This book provides the foundations and the main ideas emerging from research that underlies the applied field called nanoelectronics. Nanoelectronics promises to improve, amplify, and partially substitute for the well-known field of microelectronics. The prefix micro denotes one millionth and, as applied to electronics, it is used to indicate that the characteristic sizes of the smallest features of a conventional electronic device have length scales of approximately a micrometer. The prefix nano denotes one billionth. Thus, in nanoelectronics the dimensions of the devices should be as many as a thousand times smaller than those of microelectronics.

Such a revolutionary advance toward miniaturization of electronics is based on the recently developed ability to measure, manipulate, and organize matter on the nanoscale – 1 to 100 nanometers, i.e., 1 to 100 billionths of a meter. At the nanoscale, physics, chemistry, biology, materials science, and engineering converge toward the same principles and tools, and form new and broad branches of science and technology that can be called nanoscience and nanotechnology.

Advancing to the nanoscale is not just a step toward miniaturization, but requires the introduction and consideration of many additional phenomena. At the nanoscale, most phenomena and processes are dominated by quantum physics and they exhibit unique behavior. Fundamental scientific advances are expected to be achieved as knowledge in nanoscience increases. In turn, this will lead to dramatic changes in the ways materials, devices, and systems are understood and created.

Introduction

The evolution of microelectronics toward reduced device sizes has proceeded to a degree that renders conventional models, approaches, and theories inapplicable. Indeed, for objects with sizes of 100 nanometers or less it is frequently the case that the length scales associated with fundamental physical processes are comparable to the geometrical size of the device; also, fundamental time scales associated with physical processes are of the order of the time parameters for nanodevice operation. Therefore, on the nanoscale the theories and models underlying modern nanoelectronics become more complicated, and rely more and more on basic science.

Generally, in the nanoworld the fundamental laws of physics that govern particles and material fields differ from those that apply to familiar macroscopic phenomena such as the motion of a baseball or a train. Instead of classical mechanics, that works so well for macroscopic phenomena, the motion of particles in the nanoworld is determined by the so-called wave mechanics or quantum mechanics. An underlying principle of central importance for nanophysics is the fundamental concept that all matter, including electrons, nuclei, and electromagnetic fields, behaves as both waves and particles, that is, wave–particle duality is a basic characteristic of all matter.

At first glance, wave properties and particle properties for the same physical object are hardly compatible. To understand wave–particle duality, we will briefly review, in the following two subsections, the basic properties of particles and waves known from classical physics.

Introduction

After the previous introduction to the general properties of particles and waves on the nanoscale, we shall now overview the basic materials which are exploited in nanoelectronics. As discussed in Chapter 1, electronics and optoelectronics primarily exploit the electrical and optical properties of solid-state materials. The simplest and most intuitive classification of solids distinguishes between dielectrics, i.e., non-conducting materials, and metals, i.e., good conducting materials. Semiconductors occupy a place in between these two classes: semiconductor materials are conducting and optically active materials with electrical and optical properties varying over a wide range. Semiconductors are the principal candidates for use in nanoelectronic structures because they allow great flexibility in the control of the electrical and optical properties and functions of nanoelectronic devices.

The semiconductors exploited in microelectronics are, in general, crystalline materials. Through proper regimes of growth, subsequent modifications and processing, doping by impurities, etc., one can fabricate nanostructures and nanodevices starting from these “bulk-like” materials.

Other physical objects that demonstrate promising properties for nanoelectronicswere discovered recently, for example carbon nanotubes. These wire-like and extended objects are of a few nanometers in cross-section. They can be produced with good control of their basic properties; in particular, they can be fabricated as either semiconductors or metals. Various types of processing techniques have been shown to be viable for the fabrication of electronic nanodevices from carbon nanotubes.

Welcome to the amazing nanoworld! In this book you will find fundamental principles in nanoscience and basic techniques of measurement, as well as fabrication and manipulation of matter at the nanoscale. The book discusses how these principles, techniques, and technologies are applied to the newest generation of electronics, known as nanoelectronics.

The science of atoms and simple molecules, and the science of matter from microstructures to larger scales, are both well established. A remaining, extremely important, sizerelated challenge is at the nanoscale – roughly the dimensional scales between 10 and 100 molecular diameters – where the fundamental properties of materials are determined and can be engineered. This field of science – nanoscience – is a broad and interdisciplinary field of emerging research and development.

Nanotechnology is concerned with materials, structures, and systems whose components exhibit novel and significantly modified physical, chemical, and biological properties due to their nanoscale sizes. A principal goal of nanotechnology is to control and exploit these properties in structures and devices at atomic, molecular, and supramolecular levels. To realize this goal, it is essential to learn howto fabricate and use these devices efficiently. Nanotechnology has enjoyed explosive growth in the past few years. In particular, nanofabrication techniques have advanced tremendously in recent years. Obviously, revolutionary changes in the ability to measure, organize, and manipulate matter on the nanoscaleare highly beneficial for electronics with its persistent trend of downscaling devices, components, and integrated systems. In turn, the miniaturization required by electronics is one of the major driving forces for nanoscience and nanotechnology.

Introduction

Having reviewed the basic properties of materials exploited in nanoelectronics, we shall now study the principal methods of high-quality material growth and nanodevice fabrication. Methods for the growth of perfect materials with controllable properties are critically important for nanostructure fabrication. Indeed, stringent requirements must be met for the growth of crystals for nanosize devices. These requirements include many factors and, first of all, ultra-high quality and purity, both controlled within extremely close limits. The following examples illustrate the term “ultra-high quality.” For Si crystals used in nanodevices, concentrations of controlled impurities currently reach concentrations of less than one part in ten billion (1 in 1010). For the case of Ge, this number is in the range of 1 in 1013−1014. The quality of a silicon crystal being used for nanoelectronics can be characterized in terms of the density of defects: they must be limited to several tens per 1 m2 (!) of the Si wafer according to the Semiconductor Road Map, that was discussed in Chapter 1. The basic methods of growth of perfect crystalline materials and multilayered heterostructures we will discuss in Section 5.2.

