Oral History Transcript — Dr. Frank Herman
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Frank Herman; June 17, 1982
ABSTRACT: Herman’s scientific career from his early education through a Ph.D. at Columbia University; research in the 1950s. Numerical calculation of the band structures of diamond, silicon and germanium, using Conyers Herring’s OPW method. Also prominently mentioned are: Henry Michael Foley, Conyers Herring, George E. Kimball, Arnold Moore, and Dwight O. North, Fred Rose, Fred Rosi, Frederick Seitz; Bell Telephone Laboratories, International Business Machines Corporation, Massachusetts Institute of Technology, and Radio Corporation of America.
Szymborski: Today is June 17th, and I am in San Jose, at IBM, talking with Frank Herman. To begin, the standard question is, why did you become a physicist?
Herman:I didn’t really decide to become a physicist until I was about 23 year’s old, working as a Research Engineer at the RCA Laboratories in Princeton, New Jersey. Before discussing this decision, let me provide you with some background material. Ever since I was a small boy I was interested in understanding how machines operate. I liked to take machines apart and very often I was even able to put them back together again. I used to make model airplanes and construct mechanical toys. Originally I wanted to become a civil engineer and build bridges or a mechanical engineer and design complex mechanisms.
My interest in mathematics and science took a big leap forward when I was admitted to the Bronx High School of Science in New York City and fell under the spell of outstanding teachers who had been brought together in the late 30s to form a specialized high school that remains One of the best of its kind in the world. Not only were the teachers inspiring, but the students were exceptional, having been selected by stiff competitive examinations. Many of my classmates went on to become scientists and engineers. One of my high school (and college) classmates was Harold Brown, who later became Secretary of Defense. Others who come to mind are Norman Austern, Joseph L. Birman, and Sidney A. Bludman, now professors of physics at Pittsburg, City College/CUNY, and Pennsylvania, respectively.
I graduated from Bronx Science in January, 1943, in the fourth graduating class. I continued my education at Columbia University in New York City, receiving the bachelor’s degree in electrical engineering in the fall of 1945, just after the end of World War II. Because of the war, there was an accelerated program, and I was able to complete four years of college in 2 and 2/3 years. I then spent the next two years in the Navy, attending electronics schools and doing electronics at various communication security installations. By the time I concluded my naval service in the fall of 1947, I knew quite a bit about the practical side of electronics, and in fact was able to modify and repair rather complex electronic equipment, including advanced radar and sonar systems.
Szymborski: Was this important for your future scientific career?
Herman:Yes, this experience was most important because it gave me contact with the practical aspects of electronics, complementing my earlier academic studies. After getting out of the Navy I decided to continue my studies and work toward a Master’s degree in electrical engineering, which I received from Columbia in 1949. During the period 1947-1949 I also taught electrical engineering at The Cooper Union for the Advancement of Science, a small outstanding engineering school in New York City. One of my colleagues at Cooper Union was Jesse B. Sherman, who had worked earlier as an engineer at RCA. Sherman suggested that I might enjoy doing research for a large electronics company such as RCA, and he urged me to apply for a position at the RCA Laboratories in Princeton, New Jersey, which I did.
I joined RCA Laboratories in June, 1949 as a Research Engineer. My first six-month assignment was to do experimental research in the field of gaseous electronics under Louis B. Malter, and my second was to work in the new field of semiconductor electronics under Arnold R. Moore. By this time it was clear to me that I was more interested in physics than in engineering, so I matriculated as a candidate for the doctorate in physics at Columbia in December, 1949. During my first year and a half at RCA, I completed the Ph.D. course requirements in physics in a most unusual way. I did all the necessary laboratory work at Columbia on Saturdays, but I did not attend any classes during the week, having made a special arrangement with my teachers. As long as I did all the homework satisfactorily, and got high grades on my exams, my absence from class would be overlooked. I was very grateful to Columbia for making this accommodation, which enabled me to work full-time at RCA while continuing my studies. By working very hard days and evenings I was able to bring this off successfully. By mid-1950 I began looking for a suitable thesis problem.
Szymborski: Who was your advisor?
Herman:My first advisors at the Columbia physics department were Harold W. Webb, Chairman of the Committee on Graduate Work, and Charles H. Townes, Department Chairman. Later, Henry M. Foley became my formal thesis advisor. Actually, I had three advisors, one at Columbia, a second at RCA Laboratories, and a third at Bell Telephone Laboratories. I will explain this in due course.
But first, I should mention that I did not enjoy doing experimental research in gaseous electronics because I was left very much to myself and did not feel that I was really part of a vital activity. On the other hand, once I began doing experimental research on semiconductors with Moore, I became intrigued with this subject, and decided to get into solid state electronics or solid state physics. By a happy chance Moore and I carried out an experiment which applied television techniques (electron beam scanning in a cathode ray tube) to semiconductors. Because of the television aspect, this work was very highly appreciated by RCA. We put a germanium point-contact rectifier inside a cathode ray tube as a target, connected the rectifier to an external circuit, and scanned the electron beam across the germanium sample. When the electron beam came close to the point-contact, it generated electron-hole pairs, causing an increase in current through the external circuit. Moore and I received a patent for a device based on electron bombardment induced conductivity (EBIC). This patent was to play an important role in my career, as will be seen shortly. By the way, I hope I am not going into this in too much detail.
