Nanostructures
HOW NATURE DOES IT

Nikolai N. Ledentsov

I'll now speak about the so-called semiconductor nanoheterostructures. Basically, these are the same double heterostructures (DHS) as the ones created by Dr. Alferov. The only difference is that their typical sizes and geometry are now different. The ideology of their manufacture and use has also considerably changed. The essential idea, however, which is to use two materials to create one single-crystal object, has remained the same.
The results, of which I'll speak in my lecture, have been mostly obtained in Prof. Alferov's laboratory. The lecture's main points are as follows:

Lecture Plan:

• Review of current developments in information technologies
• The role of heterostructures; methods of obtaining them
• "Quantum dots" - what they are and how they can be used
• Conceptual change in how crystals are grown: from man-made "super-lattices" to nanostructural self-organization
• Crystal surface patterns
• How nature solves problems she creates
• Crystal microcracks and dislocations is a source of opportunities for nanostructure and nanoepitaxy scientists and technologists
• Review of achievements and future prospects
• Conclusion: Traditional and new ways of looking at semiconductors compared; everything changed compared to old ways of looking at semiconductors
  

A Nobel Prize is not awarded just for fundamental research. It is given in recognition of the fact that a particular area of research is of importance for the whole of humanity. Its role is to enhance social progress. This is why we'll start by discussing what role semiconductors and semiconductor heterostructures play in modern industry worldwide.

Here I point out how the market of compound semiconductor devices, such as GaAs or InP, has been growing over the years. This market is almost wholly dominated by heterostructure-based devices. The fastest growth is taking place in two segments - integrated circuits and heterostructure lasers. Same segments dominate in present-day information technologies. That's why a Nobel Prize was awarded - because of the social significance of this work.

Prior to this two Nobel Prizes have been given for semiconductor hetero-structures. The winners were Klaus Von Klitzing for the Quantum Hall Effect and Horst Stormer for his discovery of composite fermions (Fractional Quantum Hall Effect). In the wider sense we can also count the 1973 Nobel Prize by Leo Esaki for tunneling in semiconductor because he was very actively working on electron tunneling in composite super-lattices he invented. Of course, the prize was primarily awarded for the tunnel diode based on heavily doped homo- p-n-junction in Ge (published in 1958). We must note that Frenkel and Ioffe in our Physical-Technical Institute studied tunneling in semi-conductor structures as early as 1931.

Two thirds of Leo Esaki's Nobel Prize Lecture were dedicated specifically to the tunneling effects in heterostructures: tunneling in 5-layer heterostructure and superlattices. He understood the importance of heterostructures in this area of research and applications. The next two prizes have been awarded to Klaus von Klitzing (1985) for Hall's Quantum Effect and to Laughlin, Stormer and Tsui (1998) for their work on Fractional Quantum Hall Effect. Their work mostly concentrated on semiconductor heterostructures, were all the fundamental research of electron transport and light and matter introduction was already done by Alferov.

In view of the strategic and generally recognized importance of the subject and previous three prizes one may wonder why this Nobel Prize has been waiting for the winner for such a long time. The explanation in part at least is probably that now, more than ever before, this work has acquired importance for the whole of humanity. Let's compare trends in various branches of modern industry.

As we see, the electronics market on the whole has been growing at the rate of 7% per year. This market has recently outpaced the entire automotive industry.

The silicon semiconductor industry, which, on average, grows by 15% annually, forms the core of this market. Semiconductor industry is currently dominated by silicon and silicon-germanium heterostructures. Most of all by silicon-based metal oxide semiconductor structures.
Now let's compare these rates of growth with those of А3В5 heterostructures. The heterolaser segment has been growing 34% per year on the average for the last two decades. In peak years these rates reached 100% or even higher.
Presently the heterolaser market alone is a large as the entire semiconductor industry back in 1980. If we extrapolate these figures to the time when many of the young people present here start their own scientific or engineering careers, we will see simply fantastic numbers that can be compared to the total present size of the semiconductor market.
It is no accident then that this happy occasion for all of us, for our Institute, and for our country took place when such dynamic development of this strategically important area has become obvious and generally recognized.

Semiconductor lasers are presently used in two major market segments:

Telecommunications (the Internet) make up 70% of the total laser market. These are lasers that use mostly InP substrate and emit light in the 1.3 to 1.5 microns range, which corresponds to the transparency of optical fiber.
Optical storage and recording (presently these are red lasers). Here short wavelengths are required - the shorter the better. Presently we actively work on ultraviolet lasers because the shorter the wavelength the more information you can record on a compact disk.

Semiconductor heterostructures are obtained by two main methods and two types of equipment. These both can be successfully used to create nanoheterostructures.

1. Vapor phase epitaxy from metal-organic compounds (MOVPE).
Several substrate wafers (GaAs, sapphire etc.) are placed into the reactor of a rather complex unit. These wafers are thin single crystal slices. A chemically complex compound is delivered to them as a gas. This compound reacts with single crystal substrate maintained at high temperature. Gas flow can be switched to expose the surface to another gas. The result is a layer by layer formation of a semiconductor compound. Layers of molecules form on top of each other. This method is used, for instance, for growing GaN-bases wide band-gap semiconductors. Some examples: structures for the manufacturing of blue-green LED's or short-wave lasers for the new-generation CD-ROM's I've just mentioned.

2.The other method is MBE (Molecular Beam Epitaxy). It uses an ultra high-vacuum chamber that can accommodate a large number of substrate wafers at a time. The molecular beam is directed towards these wafers from special crucibles. Special shutters may interrupt this beam. Same as with the other method, we get a semiconductor or a multi-layered structure forming on the substrate surface.

