In Chapters 3 and 4 we have discussed electron behavior in potential wells of various profiles and dimensionalities. We have established that localization of electrons in such potential wells, regardless of their form, leads to the discretization of the electron energy spectrum whereby the distance between energy levels substantially depends on the geometrical size of the potential wells. If this size is macroscopic then the distance between the energy levels is so small that we can consider the energy spectrum to be practically continuous (or quasicontinuous). Electrons in metallic samples of macroscopic sizes have this kind of energy spectrum. Another limiting case is that of small clusters consisting of just a few atoms, where the distance between energy levels is of the order of electron-volts. Gradual decrease of one or several geometrical dimensions of the potential well from macroscopic to about 1 μm practically does not change the form of the electron energy spectrum. Very often macroscopic materials (or macroscopic crystals) are referred to as bulk materials or bulk crystals. Changes happen only when the size of structures is of the order of or less than 100 nm. Such structures are called nanostructures. The change of the electron spectrum from quasicontinuous to discrete implies changes in most of the physical properties of nanostructures compared with those in bulk crystals. In this chapter we will consider the main peculiarities of the electron energy spectrum in nanostructures of various dimensionalities.

The main characteristics of atoms and molecules are their structure and their energy spectrum. Under the term structure of an arbitrary particle we usually understand the size and the distribution of its mass and its charge in space. In quantum physics such a distribution is defined by the square of the modulus of the wavefunction of a particle. The particle itself may consist of a system of other particles that are bound by a certain type of coupling. For example, an atom consists of a nucleus and a system of interacting electrons, a molecule consists of a system of interacting atoms, and so on. If we consider an atom, the nucleus of the atom is assumed to be at rest (the so-called adiabatic approximation). This assumption can be made because the nucleus has a much larger mass than that of an electron (a proton's mass is 1836 times larger than the mass of an electron). Then, the square of the modulus of the wavefunction, ∣ψ(r1, r2, …, rn)∣2, for the system of electrons defines the probability density of finding the j th electron at the point rj. Graphically it is very convenient to depict ∣ψ∣2 in the form of an electron cloud, which can be considered as an averaged distribution of matter added to the mass of the nucleus located at the center of an atom.

Nanoelectronics is a field of fundamental and applied science, which is rapidly progressing as a natural development of microelectronics towards nanoscale electronics. The modern technical possibilities of science have reached such a level that it is possible to manipulate single molecules, atoms, and even electrons. These objects are the building blocks of nanoelectronics, which deals with the processes taking place in regions of size comparable to atomic dimensions. However, the physical laws which govern electron behavior in nanoobjects significantly differ from the laws of classical physics which define the operation of a large number of complex electronic devices, such as, for example, cathoderay tubes and accelerators of charged particles. The laws that govern electron behavior in nanoobjects, being of quantum-mechanical origin, very often seem to be very strange from a common-sense viewpoint. The quantum-mechanical description of electron (or other microparticle) behavior is based on the idea of the wave–particle duality of matter. The wave properties of the electron, which play a significant role in its motion in small regions, require a new approach in the description of the electron's dynamic state on the nanoscale. Quantum mechanics has developed a fundamentally new probabilistic method of description of particle motion taking into account its wave properties. This type of description is based on the notion of a wavefunction, which is not always compatible with the notion of a particle's trajectory. This makes electron behavior harder to understand.

A review of milestones in nanoscience and nanotechnology

It is extremely difficult to write the history of nanotechnology for two reasons. First, because of the vagueness of the term “nanotechnology.” For example, nanotechnology is very often not a technology in the strictest sense of the term. Second, people have always experimented with nanotechnology even without knowing about it. Ironically enough, we can say that the medieval alchemists were the founding fathers of nanoscience and nanotechnology. They were the first researchers who tried to obtain gold from other metals. The ancient Greek philosopher Democritus also can be considered as a father of modern nanotechnology, since he was the first to use the name “atom” to characterize the smallest particle of matter. The red and ruby-red opalescent glasses of ancient Egypt and Rome, and the stained glasses of medieval Europe, can be considered as the first materials obtained using nanotechnology. An exhibition at the British Museum includes the Lycurgus cup made by the ancient Romans. The glass walls of the cup contain nanoparticles of gold and silver, which change the color of the glass from dark red to light gold when the cup is exposed to light. In 1661 the Irish chemist Robert Boyle for the first time stated that everything in the world consists of “corpuscules” – the tiniest particles, which in different combinations form all the varied materials and objects that exist.

Nanotechnology is based on the ability to manipulate individual atoms and molecules in order to assemble them into bigger structures. Such artificial nanoscale structures, usually fabricated using self-assembly phenomena, possess new physical, chemical, and biological properties. The fabrication of various types of nanostructures and study of their properties require new technological means and new principles.

