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WITHDRAWN: Birth of semiconductor superlattices
Author's Accepted Manuscript
Birth of Semiconductor Superlattices Raphael Tsu
PII: DOI: Reference:
www.elsevier.com/locate/jcrysgro S0022-0248(15)00381-4 http://dx.doi.org/10.1016/j.jcrysgro.2015.05.018 CRYS22869
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Journal of Crystal Growth
Cite this article as: Raphael Tsu, Birth of Semiconductor Superlattices, Journal of Crystal Growth, http://dx.doi.org/10.1016/j.jcrysgro.2015.05.018 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Manuscript for Elsevier 18th International Conference on MBE, September 7-12, 12, 2014, Flagstaff, AZ
Birth of Semiconductor Superlattices Raphael Tsu University of North Carolina at Charlotte Charlotte NC 28223 USA
Abstract Superlattices were introduced 45 years ago as man-made made solids to enrich the class of materials for electronic and optoelectronic applications. Originally Esaki and I recognized the need to make properties of small things bigger, as developed by nature applying periodicity. The field developed loped to include quantum wells and quantum dots because of the role in phase coherence. Once the Genie is out of the bottle, the field of superlattices is metamorphous into surprising new twists. According to Bob Luntz of ARO who published a manuscript in 1997: The Superlattice lattice Story, reached the White House ouse for participating in Nano-Initiatives, Nano with patents on Quantum Wire + Quantum Dots + Superlattices reached 1600 and publications ublications related to superlattices have passed 10,000. Since there were subjects in public presentations regarding the introduction of resonant tunneling, not quite consistent with events taken place, I included some dates of submission in some of these references. There are plenty of similarities between superlattices and metamaterials, s, in fact many of those are presented for the first time. In 1990, while I spent a summer with Leo, Leroy invited me to his home and asking me my view about the inclusion of the experimental results of Resonant Tunneling in Esaki’s Nobel Lecture four months before our manuscript submitted to APL.. We agreed that Esaki had a hard time to win support of our research, both inside and outside of IBM. Getting additional support from the Nobel committee might be the source of what he did. The concept of metamaterials metam appeared first in the mid 1940’s, long before the introduction of superlattices, however, it was the development of superlattice that led the way for present day metamaterials.
Leo Esaki Visited Ray Tsu at Max Planck Institute for Solid State Physics 1976 1
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Introductions Prior to joining Bell Labs, I published a paper for my master’s thesis on periodic loading of a ridge-waveguide at Ohio State University Antenna Labs. I learned from the work of Brillouin and Lewin, [1-3] as well as techniques from R.E. Collin & R.M. Vaillancourt, dealing with the application of Rayleigh-Ritz Method on a wide range of periodic structures, including man-made periodic loading, [4] as well as methods involving the computations of the propagation of a wave in periodic structures using both techniques similar to band structure calculations as well as equivalent circuit approach as commonly adopted in metamaterials today for the dispersion relationships involving periodic structures.[5] This type of new technology, almost identical to today’s metamaterials, was very much in demand particularly in the DOD sponsored research, however, unlike superlattices which are active with gain, metamaterials are passive systems, no difference from tuners serving as impedance matching, mainly operating near some sort of resonances to gain efficiency, leading to breakdowns under high power. This fact has not been understood in today’s popularity of the photonic crystals and metamaterials! I made a radical change for my PhD work, engaging instead in the use of Heisenberg’s S-matrix applying to electromagnetic waves. After PhD, I worked on the ultrasonic amplifier involving the interaction of electrons with ultrasound in GaAs, and other piezoelectric solids at Bell Labs. Both of these theoretical and experimental techniques are quite similar to my training at Ohio State. I became increasingly drifting towards theoretical physics, partly because of the need to learning with complex wave propagation in elastic media, using tensor Green Function for the Cerenkov Phonon radiation in solids and plasma-phonon interactions. There was something else. I received a possible promotion at BTL by the suggestion of J.R. Pierce to Morris Tannenbaum, Director of my Department, because at the Brain-Storm-Session at BTL conducted by J.R. Pierce, I pointed out something regarding the CHIRP-RADAR system that caught Pierce’s attention: nonlinear array cannot be modeled by interference using two double sources as in a double slits. I refused the possible promotion at BTL and left for Trinity University in San Antonio TX, teaching Einstein’s general relativity. There I met and reported to Frank Witmore, the head of the Physics section of Southwest Research Institute. One day I showed Frank a letter I received including an offer from Soloman Buchsbaum, the Department Head of Research in Plasma Physics at BTL. Frank pulled out a New York Times from his drawer, showing me an article on Kink-Effect by Leo Esaki. I told Frank that I took Esaki to Chinatown for lunch, when he visited BTL. Frank asked whether Esaki liked the food. I replied that Esaki really liked the food I ordered. The next day he handed me the phone saying that he got through to Esaki on the phone. I followed through with a request for an interview, which led to my working for IBM reporting to Leo! After I showed Frank my official offer from Leo, he gave me a little book to read, by Brian Pippard, where he said that the reason why Bloch oscillation had not been observed in metals because the mean free time for electrons in metal is 10-14 sec., four to six orders of magnitude too short. I remembered discussing that with Frank, who just published a paper on negative resistance with me in electrons undergoing giant-trap at LHe temperatures. During my first year at IBM, I published two papers, one on the band structure of GeTe and one on the interaction of phonons and plasmons including Landau Damping. When Leo showed me his disclosure early 1969, having no more than two lines, stating that putting tunnel diodes in series, wonderful and intriguing I-V would have developed. The disclosure was closed by Bob Keyes, marked ‘Close’ with a large cross for lack of operating 2
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principles. I pointed out to Esaki that he should have mentioned that these tunnel diodes are placed periodically. Leo replied, “Oh, of course, placed in series forming a periodic structure.” It seemed obvious that placing things periodically has deeper meaning, nevertheless, it must be emphasized in an official disclosure! I then said that I think I know how to compute the I-V in such structures. It took no more than one weekend for me to come up with an expression on the negative resistance of a man-made superlattice, which is so well known now. [6] Why I failed to tell Esaki what I revealed here. I learned the phrase, “Dead on Arrival” at Bell Labs. I thought about it and decided I should do it when proper occasion arises. Well, every time such occasion seemed to have on hand, it somehow did not seem proper! Nevertheless, there is something I felt all along. Without Esaki pushing the superlattice at IBM with all his determination, it would never have taken off! The technical world is super-conservative, and radically new concepts are viewed as luxury with great reservations. IBM gave some support after ARO came through with a sizable program. In fact I learned from a document, entitled: The Superalattice Story by Bob Luntz of ARO written for the White House, stating that ARO’s involvement for the superlattice was delivered by one individual, John Bardeen. Furthermore, if I had revealed my association with the periodically loaded microwave structures, I was quite sure that superlattices would not have been developed! Conceptually, superlattices led to photonic crystals which evolved into metamaterials; while, in reality, it was the other way around!
