Royal Society publishing Informing the sence of the futue Recollections Author(s): C. Herring Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 371, No. 1744, The Beginnings of Solid State Physics(Jun. 10, 1980), pp 67-76 Published by: The Royal Society StableUrl:http://www.jstor.org/stable/2990277 Accessed:12/03/20100222 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp.JstOr'sTermsandConditionsofUseprovidesinpartthatunless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showpublisher?publishercode=rsl Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission JStOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about STOR, please contact support@jstor. org The Royal Society is collaborating with JSTOR to digitize, preserve and extend access to Proceedings of the Royal Society of London. Series A, Mather atical and Phvsical sciences ittp://www.jstor.org
Recollections Author(s): C. Herring Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 371, No. 1744, The Beginnings of Solid State Physics (Jun. 10, 1980), pp. 67-76 Published by: The Royal Society Stable URL: http://www.jstor.org/stable/2990277 Accessed: 12/03/2010 02:22 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=rsl. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The Royal Society is collaborating with JSTOR to digitize, preserve and extend access to Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. http://www.jstor.org
Proc. R Soc. Lond. A 371, 67-76(1980) Recollections BY C. HERRING Department of Applied Physics, Stanford University Herring, (William)Conyers. Born New York 1914. Educated Princeton Univer. y. Research physicist Bell T'elephone Laboratories. Research on many branches of physics, particularly magnetism 1. ONE-ELECTRON ENERGY BANDS As a graduate student in the 1930s I got my principal education on the electronic uantum mechanics of solids from the Sommerfeld-Bethe article in the handbuch ler Physik. It seemed quite clear from this that the one-electron wavefunctions and nergies of a self-consistent field solution for a crystal would often have character istics intermediate between those of the tight-binding approximation and those of the almost-free-electron theory, and that therefore one would need to find new and less restrictive ways of calculating them. The Wigner-Seitz method, which had just been developed, was one such, although its initial validity was limited to states ghbouring the he=0 state of the conduction band of a non-transition metal Beyond this, one very appealing handle was to study the rigorous properties of Bloch states that could be inferred from crystal symmetry. Louis Bouckaert and Roman Smoluchowski, who were working as postdoctorals with Wigner in the academic year 1935-6, undertook to study these symmetry properties for electrons n the common eubic lattices; their work culminated in the now famous B.S.w paper of 1936. I held many discussions with them, and became intrigued by the study of the topological behaviour of the functions En()describing the energies of the bands n, and particularly by the topology of the evolution of these functions as the potential energy function, i.e. the Hamiltonian of the problem, was changed continuously. The development of this interest came while Wigner, under whom I was working as a graduate student at Princeton, was away for the second term at Wisconsin. In our long-distance communications, he encouraged my interest and made the further very fruitful suggestion that it would be of interest to supplement the study of spatial symmetry properties with a study of time-reversal symmetry, a subject to whose general formulation(as distinguished from its application to crystals)he had already made fundamental contributions. Before the end of the academic year I had picked up enough ideas to keep me busy, working at home on Staten Island over the summer. The result was my thesis On energy coincidences in the theory of Brillouin zones. This had two parts. The first was an analysis of consequences of time-reversal symmetry, and the development of criteria fo predicting when it would require the 'sticking together'of bands that would be independent if only spatial symmetry were considered. The second and longer part
C. herring of the thesis dealt with energy coincidences between different bands, i. e for n+n, that were not required by symmetry, and noted the interesting fact that some such coincidences are indestructable, in the sense that they cannot be made o disappear(though they can be moved about in k-space) by any infinitesimal change in the lattice potential. I found this work intellectually fascinating, but had grave misgivings about its applicability to real electronic energy bands, because I felt that correlation effects(see below)must make the picturing of metal electrons in one-electron terms a very poor approximation. Fortunately, I realized that the results would have a much more clearly valid applicability trum of phonons, so I did not feel that i was being awarded a degree under entirely In the following academic year(1937), John Slater visited Princeton(Institute for Advanced Study for a sabbatical semester. His methods of reasoning and working were very different from Wigner's, or from my own, and did not at first appeal to me, but I was very impressed by his productivity: in that one semester, by simply barging ahead with calculations in areas that seemed to him to contain pay dirt,, he succeeded in completing four papers, two of which have emerged in historical perspective as classics. (These were the invention of the APw method and the formulation of the theory of ferromagnetic exchange coupling for an insu lator in band-theoretical terms, respectively. )In the hope that some of this facility might rub off on me, I applied to the National Research Council for a fellowship to do postdoctoral research with him at m.I.T. The fellowship was awarded, so I spent the years 1937-9 at M I T. However, my strongest intellectual contacts were not with Slater, but with John Bardeen, who had gone from Princeton to Harvard a year earlier to be a Junior Fellow there, and with some of the younger people, mostly experimental, at M.I. T. I was particularly impressed, in view of my develop ing interest in band calculations(see below), by Bardeen's improvements to the Wigner-Seitz approach, especially in the direction of accurate calculation of the effective mass at the bottom of a band My original intention in these postdoctoral years was to develop more realistic models of lattice vibrations, particularly in metals. Since I was convinced that interatomic force constants could not be adequately described in terms of mere nearest neighbour forces or in terms of simple pair potentials, I decided to try to determine the force constants from first principles by suitably generalizing the Wigner-Seitz method of calculating lattice energies. Though such calculations were eventually made in the late 1950s by Toya, and have since become quite common- place thanks to the concept of pseudopotentials, I found the task too difficult for me at the time, and decided that one would need first to develop a new and more tractable formalism for the calculation of band structures in general. For the simple metals it seemed that one ought to be able to capitalize on the great similarity of their wavefunctions to plane waves; yet it was already known that the strong
