I was born on August 25, 1928 in Weimar, Germany. My father was a civil servant working for the city administration of my home town; my mother was a classical German “Hausfrau.” Both came from simple skilled-craftsmen families. Neither had a high-school education, but there was never any doubt that they wanted to have their children obtain the best education they could afford. My mother, in particular, pushed relentlessly for top performance in school: simply doing well was not enough. Fortunately, I breezed through 12 years of school almost effortlessly, not once requiring help with homework from my parents.

Despite their insistence on excellence, my parents never pushed me in any particular academic direction; I was completely free to follow my inclinations, which ran towards math, physics, and chemistry. When I finally told my parents that I wanted to study physics, my father merely wondered what that is, and whether I could make a living with it. I certainly could become a physics teacher at a High School, or “Gymnasium,” a thoroughly respectable profession.

I did have one major problem in school, though: Discipline! I was often bored, and entertained myself in various disruptive ways. A frequent punishment was an entry into the “Klassenbuch,” the daily class ledger. These entries were considered a very serious matter, and if I had not been excellent academically, I would have risked being expelled. Once, after I had again been entered as having disturbed the class, the teacher who had overall responsibility for the class – Dr. Edith Richter, whom I adored – asked me in great exasperation: “Why again?” I told her that I had been bored, whereupon she exploded: “Mr. Kroemer, one of the purposes of a higher education is that you learn to be bored gracefully.” I will never forget that outburst – nor have I ever really learned to be bored gracefully.

Another teacher – Willibald Wimmer – had his own clever way of handling me. Before the end of the war, he had been an instructor at a local engineering college, ending up teaching math and physics at our high school. He was used to dealing with more mature students, and he treated us as adults. I was way ahead of the curriculum in math, and kept showing off. Worse, I taught some of my classmates math “thricks,” that were not part of the curriculum. So, Mr. Wimmer made a “treaty” with me: While he could not excuse me from attending class, I was guaranteed a top grade without being required to turn in the homework assignments, and was permitted to do whatever I wanted to do during the hour, provided I kept absolutely quiet – except when explicitly asked to speak up. Both of us kept that treaty.

Mr. Wimmer also became our physics teacher, a subject about which he clearly knew little more than what was in the textbook. Realizing that I was deeply into physics, he simply enlisted me and one other student to help him in lecture preparations, like setting up what apparatus had survived the war. Once I even was asked to present the lecture myself, with him sitting in the front row and enjoying the show. It was a wonderful experience.

Having graduated from the gymnasium in 1947, 1 was accepted as a physics student at the University of Jena, where I fell under the spell of the great Friedrich Hund, the most brilliant lecturer I ever encountered. The joy did not last long. In early 1948 the political suppression in East Germany became very severe, especially at rebellious universities like Jena. Every week, some of my fellow students had suddenly disappeared, and you never knew whether they had fled to the West, or had ended up in the German branch of Stalin’s Gulag, like the uranium mines near the Czech border. During the Berlin airlift, I was in Berlin as a summer student at the Siemens company, and I decided to go West via one of the empty airlift return flights.

From Berlin, I had written to several west German universities for admission, including Göttingen, but did not receive a reply before leaving Berlin (they had turned me down). I followed the advice of one of my Jena professors “why don’t you give my greetings to Professor König in Göttingen.” König told me that physics admissions were closed, but he passed me on for what was ostensibly just a friendly chat to Professor Richard Becker and his alter-ego assistant, Dr. Günther Leibfried. They in turn passed me on to Wolfgang Paul (Nobel 1989), and I think also to Robert Pohl. It soon dawned on me that this was not just a friendly social chat with people who had nothing better to do, but a thorough examination. I remember one of the questions Paul asked me: “You know that a mirror interchanges left and right? -Then why doesn’t it interchange top and bottom?” In the end, I was returned to Becker, who told me that two of the students who had been admitted were not coming, and a meeting was scheduled for the next day to select who would get the two openings. A few days later I received a postcard that I had been accepted.

Post-war Göttingen. was – intellectually – a wonderfully stimulating place. I was attracted to one of the younger instructors – “Privatdozent” Dr. Hellwege – who offered a so-called Proseminar, where pre-research students would present papers assigned to them, and I participated in this for several semesters in a row. Once, the famous Fritz Houtermans visited Hellwege, and sat in on several of the presentations, including mine. I presented someone’s data that yielded a reasonable straight line on a double-log plot, and proudly claimed a power law for the data. Houtermans was not impressed: “On a double-log plot, my grandmother fits on a straight line.” I keep quoting Houtermans’ grandmother to my own students. Eventually, I signed up with Hellwege for a Diploma Thesis, which would probably have led to an experimental study of the optical spectra of some rare-earth salts. But Hellwege had a long waiting list, and in the meantime, Professor Fritz Sauter – a refugee who had found a temporary home as a guest in Becker’s Institute for Theoretical Physics – offered me a theoretical Diploma Thesis, based on a talk that I had given in one of his seminars. Hellwege suggested that I accept Sauter’s offer: “You will be finished with him before you can start with me.” So I became a theorist.