Szymborski: Don’t worry, I’m very interested in such small details.
Herman:After completing my assignment with Moore, I joined the physical electronics group and reported to Dwight O. North, who was known affectionately as “Don” after his initials. Don was a brilliant theoretician who had carried out pioneering studies in noise theory before and during World War II. I was delighted to join this group because it was composed of some of the most eminent RCA scientists, including Albert Rose, the inventor of the image orthicon and an authority on vision; Leon S. Nergaard, an expert on high power tubes; and Henry T. Devore, an authority on photoconductivity.
Szymborski: What kinds of problems did these people work on at RCA?
Herman:We are speaking of the period 1949-1951, which was still the dawn of the modern semiconductor physics era. Most of the scientists at RCA had made their reputations in vacuum science and technology, electronic circuitry, acoustics, etc. They had invented and designed high power tubes, television camera tubes, and gas discharge devices. They had also made detailed studies of thermionic emission, cathodoluminescence, and photoconductivity. Research on these subjects was still in full swing during this period. In addition, there was a laboratory-wide crash program on color television which proved highly successful. My immediate colleagues were among the world’s leading authorities in their fields, but they did not have a strong background in the quantum theory of solids. In retrospect, I was very lucky to have worked with Moore, who had gotten his degree at Cornell working on color centers and was thus one of the few physicists with a solid state background at RCA.
Of course, the transistor had been invented a few years before, and it was already clear that semiconductor electronics would become an important subject. Many of the senior people decided to learn more about semiconductors, and a number of us organized courses in quantum mechanics, semiconductor electronics, and solid state physics. The challenge was to teach scientists and engineers with strong backgrounds in classical physics and vacuum electronics the fundamentals of the quantum theory of solids.
Szymborski: Did you teach these courses to personnel at RCA?
I was one of many people involved. Courses were usually taught by several people who would take turns lecturing. No one forced us to do this. Because they were highly motivated, most of the senior people succeeded in making a graceful transition from their earlier fields of expertise into newer fields. From my own point of view, these courses proved very useful: They greatly facilitated my getting into solid state physics, and they made up for many of the courses that I had taken “in absentia” at Columbia.
After joining the physical electronics group, I began looking for a suitable research problem, one that would be relevant to RCA’s interests, acceptable as a thesis problem at Columbia, and at the same time intellectually challenging to me. Initially, I intended to do a theoretical study of electron bombardment induced conductivity in germanium, extending the work that I had done earlier with Moore. This topic was close enough to the experimental activities at RCA that it received RCA’s blessing. By way of getting into the EBIC research, I read Seitz’s “Modern Theory of Solids” literally from cover to cover, as well as current literature on the electronic and optical properties of germanium. During this period of intensive reading, it became clear to me that we really knew very little about the electronic structure of germanium, and that many interpretations of the physical properties of germanium were based on highly simplified band structure models of doubtful validity. I became interested in band theory principally through the influence of three textbooks: Seitz’s book, Brillouin’s “Wave Propagation in Periodic Structures,” and Wilson’s “Theory of Metals.” Because of its more complicated core structure, I decided to defer a study of germanium until I had dealt with its simpler prototype diamond.
Szymborski: Could you recall more details about why you chose this problem in particular? I understand that diamond was considered to be an elemental crystal having the same structure as germanium. Did you talk to anybody about this choice or were you influenced by some literature or discussions?
Herman:The choice of problem was based primarily on reading the textbooks just mentioned and current literature on transistors and semiconductors. It was indeed astonishing how little was actually known about the band structure of germanium. As in football, I saw a hole in the line and decided to charge through.
To elaborate, there were very few people at RCA or Columbia that I could talk to about germanium. From my reading, it was evident that band structure played an important role in determining many of the electronic and optical properties of solids. It was equally evident that our understanding of the band structure of actual materials such as germanium — as opposed to idealized textbook models — was rudimentary. Details of band structure affect transport properties such as magneto resistance, and optical properties such as the shape of the absorption curve just above threshold. But these details were not understood at all at the time. I couldn’t get very excited about the phenomenological analysis of transport measurements, for example, but I became intrigued at the prospect of supplying more definitive information about the band structure, and thus hopefully contributing to a better understanding of germanium and related materials.
In the final analysis, my choice of problem was highly subjective, and was determined in part by the experimental situation at the time, by the research atmosphere in which I found myself, including the people and the facilities, and perhaps most important of all, by my own temperament. I wasn’t out for a Nobel Prize. I simply wanted to do something theoretical that would lead to a concrete result that could be verified experimentally and would move the field forward. In view of the nature of the problem, it was clear that I had to carry out what today would be called a large-scale calculation, armed only with a slide rule and a desk calculator. I wanted to work on a problem that I could solve all by myself, in keeping with the spirit of a doctoral dissertation.
