Phys 5701.001 (Spring 2017)http://www.physics.umn.edu/classes/2017/spring/Phys%205701.001/Solid-State Physics for Engineers and Scientists2017-03-25T11:40:01ZXML::Atom::SimpleFeed2017-03-23T23:12:36Z<p>Reading:</p>
<p>Simon, Chapter 18, "Semiconductor Devices," although it is rather shallow<br />
Ashcroft and Mermin, end of Chapter 28 and Chapter 29: "Inhomogeneous Semiconductors"<br />
Davies, "The Physics of Low-Dimensional Semiconductors," pages from Chapter 3</p>
<p>I am posting the pages from A&M and Davies at the link below.</p>
<p>Problem Set 8 is posted.</p>
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Reading for Week 10
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modified 24-Mar-2017 at 2:13PM
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</ul>2017-03-25T01:10:08ZPaul Crowellcid:58471.eid:438072.updated:2017-03-24 20:10:08Week 10 (Updated)2017-01-18T17:04:35Z<ul>
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<a href="/classes/2017/spring/Phys 5701.001/downloads/438282-ProblemSet8.pdf" title="299 Kbytes, application/pdf">Problem Set 8</a>
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<small><i>posted 24-Mar-2017 at 8:08PM</i></small>
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<a href="/classes/2017/spring/Phys 5701.001/downloads/436532-Problem_Set_7.pdf" title="257 Kbytes, application/pdf">Problem Set 7</a>
<small>| <a href="/classes/2017/spring/Phys 5701.001/downloads/436532-Problem_Set_7.pdf?download=1" title="257 Kbytes, application/pdf">Download</a></small>
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<small><i>posted 18-Mar-2017 at 3:25PM</i></small>
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<a href="/classes/2017/spring/Phys 5701.001/downloads/434432-Problem_Set_6.pdf" title="248 Kbytes, application/pdf">Problem Set 6</a>
<small>| <a href="/classes/2017/spring/Phys 5701.001/downloads/434432-Problem_Set_6.pdf?download=1" title="248 Kbytes, application/pdf">Download</a></small>
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<small><i>posted 7-Mar-2017 at 7:31PM</i></small>
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<a href="/classes/2017/spring/Phys 5701.001/downloads/431762-Problem_Set_5.pdf" title="376 Kbytes, application/pdf">Problem Set 5 (revised)</a>
<small>| <a href="/classes/2017/spring/Phys 5701.001/downloads/431762-Problem_Set_5.pdf?download=1" title="376 Kbytes, application/pdf">Download</a></small>
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<small><i>posted 20-Feb-2017 at 8:57PM</i></small>
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<a href="/classes/2017/spring/Phys 5701.001/downloads/429912-Problem_Set_4.pdf" title="237 Kbytes, application/pdf">Problem Set 4</a>
<small>| <a href="/classes/2017/spring/Phys 5701.001/downloads/429912-Problem_Set_4.pdf?download=1" title="237 Kbytes, application/pdf">Download</a></small>
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<small><i>posted 9-Feb-2017 at 11:27PM</i></small>
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<a href="/classes/2017/spring/Phys 5701.001/downloads/428082-Problem_Set_3.pdf" title="219 Kbytes, application/pdf">Problem Set 3</a>
<small>| <a href="/classes/2017/spring/Phys 5701.001/downloads/428082-Problem_Set_3.pdf?download=1" title="219 Kbytes, application/pdf">Download</a></small>
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<small><i>posted 2-Feb-2017 at 3:21PM</i></small>
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Solutions
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modified 22-Mar-2017 at 2:55PM
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<a href="/classes/2017/spring/Phys 5701.001/downloads/426492-Problem_Set_2.pdf" title="288 Kbytes, application/pdf">Problem Set 2 (Revised)</a>
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<small><i>posted 31-Jan-2017 at 5:11PM</i></small>
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<a href="/classes/2017/spring/Phys 5701.001/downloads/424022-Problem_Set_1.pdf" title="132 Kbytes, application/pdf">Problem Set 1</a>
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<small><i>posted 18-Jan-2017 at 11:07AM</i></small>
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</ul>2017-03-25T01:09:12ZPaul Crowellcid:58471.eid:424012.updated:2017-03-24 20:09:12Problem Sets and Solutions (Updated)2017-03-09T20:32:12Z<p>Problem Set 7 is posted. </p>
