W57
Chapter
21
Optical 1496T_c21_W57-W85
3/1/06
15:21
Page Properties
lar glass prism. Refraction occurs when the direction of the light beam is bent at both glass-air prism interfaces (i.e., as it passes into and out of the prism). And dispersion (chromatic) occurs when the degree of bending depends on wavelength (i.e., the beam is separated into its component colors). ( PhotoDisc/Getty Images.)
A
white light beam experiences both refraction and dispersion as it passes through the triangu-
WHY STUDY the Optical Properties of Materials?
When materials are exposed to electromagnetic radiation, it is sometimes important to be able to predict and alter their responses. This is possible when we are familiar with their optical properties and understand the mechanisms responsible for their optical behaviors. For example, in Section 21.14 on optical fiber materials, we note that the performance of optical fibers is increased by introducing a gradual variation of the index of refraction (i.e., a graded index) at the outer surface of the fiber. This is accomplished by the addition of specific impurities in controlled concentrations. W57
1496T_c21_W57-W85
3/1/06
15:21
Page W58
Learning Objectives
After careful study of this chapter you should be able to do the following: 1. Compute the energy of a photon given its fre5. Describe the mechanism of photon absorption quency and the value of Plancks constant. for (a) high-purity insulators and semiconduc2. Briefly describe electronic polarization that retors, and (b) insulators and semiconductors that sults from electromagnetic radiation-atomic incontain electrically active defects. teractions. Cite two consequences of electronic 6. For inherently transparent dielectric materials, polarization. note three sources of internal scattering that 3. Briefly explain why metallic materials are can lead to translucency and opacity. opaque to visible light. 7. Briefly describe the construction and operation 4. Define index of refraction. of ruby and semiconductor lasers.
21.1 INTRODUCTION
By optical property is meant a materials 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. Next to be explored are the optical behaviors of metallic and nonmetallic 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 utilization of these phenomena, and optical fibers in communications.
Basic Concepts
21.2 ELECTROMAGNETIC RADIATION
In the classical sense, electromagnetic radiation is considered to be wave-like, 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 radioactive materials) having wavelengths on the order of 10 12 m (10 3 nm), through x-rays, ultraviolet, visible, infrared, and finally radio waves with wavelengths as long as 105 m. This spectrum, on a logarithmic scale, is shown in Figure 21.2.
Figure 21.1 An electromagnetic wave showing electric field e and magnetic field H components, and the wavelength l.
Position
H
1496T_c21_W57-W85
3/1/06
15:21
Page W59
21.2 Electromagnetic Radiation W59
Figure 21.2 The spectrum of electromagnetic radiation, including wavelength ranges for the various colors in the visible spectrum.
Energy (eV) 108 106 104 102 100 102 104 106 Radio, TV 108 1010 Wavelength (m) 1014 1012 1010 108 106 104 1 millimeter (mm) 102 100 102 1 kilometer (km) 104 0.7 m Red 1 meter (m) Visible spectrum wavelength 0.4 m Violet 1 angstrom () 1 nanometer (nm) 0.5 m Green 1 micrometer ( m) 0.6 m Yellow Blue
Frequency (Hz) 1022 1020 1018 1016 1014 1012 1010 108 106 104
-Rays
X-Rays
Ultraviolet Visible Infrared
Orange
Microwave
Visible light lies within a very narrow region of the spectrum, with wavelengths ranging between about 0.4 mm (4 10 7 m) and 0.7 mm. The perceived color is determined by wavelength; for example, radiation having a wavelength of approximately 0.4 mm appears violet, whereas green and red occur at about 0.5 and 0.65 mm, respectively. The spectral ranges for the 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 lightnamely, 3 108 m/s (186,000 miles/s). This velocity, c, is related to the electric permittivity of a vacuum 0 and the magnetic permeability of a vacuum m0 through
For a vacuum, dependence of the velocity of light on electric permittivity and magnetic permeability
c
1 0 m0 1
(21.1)
Thus, there is an association between the electromagnetic constant c and these electrical and magnetic constants. Furthermore, the frequency n and the wavelength l of the electromagnetic radiation are a function of velocity according to c ln (21.2)
For electromagnetic radiation, relationship among velocity, wavelength, and frequency
Frequency is expressed in terms of hertz (Hz), and 1 Hz 1 cycle per second. Ranges of frequency for the various forms of electromagnetic radiation are also included in the spectrum (Figure 21.2).