Of course, the very first issue that had to be resolved was whether RCA would approve of this project, which was very “blue-sky” for that time. Fortunately, RCA remembered my success in getting a patent on the EBIC device with Moore shortly after joining RCA, and they reasoned that I was a practical person who would generate other patentable ideas in the course of time, particularly if I became active in a new, rapidly expanding subject. So RCA agreed to the project, and Don North as my supervisor accepted the responsibility of guiding my research, even though his own expertise was in noise theory and applied mathematics. As it turned out, Don was extremely supportive, providing mathematical guidance and considerable encouragement. He was also an excellent writer and his insistence on high literary standards definitely improved by ability to write scientific articles clearly. But bear in mind that if it hadn’t been for the EBIC patent, it is not likely that RCA would have granted me permission to work on such a “far-out” project as the band structure of diamond and germanium. In any event, I now had a research problem that was acceptable to RCA.
The next step was to find a thesis advisor at Columbia. The only member of the Columbia physics faculty who had any professional interest in solid state physics was an elderly professor (Shirley L. Quimby), who taught an excellent course in analytical dynamics. He was interested in the elastic properties of copper, but had no interest whatsoever in the quantum theory of solids.
Szymborski: I think his interests went back to the First World War.
Herman:After extensive discussions with various physics professors, I persuaded Henry M. Foley to become my thesis advisor. He was an expert on hyperfine structure in atoms and molecules and had a strong quantum mechanics background. He regarded my work as a challenge and as an opportunity for’ himself to learn something about solid state physics. Foley proved to be an excellent thesis advisor. I began working on the band structure of diamond in the fall of 1950. Before discussing the results, let me say a few words about the choice of computational method. In 1935, George E. Kimball, then a graduate student at MIT working under the direction of John C. Slater, carried out a pioneering calculation of the band structure of diamond using Slater’s cellular method. Even though this calculation was rather crude, leading to a forbidden band width of about 50 eV (the experimental value is about 5.4 eV), it provided the model that was used to represent germanium during the late 40s and early 50s. According to this model, elemental tetrahedral coordinated materials such as diamond, silicon, and germanium are direct band gap insulators or semiconductors whose valence and conduction band edges are located at the center of the reduced zone. During the mid-30s, William Shockley, then also a student at MIT working with Slater, calculated the band structure of sodium chloride, and found the top of the p valence bands to be degenerate and to lie at the center of the reduced zone. He also analyzed the complicated nature of the fluted dispersion curves in the neighborhood of the valence band edge. In the light of Shockley’s results for sodium chloride, it is surprising that nobody worried about the possible consequences of an analogous degenerate valence band edge in diamond-type crystals in the late 40s and early 50s.
After I became interested in the band structure of diamond in the fall of 1950, I spoke to Kimball, who was then a professor of chemistry at Columbia, about his classic 1935 calculation. Kimball said that his calculation explained why diamond was an insulator, but wasn’t to be trusted quantitatively because the calculation was very primitive. Kimball also said that I could probably carry out a more accurate cellular calculation than he did 16 or so years before, but it would require a great deal of computational effort. Ironically, the computational tools at my disposal at RCA in the early 50s (slide rules and desk calculators) were essentially no better than those used by Kimball at MIT in 1935. (In retrospect, it was lucky that I didn’t use the cellular method, because it would indeed have taken an enormous amount of computational effort to get accurate results, as I discovered about 25 years later using large electronic computers. Incidentally, these later calculations, done with Jose R. Leite and Bard I. Bennett at IBM, confirmed the numerical accuracy of Kimball’s results, but showed how inadequate his basis set and choice of boundary conditions really was.)
So I proceeded to examine other computational methods, and I rejected one after another because they required excessive computational effort or were based on empirical parameters that could not be estimated reliably. Thus, first-principles linear combination of atomic orbitals (LCAO) or augmented plane wave (APW) calculations would have required evaluation of multicenter integrals or many integrations of Schrodinger’s equation, while the semi-empirical LCAO method would have been based on highly uncertain parameters. Finally, I came across Conyers Herring’s beautiful 1940 paper on the orthogonalized plane wave (OPW) method and another 1940 paper by Herring and Hill on its application to metallic beryllium. With the OPW method, I could use existing self-consistent Hartree or Hartree-Fock atomic wave functions to represent the valence and conduction band orbitals in the ion core region, bypassing the need to integrate Schrodinger’s equation from scratch. (This is not rigorously true, but represents an excellent first approximation.) It was necessary to calculate Fourier transforms of atomic orbitals, but this could be readily done with a desk calculator, as could the calculation of the OPW matrix elements. The major computational problem would be evaluating high order secular equations.
Szymborski: What order were they?