To fabricate a nanostructure and a nanodevice two approaches can be undertaken. The first is based on a previously grown perfect material with further processing. This includes a number of fabrication stages and methods (nanolithography, etching, implantation, selective doping, etc.). In Section 5.3 we review these methods.

External state variables

Thermodynamics is concerned with the state of a system when left alone, and when interacting with the surroundings. By ‘system’ we shall mean any portion of the world that can be defined for consideration of the changes that may occur under varying conditions. The system may be separated from the surroundings by a real or imaginary wall. The properties of the wall determine how the system may interact with the surroundings. The wall itself will not usually be regarded as part of the system but rather as part of the surroundings. We shall first consider two kinds of interactions, thermal and mechanical, and we may regard the name ‘thermodynamics’ as an indication that these interactions are of main interest. Secondly, we shall introduce interactions by exchange of matter in the form of chemical species. The name ‘thermochemistry’ is sometimes used as an indication of such applications. The term ‘thermophysical properties’ is sometimes used for thermodynamic properties which do not primarily involve changes in the content of various chemical species, e.g. heat capacity, thermal expansivity and compressibility.

One might imagine that the content of matter in the system could be varied in a number of ways equal to the number of species. However, species may react with each other inside the system. It is thus convenient instead to define a set of independent components, the change of which can accomplish all possible variations of the content.

Experimental conditions

There will be a driving force for a phase transformation if the conditions of a system are changed in such a way that the system moves from one phase field into another in the phase diagram. In this chapter we shall examine the character of such phase transformations and we shall find that they depend upon the experimental method of controlling and changing the conditions. It is important first to realize that the possibility of efficiently controlling the various state variables is very different. For gaseous and liquid phases it is comparatively easy to control the pressure. It can be kept constant or it can be changed gradually according to an experimental programme. At any moment it is very uniform in the system apart from effects due to the surface energy of curved phase interfaces. For solid systems it is more difficult to control the pressure, in particular during a phase transformation resulting in a volume change. This may give rise to local deformation and internal stresses. On the other hand, solid phases are usually so dense and rigid that the thermodynamic effect of pressure differences and stresses can often be ignored. From a practical point of view we may often regard the pressure as an experimental variable which can be reasonably well maintained at a low enough level to have a negligible effect.

Transformations and transitions

In Chapter 12 we were mainly concerned with the question whether a transformation is sharp or gradual. The difference between those cases is very practical and straight-forward. It is based on a one-dimensional phase diagram where the only axis represents the quantity that is being varied. If that diagram shows a two-phase field of some extension between the two one-phase fields, then the transformation between the two phases will be gradual. If the two-phase field has no extension, then the transformation will be sharp. For a unary system with a transformation this will happen if one varies a potential, e.g. T. The Gibbs energy is a continuous function of T across the sharp transformation but its derivatives, yielding S and V, show discontinuous jumps. This is why the phase boundaries separate when a molar axis is introduced (see Figs 9.1 and 9.2). In other cases there is no such separation because the first-order derivatives are zero. A typical example is found in a ferromagnetic substance, which gradually loses its magnetization as the temperature is increased. At the Curie temperature it reaches zero and the substance has thus become paramagnetic. There is no temperature where ferromagnetic and paramagnetic regions coexist in a pure substance, not even if one varies a molar quantity.

General principles

By ‘modelling’ we shall understand the selection of some assumptions from which it is possible to calculate the properties of a system. Sometimes it is possible to obtain a close mathematical expression giving a property as a function of interesting variables. In this chapter and the following ones we shall mainly concern ourselves with such models. However, in many cases the model cannot be expressed in a closed mathematical form but results can also be obtained by numerical calculations using some iterative method. When the iteration in some way resembles the behaviour of a real physical system one talks about ‘simulation’. Such methods are becoming increasingly more powerful thanks to access to more and more powerful computers.

The purpose of modelling is two-fold. From a scientific point of view one likes to learn how nature functions. One way of gaining knowledge is to define some hypothesis resulting in a model and test it by comparing the predictions from the model with experimental information. Then, it does not matter much if the predictions are made by an analytical calculation or by some numerical method. From a more technological point of view one likes to predict the properties of a particular system in order to put it to efficient use in some practical construction or operation. Then it is often most convenient to have a model which yields an analytical expression.

Thermodynamic treatment of kinetics of internal processes

In Chapter 1 we considered spontaneous processes inside a system when discussing the second law but later in that chapter we only considered equilibria. We shall now discuss the thermodynamic treatment of the kinetics of such processes. This field of thermodynamics is often called irreversible thermodynamics but the full term should rather be thermodynamics of irreversible processes. The word irreversible is often replaced by the word spontaneous. A process occurring inside a system may be caused by a change imposed upon the system by some external action, but it will here be regarded as a spontaneous result of the new conditions inside the system. All processes inside a system that actually occur will thus be regarded as spontaneous. It would really be unnecessary to use either of the terms irreversible and spontaneous processes if it were not for the need to distinguish them from the limiting case of a cyclic process, e.g. the Carnot cycle, when it is carried out in such a way that the internal processes it gives rise to produce a negligible amount of entropy. Since a cyclic process is controlled by actions from the outside and they could be performed in the reverse direction, it is possible to run the cycle in the reverse direction. All the internal processes it gives rise to will also reverse and if their entropy production is again negligible the two cases will be identical in the limit, except for the sign.