1
Introduction

FOCUS AND SCOPE OF THIS REPORT

Improvement in materials has been a hallmark of the advance of civilization. Prehistoric and historic periods, such as the bronze and copper eras, indeed often carry labels in which a development in materials technology is seen as a defining feature. This also holds true in archaeological classifications. That is not to say that advances in materials technology are determinant; rather they provide a background against which events have occurred.

Scientific advances of the 20th century completely redefined the interplay between experiment and theory in the understanding of materials, providing the modern basis for the formulation and solution of scientific and technological problems. The advent of x-ray diffraction studies of the atomic architecture of materials was central to these advances. In many cases of great importance, the availability of crystalline samples, either natural or synthetic, was the crucial factor in enabling such studies.

The world is now entering a new age in which modern experimental capabilities allow manipulation at the level of the single atom and molecule, as well as interrogation and control of properties of solids at this scale. Taking full advantage of such capabilities for tailoring the properties of new functional materials requires the sophisticated control over materials preparation protocols that lies at the forefront of the development of single-crystal growth technology. Advancing the forefront of crystal growth is central to the strength of technology-based industries and to the scientific enterprise on which the technologies rest. Sensitive equipment



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1 Introduction FOCUS AND SCOPE OF THIS REPORT Improvement in materials has been a hallmark of the advance of civilization. Prehistoric and historic periods, such as the bronze and copper eras, indeed often carry labels in which a development in materials technology is seen as a defin- ing feature. This also holds true in archaeological classifications. That is not to say that advances in materials technology are determinant; rather they provide a background against which events have occurred. Scientific advances of the 20th century completely redefined the interplay between experiment and theory in the understanding of materials, providing the modern basis for the formulation and solution of scientific and technological problems. The advent of x-ray diffraction studies of the atomic architecture of materials was central to these advances. In many cases of great importance, the availability of crystalline samples, either natural or synthetic, was the crucial factor in enabling such studies. The world is now entering a new age in which modern experimental capabili- ties allow manipulation at the level of the single atom and molecule, as well as interrogation and control of properties of solids at this scale. Taking full advantage of such capabilities for tailoring the properties of new functional materials requires the sophisticated control over materials preparation protocols that lies at the forefront of the development of single-crystal growth technology. Advancing the forefront of crystal growth is central to the strength of technology-based industries and to the scientific enterprise on which the technologies rest. Sensitive equipment 

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frontiers c rys ta l l i n e m at t e r  in now essential in medical and national security areas depends on high-quality single-crystal detectors. The search for ever better radiation detector materials is an important part of the new materials work that goes hand in hand with single- crystal growth. This is just a part of the broad search for functional new materials and the research and development that follow, which are vital to the competitive health of this nation’s high-technology industries. The intent of the present study by the National Research Council’s Commit- tee for an Assessment of and Outlook for New Materials Synthesis and Crystal Growth is to investigate whether an articulated agenda on the growth of crystalline materials would serve the national interest scientifically and technologically. The formal charge to the committee is presented in Appendix A. The discovery and growth of crystalline materials (DGCM) encompass a broad range of activities involving both theory and experiment. One very substantial activity is the growth of large boules (synthetically grown single-crystal ingots), most notably defect-free silicon for the semiconductor industry. Silicon technology designed for flat-panel displays is now being adapted to produce large-area multi- crystalline solar panels. Another significant activity is the development of laser materials, using both known and new materials, for novel communications appli- cations. Various gamma-ray detection arrays in high-energy physics experiments depend on discovering new, or employing known, single-crystal materials. Single crystals are increasingly used in metallurgical settings, for example, as turbine blades in jet engines. Two-dimensional films of single crystals are increasingly used in the semiconductor industry, and the long-term projection is for even more use of such material. Diamond films are one example of an emerging technology with many applications, including wear-resistant coatings on cutting tools as well as high-power transistors. Crystalline material also promises to play an integral role in meeting homeland security needs, with semiconductors offering significant advan- tages in efforts to develop more-sensitive radiation detectors. Finally, crystallization of organic materials, highly important in biological and biochemical sciences, is receiving attention for its potential in application-based uses such as photovoltaics and electronics. All of the applications mentioned above are based on a physical functionality imbued by a material’s crystalline structure. Crystal growth is a diverse field. Crystals can be grown using a remarkable variety of techniques. Many people are familiar with the growth of rock candy sugar crystals from aqueous solution. This method is a prototype for the growth of intermetallic compounds from molten metal solvents, hydrothermal growth of quartz crystals, and flux growth of oxides, for example. In preparing this report the committee necessarily had to delineate the scope of the study, and in doing so it left out activities and research fields that arguably could have been included. The committee focused on crystalline materials, both bulk and thin-film, with unique physical properties. It did not seek to describe

