Topics covered in this course will include a review of quantum theory, atomic bonding and crystal stucture, mechanical and thermal properties of solids, and the significance of heat capacity as a measure of the lattice vibrations. The study of electrons in metals will lead to the temperature dependence of resistivity, mobilities, Hall effect, and superconductivity. The band theory of solids and the distinction between metals, insulators and semiconductors will follow from the discussion of the behavior of electrons in crystalline solids. Semiconductor topics will include the effects of doping, electron and hole conductivity, Hall effect, optical absorption, and the physics of the pn junction. The course will conclude with the equilibrium diode and the effects of bias voltages, temperature changes, and light absorption - an application of the ideas of band theory to the operation of basic junction devices.

Textbook:   Ronald Brown,  SOLID STATE PHYSICS - An Introduction for Scientists and Engineers.   El Corral, 2006

Course Syllabus

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PHYSICS 412 NOTES

[Look here occasionally for comments on the course throughout the quarter.]
[NOTE:   The following is approximately the schedule for the class last year - FALL 2007.  This year's schedule may be a bit different - and, in particular, the exams could be changed from last year's format.]

We will begin with a brief review of the elements of the quantum theory. The first chapter of the book touches on the important ideas that will come up during the later discussions in the course. Read through the chapter quickly - then look more carefully at the areas you feel need some review. You do not need to have this material "nailed" in order to proceed. But you do need to have the essential ideas, since QM will be a part of nearly every discussion. By Monday, you should be comfortable with the assigned problems.

Homework problems due Mon. - Ch 1, Probs. 5, 8, 13, 14.

You might also look carefully at Question 13, Probs. 10 and 12, and the two-dimensional hydrogen atom (and how the allowed quantum numbers lead to the structure of the periodic table in Flatland!)

Based on the structure of the periodic table (based on the hydrogen atom quantum number scheme), we will relate the atomic structure and electron configurations to bonding mechanisms. This will lead to the discussion of crystal structures. The "story" of Ch 2 is that the bonding mechanisms drive the crystal structures - and thus ultimately control the nature of the solids that form. Be making the connection between bonding and crystal structures. Look carefully at the derivation of the crystal potential energy function U(R) for the Van der Waals bonded solids in order to determine their crystal structure by Friday.

On Friday, we will talk about crystal directions, crystal planes, and crystal symmetries and unit cells. The notation used to designate and identify crystal planes (Miller indices) will be discussed. Be working the Ch 2 problems to be sure there are no surprises.

Homework problems due Wed. - Ch 2, Probs. 4, 8, 11, and 14.

We won't spend much time on X-ray diffraction. I'll respond to questions on Ch 2 stuff - and talk a little about the reciprocal lattice description of solids - then will begin the discussion of X-ray diffraction - the method for determining the crystal structures of solids. That discussion will spill over to Wednesday. How much time we talk about that is up to you.

In completing your review of X-ray diffraction. Look in particular at the development of the Bragg condition for simple cubic structures - and then what role the "center" atoms play in the diffraction patterns of bcc and fcc structures. The way to account for those atoms is through the "selection rules". You should know WHY those rules appear - ie, what their purpose is. You should look for how the application of Bragg condition and selection rules lets you determine the crystal structure and lattice parameter for cubic crystals (sc, bcc, fcc, diamond). NOTE: The x-ray diffraction material is optional - ie, use it for information about that diagnostic tool. If you plan on taking the solid state lab in Winter, this will be helpful material.

Homework problems due Mon. - Ch 3, Probs. 1 and 5.

The chapter on the mechanical properties of solids has three main parts: Basic mechanical stiffness, thermal expansion, etc., wave propagation in solids, and the thermal properties.

On Friday, we started talking about the mechanical properties of solids. It will actually be a continuation, in a way, of the discussion of the relationship between bonding mechanisms and crystal structure. The form of the potential energy function that we developed in the discussion of the Van der Waals bond - called the "crystal potential energy" - was used to examine the elasticity of crystals and thermal expansion. That discussion will continue on Monday.