Presently the quantities of compound semiconductor epitaxial structures (measured in square inches) produced by both technologies are about equal (one million). Sales have grown 5-fold in the last 5 years.

We often criticize our politicians for their failure to understand what needs to be done for the country, and where the big money is. To be fair, other countries have the same problem. The entire Europe presently finds itself in a predicament (see Slide 7). It produces only 2% of world's output of MBE epitaxial wafers and 3% of world's MOCVD (GPE MOC) epitaxial wafers. We are not the only one to fail in using our own inventions. It is a problem of the entire Europe, which made a huge contribution to the development of semiconductor physics and technology. It may be noted though that, as of recent, some positive trends can be seen also in Europe.

Before I move on to the subject of quantum dots I'd like to say a few words on double heterostructures (DHS) in general, and the differences between hetero and homostructures.

A heterostructure is essentially a single crystal that is composed of chemically different layers. For example, a layer of a different material can be added into a matrix material in such a way that the boundaries between the layer and the matrix are free of defects. Some time ago it was considered an impossible task. The issue was if the boundary itself could cause undesirable effects. It was also thought that materials with different properties, such as color of emitted light, always have different crystal lattices, i.e. different size of the crystal unit, thus making any attempt to join them bound to produce cracks and other defects. It was also thought that it would be hard to make the boundary sufficiently sharp and clear, and that most of the expected advantages would for this reason be almost entirely lost. It was also thought that microparticles consisting of parasite compounds would form at the boundary. But Alferov and his colleagues have demonstrated that all these problems can be avoided, and that the expected advantages of "ideal" heterostructures can be obtained and implemented in practice. These properties include the possibility of fixing charged particles in a layer of a narrow band-gap material, of generating the waveguide effect by this layer, of obtaining ultrahigh densities of charged particles in a narrow layer without resorting to strong doping of the entire structure, and much more.

In order to understand how semiconductor heterostructures and hetetostructure-based lasers work, we first need to look at the structure of the crystal that makes up this heterostructure. Let's begin with the most fundamental thing, which is the quantum nature of the crystal. What is it?

If you look at a thin gasoline film on a water puddle you will notice different colors. Standing waves form in a thin layer of gasoline. This is not the color of the film itself; this is the color of reflected light. The intensity of the light reflected by the film of a given thickness is different for different colors (wavelengths) within the sun spectrum. This effect is caused by interference of light and is related to its wave nature. If several half-wavelengths exactly fit to the film thickness - the light reflected from the boundary between the gasoline film and the water comes back "in phase" and adds to the light, reflected by the air-gasoline surface. In the opposite case, the reflection can be suppressed. This reflection suppression effect, by the way, is used in photocameras to increase transparency of the lenses. The given thickness of the gasoline film gives the particular wavelength (color) when the reflected light has maximum intensity. The thickness of the layer varies, so standing waves corresponding to different colors form in the layer. If we can put several layers of two liquids without mixing them - we may obtain a very good reflection coefficient for a particular wavelength or a range of wavelengths. This, for example, is the basis of interference mirrors in many optical devices.
So, an electron, including a free electron in a crystal, also has wave properties, which is one the fundamental laws of quantum mechanics.

An electron in a potential well formed by the attractive potential of the positively charged atomic nucleus behaves similarly to light. It forms standing waves within this potential well. The energy spectrum of the electron becomes discrete as opposed to a continuous spectrum of energy states in free space. In a solid body, however, the density of atoms is very high, and electron levels interact, and this interaction results in energy bands rather then levels. The last band occupied by electrons is called "valence band". Valence band is separated by "forbidden" gap from the nearest allowed energy band, which is not occupied by electrons. This forbidden gap originates from discrete energy spectrum of single atoms, where levels are separated by the forbidden states. Here is an illustration. Suppose we have a single level in a free atom [left side of the slide]. If we hit this atom with an electron or a photon, the electron could move from the filled shell to the free outer level, or, as we say, become excited. When the electron returns, it emits a quantum of light. That is why gas atoms emit light of a precise wavelength when electric current is applied. In a solid state, however, we have wide energy bands instead of discrete levels, but the principle of electrons becoming excited, and coming back to the empty site emitting photons (quanta of light) is all the same [second picture down on the slide]. Doping of crystal with foreign atoms may generate electrons that are loosely attached to the crystal lattice. At final temperatures we get free electrons in the crystal, and these electrons can move in the electric field. We also have a positive charge on a site, which lost its electron. Or one may do the reverse and use doping to create traps for valent electrons, thus creating positively charged electron-free states which are weakly bound to the negatively-charged core caused by impurity atom, which attracted valence band electron. The crystal on the whole always remains electrically neutral. These positively charged "holes" are pulled to the trap charged with captured electrons, but when the crystal is heated they are released because of their collisions with vibrating crystal lattice (phonons). Doping thus helps obtaining either electron or hole conductivity. So now, when you apply electric field to the crystal, you can make electrons move towards holes, and holes towards electrons. They meet, and free electrons fill the available holes thus emitting quanta of light. The color of the emitted light is determined by the energy difference between the bands of allowed states (the conduction and the and valence band) through which electrons and holes move. So you can make red, blue, green, or ultraviolet light-emitting diodes (LED's). Unfortunately, the electrons and holes run in opposite directions and with different velocities, and light is also emitted in all directions. To construct a laser, however, you need to have an area with a very high concentration of electrons and holes, and somehow keep light from leaving that region. So, no effective laser can be created based on homo-p-n junction, unless you switch to use heterostructures. The situation, indeed, changed with the appearance of heterostructures [second drawing from the bottom]. Now you have two materials with different band-gaps. Your electrons and holes accumulate in a potential box, and if the box has walls thick enough, they run around inside as quasi-particles. They can't escape in the neighboring layers, as there is no available states in the forbidden gap. Now all the charged particles are in a narrow layer of material with certain properties. This material also acts as an optical confinement layer - trap for photons [the lower figure], the light is localized in the plane of the layer, because of a higher refraction coefficient of the narrow band-gap layer, similar to photons trapped in water strings. The latter effect is beautifully seen for illuminated fountains in nighttime. These two effects of carrier and light confinement allow us to drastically improving laser device performance.