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introduction  comprehensively either the marvels of crystal growth or its successes, but rather to assess U.S. national strengths and weaknesses in these activities and to address what responses appear appropriate based on this assessment. The committee did not consider protein crystallography or crystals for the pharmaceutical industry. While these areas are extremely important, they lie outside the scope of the committee’s charge. The committee also did not consider nano-sized material to be within the scope of this report. While there are many overlaps in applications between nano- sized material and the crystalline material discussed here, there is much less overlap in the scientific realm. Further, the historical and current levels of programmatic support for these two research areas differ significantly. U.S. agency leaders in the physical sciences and engineering have recognized the importance of nanoscience and engineering (nanomaterials), and they have established strong national initia- tives to address those opportunities. The enduring importance of the discovery and growth of crystalline materials has not received the same recognition and support. Therefore, the committee limited its assessment to the current health and future support needs for research in bulk and thin-film crystalline material. Basic research in solid-state chemistry and condensed-matter physics uses crystal growth as a technique in the search for new materials. After creating a new material, much effort is often required to produce the large crystals needed for physical measurements of new, interesting properties (Box 1.1). Many materials of interest are significantly anisotropic and in many cases exhibit two-dimensional or even one-dimensional mechanical or electrical properties. A compelling rationale for producing single crystals of such materials clearly extends to application. The ability to grow crystals of a known material is generally not straightforward, and continuing advances are being made in growth techniques coupled with theoretical insight. For applications, the goal is often low-defect-density or defect-free crystals; achieving such perfection requires detailed understanding of the system under investigation, coupled with in-depth knowledge of crystal growth techniques. Crystal growth includes a variety of activities that have been profoundly impor- tant from both basic science and technological standpoints. Such activities are often driven by individual researchers in close symbiotic alliance with measurement and theory colleagues. Many questions arise naturally in the context of seeking to strengthen support for crystal growth: What kind or kinds of facilities provide the best approach to the science? How should the search for new materials fit with crystal growth production activities? How can it be ensured that there will be an adequate workforce with high competence in crystal growth science and technology and the new paradigms needed for conducting research in this new age of material control? These important issues are addressed later in this report (Chapter 3). It is clear that crystalline perfection is a route to new functional possibilities for mate- rials. Experimental and theoretical investigations on new as well as known materials will have important payoffs for both science and technology.

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frontiers c rys ta l l i n e m at t e r 0 in BOX 1.1 Growth of Large Crystals for the National Ignition Facility In order to meet the needs of the National Ignition Facility at the Lawrence Livermore National Laboratory (LLNL) for hundreds of half-meter-scale, high-quality single-crystal plates of potassium dihydrogen phosphate, KH2PO4 (KDP) (see Figure 1.1.1) and deuterated potassium dihydrogen phosphate, KD2PO4 (DKDP), the Laser Program at LLNL undertook a major effort to develop a method for growing these crystals at high production rates. This effort resulted in a production technology capable of producing half-meter boules at 5 to 10 times the rates previously possible. In addition, this effort led to a mechanistic understanding of the physics of KDP growth as well as the connection between growth defects and optical performance. FIGURE 1.1.1 This potassium dihydrogen phosphate (KDP) crystal, weighing 701 pounds and measuring approximately 26 inches by 21 inches by 23 inches high, was produced in a record 52 days through a rapid-growth process perfected at the Lawrence Livermore National Laboratory (LLNL). A crystal of this size would have taken 2 years to grow using conventional methods. The enormous crystal was sliced into plates for use in the National Ignition Facility (NIF), a giant laser under construction at LLNL. The crystal plates (½ inch thick and 16½ inches square) are used to convert the laser’s infrared light beams to ultraviolet light just before the beams strike the laser target. About 500 of these plates are needed for NIF. SOURCE: Courtesy of Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory, and the Department of Energy under whose auspices the work was performed.

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introduction  ORGANIZATION OF THE REPORT The balance of this introductory chapter uses four examples from history to illustrate how the discovery and growth of crystalline materials have played a lead- ing role in a range of scientific and technological advancements. Chapter 2 turns from history to the future, setting out three grand challenges facing those engaged in the discovery and growth of crystalline materials. These include meeting the needs of information and communications systems with new crystalline materials, developing materials for the next generation of energy sources, and bringing to fulfillment the long-sought capability of designing, from first principles, materials that meet specific technological requirements. Chapter 3 examines the current health of DGCM activities, including efforts to educate those entering this field, and the levels of financial support being pro- vided by industry and federal agencies. It also discusses efforts other countries are undertaking to support these activities. The final chapter contains strategies for addressing some of the shortfalls currently facing those engaged or wanting to engage in this field, and for developing the structures that will increase opportuni- ties in this field. The appendixes provide background information about the committee and those activities engaged in by the committee in preparing this report as well as discussions on synthesis techniques for crystalline growth, the classifications of materials, and a more detailed development of some of the structural recommen- dations made in the concluding chapter. HISTORICAL EXAMPLES OF CRYSTAL GROWTH AND TECHNOLOGY Following introductory remarks, this section examines four examples from the history of crystal growth that illustrate the remarkable intertwining of fundamental and applied science common to this field. These examples—from metallurgy, semi- conductors, thin films, and high transition temperature (Tc) superconductivity— represent leading-edge activities in which the ability to control the growth of crystals not only led to the advancement of science but also made a direct and significant contribution to society in general. Naturally occurring crystals have always attracted attention. A natural quartz crystal is seen in an ancient medicine bag displayed at Mesa Verde National Park in Colorado. The double refraction of Iceland spar (calcite) and its investigation opened the door to optical polarization. Pasteur’s identification of the handedness of crystals and its connection with the rotation of plane-polarized light is another remarkable observation (see Box 1.2). Such scattered findings were paralleled by a disjoint mathematical development resulting ultimately in the theory of space groups, which was complete before the discovery of x-rays and the ability to verify