<p>We will continue with the discussion of metals after break, and then turn to semiconductors. Start reading Kittel, Chapter 8. </p>
<p>Note that the semiclassical model for transport, which is used in Chapter 9 to describe magneto-oscillations in metals, in introduced for the first time in Chapter 8. Note the key fact: <br />
<img src="/texvc/d00ff5ee66cf213f7269eb29d8c79383.png" alt=" \hbar dk/dt ">
= F, where F is the external force (e.g. the Lorentz force). This may puzzle you, because \hbar k is NOT the electron momentum, and so this does not appear to be consistent with F=ma at first glance. The truth comes out on p. 93. The electron is acted on by both the external force and the periodic potential. When both the lattice and the electrons are included (see Eqs. 8.15 and 8.16), then \hbar k is a momentum (the crystal momentum). </p>
<p>The semiclassical model leads to some reasonably intuitive phenomena such as magneto-oscillations, which are really just an extension of cyclotron motion to periodic systems, and some non-intuitive ones, such as Bloch oscillations (p. 217). In the latter case, a constant electric field leads to oscillations in the group velocity. If you understand Bloch oscillations, then you understand crystal momentum.</p>
<p>I am adding below a "simple" derivation of the expression (Kittel 9.37) for the period of magneto-oscillations. In class,I just wrote down this expression, but for Fermi surfaces with a circular cross-section, it is possible to derive it accepting only the fact that the energies must be quantized in units of the cyclotron energy. <br />
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<a href="/classes/2017/spring/Phys 5701.001/downloads/437482-Magnetoscillations.pdf" title="232 Kbytes, application/pdf">Magneto-oscillations</a>
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<small><i>posted 21-Mar-2017 at 3:49PM</i></small>
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</ul>2017-03-21T20:49:32ZPaul Crowellcid:58471.eid:436542.updated:2017-03-21 15:49:32Week 9 (Updated)2017-01-17T21:20:27Z<i>This item is restricted: please visit the website to view it.</i>2017-03-20T04:22:30ZPaul Crowellcid:58471.eid:423742.updated:2017-03-19 23:22:30Lecture Notes and Related Materials (Updated)2017-03-08T00:22:11Z<i>This item is restricted: please visit the website to view it.</i>2017-03-08T00:22:57ZPaul Crowellcid:58471.eid:435602.updated:2017-03-07 18:22:57Quiz Solutions (Updated)2017-03-02T05:59:54Z<p>Problem Set 6 is posted.</p>
<p>We are going to skip over Chapter 8 for now and start Chapter 9 (Band structure of metals and the Fermi surface). Start by reading pp. 223 - 236. Tight binding is particularly important. As I mentioned in class, it is in a sense the opposite of the NFE approximation, in that we will start with individual atomic levels and let them couple to form bands. The advantage of tight binding is that (unlike the NFE model) it produces physically reasonable band structures over the entire zone. It is not perfect, and some would argue that it should not work very well for metals (but it often does). Nonetheless, a basic understanding of the tight binding philosophy is essential for anyone working in solid state physics.</p>
<p>In contrast, I will probably skip pp. 236 - 239, as this is not an exhaustive class on band structure. I will also go a bit light (relative to a traditional physics class) on Fermi surface probes, such as the de Haas van Alphen effect.</p>
<p>We will also have a discussion about the topics to be covered after break, as I will make some effort to address areas of particular interest to the class.</p>2017-03-02T05:59:54ZPaul Crowellcid:58471.eid:434442Week 82017-02-24T01:05:24Z<p>The first quiz will be on Thursday, March 1st. It will cover material through Chapter 6. It will be "closed book."</p>
<p>On Tuesday, we will continue the discussion of the nearly free electron model. Please make sure that you have read Chapter 7 and read pp. 169 - 174 particularly carefully. Note the key role played by the fact that the periodic potential can be written as a sum of plane waves that includes ONLY reciprocal lattice vectors (Eq. 23). The wavefunction itself is expanded in the usual sum over all k-states (Eq. 25), but (as you will read), solving for a Bloch function consists of solving a set of equations for each wave-vector k in the first Brillouin zone. In short, the periodic potential "mixes" the plane wave state at k0 (some wave-vector in the first BZ, see Fig. 7) only with those plane waves with k differing by reciprocal lattice vectors. </p>