GaP/GaAs Superlattice to VG-MBE Ga0.5Al0.5As & Birth of Resonant Tunneling Around late 1969 – early 1970, Gene Blakeslee was assigned in making the first superlattice using LPE GaP/GaAs. LPE was quite in fashion in those days because the highest mobility of GaAs was made with LPE. Other than showing periodicity in X-ray diffraction, there was nothing else such as the important Negative Differential Conductance, NDC. After Esaki knew that LPE was not the way to go about it, he dropped Blakeslee. However, Leo asked me if I knew someone at BTL. I interacted with Walter Brown, who invited Leo and me to see him. Well, Brown convinced us to order the Dual Plasmatron. The instrument set in Leroy Chang’s office for several months since returning from his sabbatical at MIT. Leroy made a call to his old advisor G. Pearson who advised him to work with MBE and to send back without even bother to open the box! The next thing I remember was Al Cho visiting us looking at a Vacuum Generator’s MBE at IBM. Al told me that our results were bad because Esaki smoked cigar. I naively believed him then. The first S.L. with GaPAs constructed by Blakeslee presented at the 12th International low Temperature Conf., Kyoto, 1970, showed periodic structures, but without NDC in I-V. [7] The first NDC observed more than two years later was with Ga0.5 Al0.5 As constructed with our VG-MBE system.[8] Howard was included because he wrote the computer program for the VGMBE system. Rideout was included partly because he was just hired. Chang operated the MBE, in fact, with inputs such as rates of evaporation obtained by me using the Raman scattering from Ga1-xAlxAs as calibration standard for the settings used in evaporations, with x varying from 0 to 0.9, determined by both X-ray and wet chemistry! I also set up the cathodo-luminescence for additional check for the Al/Ga ratio, involving the band structure of the ternary compound. These parameters were entered into the computations for comparison between the I-V and designed parameters such as the Al concentration x. I was not included, perhaps Esaki felt that my role has been rewarded enough! Although I felt left out for all my effort in developing the diagnostic 3
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tools for the determination of alloy compositions, primarily using Raman phonon modes for the ternary alloy systems, as well as being the first who derived the expression for the NDC. My role in Leo’s group as a theorist is in fact ignoring all the experimental role I served in providing design parameters. NDC appeared more than two years after the first attempt showing SL with X-ray diffraction confirmation. This fact was in direct contradiction to the rejection of the first Esaki-Tsu paper to Phys. Rev. stating that a laboratory like IBM should be able to show NDC quickly without resort to claims from publications! What a naive reviewer posing as an expert! Shortly after Warsaw in early fall of 1972, Esaki was ready to announce our results at IBM showing our NDC for the first time to nearly 100 present. Esaki asked me to take a vote of confidence right after his presentation. After I told Leo that over 80% present voted ‘yes’, Esaki declared that he had the mandate to continue the research on superlattices. At this point Ian Gunn stood up and said, “Leo, I am sorry that I voted no, but congratulations to you for the successful execution of a Gunn diode, [9] with domain oscillations in Ternary alloy!” Since Gunn’s office was two down from mine, I quickly caught up with him suggesting that we shall use only a single period forming tunneling while avoiding all possibility of domain formation, which I am sure would show NDC. Gunn replied, “Ray, if you show that, I would go anywhere, anytime to applaud your success.” Leroy Chang and I, two of us gang-up on Leo. Leo replied, “Who can make the thinnest tunnel junction.” I said, “You.” “What dimension?” “More than ten times our well width.” Then Leo said to Leroy and me, “I am protecting you from making a fool of yourself because of pinholes. Ray, you can compute the tunneling from a single well if you would like to do it.” That led to our paper of resonant tunneling with computed I-V for a single quantum well, QW, up to three coupled QWs [10] However, Esaki still disallowed Leroy and I to try experimental verification until late Fall when Esaki knew that he was to receive the Nobel Price. Leroy and I first tried to use something I developed, a contact with a radius of 25 µm, to a double barrier structure. However, out of 100 units, not a single one showed NDC. Next I went to the special technique shop at IBM where a new process with a smaller contact of 6 µm, was developed as the latest technology in contacts at IBM. With that, before November of 1973, we have successful NDC in nearly 10 percent out of 100 units, consisting of a single 50Å GaAs QW, in between with two barriers of 80 Å Ga0.3Al0.7As. [11] By early November, Leo Esaki asked me to teach Leo Alexander, a technician in our group, to compute a complete representation of RTD, the transmission coefficient of a tunneling structure with applied voltage for his use as something important to our project. Furthermore, Leo asked me to write up something about the resonant tunneling for him to present in his Nobel Lecture. However, in his Nobel Lecture in December of 1973, [12] our glorious measurements of I-V and dI/dV of the resonant tunneling through a single quantum well were included in his Nobel lecture, made public in December 1973, a full four months ahead of our submission to APL, received 18 March 1974, and appeared June, 1974 [13]. Although Leo did mention in his Nobel Lecture that a publication exclusively dealing with this aspect was being prepared for publication. This document also appeared in Science, on 22 March 1974, [12]. It is possible that Esaki did not know that this version came out 3 months before our submission to APL. For all fairness, I knew something about that because I distinctly remember that Leo did ask me to prepare something for him to be included in his Nobel Lecture. I did not take all that as Esaki’s self-serving motive, because I knew how difficult it was to launch some ideas so daring. 4
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Now I have a surprise for many of you. Shortly there-after, I received a phone call from Ray Wolfe at BTL, “Ray, just listen what I have to say. I am reading to you what I found from the copying machine.” I replied, “Are you the reviewer of the submitted paper by Chang, Esaki and me?” “No, but you are having company.” Then I thank Ray Wolfe, “This kind of competition is very good for us at IBM, because with challenge from BTL, we are made respectable at IBM!” The paper in question is of course the one referred above by Chang, Esaki and Tsu. Not long after, there came the paper by Dingle et al [13] from BTL with signal to noise ratio of excitons 20 times better than ours. Al Cho told me that we should not have used x = 0.5 in Ga1-xAlxAs. For keeping interfacial strain to a minimum, x should not exceed 0.3. I have a saying for my students, “Don’t tell me who is intelligent or dumb. Tell me who knows.” In those days the best source came from Knudson cells. We know that BTL has Wiegmann, a technician who made the best home-made cells. Incidentally, I spend couple of years at Univ. Sao Paulo. I hired Wiegmann for making Knudson cells during the spring of 1985. The development of quantum well, QW, and multiple quantum wells, MQW, with wide spread involvement in present and future devices owe their origins to something developed by chance, showing that NDC of superlattices is not due to domain oscillations of Gunn diodes! Another side line with MQW is the so-called modulation doping for achieving high mobility, in fact was an idea Esaki and I had described in an IBM report [14], which was asked to be removed by the editor of IBM’s own journal of Research! [6]
Origin of Type III Superlattice One day Esaki asked me if I had some insight into how to move the point of inflection, when the mass changes sign at some value of E-k of the miniband, closer to the mini-zone center, in order to lower the electric field necessary for NDC. Esaki showed me the Handbook of Electronic Materials by Neuberger, and we were looking into InAs/GaSb with the top of the valence band of GaSb being above the bottom of the conduction band of InAs would have resulted in having the peak current, NDC, located at a lower voltage. I responded by saying that perhaps I can use k.p method to find out. Leo jumped up and said to me, “Go for it. This will be something we are after!” My main theoretical approach involved the realization that whenever conduction band overlapping with the valence band, we must introduce the periodic parts of the wave functions. In other words, no more plane waves, we need the full Bloch wave-functions. Because of the overlapping conduction and valence-bands, a new bandgap must be developed, with band-width determined by how large is the superlatice period. The larger the period, the smaller is the degree of interaction per unit volume, resulting in very narrow bands! It turned out that I was to go on a sabbatical at Campinas, Brazil starting in November of 1976. I started with the basic formulation and handed my unfinished work to Sai-Halasz, needing some fairly involved computer programing. Type III Superlattice arrived! Although it did not accomplish lowering the point of inflection in NDC! However, the scheme provided us a much larger range in designing the band width and the separations of minibands in the IR region. [15,16] The physics involved may be understood simply in terms of overlapping maximum of valence band with the minimum of conduction band resulting in an interaction in opening up a new band, with the transfer of electrons to the lower conduction band resulting in a substantial increase in 5
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conductivity! Nevertheless, not much change in optical properties is expected because the new gap opened is generally very narrow! [16] THz oscillators using Bloch Oscillations has been over-shadowed by QCL, making the role of Type III Superlattice in IR detectors far more important than lowering the bias needed for NDC. Again, we have situations where major developments in technology often came from totally surprising reasons! In fact superlattices have been superseded by multiple quantum wells, MQWs, In fact, most activity today under the title of superlattices are in fact MQWs! There are few principles we must realize and remember. How do we achieve higher power handling? As we know there are two ways: putting identical devices in series to gain voltage for higher power, but usually with decrease speed. We can also putting identical devices in parallel, to gain current, which also lead to higher response time. In so doing, we are in fact using superlattice as components. And that we should be doing from the beginning. Because Esaki and I were not very familiar with devices and systems. We introduce the concept of superlattices as a bulk devices, but in fact, the end result is in fact in terms of components! Just ask ourselves whether we use a big hunk of cement to do the job, or we use smaller blocks.