ecollection s departures from plane-wave form near the atomic nuclei had very important con sequences for the energies of the states. Realizing that these departures were necessitated by the requirement that the valence electron wave functions be ortho- gonal to those of the cores, I thought of working with a non-orthogonal basis forme by orthogonalizing plane waves to the core states. To my surprise, even a single plane wave of this sort often gave a remarkably good quantitative approximation to the correct crystal wavefunction. So I started developing the approach system atically, and published an exposition of what is now known as the orthogonalized plane wave method. A fortunate opportunity presented itself immediately to test this in a full-scale band calculation: A G. Hill, with whom I was at that time sharing an apartment, had started some calculations with Seitz at Rochester on the band structure of beryllium, but had not finished them. Although primarily an experi mentalist, he was very interested in doing more work on this project, and he asked if i would be interested in collaborating with him. Since beryllium is divalent, and crystallizes in the hep structure with two atoms per primitive cell, its bands approximately fill two Brillouin zones instead of half a zone as in the alkali metals Thus calculation of its band structure and cohesive energy requires a method that is capable of handling states near the zone boundaries: an approximation using merely a parabolic band of constant effective mass would clearly be inadequate, and Shockley's'empty-lattice'test had just shown that sizable errors could occur in Slater's earlier scheme of fitting boundary conditions only at the centres of cell faces. So I proposed that we should combine OPW calculations for states at the zone boundary with Wigner-Seitz-Bardeen calculations for states near the bottom of the band. The project proved enormously laborious, but eventually we managed to get it finished, and it was on the whole quite successful In these same years at M.I.T., Marvin Chodorow, a graduate student under Slater, was working on the application of Slater's new APW method to copper feature of it was his construction of an empiricall n an this work. A noteworthy As his office adjoined mine, we had many conversations core potential for copper, significantly better than any that had been used before. Though the thesis was never published in full, use of the Chodorow potential has been revived in recent While this was going on, and afterward, I started to work on several applications of the opw method. One was an improved calculation of compressibility, etc, for lithium; another, moving towards my original goal of calculating interatomic force onstants, was an attempt, with H. B. Huntington, to evaluate the corrections to Fuchs's simple electrostatic theory of shear constants of simple metals. But such work went slowly, and after spending the next two years at Princeton and Missouri respectively, I became involved, as did everyone else, in war work for the period 1941-5. After the war, I became involved with other things, and it was with surprise that I learned several years later, in an encounter with Frank Herman at an A PS meeting in New York, that he was trying to do a thesis at Columbia University on the electronic bands of diamond, using the OPW method. I followed his work
C. Herring ith interest, as I began to think about possible band structures for the semi conductors silicon and germanium which were being intensively investigated t Bell Laboratories, where I now was. After finishing this diamond work and moving to R.C.A., Herman collaborated with a graduate student at Princeton,J Callaway, in applying similar methods. to the band structure of germanium As just noted, there was, in the late 1940s and early 1950s, a great deal of interest in energy bands, especially in valence and conduction band edges, in germanium and silicon. In the early part of this period, many theoretical discussions simply assumed'for simplicity'that the band edges would be at the centre of the Brillouin zone, and would be non-degenerate, with isotropic effective masses. My experience with calculations for beryllium, and in due course my awareness of the results Herman was getting for diamond, convinced me that such a picture for the electron and hole states in silicon and germanium was extremely unlikely.However,there remained many possibilities, and it took some years to sort them out. Transpo properties, particularly the anisotropy of magnetoresistance in single crystals seemed to provide some of the most promising handles. Early successful uses of this approach were my collaboration with G. L. Pearson to infer from his exper ments that the conduction band edge in silicon was on the A lines with a mass anisotropy of five to one, and the inference by Meiboom Abeles that the condt tion band edge in germanium was at the L points, with a much larger mass anisotropy. Both these conclusions were soon confirmed by cyclotron resonance experiments. The magnetoresistance approach was less successful for the valence bands. I became convinced that the valence band edges in germanium must be along the A lines, because of the vanishing magnetoresistance for magnetic fields in the [100] directions. Such vanishing would have to occur from symmetry for [100] valleys, but could occur only by accident for many other band structures, including the a priori plausible one of a degenerate band edge at k=0. It turned out that just thisaccident' does in fact occur. By the middle 1950s, elucidation of the band structures of semiconductors was proceeding fairly rapidly, thanks primarily to cyclotron resonance, but also to such things as piezoresistance, optical properties etc. these provided a wealth of opportunities for comparing theory and experiment By contrast, there had not occurred any great expansion in opportunities for comparing theoretical band structures with experimental data for the case of metals There were still the old standbys: electronic specific heat, paramagnetic suscepti bility, some features of optical absorption, etc, but the great modern science of Fermiology had not yet been born. One new thing, however, did along about this time: the Knight shift. C. H. Townes, who had been a colleague of mine at Bell Laboratories in the late 1940s, had moved to Columbia University, and got involved in the newly blossoming field of nuclear magnetic resonance. Working at Brookhaven, a student of his, W.D. Knight, discovered that the n. m r. frequencies of nuclei in metals are usually appreciably greater than the frequencies of the corresponding nuclei in non-metallic compounds. Townes proposed the interpre tation that the field on the nucleus was enhanced by the contact hyperfine term