Chapter 21 Optical Properties (a) Schematic diagram illustrating the operation of a Load photovoltaic solar cell. The cell is made of polycrystalline silicon that has been fabricated to form a p–n junction Sunlight Current (see Sections 18.11 and 18.15). Photons that originate as light from the sun excite electrons into the conduction band on the n side of the junction and create holes on the p side. These electrons and holes are drawn away n-type silicon from the junction in opposite directions and become part Junction of an external current. p-type silicon Photons Electron flow – – + + “Hole” flow (a) Courtesy of Research Institute for Sustainable Energy (www.rise.org.au) and Murdoch University (c) A home with a number of solar panels. © Gabor Izso/iStockphoto (b) (b) An array of polycrystalline silicon © Brainstorm1962/iStockphoto (c) photovoltaic cells. 838 • WHY STUDY the Optical Properties of Materials? When materials are exposed to electromagnetic fiber materials in communications, we note that the radiation, it is sometimes important to be able to performance of optical fibers is increased by introducing predict and alter their responses. This is possible when a gradual variation of the index of refraction (i.e., a we are familiar with their optical properties and graded index) at the outer surface of the fiber. This is understand the mechanisms responsible for their optical accomplished by the addition of specific impurities in behaviors. For example, in Section 21.14 on optical controlled concentrations. Learning Objectives After studying this chapter, you should be able to do the following: 1. Compute the energy of a photon given its 5. Describe the mechanism of photon absorption frequency and the value of Planck’s constant. for (a) high-purity insulators and semiconductors 2. Briefly describe the electronic polarization that and (b) insulators and semiconductors that con- results from electromagnetic radiation–atomic tain electrically active defects. interactions, and cite two consequences of elec- 6. For inherently transparent dielectric materials, tronic polarization. note three sources of internal scattering that can 3. Briefly explain why metallic materials are opaque lead to translucency and opacity. to visible light. 7. Briefly describe the construction and operation 4. Define index of refraction. of ruby and semiconductor lasers. 21.1 INTRODUCTION Optical property refers to a material’s response to exposure to electromagnetic radiation and, in particular, to visible light. This chapter first discusses some of the basic principles and concepts relating to the nature of electromagnetic radiation and its possible interactions with solid materials. Then it explores the optical behaviors of metallic and nonmetal- lic materials in terms of their absorption, reflection, and transmission characteristics. The final sections outline luminescence, photoconductivity, and light amplification by stimulated emission of radiation (laser), the practical use of these phenomena, and the use of optical fibers in communications. Basic Concepts 21.2 ELECTROMAGNETIC RADIATION In the classical sense, electromagnetic radiation is considered to be wavelike, consisting of electric and magnetic field components that are perpendicular to each other and also to the direction of propagation (Figure 21.1). Light, heat (or radiant energy), radar, radio waves, and x-rays are all forms of electromagnetic radiation. Each is characterized primarily by a specific range of wavelengths and also according to the technique by which it is generated. The electromagnetic spectrum of radiation spans the wide range from g-rays (emitted by ra- dioactive materials) having wavelengths on the order of 10Ϫ12 m (10Ϫ3 nm) through x-rays, ultraviolet, visible, infrared, and finally radio waves with wavelengths as long as 105 m. This spectrum is shown on a logarithmic scale in Figure 21.2. • 839 840 • Chapter 21 / Optical Properties Figure 21.1 An electromagnetic Ᏹ ␭ wave showing electric field Ᏹ and magnetic field H components and the wavelength ␭. Position H Visible light lies within a very narrow region of the spectrum, with wavelengths ranging between about 0.4 ␮m (4 ϫ 10Ϫ7 m) and 0.7 ␮m. The perceived color is deter- mined by wavelength; for example, radiation having a wavelength of approximately 0.4 ␮m appears violet, whereas green and red occur at about 0.5 and 0.65 ␮m, respec- tively. The spectral ranges for several colors are included in Figure 21.2. White light is simply a mixture of all colors. The ensuing discussion is concerned primarily with this visible radiation, by definition the only radiation to which the eye is sensitive. All electromagnetic radiation traverses a vacuum at the same velocity, that of light—namely, 3 ϫ 108 m/s (186,000 miles/s). This velocity, c, is related to the electric For a vacuum, permittivity of a vacuum P and the magnetic permeability of a vacuum m through dependence of the 0 0 velocity of light on electric 1 c = (21.1) permittivity and 1P 0 m0 magnetic permeability Figure 21.2 The Energy (eV) Wavelength (m) spectrum of electro- Frequency (Hz) magnetic radiation, 108 10–14 Visible spectrum 1022 wavelength including wavelength 0.4 ␮m ranges for the various ␥-Rays 106 10–12 20 Violet colors in the visible 10 spectrum. X-Rays 104 10–10 1 angstrom (Å) Blue 1018 1 nanometer (nm) 0.5 ␮m 102 10–8 Ultraviolet 1016 Green –Visible –6 Yellow 100 10 1 micrometer (␮m) 1014 Infrared 0.6 ␮m Orange 10–2 10–4 1012 1 millimeter (mm) Microwave 10–4 10–2 1010 Red 0.7 ␮m 10–6 100 1 meter (m) 108 Radio, TV 10–8 102 106 1 kilometer (km) 10–10 104 104 21.3 Light Interactions with Solids • 841 Thus, there is an association between the electromagnetic constant c and these electrical and magnetic constants. Furthermore, the frequency v and the wavelength ␭ of the electromagnetic radiation For electromagnetic are a function of velocity according to radiation, relationship among c = lv (21.2) velocity, wavelength, and frequency Frequency is expressed in terms of hertz (Hz), and 1 Hz ϭ 1 cycle per second. Ranges of frequency for the various forms of electromagnetic radiation are also included in the spectrum (Figure 21.2). Sometimes it is more convenient to view electromagnetic radiation from a quantum- mechanical perspective, in which the radiation, rather than consisting of waves, is photon composed of groups or packets of energy called photons. The energy E of a photon is said to be quantized, or can only have specific values, defined by the relationship For a photon of electromagnetic radiation, hc E = hv = (21.3) dependence of l energy on frequency, and also velocity and wavelength where h is a universal constant called Planck’s constant, which has a value of 6.63 ϫ 10Ϫ34 J#s. Thus, photon energy is proportional to the frequency of the radiation, or Planck’s constant inversely proportional to the wavelength. Photon energies are also included in the elec- tromagnetic spectrum (Figure 21.2). When describing optical phenomena involving the interactions between radiation and matter, an explanation is often facilitated if light is treated in terms of photons. On other occasions, a wave treatment is preferred; both approaches are used in this discus- sion, as appropriate. Concept Check 21.1 Briefl y discuss the similarities and differences between photons and phonons. Hint: You may want to consult Section 19.2. Concept Check 21.2 Electromagnetic radiation may be treated from the classical or the quantum-mechanical perspective. Briefl y compare these two viewpoints. [The answers may be found at www.wiley.com/college/callister (Student Companion Site).] 21.3 LIGHT INTERACTIONS WITH SOLIDS When light proceeds from one medium into another (e.g., from air into a solid substance), several things happen. Some of the light radiation may be transmitted through the medium, some will be absorbed, and some will be reflected at the interface between the two media. The intensity I0 of the beam incident to the surface of the solid Intensity of an medium must equal the sum of the intensities of the transmitted, absorbed, and reflected incident beam beams, denoted as I , I , and I , respectively, or at an interface is T A R equal to the sum I = I + I + I of the intensities 0 T A R (21.4) of transmitted, absorbed, and reflected beams Radiation intensity, expressed in watts per square meter, corresponds to the energy being transmitted per unit of time across a unit area that is perpendicular to the direction of propagation. 842 • Chapter 21 / Optical Properties An alternate form of Equation 21.4 is T + A + R = 1 (21.5) where T, A, and R represent, respectively, the transmissivity (IT/I0), absorptivity (IA/I0), and reflectivity (IR/I0), or the fractions of incident light that are transmitted, absorbed, and reflected by a material; their sum must equal unity because all the incident light is transmitted, absorbed, or reflected. Materials that are capable of transmitting light with relatively little absorption transparent and reflection are transparent—one can see through them. Translucent materials are those through which light is transmitted diffusely; that is, light is scattered within the translucent interior to the degree that objects are not clearly distinguishable when viewed through a specimen of the material. Materials that are impervious to the transmission of visible opaque light are termed opaque. Bulk metals are opaque throughout the entire visible spectrum—that is, all light ra- diation is either absorbed or reflected. However, electrically insulating materials can be made to be transparent. Furthermore, some semiconducting materials are transparent, whereas others are opaque. 21.4 ATOMIC AND ELECTRONIC INTERACTIONS The optical phenomena that occur within solid materials involve interactions between the electromagnetic radiation and atoms, ions, and/or electrons. Two of the most important of these interactions are electronic polarization and electron energy transitions.