Superlattice, Photonic Crystal and Meta-materials I want to take this opportunity to make an important point how we learn and how we discover. I was working at Ohio State University, Antenna Lab., with my advisor Kirschbaum, on periodic loading of waveguides, which was in almost all respect, identical to today’s Metamaterials. I was to use the approach using solutions of Maxwell’s equations applying to a periodic structures, a ridged-waveguide with periodic cuts. Following the work of L. Lewin from Royal Radar Establishment, as early as 1947, or before, who placed identical spheres on a cubic lattice sites, obtaining variable refractive index, hot subject for RADARs. However, the approach is certainly identical to the development of Photonic Crystals, more than 40 years later by Yablonovitch.[17] Let us go into more detail regarding this. Lewin’s scheme was quickly improved by confining into one dimension, developing into periodic loading in wave-guides, shown to provide better control and repeatability. Anything along this line was quickly dominated by the defense industry. Within few years, serrated waveguides, periodic loading of a ridge waveguide came onto the scene for the control of phase by periodic loadings, quickly seized by DOD for focusing microwaves. However, this work eventually disappeared from R & D because of two reasons: (1) DOD in US classified that sort of work; but more importantly, (2) unlike superlattices, it is passive, requiring operation near some sort of resonance, ending up in high field breakdowns, unsuitable for high power microwave focusing systems, prevented this sort of meta-materials to play a significant role in electronic and optical devices. Actually power handling capacity of any devise is important consideration, including superlattices! I hid this work from Esaki because I did not want to confuse the issues, with principles involved close to superlattices, having man-made components with circuit representations, indistinguishable from today’s metamaterials. Kirschbaum, who was an expert in equivalent circuits, showed me how to use circuit approach while I was using field approach, referenced earlier by Collin and Vaillancourt: basically with distinction between the propagation k, along the direction of the periodic structure, applying Floquet’s expressions, called Bloch theorem in Solid State Physics, 6
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while in the transverse direction, fields are all matched in their common boundaries. Kirschbaum told me to measure the equivalent capacitance with dc voltage and current. I protested that capacitance, like any constitutive equation, is frequency dependent. He said, “Let me teach you something. Do you know why capacitance is a function of geometry? It is true because we have Avogadro-number of electrons, pushing each other by electrostatic repulsion until they got into all cracks and surfaces, in so doing, defining the geometry involved!” Now it is quite clear had I disclosed my work regarding the periodic loading of waveguides, Esaki would not push for it. Even if he did, his chances for success would be very low! On the other hands, without superlattices, I doubt very much photonic crystals would have been introduced. In a way metamaterials, although developed somewhat independently, most obviously took a ride on the over-whelming momentum developed in the field of superlattices. Superlattices did not lead to metamaterials. Nevertheless, superlattice did prepare the technical world for rapid introduction and development of metamaterials. Furthermore, the incorporation of man-made elements represented by circuit approach widely adopted today in metamaterials, in fact, was introduced many years ago! We have earlier touched on the active and passive systems, as represented by superlattices and metamaterials respectively. By applying a dc bias, superlattice, due to the NDC, becomes an active system such as oscillators, modulators, and ultimately, an amplifiers for signal generation as well as detection. It was pointed out in Section 1.5 of my book, where the response function and Bloch oscillations have been derived with an application of a combined dc and ac fields. [16] A dc field gives the gain factor as an amplifier, and an ac-field gives modulation as well as possible applications as modulator and ultimately as parametric amplifiers! One may ask how a dc-field can affect a typical metamaterials having a periodic array of elements such as circuits. Obviously a large metallic element in the form of the letter C cannot be affected by a dc voltage, however, when the number of electrons are few, a dcfield can shift the electron distribution and affecting the capacitance of such shape! Therefore, I am calling you to start applying a bias, ac or dc, to the elements of your metamaterials!
Raman and Cathodo-luminascence for alloy concentrations in GaAlAs At the beginning at IBM, we were trying to use optical absorption and emissions for calibration of alloy concentrations in III-V systems, such as what was done at BTL. However, we did not have traditions and experience in this sort of work. Leo invited H. Kawamura to work with us. Partly because Leo knew that I was fascinated by Raman scattering. As Kawamura told Esaki that he would like to work on Raman Scattering. And Leo knew that I asked for a Spexsystem for Raman. Leo told me that Kawamura was an important physicist in Japan. So now is my chance to work with Raman. Well, there were two things against us. First we do not have the budget for a SPEX-II system. Well I got one on loan from SPEX. But the greater problem is the discovery that Kawamura thought that I was familiar with Raman because I asked Esaki to allow me working on Raman, which I had never done! When Kawamura arrived. We went to G. Burns for help. Gerry said to his technician, “Ray and Kawamura, are blind leading the blind!” Six months later, we discovered something new in Raman Scattering, Disorder activated Raman Phonons in GaAlAs systems, published in Phys. Rev. Let.! Well we developed the use of Raman as calibration of the alloy systems, by having a sample with Al concentration varying from 0.1 to 7
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0.9 completely determined by X-ray and wet chemistry! This sample allowed us to have fast turn-around. Leroy was so happy that we were able to provide him half-a-day turn-around for the determination of composition x of the ternary alloy systems. Cathodo-luminescence is so simple to operate because unlike photo-luminescence, rarely were we involved in selection rule issues. Perhaps the only complain involves too much data; sometimes with mysterious data, even after the sample had been removed from the chamber! The First Metamorphosis of Superlattices – Resonant Tunneling via Quantum Wells After the success in reducing the structure to a single period, the birth of resonant tunneling through a single quantum well became reality. It came because we tried to show that the NDC was indeed result of Bloch oscillation. Well we were correct, but then, who needs Bloch Oscillations! Esaki and I were somewhat misled by the love of physics and the lack of understanding what is a real device. We did not understand that there is no need of bulk device. All electronic devices consist of input, active region of gain, or in general, region of interaction, followed by output. Therefore, the concept of QCL, quantum cascade laser is what the expert, like Capasso has come up with. [18] What is QCL, it is, like the injection laser, having input, active region, and output, all consist of QW or MQW, for quantum well, or multiple quantum well. You may ask why we still refer to most of these devices as superlattice. Well, it came from the original concept of superlattice, however, the main feature has changed. What remains consist of devices we can construct with quantum wells, and others, for example, I was involved in filing a patent with components consisting of Type II, however, not as a single unit of quantum devices, rather as multiple components, with InAs and GaSb based Type II or Type III ingredient, but separated. In essence, the patent involves structures quite different from single entity, as superlattices. In essence, what is involved consists of parts, each having a thin layer of a given materials, in contact with another thin layer of materials. What is the connection with the concept of a superlattice? Well, not quite! The commonality with superlattice consists of regions with which its phase of de Broglie electrons forms the essence of action in a given device. Perhaps we should invent a new term – PSQS for Phase Sensitive Quantum Structure, which have been around for quite a while.