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frontiers c rys ta l l i n e m at t e r  in BOX 1.2 Pasteur and the Discovery of the Relationship Between Natural Optical Activity and Crystal Morphology The French 5-franc note honoring Louis Pasteur contained mirror images of faceted crystals (Figure 1.2.1). Pasteur, in his studies of wine fermentation, noted that tartaric acid crystallized in two mirror-image habits, only one of which occurred in grapes. He was able to separate crystals of these two morphologies under the microscope and show that one rotated plane polarized light counterclockwise, the other clockwise, reflecting a preferred handedness in the naturally occurring variant. The finicky nature of crystal growth is also demonstrated by this example, because above 27°C only one morphology forms. Thus, had Pasteur worked in a warmer climate or on a warmer day, this discovery would have been postponed. FIGURE 1.2.1 French 5-franc note honoring Louis Pasteur, containing mirror images of faceted crystals inside the vertices of the braided ellipse. SOURCE: Courtesy of Z. Fisk, University of California, Irvine. atomic crystalline order experimentally. The tensor description of material proper- ties also predates x-ray diffraction studies of solids. It is no exaggeration to state that developing the ability to analyze crystals using x-rays was key to ushering in the modern scientific and technological era. With that ability, the nature of crystalline structures began to reveal itself to researchers. Such phenomena as the double refraction of calcite and piezoelectric and ferroelectric behavior could now be understood on an atomic scale. In turn, the deeper under- standing of materials from such studies opened new avenues to industrial use in, for

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introduction  example, the advancing technological requirements of the telephone industry. As early as the 1930s, Bell Laboratories began investing in materials research, leading not only to a better understanding of many fundamental constructs of crystalline materials, but also ways to use that understanding in a wide range of applications. For example, it was discovered that the piezoelectric properties of quartz are highly dependent on crystallographic direction. As a result, the so-called ZT-cut was adopted for use when temperature insensitivity is desired. In the late 1930s, Bell Laboratories assembled a significant fraction of the nascent solid-state physics expertise in semiconductor material. Research on that material led swiftly to the realization of the dominant deleterious effect of grain boundaries on electronic properties. It also led to the discovery of the technique of zone—and later floating zone—refining: a technique that opened completely new vistas in semiconductor research and applications. The strong coupling within the semiconductor research activities that led to these discoveries spread to other areas of research at Bell Laboratories. For example, the study of the magnetic properties of oxide garnet crystals was based on the technique of flux growth of single crystals, pioneered by J.P. Remeika and L.G. Van Uitert. These single crystals allowed Bell Laboratories researchers to exploit a hunch with respect to interesting properties of the crystals that had been suggested by E.F. Bertaut of the Laboratoire de Crystallographie in Grenoble, a hunch Bertaut had not been able to explore because he had lacked a source for the single crystals. The story of crystalline thin films leading to quantum-well structures paralleled the developments in bulk crystals. Starting with the work of F. Fang and colleagues at the IBM Thomas J. Watson Research Center on silicon-based field-effect transis- tors, the artificial construction of tailored layer structures was seen as a route to create two-dimensional electron systems. Development of molecular-beam epitaxy (MBE) by A. Cho and J. Arthur at Bell Laboratories allowed unprecedented control of crystallinity in multilayer structures. The deep interplay between basic physics and application was enabled by the remarkable and continuously improving ability of the film growers to increase charge carrier mobilities through increasing crys- talline perfection. The basic physics that came from this effort proved a complete surprise, and the surprises continue. A startling development in engineering materials was the discovery that inter- metallic compounds can be used as structural materials. Conventional wisdom had held that chemically ordered intermetallic compounds were much too brittle for most usual metallurgical methods of use and handling. That intermetallic single crystals are now used as turbine blades in jet engines is remarkable both in light of that conventional wisdom and in that scientists and engineers had the courage to undertake the extensive research necessary to determine otherwise. Many materials whose properties depend on highly anisotropic crystal struc- tures find important use in polycrystalline form. The ferroelectric barium titanate,

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frontiers c rys ta l l i n e m at t e r  in whose useful properties derive from its non-centrosymmetric structure, is used in a wide range of applications, from the dielectric material in capacitors to piezoelectric material in transducers such as microphones. The active material in Polaroid film is herapathite, a crystal originally discovered growing in a container of urine from a dog fed quinine by a doctor. Under a microscope, superimposed crystals showed reduced or no light transmission. Edwin Land, founder of the Polaroid Corpora- tion, used this observation in an unusual way, grinding synthetic herapathite into small crystalline needles that could be aligned by stretching them in a plastic sheet. In this case the properties were only known from single-crystal observations, but their extremely anisotropic character was exploited by clever processing. Academia, the national laboratories, and private industry have all been impor- tant components of the crystal growth community. In the past decade the industrial research laboratories have downsized to the point that this traditional balance has been dramatically altered. Industry clearly has needs that require close focus and tightly controlled communication to the outside. This seems particularly to be the case for both the semiconductor and pharmaceutical industries. The academic and national laboratory efforts are more parallel, with national laboratories tending to cut across disciplinary divides in basic research areas more easily than do uni- versities. Materials science departments have development efforts directed toward improving the size and quality of crystals, while chemistry and physics studies of single crystal focus on new materials: new structures tend to be of interest to chemists and new functionalities of interest to physicists. The area of crystal growth has considerable commonality of purpose between the universities and national laboratories. National laboratories have the ability to assemble teams in a way not always available to universities. This raises the question of whether a more natu- ral setting for what might be called crystal-driven research would be at national laboratories, or whether an equally effective research program can be built from a distributed effort across university–national laboratory boundaries. The metallurgist R.W. Cahn, in The Coming of Materials Science, has discussed the study of crystals as a parepisteme: an inquiry at the boundary between disci- plines, not generally a freestanding study in and of itself, but one that is ancillary and important to other investigations.1 Of the many interesting paths that one can follow into the history of the subject, four that have important contemporary relevance are presented below. 1 R.W. Cahn, The Coming of Materials Science, Oxford, United kingdom: Elsevier Science, 2003.