Herman:It was difficult to estimate the highest order in advance, but I anticipated secular equations of order 150 x 150 or even 200 x 200. It all depended on how rapidly the Eigen solutions converged, particularly those representing pure p-like valence and conduction band states. For these, the orthogonalized plane waves reduced to ordinary plane waves, and in principle it might take thousands of plane waves to reach effective convergence. Although I never did achieve convergence of energy levels on an absolute scale, I did reach effective relative convergence, so that I could determine energy level differences (interband separations) reasonably well. The key, of course, was to factor the high order secular equations using group theoretical methods. In order to learn how to do this, I taught myself group theory, and in the course of reading the literature on space groups came across some very interesting papers by Herring, one dealing in fact with the diamond space group. As it turned out, the symmetrized OPW secular equations ranged in order from 4 x 4 to 16 x 16 or so. Although I still had a formidable computational job facing me, it was one that I felt confident I could handle using primitive electromechanical computers such as those located at the IBM Thomas I. Watson Computing Laboratory at Columbia. It was quite some time before electronic computers made their appearance at the RCA Laboratories in Princeton.
After getting into the calculations, I met Herring for the first time, most likely at a meeting of the American Physical Society. I told him that I was applying the OPW method to diamond, and would be interested in his opinions and advice. Herring was somewhat surprised at first that I was attempting to treat a covalent crystal by a method he had developed for metals, but he encouraged me to try the OPW method on diamond in the expectation that the results would be interesting. He also agreed to serve as an informal thesis advisor, completing the troika composed of Don North, my RCA supervisor; Henry Foley, my formal thesis advisor at Columbia; and himself. I was delighted to have the opportunity to talk about the OPW method with its originator and about group theory with an expert.
Herring was then at Bell Telephone Laboratories in Murray Hill, New Jersey, just about an hour’s drive from Princeton, and he invited me to visit him. When I came to see him, which I did many times during my doctoral studies, I was always impressed by people lining up in the hallway outside his office waiting to ask him questions on a wide variety of scientific subjects. Herring was a voluminous reader, having probably read every important paper in solid state physics. He had a dispatch case containing hundreds if not thousands of 3” x 5” index cards, each containing the essential information culled from a particular paper. Herring was a virtual encyclopedia of solid state knowledge. He would provide theoretical advice, constructive criticism, and useful references on an astonishingly wide range of topics. Incidentally, Don North and Conyers Herring both served as role models for me in my younger days: Here were two men who had carved out creative and productive careers as theoreticians in industry. Clearly one could aspire to be a theoretical solid state physicist in industry as well as at a university.
To return to the calculations, all went smoothly until I had to face up to the problem of factoring high order secular equations. I knew how to do this by hand, but the task was time consuming, and it was necessary to check and recheck the factoring to make sure no errors were made. (Years later I devised ways for automating this process using large electronic digital computers, but in 1951 I hadn’t yet learned how to use “automatic” computers.) It then occurred to me that my mother could help me with some of this work. I had read about the Hartrees, and how the younger Hartree (Douglas R.) had been aided by his father (William), who was a retired railroad engineer and enjoyed doing “sums” on a desk calculator. I showed my mother how to set up the OPW secular equations and how to factor them, and she agreed to do some of this in her spare time in order to save me time.
My mother was by no means a mathematician, but she had enormous patience and an aptitude for numbers, and she was only too happy to help me out. So she did the factoring by hand — the total effort may have taken her many hundreds of hours — and I was saved many weeks, if not months of detailed work Many years later, when I repeated these calculations using electronic computers, I found that my mother had not made a single mistake. I wanted to acknowledge my mother’s assistance in my doctoral dissertation, but she wouldn’t let me. So I am happy to have the opportunity to do so now, however belatedly. In 1954, at Cambridge, I had a conversation with D. R. Hartree and I told him how my mother had helped me in the same way that his father had helped him.
Even though the factored secular equations were of much lower order than the original unfactored ones, it was still impractical to evaluate them on a desk calculator, so I obtained permission to spend a few months at the Watson Lab at Columbia in early 1952, writing programs and carrying out the numerical work on early electromechanical computers such as the IBM 602A. I greatly enjoyed learning to program this computer, which involved wiring program boards. How different from today! Finally I was able to obtain the electronic eigenvalues and eigenvectors for diamond and from these emerged the band structure of diamond.
There were many side benefits to my sojourn at the Watson Lab. First and foremost, I met my future wife, Sondra, who was then a senior at Barnard College. Secondly, I met Leon Brillouin and Llewellyn H. Thomas, both of whom were on the staff at the Watson Lab and were also affiliated with Columbia. I had many interesting conversations with both of them. I vividly recall Brillouin discussing his development of the zone concept. In retrospect, he was delighted that a purely mathematical construct could play such an important role in determining the electronic structure of solids, and have dramatic physical and technological consequences, ranging all the way from the existence of electrons and holes, to their role as minority and majority carriers in semiconductors, to transistor action itself. Finally, the visit to the Watson Lab reinforced my interest in large-scale scientific computation, a consideration that greatly influenced my future career.
Incidentally, about the time I was completing my doctoral studies at Columbia, I was offered a position at the IBM Watson Lab by Polykarp Kusch, then a Consultant to the Director, Wallace J. Eckert. I sometimes wonder what turn my career would have taken if I had accepted this job offer and joined IBM in 1953 instead of 16 years later. As it was, I felt extremely loyal to RCA and turned the offer down. Some of my Columbia classmates — Robert Gunther-Mohr, Seymour H. Koenig, Sol Triebwasser, and Gardner L. Tucker — did join IBM at that time.