Impact of Superlattices Let us first look at the impact of superlattice, e.g. from the standpoint of the introduction of the transistors. Although transistors, as lump-devices, have its place in the device world, the greater contribution to modern technology is the development of the monolithic IC’s in the form of MOSFET’s, introduced by Kahng, D. & Atalloa, M.M. [19] However, one wonders whether MOSFET would be invented without the introduction of transistors. When man-made semiconducting devices consist of dimensions less than the mean-free-path of electrons in solids, quantum wells and even quantum dots emerged. Thus the consequences of the introduction of superlattice led the way to quantum wells, and quantum dots, including MQW, especially involving Type-II superlattices, introduced by Esaki and Tsu as a possible way to move the point of inflection of the superlative closer to the zone center of the SL band structure such that NDC may be reached at a lower applied voltage. Well, it did not happen, yet something else emerged, new possibilities such as detectors operated in long-wavelength IR, LWIR and Mid-Wavelength 8
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IR, MWIR emerged. [20, 21, 22, 23] In particular, Type III superlattices as discussed, in addition to the appearance of new energy gaps, the increase with new conducting channel serving as new devices in IR detectors, [23], actually also serving as ITO and TCO [24], the overlapping of valence and conduction bands resulting in opening new gaps with transfer of electrons leading to a significant increase in carrier concentration for conduction processes in devices, without Coulomb scattering from dopants. We were very excited by the possibility of THz devices, via RTD. [25] Among some very interesting new possible applications of SL, with which taking the field of semiconducting devices to new frontiers, are device concepts with quantum dots and nano-science in general. [Chapters 8-12 of 16] The big surprises include new fundamental physics, for example, the behavior of the dielectric constant of quantum dots and the strange role of symmetry. [26]
The Role of Periodic Loading in the Development of Superlattices As pointed out earlier that the work of material loaded with small particles on a cubic lattice sites by L. Lewin, preceded superlattice by more than 20 years. [1, 2]. And the work on periodic loading of a ridged waveguide, one dimensional periodic loading, by Kirschbaum and Tsu, preceded superlative by 10 years. [5] What are the impacts of these earlier work on the development of super lattices and eventually, the metamaterials? I think my personal knowledge of these earlier works did help me to be guided into the correct theoretical understandings, mainly involving the use of Floquet’s theorem, and the 3D version, the Bloch theorem. For the one-dimensional periodic loading, Kirschbaum taught me how to develop a 1-D loading based on circuit approach so similar to the approach used for a vast majority of metamaterials. Since metamaterials developed from Photonic crystals [17], with periodic loading of circuit elements; and superlattices developed using periodic loading involving heterojunctions; both are intimately connected with Lewin’s original work, it is obvious from what is presented here, both super lattices and metamaterials were developed independently from earlier works. In particular, periodic loading of a ridged waveguide [5] succeeded in obtaining variation of refractive index at microwave frequencies from n = 0.3 to 1.9, sufficient for microwave applications as a new type of antenna systems. However, there is something very important, not known to most workers, including those presently claimed. My work on the ridged waveguide was sponsored by Sperry Gyroscope of Sperry Rand, which in turn was funded by DOD. When it was discovered that most of the wide range of refractive index traced to resonances: a slot in a ridge is represented by an impedance varying from 0 to ∞, the typical impedance of the so-called quarter-wave transformer. Basically a transmission line has an input impedance varying from 0 to ∞, in every quarter wave change in length! This feature constitutes the universal concepts of the circuit representations in periodically loaded structures. However, resonances always restrict power handling capability, therefore, there is no secret that Type-III superlatives developed into good IR detectors. However, if we were to ask for using as focusers, resonant systems hardly can handle high power without increasing the volume of interaction to lower the field strength. And that is the key position: How to design systems to avoid breakdowns with the least increase in the volume of interaction!
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Conclusions In my nearly 60 years of involvement in physical science with main objective of promoting man-made devices, I have publicly reminded the scientific community that Darwin’s survival of the fittest for biological species should be extended to human technology. Ideas are important, but thousands of technologists working to move ahead, outdoing each other in performance, is what propels our technology. As widely accepted in research and development involving superlattices, the subject is matured while its ramifications, represented by nanodevices, would propel the field of endeavor to new directions and importance in the quest for technology superiorities. There is something worthy of note in both superlattices as well as metamaterials: If circuit elements are to be incorporated in whatever geometrical forms, the materials must not be metals because of their fantastically low carrier life-time, instead, high mobility semiconductors with modulation doping, or with Type III superlattices to avoid high scattering from dopants! Lastly, when I was leaving Shanghai, my great uncle who was in his last days of an active life in promoting industry in China, said to me, “ I want you to remember the old Chinese saying: To succeed in new human task, one needs the right tool.”
List of References 1. Lewin, L. The Electrical Constants of Materials Loaded with Spherical Particles, Proc. IEEE-3, 94, 65-68 (1947) 2. Lewin, L. Advanced Theory of Waveguides, Iliffe & Sons Ltd. London, England (1951). 3. Brillouin, L. Wave Propagation in Periodic Structures, Dover Publications, Inc. New York, NY (1953) 4. R.E. Collin & R.M. Vaillancourt. Application of Rayleigh-Ritz Method …, IRE Transections, MTT-7, 177-184 (1957) 5. Kirschbaum, H.S. and Tsu, R., A Study of a Serrated Ridge Waveguide, IRE Transactions on Microwave Theory and Techniques MTT-7, 142-147 (1959) 6. Esaki, L. & Tsu, R. Superlattice and Negative Differential Conductivity in Semiconductors, IBM J. Res. Develop., 14, 62-65 (1970) 7. Esaki, L., Chang, L.L., Tsu, R., A one-dimensional Superlattice in Semiconductors, 12th International low Temperature Conf., Kyoto, 551-553, (1970) 8. Esaki, L., Chang, L. L., Howard, W., Rideout, L. Proc.11th International Conf. Phys. of Semiconductors, Warsaw Poland, p.431, (1972) 9. Gunn, J.B., Solid State Comm.1, 88 (1963) 10. R. Tsu, and L. Esaki, Tunneling in a finite Superlattice, Appl. Phys. Lett. Received March 1973, 22, 562-564, 1 June 1973. 11. Chang, L.L., Esaki, L, and Tsu, R, Resonant Tunneling in Semiconductor Double Barriers Appl. Phys. Lett. 24, 593-595, (1974). Received 18 March 1974, and appeared June, 1974. 12. Esaki, L. Nobel Lecture, 116-133, December 12, 1973, The Nobel Foundation 1974, also in Esaki, L., Long Journey into Tunneling, Science, 183, 1149-1155, Science (1974). 13. Dingle, R., Wiegmann, W.E., & Henry, C.H. Phys. Rev. Lett. 33, 827 (1974). 14. Esaki, L., Tsu, R., Superlattice and Negative Differential Conductivity in Semiconductors, IBM Research Note RC-2418, (1969) 15. Sai-Halacz, G.A., Tsu, R., and Esaki, L. Appl. Phys. Lett., 30, 651(1977). 10
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16. Tsu, Raphael, Superlattice to Nanoelectronics, Elsevier, ISBN 978-0-08-096813-1, 2nd edition, 2011, Chapter 1. 17. Yablonovitch, E., Phys. Rev. Lett. 58, 2059 (1987). 18. Faist, J. Capasso, F., Sivco, D.L. Sittori, C. Hutchinson, A.L. Cho, A.Y. Science 264, 533, (1994) 19. Kahng, D. & Atalloa, M.M. in IRE-AIEE Solid State Device Res. Conf. (CIT) Pittsburgh, PA, (1960) 20. Tsu, R. Proc. SPIE 8631, 863106 – 1-15(2013) 21. Zhang, Y.H. Appl. Phys. Lett. 66, 118 (1995) 22. Yang, R.Q. & Pei, S.S. J. Appl. Phys. 79, 8197 (1996) 23. Razeghi, M. Tech. of Quantum Devices, Spring, NY (2009) 24. Edwards, P. P., Porch, A., Jones, M. O., Morgan, D. V., Perks, R. M. Dalton Transactions 19: 2995–3002, (2004) 25. Sollner, T.C.L.G., Goodhue, W.D., Tennenwald, P.E., Parker, C.D., Peck, D.D. Appl. Phys. Lett. 43, 588 (1983). 26. Tsu, R. & LaFave, Jr. T, Role of Symmetry in Conductance, Capacitance, and Doping of Quantum Dots, Wonder of Nanotech. SPIE Press, Razeghi, Esaki & von Klitzing, (2013)
Acknowledgments I thank the organizing committee of MBE-2015 for inviting me to give this summary, which includes interesting materials probably unknown to most.