The propagation of mechanical waves in the crystal will be discussed briefly in order to obtain a result that will be necessary to understand the heat capacities of solids. We will not go through this discussion in great detail, but there are two important points to be made: Vibrations in periodic structures yield the same results as in the idealized homogeneous solids until the vibration wavelengths become comparable to the interatomic separations. And that leads to a high frequency "cut-off" wavelength.

Thermal Properties - in particular the molar heat capacity. This is a very important topic as it ultimately explains the behavior of electrons in metals as well as how atoms vibrate in all solids. The classical theory will need to be modified to explain the behavior of solids at low temperature. The important result that follows has applications to all solids - and appears in the electrical properties discussion as well as thermal properties, including the discussion of superconductivity.

The first mid-term will follow completion of Ch. 4.

Homework problems due Mon. - Ch 4, Probs. 2, 9, 13, 14.

You should be finishing Ch 4 by Monday and bring any questions you want addressed to class. In particular, be sure that you have looked at the distinctions between the classical, Einstein, and Debye models of the molar heat capacity of solids. These all deal with the lattice vibration contribution to the heat capacity - with the important conclusion that atoms vibrate as quantum harmonic oscillators. As we will see, the lattice vibrations ultimately control (ie, limit) the flow of electrons in metals - hence limits the electrical conductivity.

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EXAM 1

Chapters 1-4

Either in class or take-home, depending.  If take-home, there would be a time limit of about three hours from when you open the exam.

Study together if you wish - then take the test independently, with no communication of any sort. (Note: Looking at worked exams from previous years is not independent work.) The work you submit must be entirely your own with the help of any books and your notes. The purpose of the time limit is to separate your study from your test-taking. Prepare first, then take the exam. Three hours should be more than ample if you are prepared when you open the exam - but it should be thought of as a guideline not an absolute limit. Don't stop in the middle of a problem you are working correctly because you ran out of time!

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We will begin the discussion of Chapter 5 - the electronic properties of solids - by looking at the resistance of metals. The basic idea that it is electron collisions with the ions that limits conductivity will be correct - but it is not the electron speeds, but rather the lattice vibrations that has the biggest effect. We will being assuming the electrons behave as classical particles moving among the ions. That will allow some success in understanding conductivity (or resistivity) and the Hall effect. But there will be an apparent paradox that can only be resolved with the quantum theory.

You need to be reading about the temperature dependence of resistivity in metals - and the Hall effect - two important areas that will help later in understanding the behavior of electrons in solids.

Introduction to Superconductivity Chapter 5, Sect. 2 - One of the most intriguiging topics in solid state physics. This will just be an intro to the basic ideas. The topic can be explored more completely by independent reading in Ch. 10.

On Monday, we will talk about superconductivity - just because it is too interesting not to talk about. Some history, some properties of superconductors, some about the experiments in superconductivity (which are, in turn, clues to the mechanisms) - and maybe something about high Tc superconductivity. We won't have time to go in depth (too bad) - but any who want to do some followup reading/thinking could always sign up for an independent study and/or stick around another year to take Phys 413!

On Wednesday, we will talk about the successes and failures of the classical model - which includes a discussion of the Hall effect (as a success - but it raises some serious concerns as well). Then we will try to address the problems that are raised in the classical model by treating the electrons quantum mechanically. The good news is that we have already solved that problem - we just have to interpret it.

By the end of the week, we will be dealing with how the quantum theory allows us to determine the electron contribution to the molar heat capacity of a metal. To do that, we will need to know the distribution of allowed states within the metal (ie, the density of states function) and how the electrons distribute themselves among those states (the Fermi distribution function).

Homework problems due Monday. - Ch 5, Probs. 3, 5, 7, 15, 18, and 20

The free electron density of states and Fermi distribution function. Assuming the conduction electrons behave as independent electrons in a box allows us to develop the density of states function - ie, the function that describes how the states are distributed in energy. Assuming the conduction electrons obey Pauli exclusion principle allows us to determine how the electrons distribute themselves among the available states as a function of temperature. That, in turn, will allow us to determine how temperature changes the energy of the electrons - one of the dilemmas from the classical theory of electrons in metals. That is, the electronic contribution to the heat capacity of a metal can be derived.