After completing my diamond calculations, I went on to study the band structure of germanium in the summer of 1952, assisted by a young graduate student at Princeton, Joseph Callaway, who has since made a name for himself in theoretical atomic and solid state physics. My doctoral dissertation covered both the diamond and germanium band structure calculations. My final oral examination took place in the fall of 1952. The doctoral committee included Brillouin, Foley, Kimball, Thomas, and Townes (chairman). My research clearly indicated that the band structure of diamond was quite different from that calculated by Kimball in 1935. While Kimball’s pioneering studies suggested that diamond was a direct band gap insulator, with the lowest conduction band level lying at the zone center, my own calculations showed that the lowest conduction band level lay somewhere along the (100) axis in the reduced zone, away from the zone center. My calculations also indicated that the valence band edge of diamond was degenerate and occurred at the zone center, thus having the same degeneracy found earlier for sodium chloride by Shockley.
The results for germanium were similar, except that the calculations were too crude for us to decide whether the lowest conduction band states occurred along the (100) axes, as in diamond, or along the (111) axes, as was later shown to be the case experimentally. Kimball questioned me closely about my calculations but in the end accepted the findings as quite reasonable.
Szymborski: He wasn’t upset?
Herman:Kimball wasn’t upset at all. He was very mature and emphasized that in contrast to mathematical theorems, numerical calculations inevitably were based on approximations, and that my results were more reliable than his because I had used fewer and better approximations as well as more powerful numerical methods. To dramatize his open-mindedness, he predicted jokingly that others would publish still better calculations for diamond in the future which might or might not confirm my own results. Actually, subsequent calculations as well as subsequent experimental studies all confirmed the essential correctness of my indirect band gap model for the diamond crystal, though some of the numerical details were certainly improved.
The first papers on diamond and germanium appeared in Physical Review in December, 1952 and January, 1953, respectively. These calculations were important because they showed for the first time that diamond and germanium had multivalley conduction band structures, and hence were indirect band gap materials. I received my Ph. D. degree in physics from Columbia in January, 1953, and my doctoral dissertation was published in Physical Review in 1954.
In late 1952 or thereabouts I wrote a letter to Frederick Seitz telling him of my results. Being closer to solid state physics than Kimball (who was by then more concerned with chemistry), Seitz recognized the technical as well as the scientific implications of my band structure results. I also discussed my results with Herring, who was very close to the semiconductor research at Bell and also appreciated the scientific and technological implications, such as the effect of complicated band structures on electron and hole scattering and hence on electron and hole mobility’s.
Szymborski: Do you still have copies of your correspondence with Seitz, Herring, and others dating from this period? I am very interested in such letters as historical documents.
Herman:Every few years I find it necessary to throw out vast quantities of accumulated papers and letters.
Szymborski: That’s what most people do, unfortunately.
Herman:Although I’ve thrown out almost everything from this period, I recall saving a few letters having special significance to me. If I still have some of this early correspondence, I will send copies to you.
After the diamond and germanium results were published, I received many invitations to lecture about the band structures. It was very exciting to discuss the results with experimentalists and to understand how they were planning to investigate the detailed band structure of diamond-type crystals. Shockley was also very interested in the results.
Szymborski: This was the first time you met Shockley?
Herman:Yes, I first met him at an American Physical Society meeting. Shockley and Herring both realized that a degenerate valence band edge and a multivalley conduction band structure could account for some of the puzzling effects observed in magnetoresistance and other types of measurements on germanium. Herring went on to do some important theoretical work dealing with transport properties in multivalley semiconductors.
Shortly thereafter, I received an invitation to present the leading invited paper at the International Conference on the Physics of Semiconductors, which would be held in Amsterdam in the summer of 1954. When I showed the invitation to the RCA management, including the section indicating that the Conference would pay all my expenses (Dutch treat), the management’s initial response was that young scientists like myself did not get sent to international conferences. Such honors were reserved for senior scientists and managers. It wasn’t a question of money. It was a question of tradition. But eventually the RCA management realized that my participation at Amsterdam would be a great honor for RCA as well as for myself, and they relented. I felt highly privileged to be an invited speaker at Amsterdam, and to have the opportunity to meet many distinguished scientists from Europe, including figures like Hendrik B.G. Casimir from the Netherlands, Georg Busch from Switzerland, and Heinrich Welker from Germany. My wife and I took our first trip to Europe, and we visited many legendary figures and places. For example, we visited the Hartrees in Cambridge. It was an exhilarating and unforgettable experience for both of us.
Szymborski: Would you tell me a little bit more about this conference?
Herman:The Amsterdam Conference was the first at which the band structure of semiconductors played a major role. Having relied on simplified models for so long, people were just beginning to realize that the band structures of actual materials could be quite complicated. They also began to realize that it was essential to understand these complicated features thoroughly if they hoped to interpret electronic and optical experiments properly. The highlight of the Amsterdam Conference was the discussion of our improved understanding of the band structure of germanium, based primarily on experimental work by the Bell, Berkeley, and MIT groups, and my own theoretical work. (Note added later: At the 16th International Conference on the Physics of Semiconductors, held at Montpellier in September, 1982, Pierre Aigrain also characterized the 1954 Amsterdam Conference in precisely these terms in his plenary address.) Experimental and theoretical studies of semiconductor band structures represented one of the major scientific themes for the next decade and a half.