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Birth of Semiconductor Superlattices Raphael Tsu
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Cite this article as: Raphael Tsu, Birth of Semiconductor Superlattices, Journal of Crystal Growth, http://dx.doi.org/10.1016/j.jcrysgro.2015.05.018 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Birth of Semiconductor Superlattices Raphael Tsu University of North Carolina at Charlotte Charlotte NC 28223 USA
Abstract Superlattices were introduced 45 years ago as man-made made solids to enrich the class of materials for electronic and optoelectronic applications. Originally Esaki and I recognized the need to make properties of small things bigger, as developed by nature applying periodicity. The field developed loped to include quantum wells and quantum dots because of the role in phase coherence. Once the Genie is out of the bottle, the field of superlattices is metamorphous into surprising new twists. According to Bob Luntz of ARO who published a manuscript in 1997: The Superlattice lattice Story, reached the White House ouse for participating in Nano-Initiatives, Nano with patents on Quantum Wire + Quantum Dots + Superlattices reached 1600 and publications ublications related to superlattices have passed 10,000. Since there were subjects in public presentations regarding the introduction of resonant tunneling, not quite consistent with events taken place, I included some dates of submission in some of these references. There are plenty of similarities between superlattices and metamaterials, s, in fact many of those are presented for the first time. In 1990, while I spent a summer with Leo, Leroy invited me to his home and asking me my view about the inclusion of the experimental results of Resonant Tunneling in Esaki’s Nobel Lecture four months before our manuscript submitted to APL.. We agreed that Esaki had a hard time to win support of our research, both inside and outside of IBM. Getting additional support from the Nobel committee might be the source of what he did. The concept of metamaterials metam appeared first in the mid 1940’s, long before the introduction of superlattices, however, it was the development of superlattice that led the way for present day metamaterials.
Leo Esaki Visited Ray Tsu at Max Planck Institute for Solid State Physics 1976 1
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Introductions Prior to joining Bell Labs, I published a paper for my master’s thesis on periodic loading of a ridge-waveguide at Ohio State University Antenna Labs. I learned from the work of Brillouin and Lewin, [1-3] as well as techniques from R.E. Collin & R.M. Vaillancourt, dealing with the application of Rayleigh-Ritz Method on a wide range of periodic structures, including man-made periodic loading, [4] as well as methods involving the computations of the propagation of a wave in periodic structures using both techniques similar to band structure calculations as well as equivalent circuit approach as commonly adopted in metamaterials today for the dispersion relationships involving periodic structures.[5] This type of new technology, almost identical to today’s metamaterials, was very much in demand particularly in the DOD sponsored research, however, unlike superlattices which are active with gain, metamaterials are passive systems, no difference from tuners serving as impedance matching, mainly operating near some sort of resonances to gain efficiency, leading to breakdowns under high power. This fact has not been understood in today’s popularity of the photonic crystals and metamaterials! I made a radical change for my PhD work, engaging instead in the use of Heisenberg’s S-matrix applying to electromagnetic waves. After PhD, I worked on the ultrasonic amplifier involving the interaction of electrons with ultrasound in GaAs, and other piezoelectric solids at Bell Labs. Both of these theoretical and experimental techniques are quite similar to my training at Ohio State. I became increasingly drifting towards theoretical physics, partly because of the need to learning with complex wave propagation in elastic media, using tensor Green Function for the Cerenkov Phonon radiation in solids and plasma-phonon interactions. There was something else. I received a possible promotion at BTL by the suggestion of J.R. Pierce to Morris Tannenbaum, Director of my Department, because at the Brain-Storm-Session at BTL conducted by J.R. Pierce, I pointed out something regarding the CHIRP-RADAR system that caught Pierce’s attention: nonlinear array cannot be modeled by interference using two double sources as in a double slits. I refused the possible promotion at BTL and left for Trinity University in San Antonio TX, teaching Einstein’s general relativity. There I met and reported to Frank Witmore, the head of the Physics section of Southwest Research Institute. One day I showed Frank a letter I received including an offer from Soloman Buchsbaum, the Department Head of Research in Plasma Physics at BTL. Frank pulled out a New York Times from his drawer, showing me an article on Kink-Effect by Leo Esaki. I told Frank that I took Esaki to Chinatown for lunch, when he visited BTL. Frank asked whether Esaki liked the food. I replied that Esaki really liked the food I ordered. The next day he handed me the phone saying that he got through to Esaki on the phone. I followed through with a request for an interview, which led to my working for IBM reporting to Leo! After I showed Frank my official offer from Leo, he gave me a little book to read, by Brian Pippard, where he said that the reason why Bloch oscillation had not been observed in metals because the mean free time for electrons in metal is 10-14 sec., four to six orders of magnitude too short. I remembered discussing that with Frank, who just published a paper on negative resistance with me in electrons undergoing giant-trap at LHe temperatures. During my first year at IBM, I published two papers, one on the band structure of GeTe and one on the interaction of phonons and plasmons including Landau Damping. When Leo showed me his disclosure early 1969, having no more than two lines, stating that putting tunnel diodes in series, wonderful and intriguing I-V would have developed. The disclosure was closed by Bob Keyes, marked ‘Close’ with a large cross for lack of operating 2
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principles. I pointed out to Esaki that he should have mentioned that these tunnel diodes are placed periodically. Leo replied, “Oh, of course, placed in series forming a periodic structure.” It seemed obvious that placing things periodically has deeper meaning, nevertheless, it must be emphasized in an official disclosure! I then said that I think I know how to compute the I-V in such structures. It took no more than one weekend for me to come up with an expression on the negative resistance of a man-made superlattice, which is so well known now. [6] Why I failed to tell Esaki what I revealed here. I learned the phrase, “Dead on Arrival” at Bell Labs. I thought about it and decided I should do it when proper occasion arises. Well, every time such occasion seemed to have on hand, it somehow did not seem proper! Nevertheless, there is something I felt all along. Without Esaki pushing the superlattice at IBM with all his determination, it would never have taken off! The technical world is super-conservative, and radically new concepts are viewed as luxury with great reservations. IBM gave some support after ARO came through with a sizable program. In fact I learned from a document, entitled: The Superalattice Story by Bob Luntz of ARO written for the White House, stating that ARO’s involvement for the superlattice was delivered by one individual, John Bardeen. Furthermore, if I had revealed my association with the periodically loaded microwave structures, I was quite sure that superlattices would not have been developed! Conceptually, superlattices led to photonic crystals which evolved into metamaterials; while, in reality, it was the other way around!