The diploma thesis was an extension of a 1939 paper by Shockley on the nature of surface states in one-dimensional potentials. As one of the elaborations, I looked at the interface between two different periodic potentials, which confronted me for the first time with what we would today call the band offsets at heterojunctions.

There was another early encounter with heterojunctions while working under Sauter. We made a field trip to the AEG research laboratories in Belecke, a small town in Westphalia. There, a Dr. Poganski gave a beautiful demonstration that the selenium rectifier was not a Schottky barrier, but a p-n junction between p-type selenium and n-type CdSe, a true heterojunction – although that term did not exist yet. This must have had an at least sub-conscious influence on me: when I later started thinking about heterojunctions in earnest, the question whether such things could actually exist as real devices had an obvious answer: Of course!

While working on my diploma, I gave another colloquium talk under Sauter, reporting on the famous Bardeen/Brattain paper “Physical Principles Involved in Transistor Action” (or some title like that). At the end I made some suggestion about some open questions raised by the authors. Sauter was intrigued and suggested that as a possible Ph.D. topic. Sometime later, he came into my office and told me to stop further work on my Diploma thesis, and to simply write up what I had done so far. When I protested, he insisted that it was time to move on to the real thing, the Ph.D. dissertation.

I had thus come into contact with one of Sauter’s strong beliefs, apparently dating back to the tradition of the 20s: that degrees should not be awarded on the basis of having “served time,” but were basically certificates that the recipient had proven capable of executing creative work independently, and no longer required supervision. In fact, he clearly preferred quick dissertations. As a result, I received my Ph.D. before my 24th birthday, fast even for a theorist: Wonderful!

The Ph.D. dissertation involved what we would today call hot-electron effects, in the collector space-charge layer of the then-new transistor. The idea was simple. Almost nothing was known about the energy band structure of Ge, but someone’s theoretical estimates suggested – quite incorrectly – very narrow bands, especially for the valence band. In this case, if the field was strong enough, any holes in the valence might undergo what we now call Bloch oscillations. A few lines of algebra suggested that, for a given current density, the traveling hole concentration would increase with increasing field (“Staueffekt”), leading to strong space charge effects. The influence of these space charges on the current-voltage characteristics of point contact diodes and transistors formed the main body of the dissertation.

My algebra also implied a decrease of electron drift velocity with increasing field, implying a negative differential conductivity. Knowing nothing about electrical circuit theory, I was unaware how useful such a phenomenon could be, until Shockley pointed it out to me in a personal discussion two years later.

But it became clear soon that my dissertation was unrelated to reality. My assumptions about the band structure and about an energy-independent mean free path had been invalid, and after the discovery of avalanche breakdown it became obvious that the huge fields required for Bloch oscillations in a bulk semiconductor could never be reached. Twenty years later, after the pathbreaking work of Esaki and Tsu on negative differential conductivity in superlattices, I realized that I had in fact anticipated their basic physics, albeit in a more primitive form: What was not possible in bulk semiconductors, appeared to become possible in superlattices with their much longer period.

Back to Sauter. He was not interested in closely supervising his students; he simply watched what they were doing on their own initiative. Still, he had a tremendous influence on me in matters of methodology. Whenever I came to him with a pure physics idea, he would invariably say, with slight sarcasm: “But Mr. Kroemer, you ought to be able to formulate this mathematically! ” If I came to him with a math formulation, I would get, in a similar tone: “But Mr. Kroemer, that is just math, what is the physics?” After a few encounters of this kind, you got the idea: You had to be able to go back and forth with ease. Yet, in the last analysis, concepts took priority over formalism, the latter was simply an (indispensable) means to an end.

This set of priorities clearly showed, and it had a profound influence on me. As a student of Sommerfeld, Sauter was a superb mathematician himself. But he detested it when people were showing off their math skills by using math that was more advanced than necessary for the problem at hand. To the contrary: You were expected to show how simple you could make it. Because he was a great expert on Bessel functions, I once felt compelled to put, into the draft of my dissertation, an ad-hoc problem that required Bessel functions. He was not amused: “This has no business here; you just put it in to impress me. Take it out!”

Richard Becker had exactly the same attitude (the two were close friends), and I later encountered it again in Shockley. Under influences such as these, I never developed into a “hard-core Theorist with a capital T,” but became basically a conceptualist who remained acutely aware of his limitations as a formalist, and whose personal role model was Niels Bohr more than anybody else amongst the Greats of Physics.