This result will tell us how the quantum nature of the electrons changes their behavior, but does not allow a quantum description of electrical conductivity (or resistivity) until the effect of the ions is reintroduced into the problem.

To understand the limitations on the conductivity of a metal requires that the electrons interact with the lattice - something that was explicitly precluded in the quantum free electron model of metals (used to understand the electron heat capacity).

On Friday, we will introduce both the atomic states model and the nearly free electron model of solids - two very different approaches that yield very similar results: the band theory. That is, either starting with individual atoms which you allow to come close enough to interact (which then breaks up the degeneracies associated with individual atomic energy levels to form bands of states) or starting with free electrons in a box and introducing the interaction with the ions as a perturbation on the free electron model BOTH yield the result that the allowed states for electrons in a solid are distributed in bands. The distinction between metals and non-metals will ultimately reside in that discussion.

We will extend the discussion of Ch 6 to include how the nearly free electron model modifies the electrical conductivity, what the significance of the E vs k diagram is in describing the dynamics of the behavior of electrons - including the ideas of hole conductivity and the effective mass of the electrons and holes. We will show how the band theory assists in describing the distinctions between metals and non-metals, monovalent, divalent, and trivalent metals. That discussion naturally leads into the first section of Ch 7 on insulators and semiconductors.

Most of this material is interpretation of the band theory ideas rather than a formal development of the band theory. But that means you will need to read it carefully to make the connections between the ideas.

The second exam will follow the discussion of Ch. 6 (with perhaps the first section of Ch. 7 included as well - since it is nearly a continuation of the material.

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EXAM II - Chapters 5, 6, and Sect. 7.1

ELECTRONS IN METALS AND THE BAND THEORY

Time limited: 4 hours (more or less) from when you open the exam (but that time does not have to be contiguous).

The test is four problems (on four pages) dealing with the classical and quantum theories of electrons in metals, the introduction to the band theory of solids, and the distinctions between metals, insulators, and semiconductors. The questions/problems will be similar to those in the text.

DUE on Monday, November 19

EXAM REVIEW SHEET

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We will then begin discussing the band gap solids - insulators and semiconductors - on Monday before Thanksgiving break. We will discuss how energy band gaps are measured in insulators and semiconductors - ie, the optical absorption experiment (which will be done in the solid state laboratory Winter quarter). Look at Sect. 7.1.

This discussion will ultimately lead to the properties of semiconductor materials, electron and hole conduction, the effects of doping to produce n-type and p-type semiconductors, how their properties differ from metals, and from each other, etc. Both the electrical and the optical properties of solids will be important in this discussion. Ultimately, the electronic properties of semiconductor devices cannot be understood without understanding this material.

We will look this week at what happens when p-type and n-type semiconductors are joined to form a pn junction. In particular, we will develop the condition for the equilibrium junction with the understanding that the only thing that can be done to such a junction is to apply bias voltages, shine light on it, or change its temperature. On Wednesday and Friday, we will look at the similarities and differences of various devices in a quick overview - including junction rectifiers, PV cells, LEDs, bipolar transistors, and FETs. It won't be a careful study, of course - given the time we have. But it should give you an overview that could become the basis for further study.

The final exam will be comprehensive, but will concentrate on the properties of solids that relate ultimately to the electronic properties. You can ignore Ch 1 (Quantum Theory) and Ch 3 (X-ray Diff) in your preparation for the final. The point of the final is to see what you are carrying away with you about the basic properties of solids. It will be closed book and notes - but you will have an equation sheet (handed out ahead of time) to remind you of the ideas and relationships throughout the course. There may be some choice on the exam - for example, six problems-do five or something. That will allow you to concentrate on the areas that you feel most confident in.

The point of the final will not be to solve a lot of problems, but to see how you have assembled the essential ideas of the course and how those ideas are connected. It will be an attempt to see how conversant you are with the material.