GaP/GaAs Superlattice to VG-MBE Ga0.5Al0.5As & Birth of Resonant Tunneling Around late 1969 – early 1970, Gene Blakeslee was assigned in making the first superlattice using LPE GaP/GaAs. LPE was quite in fashion in those days because the highest mobility of GaAs was made with LPE. Other than showing periodicity in X-ray diffraction, there was nothing else such as the important Negative Differential Conductance, NDC. After Esaki knew that LPE was not the way to go about it, he dropped Blakeslee. However, Leo asked me if I knew someone at BTL. I interacted with Walter Brown, who invited Leo and me to see him. Well, Brown convinced us to order the Dual Plasmatron. The instrument set in Leroy Chang’s office for several months since returning from his sabbatical at MIT. Leroy made a call to his old advisor G. Pearson who advised him to work with MBE and to send back without even bother to open the box! The next thing I remember was Al Cho visiting us looking at a Vacuum Generator’s MBE at IBM. Al told me that our results were bad because Esaki smoked cigar. I naively believed him then. The first S.L. with GaPAs constructed by Blakeslee presented at the 12th International low Temperature Conf., Kyoto, 1970, showed periodic structures, but without NDC in I-V. [7] The first NDC observed more than two years later was with Ga0.5 Al0.5 As constructed with our VG-MBE system.[8] Howard was included because he wrote the computer program for the VGMBE system. Rideout was included partly because he was just hired. Chang operated the MBE, in fact, with inputs such as rates of evaporation obtained by me using the Raman scattering from Ga1-xAlxAs as calibration standard for the settings used in evaporations, with x varying from 0 to 0.9, determined by both X-ray and wet chemistry! I also set up the cathodo-luminescence for additional check for the Al/Ga ratio, involving the band structure of the ternary compound. These parameters were entered into the computations for comparison between the I-V and designed parameters such as the Al concentration x. I was not included, perhaps Esaki felt that my role has been rewarded enough! Although I felt left out for all my effort in developing the diagnostic 3
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tools for the determination of alloy compositions, primarily using Raman phonon modes for the ternary alloy systems, as well as being the first who derived the expression for the NDC. My role in Leo’s group as a theorist is in fact ignoring all the experimental role I served in providing design parameters. NDC appeared more than two years after the first attempt showing SL with X-ray diffraction confirmation. This fact was in direct contradiction to the rejection of the first Esaki-Tsu paper to Phys. Rev. stating that a laboratory like IBM should be able to show NDC quickly without resort to claims from publications! What a naive reviewer posing as an expert! Shortly after Warsaw in early fall of 1972, Esaki was ready to announce our results at IBM showing our NDC for the first time to nearly 100 present. Esaki asked me to take a vote of confidence right after his presentation. After I told Leo that over 80% present voted ‘yes’, Esaki declared that he had the mandate to continue the research on superlattices. At this point Ian Gunn stood up and said, “Leo, I am sorry that I voted no, but congratulations to you for the successful execution of a Gunn diode, [9] with domain oscillations in Ternary alloy!” Since Gunn’s office was two down from mine, I quickly caught up with him suggesting that we shall use only a single period forming tunneling while avoiding all possibility of domain formation, which I am sure would show NDC. Gunn replied, “Ray, if you show that, I would go anywhere, anytime to applaud your success.” Leroy Chang and I, two of us gang-up on Leo. Leo replied, “Who can make the thinnest tunnel junction.” I said, “You.” “What dimension?” “More than ten times our well width.” Then Leo said to Leroy and me, “I am protecting you from making a fool of yourself because of pinholes. Ray, you can compute the tunneling from a single well if you would like to do it.” That led to our paper of resonant tunneling with computed I-V for a single quantum well, QW, up to three coupled QWs [10] However, Esaki still disallowed Leroy and I to try experimental verification until late Fall when Esaki knew that he was to receive the Nobel Price. Leroy and I first tried to use something I developed, a contact with a radius of 25 µm, to a double barrier structure. However, out of 100 units, not a single one showed NDC. Next I went to the special technique shop at IBM where a new process with a smaller contact of 6 µm, was developed as the latest technology in contacts at IBM. With that, before November of 1973, we have successful NDC in nearly 10 percent out of 100 units, consisting of a single 50Å GaAs QW, in between with two barriers of 80 Å Ga0.3Al0.7As. [11] By early November, Leo Esaki asked me to teach Leo Alexander, a technician in our group, to compute a complete representation of RTD, the transmission coefficient of a tunneling structure with applied voltage for his use as something important to our project. Furthermore, Leo asked me to write up something about the resonant tunneling for him to present in his Nobel Lecture. However, in his Nobel Lecture in December of 1973, [12] our glorious measurements of I-V and dI/dV of the resonant tunneling through a single quantum well were included in his Nobel lecture, made public in December 1973, a full four months ahead of our submission to APL, received 18 March 1974, and appeared June, 1974 [13]. Although Leo did mention in his Nobel Lecture that a publication exclusively dealing with this aspect was being prepared for publication. This document also appeared in Science, on 22 March 1974, [12]. It is possible that Esaki did not know that this version came out 3 months before our submission to APL. For all fairness, I knew something about that because I distinctly remember that Leo did ask me to prepare something for him to be included in his Nobel Lecture. I did not take all that as Esaki’s self-serving motive, because I knew how difficult it was to launch some ideas so daring. 4
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Now I have a surprise for many of you. Shortly there-after, I received a phone call from Ray Wolfe at BTL, “Ray, just listen what I have to say. I am reading to you what I found from the copying machine.” I replied, “Are you the reviewer of the submitted paper by Chang, Esaki and me?” “No, but you are having company.” Then I thank Ray Wolfe, “This kind of competition is very good for us at IBM, because with challenge from BTL, we are made respectable at IBM!” The paper in question is of course the one referred above by Chang, Esaki and Tsu. Not long after, there came the paper by Dingle et al [13] from BTL with signal to noise ratio of excitons 20 times better than ours. Al Cho told me that we should not have used x = 0.5 in Ga1-xAlxAs. For keeping interfacial strain to a minimum, x should not exceed 0.3. I have a saying for my students, “Don’t tell me who is intelligent or dumb. Tell me who knows.” In those days the best source came from Knudson cells. We know that BTL has Wiegmann, a technician who made the best home-made cells. Incidentally, I spend couple of years at Univ. Sao Paulo. I hired Wiegmann for making Knudson cells during the spring of 1985. The development of quantum well, QW, and multiple quantum wells, MQW, with wide spread involvement in present and future devices owe their origins to something developed by chance, showing that NDC of superlattices is not due to domain oscillations of Gunn diodes! Another side line with MQW is the so-called modulation doping for achieving high mobility, in fact was an idea Esaki and I had described in an IBM report [14], which was asked to be removed by the editor of IBM’s own journal of Research! [6]
Origin of Type III Superlattice One day Esaki asked me if I had some insight into how to move the point of inflection, when the mass changes sign at some value of E-k of the miniband, closer to the mini-zone center, in order to lower the electric field necessary for NDC. Esaki showed me the Handbook of Electronic Materials by Neuberger, and we were looking into InAs/GaSb with the top of the valence band of GaSb being above the bottom of the conduction band of InAs would have resulted in having the peak current, NDC, located at a lower voltage. I responded by saying that perhaps I can use k.p method to find out. Leo jumped up and said to me, “Go for it. This will be something we are after!” My main theoretical approach involved the realization that whenever conduction band overlapping with the valence band, we must introduce the periodic parts of the wave functions. In other words, no more plane waves, we need the full Bloch wave-functions. Because of the overlapping conduction and valence-bands, a new bandgap must be developed, with band-width determined by how large is the superlatice period. The larger the period, the smaller is the degree of interaction per unit volume, resulting in very narrow bands! It turned out that I was to go on a sabbatical at Campinas, Brazil starting in November of 1976. I started with the basic formulation and handed my unfinished work to Sai-Halasz, needing some fairly involved computer programing. Type III Superlattice arrived! Although it did not accomplish lowering the point of inflection in NDC! However, the scheme provided us a much larger range in designing the band width and the separations of minibands in the IR region. [15,16] The physics involved may be understood simply in terms of overlapping maximum of valence band with the minimum of conduction band resulting in an interaction in opening up a new band, with the transfer of electrons to the lower conduction band resulting in a substantial increase in 5
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conductivity! Nevertheless, not much change in optical properties is expected because the new gap opened is generally very narrow! [16] THz oscillators using Bloch Oscillations has been over-shadowed by QCL, making the role of Type III Superlattice in IR detectors far more important than lowering the bias needed for NDC. Again, we have situations where major developments in technology often came from totally surprising reasons! In fact superlattices have been superseded by multiple quantum wells, MQWs, In fact, most activity today under the title of superlattices are in fact MQWs! There are few principles we must realize and remember. How do we achieve higher power handling? As we know there are two ways: putting identical devices in series to gain voltage for higher power, but usually with decrease speed. We can also putting identical devices in parallel, to gain current, which also lead to higher response time. In so doing, we are in fact using superlattice as components. And that we should be doing from the beginning. Because Esaki and I were not very familiar with devices and systems. We introduce the concept of superlattices as a bulk devices, but in fact, the end result is in fact in terms of components! Just ask ourselves whether we use a big hunk of cement to do the job, or we use smaller blocks.