Two types of lasers are presently used:

1. Conventional, or stripe cavity lasers. For example, as this drawing shows, the p-contact to a layer with hole conductivity is placed on the top, and the doped substrate doped with donor impurity, having an electron conductivity is at the bottom. Between them we have an active medium, and light moves in this thin layer and leaves the system though facets that partly reflect the light back and thus act as so-called Fabry-Perot resonators. Feedback is essential for the laser to work. You need some of the light to be reflected and run back and forth in the crystal to cause chain reaction of photon multiplication. This way the same quantum state is established for the light. Lasing occurs.

Lasers have huge advantages over LED's. These advantages include greater power (up to 12Watts while the output facet aperture is only 0.1mm wide) and high power density at the exit facet (up to 40MWatts/cm2). These "edge-emitting" lasers can be created on different substrates, with a wade choice of materials, and so on. The problem is related to a narrow width of the waveguide layer, typically used in most of the commercially available devices. Small width causes self-diffraction of light at the output aperture, and very broad angular distribution of the laser beam. You need a special lens to correct this effect. Another problem is astigmatism - beam divergence is different for the in-plane direction, where it is small, as the stripe with is typically large (above 3 microns), and for the perpendicular to p-n junction direction, where it is large, as the waveguide width is about light-wave in the crystal (0.1 - 0.5 µm) to keep stable, so called "single mode" device operation.

2. Vertical cavity lasers. Another type of laser geometry is when light goes up perpendicular to the p-n junction. The physics is the same as in the case of stripe lasers, if we imagine that we put them on top of the back facet. Mirrors in this case, as a rule, are of multilayered interference type, with nearly 100% reflectance. You need mirrors like that in order to compensate for a very small length of the vertical resonator and small light amplification during each single passage of the photon through the resonator.

Vertical cavity lasers may be very small (several micrometers). They have a low threshold current, and very good beam quality, with narrow beam divergence, as the output aperture can be made of rather large size (3-15 µm). They can easily be made of a single-mode variety, when only one quantum state of light participates in laser generation. Vertical lasers are characterized by good temperature stability of the threshold current and emitted wavelength, which is simply defined by the thickness of the cavity (remember standing waves in a gasoline film?). Further, they can be used to create complex optoelectronic integrated circuits bases on one crystal. Their small size makes them cheap. They do not consume much power. The market for such lasers is growing at the rate of 200% annually. They have only one disadvantage: only GaAs-based lasers are commercially available. They have an ideal heterocouple for interference mirrors - AlAs with a refractive index greatly different from that of GaAs. At the same time, telecommunications require wavelengths of about 1.3 and 1.5 microns, which requests manufacturing active medium that emits in that range only on InP substrate.

Such is the current situation with lasers. This state of affairs is usually just accepted because you can't jump higher than the ceiling. So let's somehow get by, most people say.

The situation is, however, starting to change in a very significant way:

Here I am showing a diagram from the Opto & Laser Europe journal, May 2000 issue, entitled "Quantum Dots Could Be Set For A Quantum Leap". Its cover announces, "Quantum dots against quantum wells - make your bets now". On this diagram the author of the article show the dynamics of the threshold current density, which is the most important characteristic in semiconductor lasers. Threshold current density is how much current is to be pumped into the device of a given area for it to stop working as a heater and start efficiently emitting light. Before laser generation starts, 99% of all energy is converted into heat. After laser generation starts, however, all that is above the threshold current density efficiently turns into light. If you want your device to be more than merely an electric iron but to produce light, you try hard to lower the threshold current density.

The main stages in laser progress are as follows. 1962-63 - appearance of lasers based on p-n junction. They had giant threshold current densities and would make excellent electric irons.

Of course, as Zhores Ivanovich used to say paraphrasing famous poet Mayakovsky, "it is not important whether you use steam loco's or cigarette butts to show that two by two makes four". Laser generation is laser generation. Still, in a specific situation facing a particular person, whether you have a steam locomotive or a cigarette butt does make a difference. So real lasers of value appeared only after the concept of double heterostructure came about. Priority patent, dated March 1963, was issued to Alferov and Kazarinov. Literally a few weeks later Herbert Kroemer, the second Nobel Prize winner for semiconductor heterostructures, sent in his article. As I already said, at first no one would take heterostructures seriously. Nevertheless, Zhores Ivanovich with his group have been actively working in that direction. Their work resulted, in 1966, in the first double heterostructure (DHS) laser that would work at low temperatures. It used the GaAs/GaAsP heterostructure that had problems of mismatch between crystal lattices and thus developed cracks. This problem prevented practical implementation of light generation with low threshold current at room temperatures. But very soon, in 1967, the GaAs/GaAlAs system was discovered, and in 1968 Alferov and others built the first low-threshold laser of 4кА/см2 current density. In 1970 Zhores Ivanovich visits America. Leading scientists at Bell (which made the first transistor) went into a shock. Hayashi, one of the key participants of the laser project at Bell, wrote in his notes, published in the IEEE Transaction on Electron Devices (1994), that he was overwhelmed with Alferov's results. Following Alferov's visit, Bell doubled its efforts.