1496T_c21_W57-W85
3/1/06
15:21
Page W60
W60 Chapter 21 / Optical Properties Sometimes it is more convenient to view electromagnetic radiation from a quantum-mechanical perspective, in which the radiation, rather than consisting of waves, is composed of groups or packets of energy, which are called photons. The energy E of a photon is said to be quantized, or can only have specific values, defined by the relationship E hn hc l (21.3)
photon
For a photon of electromagnetic radiation, dependence of energy on frequency, and also velocity and wavelength Plancks constant
where h is a universal constant called Plancks constant, which has a value of 6.63 10 34 J-s. Thus, photon energy is proportional to the frequency of the radiation, or inversely proportional to the wavelength. Photon energies are also included in the electromagnetic 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 more appropriate; at one time or another, both approaches are used in this discussion.
Concept Check 21.1
Briefly discuss the similarities and differences between photons and phonons. Hint: you may want to consult Section 19.2.
[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]
Concept Check 21.2
Electromagnetic radiation may be treated from the classical or the quantummechanical perspectives. Briefly compare these two viewpoints.
[The answer 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 medium must equal the sum of the intensities of the transmitted, absorbed, and reflected beams, denoted as IT, IA, and IR, respectively, or
Intensity of incident beam at an interface is equal to the sum of the intensities of transmitted, absorbed, and reflected beams
I0
IT
IA
IR
(21.4)
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. 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,
1496T_c21_W57-W85
3/1/06
15:21
Page W61
21.4 Atomic and Electronic Interactions W61 absorbed, and reflected by a material; their sum must equal unity, since all the incident light is either transmitted, absorbed, or reflected. Materials that are capable of transmitting light with relatively little absorption and reflection are transparentone can see through them. Translucent materials are those through which light is transmitted diffusely; that is, light is scattered within the 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 light are termed opaque. Bulk metals are opaque throughout the entire visible spectrum; that is, all light radiation is either absorbed or reflected. On the other hand, electrically insulating materials can be made to be transparent. Furthermore, some semiconducting materials are transparent whereas others are opaque.
transparent translucent 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.
Electronic Polarization
One component of an electromagnetic wave is simply a rapidly fluctuating electric field (Figure 21.1). For the visible range of frequencies, this electric field interacts with the electron cloud surrounding each atom within its path in such a way as to induce electronic polarization, or to shift the electron cloud relative to the nucleus of the atom with each change in direction of electric field component, as demonstrated in Figure 18.32a. Two consequences of this polarization are: (1) some of the radiation energy may be absorbed, and (2) light waves are retarded in velocity as they pass through the medium. The second consequence is manifested as refraction, a phenomenon to be discussed in Section 21.5.
Electron Transitions
The absorption and emission of electromagnetic radiation may involve electron transitions from one energy state to another. For the sake of this discussion, consider an isolated atom, the electron energy diagram for which is represented in Figure 21.3. An electron may be excited from an occupied state at energy E2 to a vacant and higher-lying one, denoted E4, by the absorption of a photon of energy. The change in energy experienced by the electron, E, depends on the radiation frequency as follows:
For an electron transition, change in energy equals the product of Plancks constant and the frequency of radiation absorbed (or emitted) excited state ground state
E
hn
(21.6)
where, again, h is Plancks constant. At this point it is important that several concepts be understood. First, since the energy states for the atom are discrete, only specific Es exist between the energy levels; thus, only photons of frequencies corresponding to the possible Es for the atom can be absorbed by electron transitions. Furthermore, all of a photons energy is absorbed in each excitation event. A second important concept is that a stimulated electron cannot remain in an excited state indefinitely; after a short time, it falls or decays back into its ground state, or unexcited level, with a reemission of electromagnetic radiation. Several decay paths are possible, and these are discussed later. In any case, there must be a conservation of energy for absorption and emission electron transitions.
