The main change in this edition is the conversion to SI units. I have tried to be as consistent as possible and have been greatly aided in this task by the unflagging and meticulous care of the publishers. I have occasionally retained the °C particularly when referring to historical experiments and to the properties of water or ice near the melting point; 0 °C seems a more sensible point of reference than 273 K.

I have included some fresh material which fills out certain omissions in the first edition. I have also added some new themes which extend the coverage of the book; in particular the nature of van der Waals forces and the basic ideas of colloid stability. In some places, where it seemed relevant, I have added sections at a level rather more advanced than that required by the average readers; they may at some later stage find it useful to refer back to these items. Finally I have, as is inevitable in moving from c.g.s. to SI units, completely rewritten the introductory parts of the chapters dealing with the dielectric and magnetic properties of matter.

It remains for me to thank various colleagues and numerous correspondents who at various times have written to me proposing corrections and improvements. Though I have not been able to implement all their suggestions I am most grateful to them.

The description of the electronic properties of a-Si: H starts with the energy distribution of electronic states. Depending on their energy and character, the different states determine the electrical transport, recombination and doping etc. Some effects of disorder in a-Si: H on the electronic states are the broadening of the density of states distribution compared to the crystal to form the band tails; the localization of the band tail states; the reduction of the scattering length to atomic distances; and the loss of momentum conservation in the electronic transitions. The last of these necessitates the replacement of the energy-momentum band structure of a crystalline semiconductor by an energy-dependent density of states distribution,N(E). It is convenient to divide N(E) into three different energy ranges; the main conduction and valence bands, the band tail region close to the band edge, and the defect states in the forbidden gap (see Fig. 1.6). This chapter describes the first two types of state and defects are dealt with in Chapter 4. The distribution of states, N(E), is derived in this chapter and is used throughout the remainder of the book in the analysis of experimental results.

One conclusion from the structure studies in Chapter 2 is that the bonding disorder of a-Si:H is relatively small. The silicon atoms have the same tetrahedral local order as crystalline silicon, with a bond angle variation of about 10% and a much smaller bond length disorder. Fig. 3.1 shows the calculated dependence of the bond energy on bond length and bond angle (Biswas and Hamann 1987).

This book describes the material properties and physical phenomena of hydrogenated amorphous silicon (a-Si:H). It covers the growth of material, the atomic structure, the electronic and optical properties, as well as devices and device applications. Since it focusses on the specific properties of one amorphous material, there is a considerable emphasis on describing and interpreting the experimental information. Familiarity with semiconductor physics is assumed, and the reader is also referred to the excellent books by Mott and Davis, Elliott, and Zallen for further information about the general properties of amorphous semiconductors and glasses.

Research into amorphous semiconductors is directed towards an understanding of how the structural disorder leads to their unique properties. A-Si:H has sometimes been regarded as a derivative of crystalline silicon, in which the disorder simply degrades the electronic properties. Much of the interest in a-Si: H comes from the realization that this is not an accurate view. The disordered atomic structure and the presence of hydrogen combine to give new phenomena which are strikingly different from those in the crystalline semiconductors. The structural disorder results in the localized band tail states characteristic of amorphous materials, which are reflected in the optical, transport and recombination properties, while the hydrogen gives unique defect, doping and metastability effects.

The development of a new material with useful technological applications is relatively rare. Hydrogenated amorphous silicon is gaining increasing use in photovoltaic solar cells and in large area arrays of electronic devices.

Illumination creates excess electrons and holes which populate the extended and localized states at the band edges and give rise to photoconductivity. The ability to sustain a large excess mobile carrier concentration is crucial for efficient solar cells and light sensors and depends on the carriers having a long recombination lifetime. The carrier lifetime is a sensitive function of the density and distribution of localized gap states, so that the study of recombination in a-Si: H gives much information about the nature of the gap states as well as about the recombination mechanisms.

The recombination process comprises two sequential steps, as illustrated in Fig. 8.1. An excited electron or hole first loses energy by many transitions within the band, in which the energy decrements are small but frequent. This process is referred to as thermalization. The thermalization rate decreases as an electron moves into the localized band tail states and the density of available states is lower. Eventually the electron completes the recombination by making a transition to a hole with the release of a large energy. Recombination lifetimes are generally much longer than the thermalization times, so that the two processes usually occur on distinctly different time scales.