Many times some people tried convincing me in America that Bell was the first one in reality but the publication was simply stolen or something like that. I always just refer to that article by Hayashi, which relieves me from having to prove the obvious. In 1970 (Alferov and colleagues once again were first) continuous laser generation at room temperature at an even lower threshold current density of 1kA/cm2 was demonstrated. Similar results were obtained a bit later at Bell. However, after that there was no noticeable progress in further lowering the threshold current in double heterostructure lasers.

The next stage of laser development involves so called "quantum-size" effects in thin layers. Up to now we assumed that the area to which charged particles are confined in the narrow band gap is still fairly wide.

If the potential box is thin, then the electron will be subjected to interference, like light in a thin gasoline layer, we usually refer to. There appear the so-called size quantizaiton subbands. But noticeable quantization only appears at the thickness of 10 manometers, not fractions of microns or even several microns, as is the case with light interference. As early as 1970 Zhores Ivanovich synthesized his first heterostructure with ultra-thin layers, and quantum size effects could be observed in these structures. Unfortunately, technologies that allow precise growth of extra-thin layers are not being developed in the Soviet Union. Heterostructures have been obtained in the Physical-Technical Institute using liquid or chloride vapor phase epitaxy while to get thin layers you need molecular beam epitaxy or gas phase epitaxy from metal-organic compounds. Zhores Ivanovich has been actively working on making these technologies available in the Soviet Union, and they soon did appear. Production has now stopped, but what has been made is now used all over the country. We have and actively employ these units in our laboratory. Also, Zhores Ivanovich has succeeded in convincing the functionaries to buy several units abroad. We used and continue intensely using these units. While we are catching up, Bell is starting the use of layers thin enough for quantum effects in lasers, and these layers are reliable and consistently produced. First laser with quantum-size layers has been made. Initially its inventors struggled with very high threshold current density. Scientists and engineers working with conventional heterostructure lasers were laughing the new ones off: why all the fuss when it is clear the idea would not work in practice?

I recall a seminar back in 1980 where I was present as a student. It was a presentation of the group headed by Nick Holonyak Jr. The subject was quantum-sized heterostructures. Comments from the audience: such structure will not generate much power, electrons will not be able to get into a layer that thin, the role of states at hetero-boundary will be too important, etc. At the end of the seminar Zhores Ivanovich concludes: "In several years our laboratory will be working mostly with quantum-size heterostructures". Perhaps some "veterans" don't recall it, but I remember very well the hum of voices in the lecture hall and how people started looking at each other and make joking remarks to the effect that "Our chief is sort of out of it..". It is remarkable that the majority of highly qualified laboratory staff failed to understand the idea. Really, why change something if things are all right as they are, and if we know our heterostructures well. Why should we go where threshold currents are so high?

You cannot, however, stop the progress. Gradually the threshold values in quantum-size layer (or "quantum well") lasers went down. First they were higher than in DHL, but the rate of change was quite high. In 1982 Bell demonstrates the first laser that is fundamentally superior to lasers based on double heterostructures. In several years the industry switched to heterolasers with quantum-well active area. By that time MBE and MOVPE available to us have improved. Here, at the Physical-Technical Institute, the lab headed by Alferov succeeded in exceeding the record threshold current density for heterolasers by obtaining the value of about 43А/cm2. This was 10-20 times lower than in DHS lasers. I was happy to be involved in this work.

Then again a period of relative stagnation followed. There was no major progress since the end of 80-ies - beginning of 90-ies period. Then the Physical-Technical Institute has started, perhaps before anyone else in the world, research on nanoheterostructures that form by self-organization. The aim was to obtain orderly arrays of nanofacets or nanoislets from submonolayers, orderly arrays of nonoislets, or quantum dots (I'll tell you in a minute what quantum dots are) in systems where lattice parameters greatly differ. Such structures, free of defects, have been successfully created.

We were first in quantum dot lasers. In 1993 we made quantum dot lasers with average threshold current values of several kiloamperes per square centimeter. Of course, it was much worse than records for quantum well heterolasers. And we were once again asked why all of that was necessary. Skeptics told us that nothing better than a quantum well laser could possibly be made. They predicted that we would get neither higher power, nor speed, nor stability against degradation. Despite these skeptical prediction we've been able to quickly solve all of these problems and lower the threshold current density to values on part with the best ultra-thin layer lasers. Presently the record threshold current density of quantum dot lasers is only 13A/cm2, which is 3-4 times better than the best parameters obtained for quantum well lasers.

Now let's go back to the fundamental nature of three-dimensional (3D) nano-inclusions of narrow band-gap material into a single-crystalline matrix, known as quantum dots. As I already mentioned, the electron in an atom is in a potential well created by the positively charged nucleus. Since the electron has wave properties, discrete energy levels form, which are separated by forbidden zones. In essence, an electron in a crystal remembers but little about the discrete nature of the atomic electron spectrum. In the conduction band the electron is able to freely move within the crystal as a quasi-particle that can have a certain "effective mass" that is usually less than the mass of the electron in vacuum. The widths of the absorption spectrum of crystals are now in the order of one or several electron volts instead of fractions of micro-electron-volts as in the case of a single atom. What would happen if we were to put ideal walls around a very small volume of the crystal? Then electron interference would take place on the walls of this potential box and, as in the case of quantization of a free electron in the electric potential of the nucleus, we'd return to a fully discrete spectrum that is typical of a single atom. This is different from a case of quantum well, where continuous motion of electron is possible in the direction parallel to the layer interfaces and continuum of allowed states exists even in case of strong size quantization along one axis.