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introduction  Example from Metallurgy: Single-Crystal Superalloys for Jet Engine Turbine Blades A remarkable and successful example of the commercialization of single crystals involves single-crystal superalloys (alloys able to perform in extreme environments) for jet engine turbine blades. This example was chosen to illustrate the unexpected way in which control of crystal growth can be utilized for tailoring commercially important products. In turbine blade applications, the general goal is to increase the operating tem- perature of the engine. Higher temperatures provide greater fuel efficiencies, ulti- mately leading to greater thrust-to-weight ratio, as shown in Figure 1.1. However, at elevated temperatures (typically above 50 percent of the melting temperature of the engineering material), creep deformation—a slow plastic strain developing below normal yield strength—occurs. Deformed components in a rotating environment such as a spinning turbine can lead to catastrophic failures. In a polycrystalline sample, the primary mechanism for creep involves atomic movement along bound- aries of given crystals. Because these boundaries are eliminated in single crystals, such turbine blades deform less at elevated temperatures. Before the 1970s, industrial-scale production requirements for single-crystal turbine blades were considered too expensive to be a viable technology. In the early 1970s, however, improvements to casting methods, developments in cooling schemes, and advances in solidification modeling using multicomponent thermodynamics significantly improved the manufacturing of superalloys. Single-crystal turbine blades now operate in environments at 85 percent of their melting temperatures. Further improvements were achieved in the metallurgical development of the material used for the blades. The workability of metals usually depends on a plasticity coming from the ability of like atoms to slide past one another in the metallic lattice. In contrast, intermetallics with their crystallographically ordered arrays of unlike metal atoms generally show brittle fracture arising from the lack of interchangeability of unlike atoms under shear. This brittle fracture limits strength, albeit at a large value in certain cases. Superalloys for jet turbines were developed that gained the rigidity associated with intermetallics but had sufficiently elevated brittle limits at operating temperatures that they could be incorporated safely into jet turbines. The effect of this improvement in material and increased operating tempera- ture is captured for selected engines in Figure 1.1. The increased temperature capa- bility of single crystal (compared to polycrystalline) alloys is conservatively 50°C to 100°C for the base metal, which translates to an increased efficiency of roughly 25 percent and a resulting significant savings in fuel consumption. Although fundamental research in single crystals and their properties has a long history, the turbine blade example is unusual, as it represents an incremental

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frontiers c rys ta l l i n e m at t e r  in 0 FIGURE 1.1 Specific core power as a function of inlet temperature in the turbine section of selected jet engines. The data for specific engines span about 70 years and are compared to the theoretical limit. The red section shows increased operating temperatures through turbine material development (including single-crystal development), and the blue section reflects advances in cooling schemes in the jet engine materials. The increase in metal temperatures incorporated many advances, includ - ing both alloy and manufacturing advances. Most notable, the development of single-crystal turbine blades increased the operating temperature roughly 50°C to 100°C. From the figure it is apparent that this increase in operating temperature translates to an approximately 25 percent increase in engine efficiency, providing large energy savings. SOURCE: Adapted by permission of the MRS Bulletin from Dennis M. Dimiduk and John H. Perepezko, “Mo-Si-B Alloys: Developing a Revolutionary Turbine- Engine Material,” MRS Bulletin, 28, No. 9 (2003), p. 639, Figure 1. but significant improvement of an existing material. The optimized creep resis- tance in single crystals compared to that in polycrystalline solids was fundamen- tally defined and known. The incremental step to advance the industry involved methods to translate the laboratory-scale understanding to a commercial process. This is in contrast to the silicon industry, where the true properties (compared to the optimized) were only available in single crystals, whose history is considered below.

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introduction  Example from Information Technology: Single-Crystal Silicon for Microelectronics A second example of the leading role that crystal growth has had in advancing science and technology is that played by highly perfect single-crystal silicon (Si) in microelectronics. This example was chosen not only to demonstrate its absolutely central importance to modern information technology (IT) but also to illustrate how such an achievement can both make a collateral impact technologically and foster fundamental advances in the study of other single-crystalline materials. Silicon is perhaps the most important technological material of the past half-century. It is the workhorse of the semiconductor, integrated circuit, and electronics industries. The Si integrated circuit underlies the $270 billion per year semiconductor industry and the $1.5 trillion per year electronics industry.2 It also underpins the IT and communications industries. Recent estimates3 attri- bute 25 percent of the economic growth in the United States to IT-producing industries, even though these industries contribute only 3 percent of the gross domestic product. As a group, the four IT industries (semiconductors, computers, communications equipment, and software) contribute more to economy-wide productivity growth than do all other industries combined. The importance of single-crystal silicon to IT and thus to the worldwide efficiency of labor suggests a label analogous to that of prehistoric eras: Humankind lives at present in the silicon age. Unlike the prehistoric and historic eras, however, the development of silicon relied on quantitative science both in crystal growth and materials charac- terization. And an essential element in that development was the recognition that previously unattained high purity and crystalline perfection would be needed for reliable and reproducible transistor action. The need for crystal perfection in semiconductors was unprecedented in the history of materials development. Understanding why this is so requires visiting some of that history. Early in the study of solids, materials were divided into classes according to how readily they conducted electricity. Good electrical conductors, such as copper (Cu), were called metals; materials that did not conduct electricity, such as quartz, were labeled insulators. Other materials exhibited widely varying electrical conductivity, ranging from relatively high conductivity to very low con- ductivity, often in the same material system. These materials, with conductivity between that of metals and insulators, were given the disparaging label of semi- conductors because of their irreproducible properties. The earliest semiconductors discovered were oxides and sulfides. Eventually, as the elements in the periodic 2 iSuppli Corporation. Available at http://www.isuppli.com/news/default.asp?id=8718. Last accessed September 3, 2008. 3 Dale W. Jorgenson, Moore’s Law and the Emergence of the New Economy, SIA 2005 Report, Semi- conductor Industry Association, San Jose, California (2005), pp. 17-20.