The German 1952 job market for theoretical physicists was all but nonexistent. New university positions were not created, and there were plenty of more senior people waiting to occupy any vacancies that might open up. So I never even considered a university career. The situation in industry was hardly any better. As luck would have it, the small semiconductor research group at the Central Telecommunications Laboratory (FTZ) of the German postal service was looking for a “house theorist” who knew semiconductor theory, and I got the job. My duties were simple. I had to be available for whatever theoretical questions anybody had, and also take an active role by poking my nose into the work of my experimentalist and technologist colleagues, to look on my own for topics to which I could contribute – provided I would never touch any equipment. Every week or two, I had to give a talk of 1 to 2 hours to the group, on any subject of my choosing of which I thought that the group should be taught about it. Other than that, I was left completely free to pick whatever problems I felt were worth tackling. So I had become a “professor” of sorts after all, teaching a small but highly motivated “class.” From day-l I was forced to learn to communicate, not with other theorists, but with experimentalists and technologists. It was a fascinating challenge, with a range of topics far beyond what I myself had learned in Göttingen, very often going beyond physics, into metallurgy, chemistry, and electrical engineering.

Of course I ceased to be a “real” theoretical physicist – if I ever was one. Call me an Applied Theorist if you want. However, the awareness of doing something truly useful helped overcome the uneasy feelings over ending a theorist career as soon as it had begun. By hindsight, maybe it wasn’t such a bad career move after all!

As my research topic at the FTZ, I picked the problem of the severe frequency limitations of the new transistors – and what one might be able to do about them. It was this problem that led directly to heterostructure ideas. In a 1954 publication of mine there are a couple of paragraphs outlining in a rudimentary form the first ideas for what was later to be called the heterostructure bipolar transistor, or HBT. I proposed both a transistor with a graded gap throughout the base, and the simpler form of just a wide-gap emitter. The rest is history. This history is described in some detail in my Nobel Lecture, so I will give here only the highlights.

Some time afterjoining RCA Laboratories in Princeton, NJ, in 1954, I returned to heterojunctions. I actually tried – unsuccessfully – to build some HBTs with a Ge/Si alloy emitter on a Ge base. But my principal contributions to the field were two theoretical papers. One of these, in the RCA Review, is essentially unknown to this day, but it clearly spelled out the concept of quasielectric fields, which I considered the fundamental design principle for all heterostructures.

The final step came in 1963, while I worked at Varian Associates in Palo Alto, CA. A colleague – Dr. Sol Miller – gave a research colloquium on the new semiconductor diode laser. He reported that experts had concluded that it was fundamentally impossible to achieve a steady-state population inversion at room temperature, because the injected carriers would diffuse out at the opposite side of the junction too rapidly. I immediately protested: “But that’s a pile of … ; all you have to do is give the outer regions a wider energy gap.” I wrote up the idea and submitted the paper to Applied Physics Letters, where it was rejected. I was talked into not fighting the rejection, but to submit it to the Proceedings of the IEEE, where it was published, but ignored. I also wrote a patent, which is probably a better paper than the one in Proc. IEEE.

Then came the final irony: I was refused resources to work on the new kind of laser, on the grounds that there could not possibly be any applications for it. By a coincidence, the Gunn effect had just been discovered, and having a long-standing interest in hot-electron negative-resistance effects, I worked on the Gunn effect for the next ten years, and did not participate in the final technological realization of the laser.

I left Varian in 1966, and in 1968 joined the University of Colorado. There I eventually returned to heterostructures, and in the early-70s tackled the theory of band offsets together with my student Bill Frensley – now at UT Dallas – who worked out the first ab-initio theory of the band offsets. Shortly afterwards – now at UCSB – I developed a powerful method to determine band offsets experimentally, by capacitance-voltage profiling through the hetero-interface.

In the late-70s, I returned to the device that had started it all, the HBT. The technology developments that had made possible the DH laser offered great promise also for the HBT, and I became a strong advocate of developing the full potential of that device.

In addition to heterostructures, I have worked on numerous other semiconductor topics, be it in physics, materials, devices, or technology. Second only to heterostructures has been a continuing interest in hot-electron negative-resistance effects, dating back to my Ph.D. dissertation. I already mentioned the work on the Gunn effect, but there was more. During my RCA years, I had come up with a crazy scheme to obtain a negative resistance perpendicular to a strong bias field, by drawing on the fact that some of the heavy holes in Ge have negative transverse effective masses – that is, perpendicular to their velocity. Experimentally, it was another failure, but conceptually, I found it extraordinarily stimulating. So did others, and it earned me a great deal of early notoriety. Today, I am back to one of the sins of my youth: to the superlattice Bloch oscillator, an exciting combination of heterostructures and hot electron physics.

At the opposite end from hot electrons has been recent work on superconducting weak links in which a degenerately modulation-doped InAs/AlSb quantum well acts as a ballistic coupling medium between superconducting Nb electrodes. They exhibit some utterly delightful large discrepancies between experiment and accepted theory.

There are numerous additional topics scattered throughout my career. I have basically been an opportunist – and not at all ashamed of it.

This autobiography/biography was written at the time of the award and later published in the book series Les Prix Nobel/ Nobel Lectures/The Nobel Prizes. The information is sometimes updated with an addendum submitted by the Laureate.

Herbert Kroemer died on 8 March 2024.