One often hears that this "atomic-like" spectrum of a 3D nanoinclusion can be expected only for an ideal case, and that a discrete atom-like spectrum in a nano-inclusion or quantum dot cannot be achieved in practice because boundaries are not ideal, impurities are present etc. It was asserted that all the potential advantages of quantum dot lasers are mere speculations. In reality, however, all the basic qualities of quantum dot (QD) and quantum dot lasers have been experimentally confirmed. We have, for example, demonstrated that quantum dots emit monochrome spectrum and display no continuity of states that is typical for ultrathin layers. We've shown that the times of radiative recombination match the theoretically predicted values for ideal 3D-quantized structures, or "quantum dots", etc. Fundamental properties of quantum dots are now being actively researched throughout the world. Their properties agree with the fundamental laws of quantum physics of which Zhores Ivanovich spoke in his introduction.

But why have quantum dot lasers only appeared in the 90's? Why haven't they come around earlier? The idea itself was expressed a long time ago. When Dingle and Henry of Bell proposed, in 1975, to use quantum effects in lasers, their patent was not limited to just ultrathin layers, but considered also size quantization in several directions. In the 80's some scientists in both America and Japan understood that, in principal, it would be great to create a quantum dot laser. It was not possible, however, to make such a laser because the traditional growth ideology accepted at the time assumed a layer-by-layer precipitation of material. In manufacturing flat nanostructures people went the same way they did when manufacturing transistors, which is lithography. Generally, both in growth and processing, the dominating approach was that of "man is making a structure". The man grows a structure, produces a layer, covers it with another layer, and so on. It was like painting the body of a Mercedes, where up to 20 layers of paint are used. One layer is one color, another layer is another color, one layer has one function, and another layer has another function. Painting is done layer by layer. So how do you make a quantum dot? How do you make a nano-object when its size got to be very small in all dimensions? Clearly, you need to make scratches on that surface, if the owner permits. If you make a real fine distance between scratches you get a nano-object. The trick is to stop soon enough. That's what people did. They etched multi-layered structures with ion beams trying to make very fine scratches and thus create quantum dots. They've spent billions of dollars doing that, but that turned out to be a no-go for lasers. True, this approach took lithography to its limits and allowed researches to accumulate experience. This is very useful, but no quantum dot laser could be made by this method, as the side surfaces of the quantum dot were damaged. The fabrication process was also very costly hindering any practical applications.

Progress in the area of quantum dots was based on a conceptual shift away from the approach described above. It become clear that one needs not oppose nature but study nature, accept her, and simply do what nature wants. Nature in fact wants to create nano-objects. The only thing that she herself wants to determine their sizes, densities and relative positions. There is, for example, such a phenomenon as spontaneous nano-faceting on crystal surface. You take a flat crystal surface with a certain crystallographic orientation, anneal it, and all of a sudden it transforms into an accordion-like structure consisting of nano-facets. This structure has a regular period, nanofacet heights are uniform, and elements show a height level of ordering. Or you take a solid solution and anneal it, or grow it under certain conditions. When you look at it from the top through an electron microscope, you see an ordered pattern of nano-areas of different composition, and these areas are of the same size. Or you deposit a sub-monolayer of one material onto another, and you get islets of a very regular shape and size. And, finally, if you deposit onto a crystal lattice a material with different lattice parameters you can also get, under certain condition, nano-hillocks. These hillocks are at this time most widely used in quantum dot lasers.

Generally speaking, the phenomenon of spontaneous formation of nano-islets has been known for a long time. Most researchers, however, did not believe that such structures could be free of defects and thus usable in devices. Let's go back to our Mercedes example. Here is how people used to look at the process: you paint your Mercedes, and all of a sudden this paint starts forming bubbles or flaking off. This, of course, is bad.

What is important is not just that the islets or hillocks form spontaneously, but that these nano-structures form in an orderly and defect-free manner.

Our achievement is that we tried to understand the processes of nanostructure formation scientifically. We've been researching the physics of this phenomenon, we've conducted a huge number of crystal growth experiments, heated and cooled the nano-islets before completing their growth, and so on. As a result we've succeeded in forming nanostructures of the required characteristics. We made nanostructures that are defect-free, very small, and closely spaced, which is required for their use in devices. All that was a result of comprehensive research. Their growth, the study of their optical properties, structural research, post-growth technology - all these have mutually supplement each other and allowed creating nanostructures of the required quality.

There are several possible epitaxy mechanisms. One is layer growth, which is most commonly used for making traditional layered heterostructures (the Frank-van der Merwe process). Such growth takes place if the sum of surface energy of precipitated layer and hetero-interface is less than the surface energy of the substrate. The surface is said to be wetted with precipitated material. There also is the Volmer-Weber method, when the precipitated material forms three-dimensional crystals on the surface. That is, it does not wet the substrate. This would happen if you painted your Mercedes without first degreasing the surface. You get paint assembling into droplets and little balls. Bad, right? That's exactly what people thought. Finally, there is the Stranski-Krastanow growth mechanism. Incidentally, Volmer was a professor at the Technical University in Berlin that at the time was called the Technical High School of Charlottenburg, and Bulgarian scientist Ivan Stranski became his successor. If growth is taking place by the Stranski-Krastanow mechanism, you first get a homogeneous film of the deposited material and then three-dimensional small islands form on this layer. That is, the deposited material first wets the surface. Why do the islets form? The explanation is the difference in the crystal lattice parameters. Imagine two mattresses. One has large and another has small sections. You take the large-sectioned mattress and try to stretch it and attach it with strings to the one with small sections. If springs are strong and strings are weak, the sections will break apart and the upper mattress will not stay attached. That's an illustration of the Volmer-Weber growth mechanism. If the strings are strong, we have an illustration of wetting. The sections would stay in place, but the whole system may bend or form swellings. This happens when crystal lattices of deposit and substrate are different. You might succeed in putting on a thin layer, but then the material will form islets that bend into vacuum. If this islets or swells are of very different sizes and have defects, then such a system is not usable for making good semiconductor devices.