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frontiers c rys ta l l i n e m at t e r  in FIGURE 1.3 Transmission electron micrograph of a silicon-silicon dioxide (Si-SiO 2) interface. With advances in electron microscopy, the interfaces in a modern integrated circuit can be imaged, as seen here in an atomic resolution micrograph of an interface between electrically conductive crystalline Si (bottom) and its nonconductive amorphous thermal oxide, SiO2 (top). This interface is the basis of the Si field-effect transistor, which is used in all modern electronics and computers. SOURCE: Courtesy of Stephen Goodnick, Arizona State University. the discovery of elegant new fundamental physics. These advances are illustrated for the gallium arsenide (GaAs) system in the following subsection. Example in the Area of Thin Films: Gallium Arsenide-Based Heterostructures A third example of crystallography leading to major discoveries in both science and technology is the development of gallium arsenide-based heterostructures. These single-crystal GaAs films are a natural extension of the deep experience of the scientific community with single-crystal Si. This work was chosen to illustrate the essential coupling between high-quality crystal growth and the discovery of completely new and unexpected physical phenomena. It also illustrates how the ability to produce single-crystal films of ever higher quality is the determining factor in making progress in this field of physics. A search by physicists for a more perfect semiconductor-insulator interface than Si-SiO2 led to the development of the GaAs-aluminum arsenide (AlAs) sys- tem, in which both the conducting GaAs and the insulating AlAs are incorporated in the same single crystal. Interestingly, these crystallize in the same tetrahedrally bonded diamond structure as that of Si, having the same average valence electron count. Using advances made in techniques to epitaxially grow single-crystal films, near-perfect crystal interfaces can be produced. Figure 1.4 is an atomic-scale micro- graph showing 12 atomic layers of semiconducting GaAs (darker layer) sandwiched between layers of semi-insulating AlAs (lighter layers). Notice that in this figure the atomic layers of GaAs cleanly link up to the adjacent atomic layers of AlAs,

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introduction  FIGURE 1.4 Cross-section transmission electron micrograph at atomic resolution of a crystal, grown by molecular-beam epitaxy, containing 12 molecular layers of aluminum arsenide (AlAs), then 12 layers of gallium arsenide (GaAs) and 12 layers of AlAs. SOURCE: Courtesy of Loren Pfeiffer, Bell Laboratories, Alcatel-Lucent. in marked contrast to the Si-SiO2 micrograph in Figure 1.3. Thus, the GaAs-AlAs system has the potential for no dangling chemical bonds at the electronic interfaces, and thus no interface traps. The absence of a disordered electronic interface gives the freedom to reduce the conducting channel thickness to about 10–6 cm, which is about the quantum size of the conduction electrons in GaAs. The motion of the electrons then becomes

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frontiers c rys ta l l i n e m at t e r  in two-dimensional. The electrons can move in the plane of the GaAs channel but not out of the GaAs layer because of the AlAs insulating barriers. The nature of the two-dimensional electrons can be probed in the experiment shown in Figure 1.5. In the sketch, the two-dimensional conducting GaAs channel just below the sample surface is placed in a perpendicular B-field, and a current, Ixx, is caused to flow in the long direction. The sample is characterized by a longitudinal resistance Rxx and a transverse Hall resistance, Rxy, named for E. Hall, who first observed it in 1878. For metal samples such as the gold leaf foil used by Hall, Rxy grows smoothly and linearly with increases in the magnetic field B. For high-purity semiconducting systems at low temperatures, however, the Hall resistance shows a series of discrete plateau steps that cannot be understood without considering the quantum proper- ties of the conducting electrons. An example of these remarkable quantum steps in the Hall resistance is shown in Figure 1.6(a) for a GaAs-AlGaAs sample. Even more striking is that the numerical values of the various resistance plateaus are given by exact ratios of fundamental physical constants, 1h Rxy = , ν e2 where h is Planck’s constant, e is the electron charge, and ν is a quantum number having integer values 1, 2, 3 . . . . This quantum Hall experiment was first performed by von klitzing, Dorda, and Pepper in 1980 using a high-quality version of the Si-SiO2 interface shown in Figure 1.3.5 The theoretical picture of the quantum Hall effect is that the resistance plateaus are due to electrons making cyclotron orbits around the magnetic flux lines of the B-field. A natural interpretation of the experiment has the magnetic B-field quantized from the point of view of the conduction electrons, in units of h/e = 4.1 × 10–7 gauss cm2. Thus the integer quantum number, ν, becomes the number of electrons, 1, 2, 3 . . . in cyclotron orbits around each magnetic flux quantum. The plateau resistivity values are the same for an Si-SiO2 interface as for a GaAs-AlAs interface. Indeed, this universal material-independent behavior, along with extreme accuracy of the h/e2 determination, has led to the adoption of these Hall resistance plateaus as the international standard for resistance, thereby defining the ohm in terms of h and e. The effect has become known as the quantum Hall effect, and its discoverer, klaus von klitzing, was awarded the Nobel Prize in physics in 1985. The discovery was not anticipated in the earlier quantum mechani- cal treatments of two-dimensional electrons, but instead was the direct result of the new availability of high-quality crystalline samples. 5 k. von klitzing, G. Dorda, and M. Pepper, “New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance, Physical Review Letters, 45, 494 (1980).

