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4 CONTENTS 5.1 Bands and Brillouin zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.2 Examples of band structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.3 Semiclassical dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6 Experimental probes of the band structure 87 6.1 Optical transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.2 Photoemission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 6.3 Quantum oscillations – de Haas van Alphen effect . . . . . . . . . . . . . . . . . 90 6.4 Tunnelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 7 Semiconductors 99 7.1 Semiconductor band structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7.2 Intrinsic carrier concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 7.3 Doped semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 8 Semiconductor devices 105 8.1 Metal - semiconductor contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 8.2 p-n junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 8.3 Solar cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 8.4 Field effect transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 8.5 Compound semiconductor heterostructures . . . . . . . . . . . . . . . . . . . . . 119 9 Electronic instabilities 123 9.1 Charge Density Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 9.2 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 10 Fermi liquid theory 145 10.1 The problem with the Fermi gas . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 10.2 Collective excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 10.3 Total energy expansion for Landau Fermi liquid . . . . . . . . . . . . . . . . . . 149 10.4 Fermi liquids at the limit: heavy fermions . . . . . . . . . . . . . . . . . . . . . 154
CONTENTS 5 Preface Books There are many good books on solid state and condensed matter physics, but the subject is rich and diverse enough that each of these contains both much more and much less than the topics covered in this course. The two classic textbooks are Kittel, and Ashcroft and Mermin. These are both at the correct level of the course, and have the virtue of clear exposition, many examples, and lots of experimental data. Slightly more concise, though in places a little more formal is Ziman. Grosso and Parravicini has a somewhat wider coverage of material, but much of it goes well beyond the level of detail required for this course. Marder is at about the right level (though again with more detail than we shall need), and has a nice blend of quantum properties with statistical and classical properties. A well illustrated modern treatment of most topics in this course is also given by Ibach and Lüth. OUP have recently issued a series of short texts in condensed matter physics. They are more detailed than needed for this course, but are quite accessible and excellent for reference. The most relevant for this course is Singleton. • C.Kittel, Introduction to Solid State Physics, 7th edition, Wiley, NY, 1996. • N.W.Ashcroft and N.D.Mermin, Solid State Physics, Holt-Saunders International Editions, 1976. • J.M.Ziman, Principles of the Theory of Solids, CUP, Cambridge, 1972. • H. Ibach and H. Lüth, Solid State Physics, Springer 1995. • J. Singleton, Band Theory and the Electronic Properties of Solids, OUP 2001. • M.P. Marder, Condensed Matter Physics, Wiley, NY, 2000. Covers both quantum matter and mechanical properties. • G.Grosso and G.P.Parravicini, Solid State Physics, AP, NY, 2000. A wide coverage of material, very bandstructure oriented, very detailed. • A very good book, though with a focus on statistical and “soft” condensed matter that makes it not so relevant for this course, is P.M.Chaikin and T.Lubensky, Principles of Condensed Matter Physics, CUP, Cambridge, 1995. These notes Treat these notes with caution. If you are looking for text book quality, then you should look at text books. Polished and optimised treatments of most of the topics covered here have been published in a number of excellent books, listed above. For much of its duration the course follows the book by Singleton, and where it does not, the books by Ashcroft&Mermin, as well as Kittel, give essential support. Reading up in text books is not only useful revision of the lecture material, it
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