Fortunately, sometimes these swellings happen to have a natural order that can be described in terms of nanoparameters. For example, GaAs has smaller sections than InAs. First you put InAs onto gallium arsenide. You succeed because the ties are strong enough to hold a flat layer of InAs atoms, but when you add more InAs layers, the full elastic energy grows until the ties start breaking. Atoms partly break free, and when a certain final temperature is reached we get a partial redistribution of material with the formation of three-dimensional islets.

Once the islet is formed, the InAs crystal lattice straightens out, and its relaxation releases energy. Then we once again cover these islets with gallium arsenide or other wide band-gap material, so we get these interesting quantum dots, indium arsenide within the gallium arsenide matrix. So now our devices are based not on layers, but on such neat densely located points. Here I am showing a transmission electron microscopy image of the structure from the sample surface side. What a surprise: you see a certain order, and islands have a characteristic size, which is identical within the error of measurement. This is exactly what you need for your device. You can get exactly the sizes and densities you require for a specific practical application. Of course, all the conditions - temperature, precipitation speed, atom streams etc. - need to be just right. We found the right conditions and thus succeeded in building the first quantum dot lasers.

Not all was as simple as it sounds now. There are many unsuitable growth conditions that result in defects. When you study islet formation, you see that under certain conditions the same amount of precipitated InAs results in the formation of ordered dots, while under other conditions these islets by some reason stick together, their uniformity is distorted, defects are concentrated, and you get large objects of some sort that have no practical use but instead result in the degradation of device quality. Overcoming undesirable effects is a science in itself. Our greatest achievement, I think, is that we figure out the main laws of nanoepitaxy and learned how the processes of defect formation can be managed. The key factor, as we found out, is not only the lowering of the elastic energy during islet formation, but change in the surface energy related to their elastic relaxation. In this figure elastic energy is represented by color. Violet is zero deformation and red is maximal tension. Here you see GaAs that plays the role of the lower mattress. This "multilayer" mattress has no internal stress in its thickness because it is big. The upper mattress that you stretch over the first one is swollen. You see that there is no tension at swollen locations, so these areas are shown in violet. It is obvious why the swelling took place. If you take an eraser and squeeze it, it bulges and tries to break free, right? It bends because of the relaxation of elastic energy. But it can also break if bending is too sharp. If too large of an islet forms, it breaks, which is very bad. What can keep a large islet from forming? We discovered that it is surface energy. You can get ordered systems of nano-islets only when the surface energy of each nano-islet is lower than the surface energy of the wetting layer it occupies. Then the islets themselves act as a wetting layer and try to fill as much of the surface as they can. The smaller and more numerous they are, the more effective is the process of filling the substrate surface. Surface energy may become lower despite greater area that is a result of the three-dimensional shape of the islets. It is now a totally different surface. It is a crystallite surface with no elastic strain that was present in the flat wetting layer. Nor can an islet be very small. There is an optimal size for these islets. A single atom located on the surface is energetically expensive because broken bonds sticking from all sides make it a radical that tries to form a surface cluster in order to use up at least some of the bonds. A precise calculation would tell us what the optimal islet size is in a system of certain parameters (surface energy, chemical composition, and disparity between lattices, temperature, and so on).

So we've investigated all the main factors and found good growth conditions. Once again I want to emphasize that we let self-organization take place. Strictly speaking we did nothing other than letting the material precipitate. Nature took care of the rest. Our aim was to understand and apply natural phenomena. When, for example, we precipitate two InAs monolayers, we get small dots, but with four monolayers we get larger islets of more consistent size than in the case of small dots. There is a size beyond which the islets wouldn't grow under optimal growth conditions. If you deposit two monolayers but wait awhile, you'll get islets of the greatest possible size. If, however, you wait for too long, you start getting defects, because thermal fluctuations may statistically lead to processes of defect formation. This is the sort of research we did to learn about the nature of these islets and conditions required for their growth. Here I'm showing the effect of temperature on islet formation. Lower temperature results in narrow, taller and denser placed islets or quantum dots. Higher temperature results in shorter and wider dots that are also less concentrated. You also get a higher concentration of adsorbed atoms of indium on the surface and thus greater thickness of the effective "wetting layer" when putting the top layer on. Also, higher temperature results in more defects: large islets, which have dislocations and micro-cracks, as statistical size fluctuations per time unit become more probable.

Here, please notice that many of the pictures display defects that are highly undesirable for any device.
What else can I show you? You can play with nature another way.

Here are dots formed at low temperature (450 degrees centigrade). Here are dots grown at 500 degrees. And here are dots precipitated at 500, but substrate was then cooled to 450 degrees. Then your dot is high and not quite as wide as that grown at 500oC. Plus you get a higher concentration of dots. Dots formed at 500 and then cooled look more like 450 than 500-degree dots. So, the process of dot formation is partly reversible. Here are, in very general terms, the leverages natural properties of materials give you.