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introduction  R xy Ixx Rxx e ld B- fi FIGURE 1.5 Experimental setup for a Hall-effect measurement. The two-dimensional electron system lies in the plane of the sample; electrical contacts are indicated by dark patches. The magnetic B-field figure 1-5.eps is perpendicular to the two-dimensional electron system. SOURCE: Adapted from E.H. Hall, American Journal of Mathematics, 2, 287 (1879). The realization that increasing the crystalline quality in the two-dimensional region could lead to a more robust quantum Hall effect led to experiments similar to that of von klitzing, but with the potentially higher-quality GaAs-AlGaAs inter- face. In 1982, H.L. Stormer, D.C. Tsui, and A.C. Gossard published a truly shocking experimental result shown in Figures 1.6(a) and 1.6(b). Not only did they see the integer von klitzing effect, but they also saw a clear Rxy plateau at ν = 1/3, and in the longitudinal Rxx signal a hint of something also at ν = 2/3. They had discovered the fractional quantum Hall effect (FQHE). Since the physical interpretation of the integer quantum Hall theory relied on ν being the number of electrons in a cyclotron orbit around each B-flux quantum, the existence of fractional values of ν seems to suggest a state whereby the electron itself is breaking up into frac- tional charges. However, particle physics tells us that an electron cannot be broken apart. Instead the FQHE experiments reveal a new state of matter, one in which new, particle-like excitations emerge owing to particle-field interactions that are qualitatively different from the interactions of elementary particles in free space. But this was only the first sighting of new families of emergent excitations in these two-dimensional electron systems. The discovery of the fractional quantum Hall effect in GaAs launched a world- wide effort to further improve the quality of the GaAs crystal samples. Figure 1.6 shows the increasing richness of observed fractional states as the sample quality (measured by the electron mobility µ) has improved. In the Figure 1.6(c) trace, for a sample of mobility 500,000 cm2/Vsec, one sees that the states at 1/3 and 2/3 are joined by states at 2/5 and 3/5, and in the Figure 1.6(d) trace, these states are

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frontiers c rys ta l l i n e m at t e r  in FIGURE 1.6 Improvement in mobility through improvement in crystal quality of two-dimensional electron gas samples leading to new states of quantum matter: (a) The quantum Hall effect Rxy in a gallium arsenide (GaAs)/aluminum gallium arsenide (AlGaAs) heterojunction at T = 0.48 K, as a function of magnetic field, or equivalently as the filling factor or number of electrons per magnetic flux line. The dashed line is the classical Hall effect as it would be seen at room temperature (D.C. Tsui, H.L. Stormer, and A.C. Gossard, “Two-Dimensional Magnetotransport in the Extreme Quantum Limit,” Physical Review Letters, 48, 1559 [1982]). Panels (b), (c), and (d) show longitudinal resistance Rxx for three different GaAs/AlGaAs two-dimensional electron gas samples indicating the appearance of new quantum states with increased purity as represented by mobility, µ, in units of cm 2/Vsec. (b) The first observation of fractional filling at ν = 1/3 and T = 0.48 K in the same sample as panel (a) (D.C. Tsui, H.L. Stormer, and A.C. Gossard, “Two-Dimensional Magnetotransport in the Extreme Quantum Limit,” Physical Review Letters, 48, 1559 [1982]). (c) New states at ν = 1/3, 2/5, 2/3 achieved in a higher-mobility sample at T = 0.55 K (H.L. Stormer, A. Chang, D.C. Tsui, J.C.M. Hwang, A.C. Gossard, W. Wiegmann, “Fractional Quantization of the Hall-Effect,” Physical Review Letters, 50, 1953 [1983]). (d) Data from a typical modern high-mobility sample at T = 0.035 K (W. Pan, H.L. Stormer, D.C. Tsui, L.N. Pfeiffer, K.W. Baldwin, K.W. West, “Fractional Quantum Hall Effect of Composite Fermions,” Physical Review Letters, 90, 16801 [2003]). This sample exhibits self similarity between the ν = 0 and ν = ½ states that is the basis for the “composite fermion” description of electronic states, which are described in Chapter 2 of this report.

