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This chapter discusses noise in homogeneous semiconductors which can all be treated by the Lax–Onsager regression theorem. In a homogeneous sample, the density of free carriers of electrons can be expressed in a form that takes into account the density of electronic states per unit energy and the probability that any one of these states is occupied. The energy is the energy at the bottom of the conduction band. If the conduction band is isotropic near its minimum, the energy takes the simple form that includes the effective mass of electrons in the conduction band. This chapter examines density of states and statistics of free carriers, conductivity fluctuations, thermodynamic treatment of carrier fluctuations, general theory of concentration fluctuations, and influence of drift and diffusion on modulation noise.

The applied voltages that drive electrochemical processes (see Chapter 11) are only one of many energy sources that can be used to activate reactions in oxide molecules and materials. Another common energy source that drives many environmental and technological oxide reactions is light from the sun. Water plays a key role in many of these reactions. Imagine that you are on vacation floating in a warm ocean bathed by the sun. Many of the phenomena you experience, from your painful sunburn to the photosynthetic growth of the seaweed you see beneath you, are photoactivated processes. In this chapter, we highlight the roles that oxides play in photon-activated solar energy technologies. Also included are reactions stimulated by other nonthermal energy sources, including electrons in high-energy plasmas. Titanium oxide, found in common white paint, is the basis for much of the discussion, because this oxide is used in many photoelectrochemical energy storage technologies. The photochemistry of colloidal manganese- and iron-oxide particles suspended either in atmospheric droplets or in the upper photic zone of the ocean where the sunlight penetrates are discussed in Chapter 18. Such oxide reactions are important globally in the elimination of pollutants. Both industrial and environmental examples illustrate how oxides participate in a wide range of photoactivated chemical reactions, including the catalytic decomposition of water, photoelectrochemistry, and photoactivated dissolution and precipitation reactions. Before exploring excited-state reactions, we need to introduce the energy sources that provide such excitation. In most of this chapter, the excitation source of interest is light. Most of us are familiar with the electromagnetic spectrum, in which the energy of a photon is given by … E=hv=hc/λ=hcω (13.1)… Here, h is Planck’s constant (h = 6.6 ·10 ^–34 J/second), c is the speed of light (3 ·1010cm/second), ν is the frequency of light (measured in Hertz or per second), λ is the wavelength of light (in centimeters), and ω is the wavelength expressed as wave number (measured per centimeter in infrared spectroscopy).

The so-called k·p theory provides an effective framework for modeling the band structures of III–V semiconductors. This approach starts with a handful of bands that are coupled in accordance with the crystal symmetry discussed in Chapter 1. This chapter describes the k·p theory and lays out the assumptions that underlie its most common versions, including Kane’s model. It also shows how the spin–orbit coupling affects the band structure of semiconductors.

This chapter discusses short wavelength quantum cascade lasers covering conduction band discontinuity and performance, heterostructure materials, and strain-compensated In_xGa_1−xAs/Al_yIn_1−yAs/InP material system.

Chapter 2 introduces the concept of excitons. Excitons are spatially coherent excitations extending over a macroscopic volume. Such coherent excitations can result either from atomic excitation delocalized by intersite interatomic-level Coulomb processes, as in the case of Frenkel excitons, or from the excitation of valence electrons into the conduction band, as in the case of Wannier excitons. In the latter case, the resulting electron in the conduction band and the hole left in the valence band can form a bound state through attractive intraband Coulomb processes. Wannier and Frenkel excitons follow from the same crystal Hamiltonian—electrons in a periodic ion lattice—but the various Coulomb terms are associated in a different way because of their physical differences at the one-electron level.

The study of dynamics of molecular processes in condensed phases necessarily involves properties of the condensed environment that surrounds the system under consideration. This chapter provides some essential background on the properties of solids while the next chapter does the same for liquids. No attempt is made to provide a comprehensive discussion of these subjects. Rather, this chapter only aims to provide enough background as needed in later chapters in order to take into consideration two essential attributes of the solid environment: Its interaction with the molecular system of interest and the relevant timescales associated with this interaction. This would entail the need to have some familiarity with the relevant degrees of freedom, the nature of their interaction with a guest molecule, the corresponding densities of states or modes, and the associated characteristic timescales. Focusing on the solid crystal environment we thus need to have some understanding of its electronic and nuclear dynamics. The geometry of a crystal is defined with respect to a given lattice by picturing the crystal as made of periodically repeating unit cells. The atomic structure within the cell is a property of the particular structure (e.g. each cell can contain one or more molecules, or several atoms arranged within the cell volume in some given way), however, the cells themselves are assigned to lattice points that determine the periodicity. This periodicity is characterized by three lattice vectors, ai, i = 1, 2, 3, that determine the primitive lattice cell—a parallelepiped defined by these three vectors.

A semiconductor can be regarded as an insulator with a narrow band gap, ε_g. Semiconductors may be divided into two classes: those for which the points in k-space corresponding to the highest occupied valence band state, ε_v, and the lowest unoccupied conduction band state, ε_c, lie directly above each other (a direct band gap material); and those for which these two points are separated in k-space by some amount k₀ (an indirect band gap material). At absolute zero, all the states associated with the valence bands are filled while those of the conduction bands are empty. The empty state is referred to as a hole. In the presence of an applied electric field, transitions will occur from the lower lying (occupied) electron state into the empty hole state, i.e., the hole will move lower in energy. However, since the hole represents the absence of an electron, this downward motion of the hole represents an increase in the energy of the system. In steady state, where the energy gained from an external potential drop is lost to the rest of the system through scattering, the hole will drift at a constant velocity. A completely filled band carries no current, and therefore the holes contribute a current of the opposite sign — they behave like positively charged electrons. This chapter discusses the following: parabolic bands, carrier densities and densities of states, band properties in some specific materials, holes in Si and Ge, impurity states, calculating the occupancy of donors and acceptors, carrier concentrations in the presence of donors and acceptors, impurity band conduction, and qualitative behavior on doping.

Energy and momentum relaxation can be characterised by time constants that are often picoseconds or less. At times longer than this, the typically slower processes of trapping and recombination are described by time constants that are generally longer than a nanosecond. The so-called hydrodynamic model of transport can be derived by defining statistical averages and moments from the Boltzmann equation. When momentum and energy relaxation is relatively so fast, simple phenomenological quantities such as the mobility and the diffusion constant can be used. This results in the simplest transport model, known as the drift-diffusion model. This chapter examines space-charge waves in semiconductors by focusing on a selection of special transport phenomena that can be described by a drift-diffusion model. It considers the case of non-degenerate distributions of electrons in a conduction band and holes in a valence band of a piezoelectric semiconductor. After discussing phenomenological equations, the chapter provides an overview of space-charge and acoustoelectric waves and then discusses parametric processes, domains and filaments, and recombination waves.