Of course, while the nature does it for you, you need to understand what it is she is doing in order for both man and nature to create the required structure. Sometimes it is hard to understand nature. In this case you proceed empirically. Let me tell you of one totally unexpected effect we've stumbled upon. When substrate temperature is really low, quantum dots all of a sudden start spontaneously forming some sort of a chain. These chains are either uni- or two-dimensional. That is, you get a densely packed crystal made of nano-islets on the surface of the substrate crystal. Electrons and holes in different places of such a quasi-crystal are tied to each other, which gives you a way to drastically alter the properties of the material including, of course, the wavelength it emits. Your emission is no longer generated by just a single dot, but by a crystallite formed by a cluster of dots, thus allowing you to move into the 1.4-1.7 micrometer range. This is of strategic importance in telecommunications.

And now an interesting example for young men. When you grow and then close one quantum dot, its strain forms a strain field on the surface above it, so the next quantum dot you form in the same cycle can be located exactly over the first one. So you can grow beads from quantum dots, and these beads are held by an invisible vertical string. Beautiful beads to present to your girls. Under other conditions, when the separating layers are thicker, strain fields originating from several dots interact, and the islets shift sideways. So girls can grow chessboard patterns for their young men.

Go ahead, do it, nature allows you all that, but you need first to study her and understand what she wants, and cooperate with her.

Here is another example of the chessboard pattern forming at certain thicknesses for submonolayer precipitates of CdSe in the ZnSe matrix.
Here is one more example that turned out very fortunate for the use in devices. You precipitate very little of the material, form a dense mass of many small islets, and then cover them with a solid solution of InGaAs, which is composed molecules of both InAs quantum dot and GaAs substrate.If you use this process, InAs molecules preferentially precipitate where you have these InAs nano-islets because this is more energetically advantageous for them because of elastic relaxation. On the other hand, GaAs is pushed away from a quantum dot with other lattice parameters. You can gradually change the composition and size of quantum dots. Here you see islets that are simply covered with GaAs. These are covered with a solid solution of InGaAs. Two major differences here. The conclusion is that you can get nearly all you want when you know what the nature wants even if in most general terms.

Self-organization also happens in the other direction.

As I've shown you on many pictures already, defects prevent us from being completely happy. We get these huge ugly islets that crack, thus spoiling our plans and not allowing us to build our devices of the quality we want. As I said before, we can select growth conditions at which the islets wouldn't form. Yes, you can do that. Still, the bigger the quantum dot we want, the more likely it is to crack. And it will crack for the simple reason that it is big. Yet, for many practical applications the big dots are of the greatest value! The question is: can we fix defects after they form? And the answer is yes! If you cover your islets with a thin layer of GaAs, it will cover the little ones, but not the large defective islets. A large defective dot is taller than a good one. Even if it is not taller, its lattice parameters are very different from GaAs, and GaAs will be repelled from this region. Then you raise your temperature and this InAs dot effectively evaporates, leaving just an empty sport in its place. GaAs has good thermal stability, and dots that are covered by GaAs remain. If, after such a procedure, you overgrow your temperature-etched structure with gallium arsenide, you will be left with defect-free quantum dots. There will be no clusters left. Here I am showing two transmission electron spectroscopy images. Here is the structure before the defective dots have been evaporated. Here it is after evaporation. As you see, everything is exactly as we want in the second example. One can get a laser.

One more case. At the beginning we spoke of the early heterolasers that used rather thick layers with different lattice constants and couldn't work at room temperature because of crystal defects, or dislocations. The first lasers were built by Zhores Ivanovich and his colleagues in 1966 using the GaAs/GaAsP system. This system has mismatched lattice parameters. Dislocations form!. Cracking crystal is a disaster for a laser. So that's why no heterolaser that works at room temperature could be made in 1966, and another two years had to pass till the AlGaAs-GaAs system, where lattice parameters accidentally happened to match, has been developed. But a laser could have been made in 1966! Using self-organization, of course! Now, when we understand the physics of self-organization, we say OK, so we have a layer that has a different lattice pattern than the substrate. So the layer cracks. Let's say it is InGaAs. Let's say we have a lot of cracks. So we have it on a GaAs substrate. At the places of cracks our material has accepted lattice parameters of the InGaAs, broken rubber is not strained anymore, that it should have with no tension. But patches of InGaAs that are distant from dislocations still have some tension left, and they have lattice parameters of GaAs if you look from the top. They are away from the boundary, where the material may relax. Now let us deposit a layer of AlAs. Of course it will settle where lattice parameters are closer to its own because it does not want to bulge like a mattress. It will simply settle where it is most comfortable, where the lattice parameters are closer to its own, farther away from dislocations. And now you raise temperature, and areas not covered by AlAs evaporate while those protected by AlAs remain. Aluminum arsenide has great thermal stability. It does not evaporate. It is like a cover on the surface of a wet stove. Let's say you make your stove wet and put pot covers on it, and turn the stove on. Water will stay for some time under the lids, but it will very soon evaporate where it is not protected. So when you raise your temperature, InGaAs stays where it is protected by AlAs. Then you put some more material on to cover the evaporated areas. The end result is that you selectively remove all defects from your structure while leaving the defect-free areas covered by AlAs. So the intensity of luminescence increases four orders of magnitude. Another advantage, you can formed nano-pedestals for further growth on top of them - and nanoepitaxy is a very important direction in modern physics. It is when you grow things on very small pedestals. But they are usually prepared by lithography, which is expensive. But with this approach they can be made directly in the technological unit. To be more precise, nature herself makes them. This idea works - here you see InGaAs domains in cross-section, and here you see that a dislocation was somewhere in this area, the layer broke, and mushroom-shaped domains formed. We then healed the structure, and not a single defect is left!

Now you are experts in self-organization, and we can move on to applications in devices. This is intended mostly as an illustration, and I will not speak of it in great detail. This is not the main point of this lecture.