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introduction  joined by a hierarchy of many more states at 3/7 and 4/7 and so on, all having odd denominators and all organized around an absent state at ν = ½. The full story of how the new states are organized around ½, and the dramatic evidence for a series of new emergent particles called composite fermions, will be continued in Chapter 2 of this report. The Stormer-Tsui-Gossard FQHE experiment uncovered deep new physics emerging from a system that is simple to describe, namely, electrons interacting through the Coulomb potential but confined to two dimensions. As the crystal- line quality of the samples improved, these electron-electron interactions became important over larger and larger distances, revealing electronic states that previ- ously were hidden by disorder. In 1998, Stormer, Tsui, and theorist Robert Laughlin were awarded the Nobel Prize for their work on the fractional quantum Hall effect;6 as the perfection of the samples was further improved, new hierarchies of states whose full explanations are beyond the Laughlin theory were uncovered. At present, the progress in uncovering new quantum states through ever-purer samples continues unabated. The recent increase in GaAs sample mobility to 31,000,000 cm2/Vsec revealed new surprises, such as striped regions of alternating- integer filling factor, non-Laughlin-even-denominator states, and the formation of re-entrant insulating states. For GaAs heterostructures of the highest crystal perfection, the magneto- transport data now contain enough information to make a compelling argument for the existence of a new fundamental particle called the composite fermion. The blue trace of Figure 1.7 (bottom panel) reproduces the data in Figure 1.6(d) showing the FQHE in a 15,000,000 cm2/Vsec mobility GaAs-AlGaAs sample grown recently at Bell Laboratories. The data are plotted versus magnetic B-field up to 18 tesla, and the principal filling factors previously discussed are labeled. The raw data show that, in addition to the fractional organizational state at ν = ½, there is another such organizational state at ν = ¼. Around each of these organizational states, a complete array of quantum Hall fractions is seen with the usual odd denominators given by the empirical formulas ν = j/(2j ± 1) near ν = ½, and ν = j/(4j ± 1) near ν = ¼, where j is an integer, j = 0, 1, 2, . . . . If two identical copies of this spectrum (arbitrarily colored blue and red) are arranged so that ν = ½ at 8.3 tesla in the red copy is placed exactly above the zero tesla starting point of the blue copy, as shown in the figure, all of the fractional quantum Hall states to the right of ν = ½ in the red copy of the data line up perfectly, state for state, with the original integer quantum Hall states in the lower, blue copy. It is as if the 8.3 tesla magnetic field at ν = ½ was somehow reset to zero, and the data started over with the pattern of the integer quantum Hall effect. Further, this 6 It is worth noting that Arthur C. Gossard, the person who grew the samples that enabled this groundbreaking experiment, was not included among the Nobel Prize winners.

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frontiers c rys ta l l i n e m at t e r  in 33 _ p p 13 2 _ 22 3 _3_ 2 2_ _1 _ 1 3 4p ± 1 7 2p ± 1 _ 35 5 3 44 _ _3 _ 3 11 7 44 _ 7 44 _ 44 _ 55 _ 17 15 9 9 1 _ 2 1 _ 4 33 _ p p 13 2 _ 2 23 3 __ 2 2_ _1 _ 1 5 2p± 1 3 4p ± 1 7 35 5 3 _ 643 2 1 44 _ 33 _ 11 7 7 44 _ 44 _ 44 _ 55 _ 17 15 9 9 1 _ 2 1 _ 4 0 6 12 18 Ma gn etic Field (T ) FIGURE 1.7 Longitudinal resistance Rxx data taken on a modern GaAs/AlGaAs high-mobility two- dimensional electron system exhibiting the fractional quantum Hall effect and composite fermion fractions. The red (top) and blue (bottom) traces are identical copies of the same data set. SOURCE: W. Pan, H.L. Stormer, D.C. Tsui, L.N. Pfeiffer, K.W. Baldwin,s K.W. West, “Fractional Quantum Hall figure 1-7.ep and Effect of Composite Fermions,” Physical Review Letters, 90, 16801 (2003). resetting of the B-field happens again at ν = ¼. Now all the states around ν = ¼ in the red data line up state for state with the ν = ½ states in the blue data, and if the red data are slid farther to the left until ν = ¼ at 16.6 tesla is lined up to zero tesla on the blue trace, the fractional states in the red trace would again line up state for state with the integer states of the blue trace. Theorists have accommodated this apparent resetting to zero of the 8.3 tesla and 16.6 tesla magnetic fields by proposing the existence of two new particles that incorporate the flux quanta of the B-field in their creation. The new particles are called composite fermions. The composite fermion associated with ν = ½ is made up of an electron and two magnetic flux quanta. The composite fermion associated with ν = ¼ is an electron and four magnetic flux quanta. The magnetic flux quanta incorporated in these new particles are no longer available, and the magnetic field is naturally reset to zero at ν = ½ and again at ν = ¼. With this new theoretical picture, the fractional quantum Hall effect becomes much easier to understand. It is just the integral quantum Hall effect of these new composite fermion particles! The beauty in this hierarchy of structure suggests further levels and more exotic particles.

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introduction  Shortly after the discovery of composite fermions, new theoretical work sug- gested a new chapter in the story of emergent particles in two-dimensional electron systems: the possible existence of emergent non-abelian quasi-particles. Non- abelian quantum particles can only exist in a two-dimensional environment, such as the one under discussion at the heterointerface in GaAs-AlGaAs. The known quantum particles occupy three-dimensional space and thus are all abelian. Non- abelian quasi-particles would have bizarre properties. In a two-dimensional sheet of quasi-particles, if a quasi-particle is caused to make an encircling path around one of its nearest neighbors and then comes back to where it started, for abelian particles nothing would change, but for non-abelian particles such an encircle- ment would cause quantum entanglement. Moreover, the quantum entanglement would not be affected by the usual processes that cause quantum decoherence of abelian particles. The only way that the entanglement of non-abelian particles could be undone is by reversing the original topological path or making topologically complicated additional loops. Thus, if non-abelian quasi-particles can be found in these two-dimensional systems, they could in principle be used as a topological lock against quantum decoherence. Such a topological lock may be just what is needed to make quantum computing a future reality. The story of the continuing interaction between GaAs MBE and the search for new semiconductor physics nicely demonstrates how the improvements in the perfection of the crystal interface between a semiconductor and its surroundings have led to profound insights in low-dimensional semiconductor physics, and how, in turn, this success has led to an ongoing effort to make still more perfect semiconductor interfaces. Example of High-Temperature Superconductivity The final example illustrating the historical role played by crystal growth in advancing both applied and basic science is in the field of high-Tc superconductivity. This example was chosen for several reasons. First, because of the complex structure of the metallic oxide materials involved, it demonstrates the absolute necessity of being able to control the growth of the materials precisely in order to gain a funda- mental understanding of their nature. Second, it is a highly active area of research with much promise, not only for expanding current knowledge of solid-state physics but also for the technological opportunities that it presents. Superconductivity, discovered in 1911 by k. Onnes shortly after his achieve- ment of liquefying helium, resisted understanding until the Bardeen-Cooper- Schrieffer theoretical breakthrough in 1957. Superconductivity was long thought to be a rare occurrence; the highest known superconducting transition temperature was 23.2 kelvin (k) until Bednorz and Müller stunned the science community in 1986 with their discovery of 28 k superconductivity in barium-doped La2CuO4,