Superlattice, Photonic Crystal and Meta-materials I want to take this opportunity to make an important point how we learn and how we discover. I was working at Ohio State University, Antenna Lab., with my advisor Kirschbaum, on periodic loading of waveguides, which was in almost all respect, identical to today’s Metamaterials. I was to use the approach using solutions of Maxwell’s equations applying to a periodic structures, a ridged-waveguide with periodic cuts. Following the work of L. Lewin from Royal Radar Establishment, as early as 1947, or before, who placed identical spheres on a cubic lattice sites, obtaining variable refractive index, hot subject for RADARs. However, the approach is certainly identical to the development of Photonic Crystals, more than 40 years later by Yablonovitch.[17] Let us go into more detail regarding this. Lewin’s scheme was quickly improved by confining into one dimension, developing into periodic loading in wave-guides, shown to provide better control and repeatability. Anything along this line was quickly dominated by the defense industry. Within few years, serrated waveguides, periodic loading of a ridge waveguide came onto the scene for the control of phase by periodic loadings, quickly seized by DOD for focusing microwaves. However, this work eventually disappeared from R & D because of two reasons: (1) DOD in US classified that sort of work; but more importantly, (2) unlike superlattices, it is passive, requiring operation near some sort of resonance, ending up in high field breakdowns, unsuitable for high power microwave focusing systems, prevented this sort of meta-materials to play a significant role in electronic and optical devices. Actually power handling capacity of any devise is important consideration, including superlattices! I hid this work from Esaki because I did not want to confuse the issues, with principles involved close to superlattices, having man-made components with circuit representations, indistinguishable from today’s metamaterials. Kirschbaum, who was an expert in equivalent circuits, showed me how to use circuit approach while I was using field approach, referenced earlier by Collin and Vaillancourt: basically with distinction between the propagation k, along the direction of the periodic structure, applying Floquet’s expressions, called Bloch theorem in Solid State Physics, 6
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while in the transverse direction, fields are all matched in their common boundaries. Kirschbaum told me to measure the equivalent capacitance with dc voltage and current. I protested that capacitance, like any constitutive equation, is frequency dependent. He said, “Let me teach you something. Do you know why capacitance is a function of geometry? It is true because we have Avogadro-number of electrons, pushing each other by electrostatic repulsion until they got into all cracks and surfaces, in so doing, defining the geometry involved!” Now it is quite clear had I disclosed my work regarding the periodic loading of waveguides, Esaki would not push for it. Even if he did, his chances for success would be very low! On the other hands, without superlattices, I doubt very much photonic crystals would have been introduced. In a way metamaterials, although developed somewhat independently, most obviously took a ride on the over-whelming momentum developed in the field of superlattices. Superlattices did not lead to metamaterials. Nevertheless, superlattice did prepare the technical world for rapid introduction and development of metamaterials. Furthermore, the incorporation of man-made elements represented by circuit approach widely adopted today in metamaterials, in fact, was introduced many years ago! We have earlier touched on the active and passive systems, as represented by superlattices and metamaterials respectively. By applying a dc bias, superlattice, due to the NDC, becomes an active system such as oscillators, modulators, and ultimately, an amplifiers for signal generation as well as detection. It was pointed out in Section 1.5 of my book, where the response function and Bloch oscillations have been derived with an application of a combined dc and ac fields. [16] A dc field gives the gain factor as an amplifier, and an ac-field gives modulation as well as possible applications as modulator and ultimately as parametric amplifiers! One may ask how a dc-field can affect a typical metamaterials having a periodic array of elements such as circuits. Obviously a large metallic element in the form of the letter C cannot be affected by a dc voltage, however, when the number of electrons are few, a dcfield can shift the electron distribution and affecting the capacitance of such shape! Therefore, I am calling you to start applying a bias, ac or dc, to the elements of your metamaterials!
Raman and Cathodo-luminascence for alloy concentrations in GaAlAs At the beginning at IBM, we were trying to use optical absorption and emissions for calibration of alloy concentrations in III-V systems, such as what was done at BTL. However, we did not have traditions and experience in this sort of work. Leo invited H. Kawamura to work with us. Partly because Leo knew that I was fascinated by Raman scattering. As Kawamura told Esaki that he would like to work on Raman Scattering. And Leo knew that I asked for a Spexsystem for Raman. Leo told me that Kawamura was an important physicist in Japan. So now is my chance to work with Raman. Well, there were two things against us. First we do not have the budget for a SPEX-II system. Well I got one on loan from SPEX. But the greater problem is the discovery that Kawamura thought that I was familiar with Raman because I asked Esaki to allow me working on Raman, which I had never done! When Kawamura arrived. We went to G. Burns for help. Gerry said to his technician, “Ray and Kawamura, are blind leading the blind!” Six months later, we discovered something new in Raman Scattering, Disorder activated Raman Phonons in GaAlAs systems, published in Phys. Rev. Let.! Well we developed the use of Raman as calibration of the alloy systems, by having a sample with Al concentration varying from 0.1 to 7
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0.9 completely determined by X-ray and wet chemistry! This sample allowed us to have fast turn-around. Leroy was so happy that we were able to provide him half-a-day turn-around for the determination of composition x of the ternary alloy systems. Cathodo-luminescence is so simple to operate because unlike photo-luminescence, rarely were we involved in selection rule issues. Perhaps the only complain involves too much data; sometimes with mysterious data, even after the sample had been removed from the chamber! The First Metamorphosis of Superlattices – Resonant Tunneling via Quantum Wells After the success in reducing the structure to a single period, the birth of resonant tunneling through a single quantum well became reality. It came because we tried to show that the NDC was indeed result of Bloch oscillation. Well we were correct, but then, who needs Bloch Oscillations! Esaki and I were somewhat misled by the love of physics and the lack of understanding what is a real device. We did not understand that there is no need of bulk device. All electronic devices consist of input, active region of gain, or in general, region of interaction, followed by output. Therefore, the concept of QCL, quantum cascade laser is what the expert, like Capasso has come up with. [18] What is QCL, it is, like the injection laser, having input, active region, and output, all consist of QW or MQW, for quantum well, or multiple quantum well. You may ask why we still refer to most of these devices as superlattice. Well, it came from the original concept of superlattice, however, the main feature has changed. What remains consist of devices we can construct with quantum wells, and others, for example, I was involved in filing a patent with components consisting of Type II, however, not as a single unit of quantum devices, rather as multiple components, with InAs and GaSb based Type II or Type III ingredient, but separated. In essence, the patent involves structures quite different from single entity, as superlattices. In essence, what is involved consists of parts, each having a thin layer of a given materials, in contact with another thin layer of materials. What is the connection with the concept of a superlattice? Well, not quite! The commonality with superlattice consists of regions with which its phase of de Broglie electrons forms the essence of action in a given device. Perhaps we should invent a new term – PSQS for Phase Sensitive Quantum Structure, which have been around for quite a while.