On a more personal level, the greatest benefit of attending the conference was meeting experimentalists and theoreticians interested in fundamental semiconductor research. At this and subsequent national and international conferences I formed friendships that I have maintained to this day. These friendships represent a vital communication network, leading to advance information on research in progress, postdocs looking for jobs, etc. I also remember after dinner speeches by Casimir (Philips, Eindhoven) on broken English and by Busch (ETH, Zurich) on the current state of semiconductor research. I was fascinated by Casmir’s urbanity, and by Busch’s facility to switch from English to French to German to Swiss-Deutch virtually in mid-sentence. Up to that time I had stood in awe of great men of science, but it was refreshing to meet so many of them face to face and discover their human side.
Szymborski: These were physicists? Or also people interested in technological aspects of solid state.
Herman:These were primarily the physicists. After Amsterdam, I continued to study the band structure of semiconductors, and learned quite a bit more about diamond-type crystals and alloys. Let me illustrate this period with a few examples. About this time, two of my RCA colleagues, Everett R. Johnson and Schuyler M. Christian, showed me some optical absorption curves for a series of germanium-silicon alloys covering the entire composition range from pure germanium to pure silicon. The striking feature about the absorption threshold (band gap) vs. composition curve was a discontinuity at about 15 atomic percent silicon. The curve was roughly linear on both sides of this composition, but the slopes were significantly different above and below this composition. Having found from my theoretical studies that different types of conduction band minima V responded differently to various types of perturbations (changes in crystal potential), I was able to interpret this discontinuity along the following lines:
As silicon is added to germanium, the lowest-lying (111) conduction band edge characteristic of pure germanium moves upward in energy relative to the valence band edge, but more rapidly than the higher-lying (100) conduction band edge. Beyond 15 atomic percent silicon, where the two sets of minima cross, the (100) minima lie below the (111) minima, thus defining the conduction band edge between this critical composition and pure silicon. The discontinuity arises from the fact that the (111) and (100) minima recede from the valence band edge at different rates in response to changes in the effective “crystal” potential produced by changing the chemical composition of the alloy. Incidentally, the (000) conduction band minimum, while lies slightly above the (111) minima in germanium, rises even more rapidly than the (111) minima with increasing silicon content, so that the (000) minimum never defines the absorption threshold at any composition.
This picture of the band structure of germanium-silicon alloys was subsequently confirmed by magnetoresistance measurements carried out by Maurice Glicksman, who had just come to RCA after working in nuclear physics with Fermi at Chicago. More detailed studies of the optical absorption process were later carried out at RCA by Ruben Braunstein, Moore, and myself, and much additional work on the germanium-silicon alloy system was done by others still later at RCA and elsewhere. Initially, it was thought that these alloys would make better transistors than silicon or germanium, because suitably chosen alloys would combine the high temperature performance of silicon with the higher mobility of germanium. It was eventually realized that these alloys were unsuitable for transistors because carrier mobility’s were greatly reduced by disorder scattering, so research on these alloys was discontinued. Somewhat later, it occurred to some RCA scientists, particularly Fred Rosi that these alloys would make excellent thermoelectric elements for auxiliary power sources in spacecraft, and indeed this is one of their major applications today. This story clearly illustrates how fundamental research begun with one practical objective in mind ended up with an entirely different, originally unanticipated practical outcome. In any event, RCA’s investment in basic research paid off handsomely, as it so often did.
My original explanation of the optical threshold of germanium-silicon alloys was important because it showed that such disordered semiconductors actually did have band structures that are well enough defined in the reduced zone to exhibit different conduction band symmetry properties, as evidenced by magnetoresistance studies. When I first discussed the band structure of such alloys in 1954, many people said that semiconductor alloys didn’t have band structures because of the disorder. Of course, the fluctuating potential associated with the disorder in the germanium-silicon alloy system is rather small. First of all, these alloys form solid substitutional solutions at all compositions, so that all the diamond structure is retained. Moreover, the effective atomic potentials of silicon and germanium — or pseudo potentials, as they would be called today — are rather similar, so that substitutional replacement of one atom by the other introduces only a weak perturbation locally. This all seems rather obvious today, but it came as a big surprise to many people in 1954.
Another perturbation that I studied was that associated with the hypothetical transformation of a column IV elemental semiconductor such as Ge into other members of its isoelectronic series, in this case GaAs, ZnSe, and CuBr. Because the lattice constants of the members of this series are essentially the same, I assumed that the symmetric part of the potential in the unit cell (which contains two atoms) remains the same for all members, while the antisymmetric part becomes increasingly larger as one proceeds along the series. This work was important because it showed that the band structures of structurally and chemically related semiconductors could be related to one another in a very simple and physically compelling manner. I have always been very proud of this particular theoretical idea, which was published in 1955. It showed that once you had paid your dues and done detailed calculations for a few representative crystals, you could draw many important conclusions for a wide class of materials without doing additional detailed calculations. The perturbation theory that I introduced could be done on the back of the proverbial envelope.