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frontiers c rys ta l l i n e m at t e r 0 in followed quickly by 90 k in yBa2Cu3O7 (see Figure 1.8). This discovery was made in polyphase ceramic powders, and determination of the actual superconducting crystal structure and its composition involved intense competition within the materials community. A succession of related materials with still higher transi- tion temperatures (Tc) was discovered, with Tc reaching the remarkable level of 156 k under pressure in a mercury-based cuprate material. This Tc is well beyond that thought possible based on existing theory. Exceeding a Tc of 77 k is a major technological triumph, since superconductivity could now be attained by cool- ing with liquid nitrogen rather than the more expensive and much less abundant liquid helium. While holding the promise of important industrial use, these new super- conducting materials also were intriguing from a fundamental science perspec- tive, having electrical and magnetic characteristics quite different from those of more familiar materials such as copper. Before it could understand and explain the physics of such materials though, the research community first had to determine their physical properties precisely. This, in turn, required a high level of control in growing the materials to remove effects of impurities and defects. The cuprate La2CuO4 YBa2Cu3O7 FIGURE 1.8 Crystalline structures of two superconductors: (left) La2CuO4, consisting of a sublattice of copper-oxygen pyramids (blue, with oxygen atoms shown in red) and the larger lanthanum atoms (yellow); and (right) YBa2Cu3O7, consisting of a sublattice of the copper-oxygen pyramids (blue) and the larger yttrium (yellow) and barium (green) atoms. SOURCE: Courtesy of M.A. Subramanian, Oregon State University.

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introduction  superconductors and their relatives have layered crystal structures with large anisotropy between in-plane and out-of-plane properties; single crystals are essen- tial to deeply probing the physics of these materials. Perfecting this crystal growth has proven to be difficult. In the 20 years since their discovery, only recently have crystals of sufficient quality been grown to allow “classical” types of experiments common in single-crystal metal physics to be conducted—namely, measurement of de Haas-van Alphen oscillations. These experiments determine aspects of the electronic structure, which appears to lie at the heart of understanding the high-Tc phenomena. Single-crystal growth of these high-melting-point oxides is performed in an optical furnace, where a hot floating zone is achieved by focusing light from high-power lamps, the optical offspring of the much older radio-frequency and electron-beam floating zone crystal growth of semiconductors. This technological development was perfected in Japan, and recent advances in the still-incomplete understanding of high Tc are coming from continued improvement of crystal quality resulting from this technology. After more than 20,000 publications, experimental research in high-Tc super- conductivity is finally making reasonable progress, although a consensus micro- scopic theory is still sought. Crystal growth played an essential role, not only for this field but also for progeny fields such as quantum criticality, orbital-ordered magnets, colossal magnetoresistance, and geometrical frustration. Understanding high-Tc superconductivity has served as a major motivation for increased develop- ment of experimental probes such as angle-resolved photoemission spectroscopy, scanning probe microscopy, tricrystal tunneling, pulsed laser deposition, high field magnets, and neutron scattering. Starting as a small-scale discovery of a new com- pound by two researchers, this topic spawned a great multitude of new scientific discoveries and extensive fundamental questioning of how well we understand solids. Such is the ongoing promise of growth of crystalline matter. The search for new materials with even higher transition temperatures continues, there being no reason to suppose that the cuprates represent any limit as to what is possible. CONCLUDING COMMENTS The return on investment to the public that ultimately pays for research such as that exemplified above comes in several forms: new technologies are enabled that simply would not exist without the continuing advances in single-crystal growth. It is not an exaggeration to say that these new technologies have transformed modern life. The transistor is based on single-crystal technology, and in a very real sense the computer would not be possible in any useful way without the transistor. One has only to look at a wristwatch to appreciate a remarkable and inexpensive result of very sophisticated single-crystal technology based on synthetic quartz crystal oscillators as a highly stable frequency device.

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frontiers c rys ta l l i n e m at t e r  in The ways in which crystal growth is intertwined with technology are many and varied, as seen by the contrast between the example of Si technology and that of the commercialization of single-crystal turbine blades. In the case of Si, pure material was required to lead to the understanding of the science and technology needed to develop commercial applications. In contrast, crystalline turbine blade commercialization was based on improvements in existing industrial processes. Commercial processes can and do benefit from the use of single crystals with sig- nificant economic consequence. Beyond this, single-crystal research has been and continues to be the path to new science. Maintaining scientific leadership in the world demands ready access to the advanced materials from single-crystal synthesis. Advances in the science of crystal growth yield ever-increasing control over materials and their uses, as well as new uses enabled by such control. These and many other examples illustrate a return on investment that can be economic or scientific, and often is both. The world is entering a new age of materials and is gaining the ability to inves- tigate, interrogate, and potentially control materials at a level approaching that of individual atoms. Single crystals are the stage on which the new capabilities play, and the ability to create these single crystals and then to produce them well is of primary scientific and technical concern. Not all materials are equal: some can be perfected much more effectively than others. The importance of a strong continu- ing search in the wide materials phase-space for ever-better functional materials cannot be overstated.