1496T_c21_W57-W85
3/1/06
15:21
Page W62
W62 Chapter 21 / Optical Properties
Figure 21.3 For an isolated atom, a schematic illustration of photon absorption by the excitation of an electron from one energy state to another. The energy of the photon (hn42) must be exactly equal to the difference in energy between the two states (E4 E2).
E5 E4 E3 Electron excitation, E = E4 E2 = h 42 Energy
E2
Incident photon E 1 of frequency
42
As the ensuing discussions show, the optical characteristics of solid materials that relate to absorption and emission of electromagnetic radiation are explained in terms of the electron band structure of the material (possible band structures were discussed in Section 18.5) and the principles relating to electron transitions, as outlined in the preceding two paragraphs.
O p t i c a l P ro p e r t i e s o f M e t a l s
Consider the electron energy band schemes for metals as illustrated in Figures 18.4a and 18.4b; in both cases a high-energy band is only partially filled with electrons. Metals are opaque because the incident radiation having frequencies within the visible range excites electrons into unoccupied energy states above the Fermi energy, as demonstrated in Figure 21.4a; as a consequence, the incident radiation is absorbed, in accordance with Equation 21.6. Total absorption is within a very thin outer layer, usually less than 0.1 mm; thus only metallic films thinner than 0.1 mm are capable of transmitting visible light. All frequencies of visible light are absorbed by metals because of the continuously available empty electron states, which permit electron transitions as in Figure 21.4a.
E Energy
Empty states Fermi energy Filled states Energy
E Fermi energy
Photon absorbed
Photon emitted
(a)
(b)
Figure 21.4 (a) Schematic representation of the mechanism of photon absorption for metallic materials in which an electron is excited into a higher-energy unoccupied state. The change in energy of the electron E is equal to the energy of the photon. (b) Reemission of a photon of light by the direct transition of an electron from a high to a low energy state.
1496T_c21_W57-W85
3/1/06
15:21
Page W63
21.5 Refraction W63 In fact, metals are opaque to all electromagnetic radiation on the low end of the frequency spectrum, from radio waves, through infrared, the visible, and into about the middle of the ultraviolet radiation. Metals are transparent to high-frequency (x- and g-ray) radiation. Most of the absorbed radiation is reemitted from the surface in the form of visible light of the same wavelength, which appears as reflected light; an electron transition accompanying reradiation is shown in Figure 21.4b. The reflectivity for most metals is between 0.90 and 0.95; some small fraction of the energy from electron decay processes is dissipated as heat. Since metals are opaque and highly reflective, the perceived color is determined by the wavelength distribution of the radiation that is reflected and not absorbed. A bright silvery appearance when exposed to white light indicates that the metal is highly reflective over the entire range of the visible spectrum. In other words, for the reflected beam, the composition of these reemitted photons, in terms of frequency and number, is approximately the same as for the incident beam. Aluminum and silver are two metals that exhibit this reflective behavior. Copper and gold appear red-orange and yellow, respectively, because some of the energy associated with light photons having short wavelengths is not reemitted as visible light.
Concept Check 21.3
Why are metals transparent to high-frequency X-ray and g-ray radiation?
[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]
O p t i c a l P ro p e r t i e s o f N o n m e t a l s
By virtue of their electron energy band structures, nonmetallic materials may be transparent to visible light. Therefore, in addition to reflection and absorption, refraction and transmission phenomena also need to be considered.