Still another perturbation that I studied was that associated with a change in lattice constant. By carrying out band structure calculations for germanium using a series of different lattice constants, you could see how the various conduction band edges respond to the application of hydrostatic pressure. In view of the similarities in the band structures of chemically and structurally related semiconductors, it is reasonable to assume that the (000) conduction band edges in all cubic tetrahedral coordinated semiconductors (diamond or sphalerite structure) respond more or less one way, (100) edges respond another way, and (111) edges respond still another way. In short, the hydrostatic pressure dependence of an absorption edge provides a signature which could be used (ideally) to deduce the type of conduction band edge from experimental observations. Such ideas grew out of my own theoretical work, and were pursued independently by Harvey Brooks and William Paul of Harvard. These ideas were used to great advantage by Richard Zallen of Harvard and Harry G. Drickamer of Illinois in systematic studies of the optical properties of semiconductors under pressure.
Szymborski: Did you suggest these experiments subjecting germanium to pressure? Was it your idea?
Herman:No, others such as Brooks and Paul had done this earlier, but it was only after the band structures of silicon and germanium were understood in sufficient detail that their different pressure coefficients could be understood in terms of different types of conduction band minima.
Szymborski: You were still working at RCA and you were more or less alone, but there were many people who were interested in the band structure of semiconductors at this time. What interactions did you have with those people? I know about Japanese school work done on multi-valley semiconductors already soon after ‘53. I think they did some theoretical and experimental work.
Herman:These ideas spread very fast. I was in touch with several individuals interested in group theoretical aspects of the band structure of diamond-type crystals. In addition to Herring, they included Roger J. Elliott and Gene F. Dresselhaus, both then at Berkeley, and a number of Japanese, including R. Sugita and E. Yamaka. Some of the formal work by the Japanese had been published only in Japanese. A number of Japanese theoreticians sent me copies of their articles in Japanese as well as English translations apparently prepared primarily for my benefit. They were very kind. I also maintained close ties with theoreticians interested more explicitly in band structure calculational methods and techniques, particularly Slater’s group at MIT. The scientific community was rather small at that time, and you could meet virtually everybody in the field by attending a few conferences in the United States and Europe. I didn’t get to Japan until 1966.
Szymborski: Woodruff got involved about that time.
Herman:Yes, Truman Woodruff told me that he was interested in learning more about the OPW method so I got him started doing the band structure of silicon. I should say that band structure calculations during the 50s were rather primitive compared with those being done today, but the computational facilities were also more primitive. The subject was much more exciting than it is now because there was still so much to learn.
Szymborski: Well, how did the general situation in solid state theory evolve during the 50s?
Herman:As you know, the growth of solid state theory was most dramatic during the 50s. The explosion in solid state physics generally was a direct consequence of the interplay between theory and experiment and a reflection of the richness and diversity of the subject matter. The explosion was fuelled by the availability of industrial and governmental support arising from the tangible transfer of basic research ideas into important commercial and military products. In contrast to high energy physics, which requires big machines, solid state physics could be done by small groups using modest experimental equipment and relatively small electronic computers. More interesting than its rapid growth in the 50s and 60s are the reasons for its reduced growth in subsequent decades.
During the 50s and going into the 60s there was a sharp dichotomy between those doing formal and computational theoretical solid state research. Many physicists were strog1y prejudiced against numerical studies. Considerable prestige was attached to formal theory. Those doing calculations were not doing physics, but rather engineering.
Szymborski: The feeling was that the calculationally oriented scientists didn’t try to solve the problems analytically.
Herman:These attitudes persisted for a long time. For example, at the Electronic Density of States Conference held at the National Bureau of Standards, Gaithersburg, Maryland in 1969, John Ziman, a distinguished British theoretician, referred to electronic computers as elephants and to band theoreticians as their mahoots. In my rebuttal, I pointed out that our understanding of the band structure of solids did not progress very far while this subject was confined to the textbooks and treated in terms of Kronig-Penney models and similar idealizations. But once the band theoreticians rolled up their sleeves and began doing realistic calculations on actual materials, and checking their results against experiment, real progress began to be made.
Many physicists have gotten over this prejudice by now, having seen how important the results of numerical studies can be, and how ingenious the methods themselves can be. What is now happening is that the most sophisticated computational methods are being adapted to implement some of the most advanced formal theories. This may have been the case also in the 50s, but computations hadn’t yet achieved the speed and accuracy that is almost taken for granted today, so that the power of formal theory overshadowed the computational studies.
During the 50s, when I was at the RCA David Sarnoff Research Center in Princeton, and during the 60s, when I was at the Lockheed Research Laboratory in Palo Alto, I found considerable prejudice against theoreticians doing numerical studies, particularly those who wrote their own computer programs. But when I came to the IBM Research Laboratory in San Jose in 1969 as Manager of the Large-Scale Scientific Computations Department, I found the situation totally reversed. The very best theoreticians at IBM designed and wrote their own computer programs, using very sophisticated algorithms and programming techniques. In this way, they were able to take full advantage of the computational facilities. Many of the best theoreticians were as outstanding in purely formal theory as in computational physics or chemistry.