Recombination is either radiative or non-radiative. The radiative process is accompanied by the emission of a photon, the detection of which is the basis of the luminescence experiment. The radiative transition is the inverse of optical absorption and the two rates are related by detailed balance.

The previous chapters are concerned with the structure and the density of states distribution of a-Si: H, describing the effects of growth, doping and defect reactions. The remainder of the book addresses the various electronic phenomena which result from the electronic structure. Foremost amongst these properties is the electrical conductivity, σ. The distinction between localized and extended electronic states is one of the fundamental concepts in the study of amorphous semiconductors. At zero temperature, carriers in extended states are conducting, but in localized states are not. Most of the experimental measurements of the localized state distribution rely on this property. Although both the concept of electrical conduction and its measurement seem simple, it is a complex process. The conductivity is a macroscopic quantity which represents an average property of the carriers as they move from site to site. The calculation of the conductivity therefore involves the transfer rate, scattering and trapping processes, as well as the appropriate average over the distribution of states. The averaging due to the disorder is the most difficult and leads to many of the interesting effects. The theory of conductivity near a mobility edge in disordered systems has been debated for many years and is still not completely agreed. The theory has applications beyond the boundaries of amorphous semiconductors, for example, in doped crystals, amorphous metals and low-dimensional materials. The discussion of the theory in this book is necessarily abbreviated and describes only the main ideas and how they apply to a-Si:H.

Amorphous materials do not have the regular atomic structure characteristic of a crystal. Instead, the specific bonding arrangement within a particular volume of material represents one of many alternative configurations. Hydrogenated amorphous silicon has the added variability of a hydrogen content which can reach 50 at %. Most features of the a-Si: H network structure are defined at the time of growth and therefore depend on the details of the deposition process. Thus it is anticipated that the electronic properties vary with the growth conditions and that a detailed understanding of the growth mechanisms is essential for the optimization of the electronic properties. Indeed, a-Si:H does exhibit a great range of specific properties. However, the optimization of the growth process produces films which are remarkably independent of the detailed growth process. The best films are all similar, while low quality films are defective in many different ways. It is now recognized that the electronic structure is influenced by defect reactions taking place within the material after growth, which are largely independent of the growth process. These are described in Chapter 6 and explain why the properties of low defect density material are not so sensitive to the deposition method.

Growth of a-Si:H

The usual method of depositing a-Si:H is by plasma decomposition of silane gas, SiH4, with other gases added for doping and alloying. Silane decomposes in the absence of the plasma above about 450 °C and high temperature pyrolitic decomposition is used to make polycrystalline or epitaxial silicon.

In 1975 Spear and LeComber reported that a-Si:H could be doped by the addition of boron or phosphorus; their conductivity data are reproduced in Fig. 5.1. This first observation of electronic doping in an amorphous semiconductor set the stage for the subsequent development of a-Si: H electronic technology. The addition of small quantities of phosphine or diborane to the deposition gas results in changes in the room temperature conductivity by more than a factor 108. The activation energy decreases from 0.7 –0.8 eV in undoped material to about 0.15 eV with phosphorus doping and 0.3 eV for boron. Subsequent experiments confirmed that the conductivity change was due to a shift of the Fermi energy, and that n-type and p-type conduction was occurring (Spear and LeComber 1977). The explanation of the results in terms of substitutional doping has never been doubted.

Examples of the conductivity temperature dependence o(T) of ntype and p-type a-Si: H are shown in Fig. 5.2 (Beyer and Overhof 1984). The thermally activated G(T) implies that the Fermi energy always remains in localized states and there is never metallic conductivity. EF is prevented from reaching the conducting states above the mobility edge by the high density of band tail localized states and also by a low doping efficiency. The conductivity is lower in p-type samples than ntype, primarily because the wider valence band tail keeps EF farther from the mobility edge.