21.5 REFRACTION
refraction index of refraction Definition of index of refractionthe ratio of light velocities in a vacuum and in the medium of interest
Light that is transmitted into the interior of transparent materials experiences a decrease in velocity, and, as a result, is bent at the interface; this phenomenon is termed refraction. The index of refraction n of a material is defined as the ratio of the velocity in a vacuum c to the velocity in the medium v, or n c v (21.7)
Velocity of light in a medium, in terms of the mediums electric permittivity and magnetic permeability
The magnitude of n (or the degree of bending) will depend on the wavelength of the light. This effect is graphically demonstrated by the familiar dispersion or separation of a beam of white light into its component colors by a glass prism. Each color is deflected by a different amount as it passes into and out of the glass, which results in the separation of the colors (see the chapter-opening photograph for this chapter). Not only does the index of refraction affect the optical path of light, but also, as explained below, it influences the fraction of incident light that is reflected at the surface. Just as Equation 21.1 defines the magnitude of c, an equivalent expression gives the velocity of light v in a medium as v 1 1m (21.8)
1496T_c21_W57-W85
3/1/06
15:21
Page W64
W64 Chapter 21 / Optical Properties where and m are, respectively, the permittivity and permeability of the particular substance. From Equation 21.7, we have n c v 1 0 m0 1 (21.9) 1m 1 r mr
Index of refraction of a mediumin terms of the mediums dielectric constant and relative magnetic permeability Relationship between index of refraction and dielectric constant for a nonmagnetic material
where r and mr are the dielectric constant and the relative magnetic permeability, respectively. Since most substances are only slightly magnetic, mr 1, and n
r
(21.10)
Thus, for transparent materials, there is a relation between the index of refraction and the dielectric constant. As already mentioned, the phenomenon of refraction is related to electronic polarization (Section 21.4) at the relatively high frequencies for visible light; thus, the electronic component of the dielectric constant may be determined from index of refraction measurements using Equation 21.10. Since the retardation of electromagnetic radiation in a medium results from electronic polarization, the size of the constituent atoms or ions has a considerable influence on the magnitude of this effectgenerally, the larger an atom or ion, the greater will be the electronic polarization, the slower the velocity, and the greater the index of refraction. The index of refraction for a typical sodalime glass is approximately 1.5. Additions of large barium and lead ions (as BaO and PbO) to a glass will increase n significantly. For example, highly leaded glasses containing 90 wt% PbO have an index of refraction of approximately 2.1. For crystalline ceramics that have cubic crystal structures, and for glasses, the index of refraction is independent of crystallographic direction (i.e., it is isotropic). Noncubic crystals, on the other hand, have an anisotropic n; that is, the index is greatest along the directions that have the highest density of ions. Table 21.1 gives refractive indices for several glasses, transparent ceramics, and polymers. Average values are provided for the crystalline ceramics in which n is anisotropic. Table 21.1 Refractive Indices for Some Transparent Materials
Material Ceramics Silica glass Borosilicate (Pyrex) glass Sodalime glass Quartz (SiO2) Dense optical flint glass Spinel (MgAl2O4) Periclase (MgO) Corundum (Al2O3) Polymers Polytetrafluoroethylene Poly(methyl methacrylate) Polypropylene Polyethylene Polystyrene Average Index of Refraction 1.458 1.47 1.51 1.55 1.65 1.72 1.74 1.76 1.35 1.49 1.49 1.51 1.60
1496T_c21_W57-W85
3/1/06
15:21
Page W65
21.7 Absorption W65
Concept Check 21.4
Which of the following oxide materials when added to fused silica (SiO2) will increase its index of refraction: Al2O3, TiO2, NiO, MgO? Why? You may find Table 12.3 helpful.
[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]
21.6 REFLECTION
When light radiation passes from one medium into another having a different index of refraction, some of the light is scattered at the interface between the two media even if both are transparent. The reflectivity R represents the fraction of the incident light that is reflected at the interface, or
Definition of reflectivityin terms of intensities of reflected and incident beams Reflectivity (for normal incidence) at interface between two media having indices of refraction of n1 and n2
R
IR I0
(21.11)
where I0 and IR are the intensities of the incident and reflected beams, respectively. If the light is normal (or perpendicular) to the interface, then R a n2 n2 n1 2 b n1 (21.12)
where n1 and n2 are the indices of refraction of the two media. If the incident light is not normal to the interface, R will depend on the angle of incidence. When light is transmitted from a vacuum or air into a solid s, then R a ns ns 12 b 1 (21.13)
since the index of refraction of air is very nearly unity. Thus, the higher the index of refraction of the solid, the greater is the reflectivity. For typical silicate glasses, the reflectivity is approximately 0.05. Just as the index of refraction of a solid depends on the wavelength of the incident light, so also does the reflectivity vary with wavelength. Reflection losses for lenses and other optical instruments are minimized significantly by coating the reflecting surface with very thin layers of dielectric materials such as magnesium fluoride (MgF2).