Impact of Superlattices Let us first look at the impact of superlattice, e.g. from the standpoint of the introduction of the transistors. Although transistors, as lump-devices, have its place in the device world, the greater contribution to modern technology is the development of the monolithic IC’s in the form of MOSFET’s, introduced by Kahng, D. & Atalloa, M.M. [19] However, one wonders whether MOSFET would be invented without the introduction of transistors. When man-made semiconducting devices consist of dimensions less than the mean-free-path of electrons in solids, quantum wells and even quantum dots emerged. Thus the consequences of the introduction of superlattice led the way to quantum wells, and quantum dots, including MQW, especially involving Type-II superlattices, introduced by Esaki and Tsu as a possible way to move the point of inflection of the superlative closer to the zone center of the SL band structure such that NDC may be reached at a lower applied voltage. Well, it did not happen, yet something else emerged, new possibilities such as detectors operated in long-wavelength IR, LWIR and Mid-Wavelength 8
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IR, MWIR emerged. [20, 21, 22, 23] In particular, Type III superlattices as discussed, in addition to the appearance of new energy gaps, the increase with new conducting channel serving as new devices in IR detectors, [23], actually also serving as ITO and TCO [24], the overlapping of valence and conduction bands resulting in opening new gaps with transfer of electrons leading to a significant increase in carrier concentration for conduction processes in devices, without Coulomb scattering from dopants. We were very excited by the possibility of THz devices, via RTD. [25] Among some very interesting new possible applications of SL, with which taking the field of semiconducting devices to new frontiers, are device concepts with quantum dots and nano-science in general. [Chapters 8-12 of 16] The big surprises include new fundamental physics, for example, the behavior of the dielectric constant of quantum dots and the strange role of symmetry. [26]
The Role of Periodic Loading in the Development of Superlattices As pointed out earlier that the work of material loaded with small particles on a cubic lattice sites by L. Lewin, preceded superlattice by more than 20 years. [1, 2]. And the work on periodic loading of a ridged waveguide, one dimensional periodic loading, by Kirschbaum and Tsu, preceded superlative by 10 years. [5] What are the impacts of these earlier work on the development of super lattices and eventually, the metamaterials? I think my personal knowledge of these earlier works did help me to be guided into the correct theoretical understandings, mainly involving the use of Floquet’s theorem, and the 3D version, the Bloch theorem. For the one-dimensional periodic loading, Kirschbaum taught me how to develop a 1-D loading based on circuit approach so similar to the approach used for a vast majority of metamaterials. Since metamaterials developed from Photonic crystals [17], with periodic loading of circuit elements; and superlattices developed using periodic loading involving heterojunctions; both are intimately connected with Lewin’s original work, it is obvious from what is presented here, both super lattices and metamaterials were developed independently from earlier works. In particular, periodic loading of a ridged waveguide [5] succeeded in obtaining variation of refractive index at microwave frequencies from n = 0.3 to 1.9, sufficient for microwave applications as a new type of antenna systems. However, there is something very important, not known to most workers, including those presently claimed. My work on the ridged waveguide was sponsored by Sperry Gyroscope of Sperry Rand, which in turn was funded by DOD. When it was discovered that most of the wide range of refractive index traced to resonances: a slot in a ridge is represented by an impedance varying from 0 to ∞, the typical impedance of the so-called quarter-wave transformer. Basically a transmission line has an input impedance varying from 0 to ∞, in every quarter wave change in length! This feature constitutes the universal concepts of the circuit representations in periodically loaded structures. However, resonances always restrict power handling capability, therefore, there is no secret that Type-III superlatives developed into good IR detectors. However, if we were to ask for using as focusers, resonant systems hardly can handle high power without increasing the volume of interaction to lower the field strength. And that is the key position: How to design systems to avoid breakdowns with the least increase in the volume of interaction!
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Manuscript for Elsevier 18th International Conference on MBE, September 7-12, 2014, Flagstaff, AZ
Conclusions In my nearly 60 years of involvement in physical science with main objective of promoting man-made devices, I have publicly reminded the scientific community that Darwin’s survival of the fittest for biological species should be extended to human technology. Ideas are important, but thousands of technologists working to move ahead, outdoing each other in performance, is what propels our technology. As widely accepted in research and development involving superlattices, the subject is matured while its ramifications, represented by nanodevices, would propel the field of endeavor to new directions and importance in the quest for technology superiorities. There is something worthy of note in both superlattices as well as metamaterials: If circuit elements are to be incorporated in whatever geometrical forms, the materials must not be metals because of their fantastically low carrier life-time, instead, high mobility semiconductors with modulation doping, or with Type III superlattices to avoid high scattering from dopants! Lastly, when I was leaving Shanghai, my great uncle who was in his last days of an active life in promoting industry in China, said to me, “ I want you to remember the old Chinese saying: To succeed in new human task, one needs the right tool.”
List of References 1. Lewin, L. The Electrical Constants of Materials Loaded with Spherical Particles, Proc. IEEE-3, 94, 65-68 (1947) 2. Lewin, L. Advanced Theory of Waveguides, Iliffe & Sons Ltd. London, England (1951). 3. Brillouin, L. Wave Propagation in Periodic Structures, Dover Publications, Inc. New York, NY (1953) 4. R.E. Collin & R.M. Vaillancourt. Application of Rayleigh-Ritz Method …, IRE Transections, MTT-7, 177-184 (1957) 5. Kirschbaum, H.S. and Tsu, R., A Study of a Serrated Ridge Waveguide, IRE Transactions on Microwave Theory and Techniques MTT-7, 142-147 (1959) 6. Esaki, L. & Tsu, R. Superlattice and Negative Differential Conductivity in Semiconductors, IBM J. Res. Develop., 14, 62-65 (1970) 7. Esaki, L., Chang, L.L., Tsu, R., A one-dimensional Superlattice in Semiconductors, 12th International low Temperature Conf., Kyoto, 551-553, (1970) 8. Esaki, L., Chang, L. L., Howard, W., Rideout, L. Proc.11th International Conf. Phys. of Semiconductors, Warsaw Poland, p.431, (1972) 9. Gunn, J.B., Solid State Comm.1, 88 (1963) 10. R. Tsu, and L. Esaki, Tunneling in a finite Superlattice, Appl. Phys. Lett. Received March 1973, 22, 562-564, 1 June 1973. 11. Chang, L.L., Esaki, L, and Tsu, R, Resonant Tunneling in Semiconductor Double Barriers Appl. Phys. Lett. 24, 593-595, (1974). Received 18 March 1974, and appeared June, 1974. 12. Esaki, L. Nobel Lecture, 116-133, December 12, 1973, The Nobel Foundation 1974, also in Esaki, L., Long Journey into Tunneling, Science, 183, 1149-1155, Science (1974). 13. Dingle, R., Wiegmann, W.E., & Henry, C.H. Phys. Rev. Lett. 33, 827 (1974). 14. Esaki, L., Tsu, R., Superlattice and Negative Differential Conductivity in Semiconductors, IBM Research Note RC-2418, (1969) 15. Sai-Halacz, G.A., Tsu, R., and Esaki, L. Appl. Phys. Lett., 30, 651(1977). 10
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16. Tsu, Raphael, Superlattice to Nanoelectronics, Elsevier, ISBN 978-0-08-096813-1, 2nd edition, 2011, Chapter 1. 17. Yablonovitch, E., Phys. Rev. Lett. 58, 2059 (1987). 18. Faist, J. Capasso, F., Sivco, D.L. Sittori, C. Hutchinson, A.L. Cho, A.Y. Science 264, 533, (1994) 19. Kahng, D. & Atalloa, M.M. in IRE-AIEE Solid State Device Res. Conf. (CIT) Pittsburgh, PA, (1960) 20. Tsu, R. Proc. SPIE 8631, 863106 – 1-15(2013) 21. Zhang, Y.H. Appl. Phys. Lett. 66, 118 (1995) 22. Yang, R.Q. & Pei, S.S. J. Appl. Phys. 79, 8197 (1996) 23. Razeghi, M. Tech. of Quantum Devices, Spring, NY (2009) 24. Edwards, P. P., Porch, A., Jones, M. O., Morgan, D. V., Perks, R. M. Dalton Transactions 19: 2995–3002, (2004) 25. Sollner, T.C.L.G., Goodhue, W.D., Tennenwald, P.E., Parker, C.D., Peck, D.D. Appl. Phys. Lett. 43, 588 (1983). 26. Tsu, R. & LaFave, Jr. T, Role of Symmetry in Conductance, Capacitance, and Doping of Quantum Dots, Wonder of Nanotech. SPIE Press, Razeghi, Esaki & von Klitzing, (2013)
Acknowledgments I thank the organizing committee of MBE-2015 for inviting me to give this summary, which includes interesting materials probably unknown to most.
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