As I mentioned in the beginning, 1.3 to 1.55 micrometers is the most technologically important range in lasers. This range makes up 70% of the lasers market. They are presently grown on the InP substrate because up to recently it was necessary to make sure the emitting wavelength agrees with substrate parameters. I'd say that the InP substrate is not very good for practical applications. It has a very poor thermal conductivity. Thermal stability of threshold current of InP lasers is poor, and the substrates are expensive and brittle. GaAs is much better. So, we build the first powerful 1.3-micron laser on GaAs. It used InAs quantum dots obtained by phase separation of a solid solution. I spoke of this method. So, if the key characteristic is the threshold current density, then such a laser is drastically better one on the InP substrate. We are sure that in the near future all lasers in this range will be grown on GaAs.

The so-called vertical cavity lasers will for the near future dominate the market of transmitter lasers used in telecommunications. Why? I already said few words about this topic. In this kind of laser light goes upward rather than parallel to the plate. A vertical cavity laser works as a cheap light emitting diode except that it has an ideal spectrum quality, narrow angular pattern, and high efficiency. You can create matrices or place many lasers in one area. In the field of lasers we are going through that initial childhood period when single discrete units are used while in transistors we are way past that stage and now have integrated circuits with packaging factor of up to 108 elements per chip. Just one condition to fabricate good VCSEL- you need multi-layered and strongly reflexive interference mirrors (Bragg mirrors). There is no such device based on InP. You can only build it on gallium arsenide, but until very recently one couldn't even think of a 1.3 micron GaAs laser. With self-organization, however, we got a vertical laser active in the 1.3-micron range, which is of a key importance for telecommunications.

And now the last example. For optical storage applications: reading and recording, you need to build the same vertical laser except that is has to work in the ultraviolet range. Up to now optical injection was used by us, but we obtained very promising results using current injection. It is the implementation of the vertical laser based on GaN, which is a wide band-gap material, with dense raws of very small InGaN quantum dots inserted into the GaN matrix.

I cannot go on forever about many new scientific ideas that may at the moment appear totally fantastic. They can drastically transform our understanding of modern optoelectronics. It may be worth mentioning that an exciton works in a quantum dot, i.e. an electron and a hole that are tied together. Exciton, which was predicted by Frenkel from our Physical-Technical Institute, is a key quasi-particle that determines many optical properties of solid bodies. Exciton interaction, i.e. coulomb attraction between an electron and a hole, allows implementing many new, exciting and yet fundamental ideas that follow from the exciton physics but that have not yet been applied to lasers. By the way, exciton was experimentally discovered by Gross also in our Physical-Technical Institute. So now, for the first time, excitons are used in lasers too, at room temperature, and these are double-heterostructure lasers that have been proposed and practically implemented by Zhores Ivanovich Alferov in the Physical-Technical Institute.

Self-organization is not just a fashionable field. It is a conceptual shift, it is a change of paradigm. I hope I have convinced you of this. The paradigm through which we view crystal growth is changing. First there were only natural structures - crystals. Then man-made layered hererostructures came about, make according to man's will. It was a giant achievement, and they soon found practical application. What we have now is a move to self-organizing nanostructures. They are of course man-made in a sense, but in essence man is merely a researcher. Nature is the true maker of these structures. This is what we call self-organization.

Let us see how the main ideas on the physics and technique of crystal growth have changed:

Lattice parameters of layered double heterostructures must match for quality devices.

In case of self-organization this condition is not essential. In fact, it is harder to get quantum dots if lattice parameters are identical.

One class of related materials is required for forming a heterostructure, e.g. GaAs-AlGaAs or silicon/germanium.

It is no longer an essential condition. You can combine very different materials, such as silicon and InAs in single crystal.

Defects and dislocated clusters result in degradation of DHS lasers.

With self-organizing nanostructures defects can be selectively eliminated.

Dislocations and dislocation matrices are not compatible with practical use in devices.

Dislocation matrices may be used for producing nanostructures or nanoepitaxy. They can be very useful.

That is, cardinal changes have taken place in the entire area of growing crystals for use in devices.

Let me show you nano-inclusions of InAs into a silicon matrix. These dots are separate atoms. You can see them in an electron microscopy image when you look through the sample at high resolution. Here you see areas that are different from the silicon matrix. These InAs nano-inclusions are inserted into the silicon matrix. Silicon technology could potentially be merged with the InAs technology for laser applications.

In conclusion I want to say that new generation technologies of making semiconductor devices based on zero sized objects - quantum dots - have been developed. Advantages of quantum dot lasers over lasers based on layered systems have been demonstrated. Quantum dot lasers have a wider spectrum compared to layered systems. Methods of using self-organization to fix defects in semiconductor structures and for nano-epitaxy have been developed.

One more thing. We are often asked about our work's recognition around the world. Perhaps, skeptics may think, we have no reason to be so proud of yourself.
Now I just want to show you the list of some plenary and invited talks at leading international conferences given by scientists of Zhores Alferov's laboratory of the Physical-Technical Institute. Among these, two invited talks by Victor Mikhailovich Ustinov. Dr. Ustinov spoke twice at a very important international conference on molecular beam epitaxy. The opening plenary report by Zhores Ivanovich at a major optoelectronics conference "Photonics West" must be mentioned. My plenary talks at the International Conference on the Physics of Semiconductors, Annual Meeting of the Institute of Physics (Great Britain), and International Conference on Indium Phosphide and Related Materials in Japan. Invited talks at international conferences on crystal growth, optoelectronics, vapor phase epitaxy from metal-organic compounds and many others. Our priority in this field is recognized throughout the world. Some, perhaps, would be happy to muffle our work but they won't succeed also this time.

Thank you for your attention.