Electronic defects reduce the photosensitivity, suppress doping and impair the device performance of a-Si:H. Their high density in pure amorphous silicon makes this material of lesser interest and is the reason for the attention on the hydrogenated material, in which the defect density is greatly reduced. The remaining defects in a-Si:H control many electronic properties and are centrally involved in the substitutional doping process. The phenomena of metastability, which are described in Chapter 6, are caused by the defect reactions.

Defects are described by three general properties. First is the set of electronic energy levels of their different charge states. Those defects with states within the band gap are naturally of the greatest interest in understanding the electronic properties because of their role as traps and recombination centers. Second is the atomic structure and bonding of the defect, which determine the electronic states. Third are the defect reactions which describe how the defect density depends on the growth and on the treatment after growth. This chapter is mostly concerned with the first two properties, and the defect reactions are discussed in Chapters 5 and 6.

The defects are one of the more controversial aspects of a-Si:H. Many models have been proposed and there is active debate about the interpretation of several of the important experiments. This chapter concentrates on what is currently the most widely accepted model, but also compares the different possibilities and discusses the underlying reasons for disagreement.

Early research

Hydrogenated amorphous silicon (a-Si: H) was a late arrival to the research on amorphous semiconductors, which began to flourish during the 1950s and 1960s; studies of insulating oxide glasses, of course, go back much further. Interest in the amorphous semiconductors developed around the chalcogenides, which are materials containing the elements sulfur, selenium and tellurium; examples are As2 Se3, GeS2 etc. The chalcogenides are glasses which may be formed by cooling from the melt, with structure similar to the oxides but with smaller energy band gaps. Research in these amorphous semiconductors addressed the question of how the disorder of the noncrystalline structure influences the electronic properties. The study of chalcogenides was further promoted by the introduction of xerographic copying machines. Xerography was invented in 1938 and the first successful copier was made in 1956, using selenium as the photoconductive material.

A-Si:H was first made in the late 1960s. Before that time there was research on amorphous silicon without hydrogen, which was prepared by sputtering or by thermal evaporation. The unhydrogenated material has a very high defect density which prevents doping, photoconductivity and the other desirable characteristics of a useful semiconductor. Electronic measurements were mostly limited to the investigation of conduction through the defect states.

Chittick and coworkers in the UK were the first to make a-Si:H, using glow discharge as the deposition technique (Chittick, Alexander and Sterling 1969). Silane gas (SiH4) is excited by an electrical plasma which causes the gas molecules to dissociate the deposit on heated substrates.

In a thin film such as a-Si: H, surface and interface effects can exert an influence throughout the entire material. The surface has different electrical and structural properties from the bulk for various reasons. There are chemical reactions which change the composition, such as oxidation or reactions with metals. There is also transfer of electrical charge across the interface which causes band bending. Possible origins of the charge transfer are the different work functions of the materials in contact or charged species attached to the surface. This chapter describes metal contacts, the free surface, semiconductor and dielectric interfaces, and, lastly, multilayer structures in which a series of very thin layers is grown which has properties which differ markedly from those of the bulk material.

Metallic contacts

When a metal is brought into contact with a semiconductor, there is a transfer of charge across the interface to bring the two Fermi energies into alignment. The space charge in the metal remains very close to the contact, but extends much farther in the semiconductor because of the low density of states in the band gap. The resulting Schottky contact has rectifying electrical properties. A similar barrier is formed between doped and undoped a-Si: H layers. The nature of the metal contact is important in virtually all electrical measurements, as it determines whether charge can flow easily across the contact. Schottky contacts are used in transient capacitance techniques to measure the defect states (see Chapter 3) and in photosensing devices, where the blocking contact reduces the dark current and minimizes noise.

Although amorphous silicon has poorer electronic properties than crystalline silicon, it offers the important technical advantage of being deposited inexpensively and uniformly over a large area. The applications are therefore almost entirely in situations in which either a large device or a large array of devices is needed. The technology which has received the most attention is the photovoltaic solar cell - large scale power production obviously depends on the ability to cover very large areas at a low cost. Input and output devices such as displays, photocopiers and optical scanners also take advantage of the large area capability. Each of these applications requires an electronic device whose size matches the interface with human activity - either a display screen or a sheet of paper - with typical dimensions of 25 cm or larger.