Nanotechnology has initiated a new so-called bottom-up technology. The bottom-up technology is based on the self-assembly phenomenon, i.e., the process of formation of complex ordered structures from simpler ones. The main idea of this technology is in the development of the controlled self-assembly of the atoms, molecules, and molecular chains into nanoscale objects. The bottom-up technology allows the fabrication of nanoobjects, such as quantum dots, quantum wires, and superlattices.

The bottom-up approach is opposite in principle to the traditional approach, which may be called the top-down approach, which is based on the sequential decrease of the object's size by means of mechanical or chemical processing for the fabrication of objects of nanoscale size (nanoobjects). Thus, for example, some of the nanoparticles can be obtained by grinding material consisting of particles of micrometer or larger size in a special grinder. The traditional technologies include laser methods for the processing of semi-conductor surfaces and making masks of various configurations and sizes for photolithography.

In this chapter we will briefly consider the main fabrication and characterization techniques for nanostructures and will give some examples of applications of nanostructures in modern nanoelectronics.

Laser heating

Carbon dioxide (CO2) infrared lasers provide a natural choice of heating system in conjunction with aerodynamic levitation. For the CNL setup shown in Fig. 2.1, a Synrad Model 60–2 270-W cw CO2 laser in the infrared range is used to heat and melt the samples. The laser beam is tilted with respect to the vertical plane by approximately 15° to avoid interference with the motion of the X-ray detector. It is directed at the sample by means of two mirrors and a ZnSe lens placed between them. Two controllers, one located inside the X-ray hutch and the other outside it, were used to control the laser power independently.

Heating with a single laser leads to significant temperature gradients, especially with insulating samples. More recent setups (Krishnan et al., 2005; Hennet et al., 2006) incorporate a second laser heating the sample from below through a small hole in the conical nozzle in order to reduce these gradients. In the CRMHT apparatus, there are actually two lasers heating the sample from above. At the lowest specimen temperatures, the power delivered to the specimen from below is roughly equal to the power delivered from above. With these modifications, temperature gradients from top to bottom of the sample are expected to be reduced below 25 °C, even for oxide samples.

Laser heating, generally with one or two CO2 infrared lasers, is also used in recent high-temperature experiments with electrostatic levitation.

The present time appears appropriate for a monograph summarizing the current state of the art of investigation of high-temperature materials with levitation techniques. Although methods for levitating solid and liquid samples in a containerless environment have existed for the best part of the century – the patent for electromagnetic levitation dates back to 1923 – it is only in the past 20 years that their potential has been fully exploited by combining the levitation and heating aspects with new capabilities for structural and dynamic studies at synchrotron X-ray and high-flux neutron sources and refined techniques for thermophysical and transport property studies such as digital imaging, noncontact modulation calorimetry and electrodeless conductivity measurements. There has also been a rapid diversification in the types of levitation methods – aerodynamic, electromagnetic, electrostatic, and others – each of which have special advantages and disadvantages. The 2006 American Physical Society meeting in Baltimore, USA, featured a symposium of invited talks focusing on just one of these methods, electrostatic levitation combined with synchrotron X-ray studies.

Measurements of the structural, dynamical, thermophysical and transport properties of materials at high temperature are important in advancing condensed matter theory, in developing predictive models, and in establishing structure–property–process. Major experimental difficulties are encountered in obtaining reliable data on contained materials at temperatures above 1000 K owing to reactions of the samples with container walls and to the influence of the containers on scattering measurements. These problems are compounded when dealing with high-melting, corrosive liquids.

It is hoped that the reader who has conscientiously struggled through the previous eight chapters has acquired a sense of the achievements and potential of investigating high-temperature materials with levitation techniques.

The acquisition of reliable thermophysical data on solids and liquids at high temperature must be considered among the major achievements, bearing in mind the difficulties that previous workers had in obtaining consistent and reliable data on contained samples at high temperature, especially those of a corrosive nature. One need only take the example of the density, an apparently humdrum quantity that is not only technologically important, for example in determining the ideal conditions for synthesis of crystalline silicon for the semiconductor industry, but also a vital parameter in materials research: a knowledge of the number density is needed to obtain useful real-space information from diffraction experiments, and furthermore it is the unique quantity that enters into a version of mode-coupling theory that has provided one of the most successful routes to understanding the dynamics of simple liquids, as well as an important parameter in ab initio numerical simulations.

A second achievement has been the ability to access metastable solid states. We have encountered several examples of new solid phases, especially glassy phases, that are not accessible with conventional techniques. Undoubtedly such phases will prove to have important technological applications in the optical and optoelectronic industries.

From the point of view of fundamental science, some striking accomplishments have resulted from the ability to access the deeply undercooled liquid state.

