Received 28 June In final form 21 September Create citation alert. Buy this article in print. Journal RSS feed. Sign up for new issue notifications. By the year electronics will probably be the basis of the largest industry in the world.
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The review begins with a brief and general introduction in which we elucidate the current state of the art and the trends in silicon microelectronics. Afterwards we examine the involvement of physics in silicon microelectronics in the two main sections. The first section concerns the processes of fabrication of ICs: lithography, oxidation, diffusion, chemical and physical vapour deposition, rapid thermal processing, etching, interconnections, ultra-clean processing and microcontamination.
The second section concerns the electrical operation of the ULSI devices. It defines the integration scales and points out the importance of the intermediate scale of integration which is the scale of the next generation of ICs. The emergence of cryomicroelectronics is also reviewed and an extended paragraph is dedicated to the problem of reliability and ageing of devices and ICs: hot carrier degradation, interdevice coupling and noise are considered. We were thus led very naturally to the question of why Mayers theory of condensation gave isotherms that stayed flat into the liquid phase, instead of becoming curves in the liquid phase.
The Mayer theory of condensation was a milestonc in cquilibriurn statistical mechanics, for it broke away from the mean field type of approach to phase rransi- tions. Mayers theory led to a number of papers by Mayer himself, by B. Kahn and G. Uhlenbeck, and by others in succeeding years. In the early s I had attended a series of lectures by J. Wang in Kunming on these devel- opments and had been very much interested in the subject ever since.
Using the lattice gas model, for which we had a lot of exact information, Lee and I examined Mayers theory as applied to this case. This led to a study of the limiting process in the evaluation of the grand partition function for infinite volume. Paper [SZbn resulted from this study. In late , after 1[52b]had appeared in print, Einstein sent Bruria Kaufman, who was then his assistant, to ask me to see him. I went with her to his office, and he expressed great interest in the paper. That was not surprising, since thermodynamics and statistical mechanics were among his main interests.
Unfortunately I did not get very much out of that conversation, the most extensive one I had with Einstein, since I had difficulty understanding him. He spoke very softly, and I found it difficult to concentrate on his words, being quite overwhelmed by the nearness of a great physicist whom I had admired for so long. Back in the fall of , Lee and I, in familiarizing ourselves with lattice gases, computed the partition function for several small lattices with 2, 3,4, 5 , etc.
We discovered to our amazement that the roots of the partition functions, which are polynomials in the fugacity, are all on the unit circle for attractive inter- actions. We were fascinated by this phenomenon and soon conjectured that it was a general theorem for a lattice of any size with attractive interactions.
The theorem, later called the unit circle theorem, became the main element that was exploited in [[52c] to discuss the thermodynamics of a lattice gas. Our attempt at proving the conjecture was a struggle, which I described in a letter to M. I quote now from that letter:. W e then formulated a physicists proof based on no double roots when the strength of the couplings were varied.
Very soon we recognized this was incorrect; and for, I would guess, at least six weeks we were frustrated in trying to prove the conjecture. W e were, of course, in constant contact with you all along and 1 remember with pleasure your later help in showing us Wintners work, which we acknowl- edged in our paper.
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Sometime in early December, I believe, you showed us the proof of the special case when all the couplings are there and are of equal strength, the case that you are now writing about in connection with Polyas collected works. The proof was fine, but we were still stuck on the general problem. Then one evening around December 20, working at home, I suddenly recognized that by making zl,zz,.
Once this idea was there, it took only a few minutes to tighten up all the details of the argument. The next morning I drove Lee to pick up some Christmas trees, and I told him the proof in the car. Later on, we went to the Institute; and I remember telling you about the proof at a blackboard. I remember these quite distinctly because Im quite proud of both the conjecture and the proof.
I t is not such a great contribution, but I fondly consider it a minor gem. We thought that, with the exact expressions for the free energy and the magnetization already known, we had powerful handles on the structure of g 8. Unfortunately these handles were not powerful enough, and the exact form of g 0 remains unknown today. The exact form of g e is of course transformable into the exact partition function of the Ising model in a magnetic field. But our efforts in this direction did lead to two useful results. In listening to a seminar around the end of February, , I learned about the new, ingenious combinatorial method of M.
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Kac and J. Ward for solving the Ising problem without a magnetic field. It was finally proved by B. McCoy and T. Wu in Suzuki, Progress of Theoretical Physics 40, ; T. Asano, Progress of Theoretical Physics 40, ;M. Suzuki and M. Fischer, Journal of Mathematical Physics 12, Ward, The Physical Review 88, Wu, The Physical Review , Commentary on 1[52d] Letter to E.
Fermi dated May 5, Unpublished Article C.
Commelztary [52d] was written while I was visiting the University of Washington in Seattle in the spring and summer of The academic year was unproductive for me. I flirted with the strong coupling theory and the strong focusing principle in accelerator design invented by E. Courant, S. Livingston, and H. I also kept up my interest in pion-nucleon scattering and cosmic ray experiments. My efforts did not lead to any useful results.
Perhaps the best thing I did that year was to get interested in J. Fortunately I was secure and confident enough not to be overly disturbed by the lack of productivity. In mid-December , I received a letter from G. Collins, Chairman of the Cosmotron Department at the Brookhaven National Laboratory, inviting me to visit Brookhaven for a year, Serber told me more about the Laboratory and the offer, and I decided to accept.
In the summer of , I moved to Brookhaven on Long Island. Brookhaven had at that time the largest accelerator in the world, the Cosmotron, operating at 3 GeV. It produced pions and strange particles, and very interesting results were pouring out of various experimental groups working there.
I made it a custom to visit the groups once every few weeks to acquaint myself with their experiments. It was a very different exposure to physics for me compared to the one in Princeton, and I recog- nized that each had its advantages. During the summer there were many visitors at Brookhaven.
Physics discussions, beach-going, and social activities were all at high gear. Then fall came, the visitors left, and my wife, son, and I settled into a quiet life in one of the apartments converted from old barracks on site. The laboratory was situated at the old Upton Army Camp. It was surrounded by woods, in which we took long walks. During weekends, we drove to explore various parts of Long Island. We grew to like Montauk Point, the Atlantic beaches, Wildwood Park, and the unpretentious island- ers around Brookhaven. One snowy Sunday, quite without aim, we drove along the north shore and came upon a charming little village.
We admired the atmosphere around the nice shopping center and looked in the map to find its name-Stony Brook. We did not know then that the next time we came to Stony Brook, in , it was to become home. A number of the experiments done at Brookhaven in the year were about multiple meson production.
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Christian and I made an effort to compute the phase space volumes for different multiplicities. We quickly concluded that we needed to use a computer. Christian knew how to write pro- grams, and we wrote a simple one.
We had to constantly esti- mate the magnitude of quantities and shift the registers right or left in order not to wipe out the significant figures, Christian was a master of programming, and I found it at first to be great fun. But then we began to debug, and I was disheartened to find so many careless mistakes in our statements.