time.
Quizzes (50% of total grade)
There will be 5 quizzes held throughout the summer to test your learning progress. The quizzes will be performed electronically through Canvas and are open note, though communication with others is forbidden. Typical quiz questions cover the online course content, similar to the knowledge checks at the end of a lesson and less-involved problems from the homeworks.
Final Exam (20% of total grade)
There will be a cumulative final exam at the end of the course. The final exam is also open note, and again communication with others is forbidden. The final exam questions will be reminiscent of quizzes, knowledge checks, and less-involved homework problems.
Course Schedule
| Module | Week | Topic | Assignment |
|---|---|---|---|
| Module 1 | 1 | Solid state materials The origin of attractive interaction Macroscopic properties | Homework 1 |
| Module 1 | 2 | The covalent bond The metallic bond The ionic bond | Homework 2 |
| Module 2 | 3 | The atomic lattice Symmetries in lattices and the atomic basis Lattice planes and X-ray diffraction | Homework 3 Quiz 1 |
| Module 2 | 4 | The reciprocal lattice From the direct to the reciprocal lattice From Bragg's Law to the von Laue condition | Homework 4 |
| Module 3 | 5 | Oscillations and waves in crystals Lattice vibrations The monatomic chain | Homework 5 Quiz 2 |
| Module 3 | 6 | Lattice vibrations in real solids The diatomic chain Generalization to 3D solids | Homework 6 |
| Module 4 | 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 | 8 | A way out of the dilemma: The Schrodinger equation The postulates of quantum mechanics The infinite quantum well | Homework 8 |
| Module 5 | 9 | Scattering at a potential steps The tunneling effect | Homework 9 Quiz 4 |
| Module 6 | 10 | The finite quantum well Sketching wave functions | Homework 10 |
| Module 6 | 11 | Electrical conduction The classical Drude model The Hall effect | Homework 11 |
| Module 6 | 12 | The Sommerfield model Electrical conduction: a semiclassical picture The Kronig Penney Model | Homework 12 Quiz 5 |
| Final Exam | |||