<p>The difficult part is deciding on the number of equations (copies of Eq. 27) to include in the system to be solved, given that the number of equations must equal the number of unknowns. The usual approach is to keep only those k's for which the free electron energies are the same (or nearly so) AND which are separated in reciprocal space by a reciprocal lattice vector G for which U_G is non-zero. In one-dimension, this means that the system is 2 x 2, becuase the Brillouin zone boundaries are just two points. In higher dimensions things can be more complicated, because there can be multiple points (even planes) on the zone-boundary for which the free electron energies are degenerate or nearly so. </p>
<p> </p>2017-02-26T19:54:32ZPaul Crowellcid:58471.eid:433292.updated:2017-02-26 13:54:32Week 7 (Updated)2017-02-17T05:33:16Z<p>On Tuesday, we will cover basic electronic and thermal transport in metals. Note that the Drude model (see Simon, Chapter 3 or Ashcroft and Mermin, Chapter 1) provides an adequate picture of transport in electric and magnetic fields, extending out to optical frequencies. I recommend reading one of these, which also provide a discussion of how the Drude model fails for thermal transport. Note that the Drude model is not simply a vestige of 19th century physics. As noted here, it is adequate for basic magneto-transport and is even more appropriate for doped semiconductors. It is also a good tool for understanding the optical properties of metals. A good book on optical properties of matter is Dressel and Gruner, "Electrodynamics of Solids." Metals are covered in Chapter 5. We willl return to this topic later in the semester.</p>
<p>On Thursday, I will introduce the periodic potential and Bloch's theorem (Chapter 7).</p>
<p>Problem Set 5 is posted.</p>2017-02-20T00:49:17ZPaul Crowellcid:58471.eid:431682.updated:2017-02-19 18:49:17Week 6 (Updated)2017-02-10T05:36:25Z<p>Tuesday's lecture will finish our first pass through phonons. I will cover thermal expansion and thermal conductivity only briefly, but I will introduce the concept of crystal momentum.</p>
<p>We will then start Chapter 6. I expect to cover the first half of this chapter this week. Please review the following concepts from quantum mechanics: wave function for free electrons, the momentum operator and its physical interpretation (see Eq. 6.13), the Pauli exclusion principle, Fermi-Dirac statistics.</p>
<p>Problem Set 4 is posted. </p>2017-02-10T05:36:44ZPaul Crowellcid:58471.eid:429922.updated:2017-02-09 23:36:44Week 5 (Updated)2017-02-02T21:25:37Z<p>Kittel: Chapter 5</p>
<p>This week will be devoted to thermal properties of solids based on the phonon description.</p>
<p>Discussion of thermal properties requires the following concepts from quantum mechanics and statistical mechanics: quantization of phonon modes (i.e., the quantum harmonic oscillator), density of states, and the Boltzmann distribution. For those who are not familiar with these topics: please read about them before class on Tuesday. </p>2017-02-02T23:49:39ZPaul Crowellcid:58471.eid:428162.updated:2017-02-02 17:49:39Week 4 (Updated)2017-01-16T05:06:28Z<p>Reading: Kittel, Chapters 1 and 2<br />
Alternatives: Simon, Chapters 12 and 13, A&M, Chapters 4 - 7</p>
<p>We will spend the first two weeks on "structure and symmetry," with an emphasis on the important crystalline systems and the notion of reciprocal space. I am not going to emphasize the mathematical aspects of symmetry, such as point groups and space groups. If you are interested, Ashcroft and Mermin address these (slightly) in their Chapter 7.</p>
<p>The first problem set will be due Thursday, January 26th and will be posted shortly.</p>
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<a href="/classes/2017/spring/Phys 5701.001/downloads/427742-PS1.pdf" title="506 Kbytes, application/pdf">Problem Set #1 Solution</a>
<small>| <a href="/classes/2017/spring/Phys 5701.001/downloads/427742-PS1.pdf?download=1" title="506 Kbytes, application/pdf">Download</a></small>
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<small><i>posted 1-Feb-2017 at 3:54PM</i></small>