21.7 ABSORPTION
Nonmetallic materials may be opaque or transparent to visible light; and, if transparent, they often appear colored. In principle, light radiation is absorbed in this group of materials by two basic mechanisms, which also influence the transmission characteristics of these nonmetals. One of these is electronic polarization (Section 21.4). Absorption by electronic polarization is important only at light frequencies in the vicinity of the relaxation frequency of the constituent atoms. The other mechanism involves valence band-conduction band electron transitions, which depend on the electron energy band structure of the material; band structures for semiconductors and insulators were discussed in Section 18.5. Absorption of a photon of light may occur by the promotion or excitation of an electron from the nearly filled valence band, across the band gap, and into an empty state within the conduction band, as demonstrated in Figure 21.5a; a free
1496T_c21_W57-W85
3/10/06
07:14
Page W66
W66 Chapter 21 / Optical Properties
Figure 21.5 (a) Mechanism of photon absorption for nonmetallic materials in which an electron is excited across the band gap, leaving behind a hole in the valence band. The energy of the photon absorbed is E, which is necessarily greater than the band gap energy Eg. (b) Emission of a photon of light by a direct electron transition across the band gap.
Conduction band Conduction band
Excited (free) electron
Energy
Eg
Band gap
Band gap
E
E Hole
Valence band
Photon absorbed (a) (b)
Valence band
Photon emitted
For a nonmetallic material, condition for absorption of a photon (of radiation) by an electron transition in terms of radiation frequency For a nonmetallic material, condition for absorption of a photon (of radiation) by an electron transition in terms of radiation wavelength Maximum possible band gap energy for absorption of visible light by valenceband-to-conductionband electron transitions
electron in the conduction band and a hole in the valence band are created. Again, the energy of excitation E is related to the absorbed photon frequency through Equation 21.6. These excitations with the accompanying absorption can take place only if the photon energy is greater than that of the band gap Egthat is, if h n 7 Eg or, in terms of wavelength, hc 7 Eg l (21.15) (21.14)
The minimum wavelength for visible light, l(min), is about 0.4 mm, and since c 3 108 m/s and h 4.13 10 15 eV-s, the maximum band gap energy Eg(max) for which absorption of visible light is possible is just Eg 1 max 2 hc l 1 min 2 1 4.13 10
15
4
eV-s 2 1 3 10
7
m
108 m/s 2
(21.16a)
3.1 eV Or, no visible light is absorbed by nonmetallic materials having band gap energies greater than about 3.1 eV; these materials, if of high purity, will appear transparent and colorless. On the other hand, the maximum wavelength for visible light, l(max), is about 0.7 mm; computation of the minimum band gap energy Eg(min) for which there is absorption of visible light is according to
Minimum possible band gap energy for absorption of visible light by valenceband-to-conductionband electron transitions
Eg 1 min 2
hc l 1 max 2 1 4.13 10
15
7
eV-s 21 3 10
7
m
108 m/s 2
1.8 eV
(21.16b)
1496T_c21_W57-W85
3/1/06
15:21
Page W67
21.7 Absorption W67 This result means that all visible light is absorbed by valence band-to-conduction band electron transitions for those semiconducting materials that have band gap energies less than about 1.8 eV; thus, these materials are opaque. Only a portion of the visible spectrum is absorbed by materials having band gap energies between 1.8 and 3.1 eV; consequently, these materials appear colored. Every nonmetallic material becomes opaque at some wavelength, which depends on the magnitude of its Eg. For example, diamond, having a band gap of 5.6 eV, is opaque to radiation having wavelengths less than about 0.22 mm. Interactions with light radiation can also occur in dielectric solids having wide band gaps, involving other than valence band-conduction band electron transitions. If impurities or other electrically active defects are present, electron levels within the band gap may be introduced, such as the donor and acceptor levels (Section 18.11), except that they lie closer to the center of the band gap. Light radiation of specific wavelengths may be emitted as a result of electron transitions involving these levels within the band gap. For example, consider Figure 21.6a, which shows the valence bandconduction band electron excitation for a material that has one such impurity level. Again, the electromagnetic energy that was absorbed by this electron excitation must be dissipated in some manner; several mechanisms are possible. For one, this dissipation may occur via direct electron and hole recombination according to the reaction