Szymborski: They were much closer to the computer.
Herman:Very much so. Of course, one also has to distinguish theoreticians who are more interested in doing order-of-magnitude estimates in the tradition of Fermi, those who prefer to do more elaborate theories involving heavy formalism, and those who prefer to gain their insights from carefully constructed calculations.
Szymborski: These approaches are complementary. What was Seitz’s style?
Herman:Seitz was usually interested in simple explanations. He himself was eclectic, doing what was most appropriate for the problem at hand. He appreciated all three approaches. He had no prejudice against computational work as such. The question was whether the results could be trusted in the light of the approximations, and what the results meant. Seitz was less interested in the numbers than in what the numbers implied.
Szymborski: I think for him it was very important to gain physical insight. In his review papers on color centers, for example, there were no calculations at all. But he tried to understand physically what was going on. It was different, for instance, when I read Japanese papers which were much more formally theoretical. The Japanese did not even try to challenge Seitz’s views on the physics. My impression was that they had a very formal approach. They did not have a good feeling for what was going on physically. They were too closely attached to the models they had created and took the models too literally, forgetting that they were just models.
Herman:My own guess is that Japanese science was then very strongly influenced by the model of Yukawa, who represented formal theory transcendent. Yukawa became a role model for young Japanese theoreticians.
Szymborski: Everybody wanted to be an elementary particle physicist and only reluctantly decided to become a solid state physicist, which is what happened to many Japanese at that time.
Herman:At first, the Japanese were handicapped by their formal training and by their lack of adequate computing facilities. In the course of time, many young Japanese theoreticians spent time in the States and in Europe, and brought back the scientific flavor of other countries. The situation is quite different today, with the Japanese making major contributions in all aspects of solid state physics.
This exchange was really very vital for them to make this progress. This is different with the Russians. I think they are still relatively isolated. I don’t know if you followed the Russian work during the 50s. How much did you know about what was going on there?
Herman:I followed the Russian literature in translation, and I was generally aware of what was going on behind the Iron Curtain, but not to the same extent that I was familiar with American and West European literature. Like the Japanese, the Russians suffered from a fixation on formal theory (read Landau instead of Yukawa), and a lack of good computers. When I first met Russian solid state theoreticians at International Conferences on the Physics of Semiconductors in Rochester (1958) and in Prague (1960), I was astonished to discover how carefully they had studied the world literature. Many of the Russian theoreticians had read my papers so carefully that they could ask me very penetrating questions indeed. I must confess that I was not as familiar with their work as they were with mine. Again, the situation has changed during the past few years, with increasing availability of large-scale computers and greater interest in numerical studies. But yes, the Russians are still rather isolated due to lack of travel opportunities abroad.
Szymborski: I’m interested in the whole structure of interactions between different groups working in America and the world-wide system of interaction. Who did you interact with? At the very beginning I noticed you had a lot of contact with people all over the East Coast: Princeton, Bell, and Columbia. Did you have any interaction with the Chicago group or Kittel’s group at Berkeley?
Herman:My closest contacts were on the East Coast, but I also had good ties with scientists all over the country, including those at Chicago and Berkeley. As I attended more and more scientific conferences and lectured at various universities, the range of my contacts broadened. I was in touch with most of the active workers in my field in the United States and Europe, and to a lesser extent in Japan.
Szymborski: I asked that because I am interested in the flow of information. Did you wait until your papers were published or did you send the preprints to some friends or make phone calls if you had some interesting results to present?
Herman:After I wrote a paper, I usually gave copies to a few colleagues for detailed technical criticism. I would also ask my wife for stylistic criticism. In spite of her own busy schedule raising our growing family and working toward her doctorate in intellectual history, my wife would always find the time to edit my papers scrupulously, sharpening the argument and strengthening the logical development. After submitting the paper for publication, I would send preprints to selected individuals. I never had a fixed mailing list. I also used the telephone a great deal. But perhaps the most effective means of communication was attending scientific conferences and visiting other laboratories.
Szymborski: How many people would you select to send preprints to?
Herman:I would usually send preprints to people whose work I mentioned in my paper, and to others who might be interested. The actual number might range from 5 to 50. I also used to receive large numbers of reprint requests.
Szymborski: Who were these people in the 50s who were interested in this sort of work?
Herman:Mostly solid state theorists and experimentalists concerned with the fundamental properties of semiconductors, judging from the reprint requests. Some of the papers I wrote during the 50s were reviews, and these received a lot of attention because many people used these reviews as a way of getting into this subject. It is particularly satisfying to see your own work entering the textbooks and monographs. For a while your name is still attached to some of the original figures and ideas, but after a time much of this becomes part of the general pool of knowledge. In any event, it is gratifying to see your own work used by other people.
Szymborski: Well, thank you very much.