The electronic devices are made up of a few different circuit elements, such as transistors, sensors, light emitting diodes etc. Sections 10.1-10.3 describe how the design of these elements is adapted to the specific properties of a-Si:H. A few of the actual and potential applications are then discussed.

Light sensors

Light sensors made from a-Si: H are either p-i-n or Schottky barrier structures. Unlike crystalline silicon, a p-n junction is ineffective without the undoped layer, because of the high defect density in doped a-Si:H. Illumination creates photoexcited carriers which move to the junction by diffusion or drift in the built-in potential of the depletion layer and are collected by the junction.

In Chapter 5, the doping properties of a-Si:H are described in terms of the alternative bonding structures of the dopants and the silicon network. The doping efficiency, η, is derived from the defect reaction, Eq. (5.27), by assuming thermal equilibrium between the different bonding configurations. This chapter applies the ideas of defect equilibrium to several phenomena, including a more detailed analysis of doping and compensation, the intrinsic defect density and the impurity distribution coefficients. The phenomenon of metastability, in which an external electronic excitation, such as light illumination, causes a reversible change in the density of electronic states, are also explained in the context of the defect reactions of the structure. The equilibration of the material represents a considerable simplification in our understanding of a-Si: H, because thermodynamic models can be used to predict the electronic properties.

It may seem surprising to apply thermal equilibrium concepts to amorphous silicon, because the amorphous phase of a solid is not the equilibrium phase. However, a subset of bonding states may be in equilibrium even if the structure as a whole is not in its lowest energy state. The attainment of equilibrium is prevented by bonding constraints on the atomic structure. The collective motion of many atoms is required to achieve long range crystalline order and the topological constraints are formidable. On the other hand the transformation of point defects requires the cooperation of only a few atoms. Therefore any partial thermal equilibrium may be expected at point defects or impurities.

Spin glass theory has had a rather large and unexpected impact on some problems far removed from spin glasses themselves. It turns out that a number of problems in fields outside physics share some of the essential features — randomness and frustration — that characterize spin glasses, and insights and techniques can be borrowed from spin glass theory and brought usefully to bear on them. This is especially true of the special novel concepts of mean field theory: broken ergodicity is a fundamental concept and broken replica symmetry may be a basic tool for analysing complex systems. While these methods probably do not apply to real spin glasses, many of these other problems have effectively infinite-ranged interactions, and mean field theory (sometimes with replica symmetry breaking) is applicable to them.

In the long run, these problems, rather than spin glasses themselves, may be the reason for reading the first part of this book. The hope that understanding spin glasses could be a key that unlocks the secrets of many other complex systems in and out of physics has been an important factor in making spin glass theory such an active field in the last decade.

In this chapter we describe a few representative examples of such problems. We will examine first some combinatorial optimization problems, in particular, the weighted matching, ‘travelling salesman’, and graph bipartitioning problems. Then we will describe some of the recent progress in understanding collective computational networks.

Renormalization in pure systems

In Section 2.2 we reviewed the basic facts about broken symmetry and phase transitions in pure systems, within mean field theory. This helped set the stage for the mean field description of spin glasses that we studied in Chapters 3–6. We will now want to study the phase transition and the nature of the low-temperature phase for spin glasses with fairly short-ranged interactions in low dimensionality (2 or 3). This situation is far from the region where mean field theory is a good guide, so we will have to learn new methods. Again, we start by learning about them in pure systems.

Renormalization is a very general approach to problems with many strongly interacting degrees of freedom. In a statistical mechanical problem, the basic idea is to carry out the trace in the partition function over some of the variables, leaving a new problem with fewer degrees of freedom. One follows how the parameters in the Hamiltonian of the system change as this procedure is iterated many times. Generally, the partial trace corresponds to removing the short-distance degrees of freedom, so each successive effective Hamiltonian has a larger lattice constant (or equivalent microscopic length) than its predecessor: each renormalization step corresponds to a change of scale. Different thermodynamic phases are identified with flows to different fixed points in the parameter space of the Hamiltonian under this semigroup.