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</ul>2017-02-01T21:54:59ZPaul Crowellcid:58471.eid:423232.updated:2017-02-01 15:54:59Week 1 (Updated)2017-01-27T00:28:53Z<p>Reading: Kittel, Chapters 3 (bonding) and 4 (phonons). I will not be assigning problems on elastic constants, but you should know the terminology (stress, strain, bulk modulus, compressibility, longitudinal and transverse sound modes, etc.) <br />
Alternatives: Chapter 6 of Simon covers bonding in solids. Chapters 9 and 10 of Simon cover phonons (using the 1D model).<br />
Problem Set 2 is posted. I revised it this weekend to include another optional part to the diffraction simulation. I also improved (I hope) the explanation of the superlattice problem.</p>
<p>Optional means genuinely optional. These are problems from my old 8711 problem sets that I think provide some insight. They will not be graded but I will attempt to post solutions. </p>
<p>It is important to know the principal classes of bonding in solids, but I am not a chemist and will spend at most one lecture on the topic.</p>
<p>Phonons (excitations of the atomic cores about their equilibrium positions) are the second piece of our picture of solids. Having established the basics of structure and symmetry, we are now going to let the atoms move. I will follow the traditional practice of developing the basic physics in one dimension, extrapolating to higher dimensions using symmetry arguments and hand-waving. The reciprocal lattice will play an important role. If you want to see how the math works in higher dimensions, look at the relevant chapters in Ashcroft and Mermin. </p>
<p>Phonons are essential to understanding the thermal properties of solids, which we will get to next week. </p>
<p> </p>2017-01-30T18:27:52ZPaul Crowellcid:58471.eid:426522.updated:2017-01-30 12:27:52Week 3 (Updated)2017-01-22T06:09:57Z<p>This week we will finish introducing reciprocal space and consider the case of x-ray diffraction, which is an example of elastic scattering.</p>
<p>Reading: Kittel, Chapter 2<br />
Simon (note the web address for this book posted on this page), Chapter 14 has a more comprehensive discussion of scattering than Kittel. Simon's discussion does refer to Fermi's golden rule, which follows from the quantum mechanical treatment of elastic scattering. All you need to know is that the probability of an incoming wave of wave-vector k scattering into a wave of wave-vector k' is proportional to the square of the Fourier transform of the scattering potential with respect to the wave-vector k-k'. </p>
<p>Problem Set 2 will be posted later. </p>2017-01-22T06:09:57ZPaul Crowellcid:58471.eid:424902Week 22017-01-18T01:21:38Z<p>You will need to know some quantum mechanics and statistical mechanics in order to practice the art of solid state physics. If you are looking for two elementary textbooks, try</p>
<p>For quantum mechanics:<br />
D. J. Griffiths, "Introduction to Quantum Mechanics"</p>
<p>For statistical mechanics:<br />
D. V. Schroeder, "An Introduction to Thermal Physics,"<br />
OR<br />
Kittel and Kroemer, "ThermalPhysics"</p>
<p>Kittel and Kroemer is a good book marred by an unfortunate choice not to use Boltzmann's constant. If you can get past that, it is at a somewhat higher level than Schroeder and gets to statistical mechanics more efficiently.</p>
<p> </p>2017-01-18T01:21:38ZPaul Crowellcid:58471.eid:423892Quantum Mechanics and Statistical Mechanics2017-01-14T23:56:07Z<ul>
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<a href="/classes/2017/spring/Phys 5701.001/downloads/423162-PHYS_5701_Syllabus_2017.pdf" title="972 Kbytes, application/pdf">PHYS 5701 Syllabus</a>
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<small><i>posted 14-Jan-2017 at 5:56PM</i></small>
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</ul>2017-01-14T23:56:39ZPaul Crowellcid:58471.eid:423152.updated:2017-01-14 17:56:39Syllabus (Updated)2016-11-03T00:13:54Z<p>A note on the text:</p>
<p>Kittel, Introduction to Solid State Physics, 8th edition. Used or borrowed copy is fine.</p>
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<a href="/classes/2017/spring/Phys 5701.001/downloads/421992-Background_on_5701.pdf" title="108 Kbytes, application/pdf">Scope of the class and comparison to PHYS 4211</a>
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<small><i>posted 2-Jan-2017 at 11:46PM</i></small>
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</ul>2017-01-14T23:55:48ZPaul Crowellcid:58471.eid:410571.updated:2017-01-14 17:55:48Background Information (Updated)