Advantages of levitation methods

Investigations of contained materials at high temperature have to contend with two distinct problems: (a) interactions between the sample and container and the resulting possibility of contamination, and (b) the effects of the container walls on the measurements, causing, for example, additional background and beam attenuation in scattering experiments. Both types of problem are removed by the use of levitation. Figure 5.1 shows the melting points and sound velocities (in the solid phase) of some representative materials. Levitation methods (with laser or other kinds of heating) are generally advantageous for measurements at temperatures above the line marked ‘levitation’. This is of course especially true for liquids, but levitation may also be beneficial for studying solid phases at high temperature. For corrosive materials, including many oxide melts, levitation methods may also be advisable at lower temperatures.

The regions marked ‘n’ and ‘x’ in Fig. 5.1 indicate roughly the regions where inelastic neutron and X-ray scattering, respectively, will be advantageous for studying collective excitations, taking into account the higher energy resolution of neutron spectrometers as opposed to the greater ability of X-ray experiments to sample larger regions of Q and E, given the requirement that the velocity of the probe must be considerably larger than that of the excitation being studied (Price & Sköld, 1986).

In the following three chapters we will give some examples of such investigations in different kinds of high-temperature solids and liquids.

The origins of this monograph can be found in a game of bridge played one evening at the 1994 Gordon Conference on High-Temperature Chemistry in Meriden, USA, the participants being Jimmie Edwards of the University of Toledo, Shankar Krishnan, then at Containerless Research Inc. (CRI), and Marie-Louise Saboungi and myself, then at Argonne National Laboratory (ANL). The outcome of the game is best left unrecorded, but a more fortunate consequence of the evening's proceedings was the inauguration of a CRI–ANL collaboration on structural studies of aerodynamically levitated liquids, first with neutrons at the Intense Pulsed Neutron Source at Argonne and subsequently with X-rays at the National Synchrotron Light Source at Brookhaven, supported by a Small Business Innovative Research Grant from the US Department of Energy. Many interesting experiments ensued, some of which are described in this work. A few years later, Marie-Louise Saboungi and I were invited by Jean-Pierre Coutures, Director of the Center for Research on Materials at High-Temperature (CRMHT), Orléans, France, for a three-month visit. This led to an eventual move to Orléans, with occasional breaks at places like Trinity College, Cambridge, where the idea of writing a book for Cambridge University Press came up.

The monograph that resulted aims to summarize the state of the art of the measurement of structural, dynamic and physical properties with levitation techniques, the considerable progress made in the past two decades and the prospects for the future.

Since all the levitation techniques described in Chapter 2 work with conducting materials, it is not surprising that they form the subject of the majority of investigations carried out to date. In this chapter we discuss some representative systems, chosen either because several of their properties have been investigated, especially by levitation techniques, or because they exhibit especially interesting phenomena.

Early transition metals

It is convenient to divide the results obtained on levitated samples of transition metals into early (Groups IVB–VIIB) and late (Group VIIIB) transition metals. The earlier group contains the refractory metals, conventionally taken as Nb, Ta, Mo, W and Re, although relatively few measurements have been made in these even with levitation techniques, presumably because of their very high melting points. A notable exception are the early optical property measurements made on Nb by Krishnan et al. (1991a), using EML in conjunction with laser heating. Values obtained for the high-temperature solid and liquid are shown in Figs. 6.1 and 6.2. It can be seen that the values exhibit rather small discontinuities at the melting point but their temperature dependences change considerably, in the case of n and k going from small negative to large positive temperature coefficients. According to Eq. (4.26), the temperature dependence of the emissivity required a 16% correction to the previous value for the specific heat of liquid Nb at the melting point, with a revised value of 35 ± 1 J mol−1 at Tm.

High-temperature melts with low electrical conductivity have largely been the province of CNL since the other main levitation techniques, EML and ESL, are inconvenient if not impossible for measurements on insulating systems. In fact, from its inception, non-conducting liquids, and in particular refractory molten oxides, have presented the heaviest application of CNL.

Pure trivalent oxides

The molten trivalent oxides Al2O3 and Y2O3, together with their mixtures, by themselves account for the vast majority of measurements with CNL. This is due in part to the scientific as well as technical importance of yttrium aluminium garnet (YAG), Y3Al5O12, an important laser material, discussed in the next section. In addition, pure Al2O3 is of technological interest as the reaction product in rocket engines fuelled by aluminium metal (Parry & Brewster,1991). As a result, molten Al2O3 has often been the material of choice when the opportunity arose for exploiting a new experimental technique with CNL.

The conductivity of molten Al2O3, measured with a contactless technique by Enderby et al. (1997) and Saboungi et al. (2002), is about 6 Ω−1cm−1 at the melting point, indicating the presence of ionic but not electronic conduction. Later measurements (Saboungi et al., unpublished work, 2003) probed the effect of changing the gaseous environment in the levitation system and found a substantial drop in conductivity in a reducing environment (Fig. 8.1). The earlier results of Shpil'rain et al. (1976) on contained samples of molten Al2O3 under argon and in vacuo are in reasonably good agreement with the upper curve in Fig. 8.1.