Reaction describing electron-hole recombination with the generation of energy
electron
hole energy 1 E 2
(21.17)
which is represented schematically in Figure 21.5b. In addition, multiple-step electron transitions may occur, which involve impurity levels lying within the band gap. One possibility, as indicated in Figure 21.6b, is the emission of two photons; one is emitted as the electron drops from a state in the conduction band to the impurity level, the other as it decays back into the valence band. Alternatively, one of the transitions may involve the generation of a phonon (Figure 21.6c), wherein the associated energy is dissipated in the form of heat. The intensity of the net absorbed radiation is dependent on the character of the medium as well as the path length within. The intensity of transmitted or
Impurity level Energy E
Conduction band
E1
E1
Band gap
E2 Photon emitted,
1=
E1 h
E2 Phonon generated having energy E1 Photon emitted, (c)
2=
E2 h
Valence band
Photon absorbed (a) (b)
Photon emitted,
2=
E2 h
Figure 21.6 (a) Photon absorption via a valence band-conduction band electron excitation for a material that has an impurity level that lies within the band gap. (b) Emission of two photons involving electron decay first into an impurity state, and finally to the ground state. (c) Generation of both a phonon and a photon as an excited electron falls first into an impurity level and finally back to its ground state.
1496T_c21_W57-W85
3/1/06
15:22
Page W68
W68 Chapter 21 / Optical Properties nonabsorbed radiation IT continuously decreases with distance x that the light traverses:
Intensity of nonabsorbed radiation dependence on absorption coefficient and distance light traverses through absorbing medium
IT
I0 e
bx
(21.18)
where I0 is the intensity of the nonreflected incident radiation and b, the absorption coefficient (in mm 1), is characteristic of the particular material; furthermore, b varies with wavelength of the incident radiation. The distance parameter x is measured from the incident surface into the material. Materials that have large values are considered to be highly absorptive.
EXAMPLE PROBLEM 21.1 Computation of the Absorption Coefficient for Glass
The fraction of nonreflected light that is transmitted through a 200 mm thickness of glass is 0.98. Calculate the absorption coefficient of this material. Solution This problem calls for us to solve for b in Equation 21.18. We first of all rearrange this expression as IT I0 ln a IT b I0 e
bx
Now taking natural logarithms of both sides of the above equation leads to bx 0.98 and x 200 mm, yields
And, finally, solving for b, realizing that IT I0 b IT 1 ln a b x I0 1 ln 1 0.98 2 200 mm 1.01
10
4
mm
1
Concept Check 21.5
Are the elemental semiconductors silicon and germanium transparent to visible light? Why or why not? Hint: you may want to consult Table 18.3.
[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]
21.8 TRANSMISSION
Intensity of radiation transmitted through a specimen of thickness l, accounting for all absorption and reflection losses
The phenomena of absorption, reflection, and transmission may be applied to the passage of light through a transparent solid, as shown in Figure 21.7. For an incident beam of intensity I0 that impinges on the front surface of a specimen of thickness l and absorption coefficient b, the transmitted intensity at the back face IT is IT I0 1 1 R 2 2e
bl
(21.19)
1496T_c21_W57-W85
3/1/06
15:22
Page W69
21.9 Color W69
Figure 21.7 The transmission of light through a transparent medium for which there is reflection at front and back faces, as well as absorption within the medium. (Adapted from R. M. Rose, L. A. Shepard, and J. Wulff, The Structure and Properties of Materials, Vol. 4, Electronic Properties. Copyright 1966 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)
Incident beam I0 Transmitted beam IT = I0(1 R)2 e l
Reflected beam IR = I0R
l
where R is the reflectance; for this expression, it is assumed that the same medium exists outside both front and back faces. The derivation of Equation 21.19 is left as a homework problem. Thus, the fraction of incident light that is transmitted through a transparent material depends on the losses that are incurred by absorption and reflection. Again, the sum of the reflectivity R, absorptivity A, and transmissivity T, is unity according to Equation 21.5. Also, each of the variables R, A, and T depends on light wavelength. This is demonstrated over the visible region of the spectrum for a green glass in Figure 21.8. For example, for light having a wavelength of 0.4 mm, the fractions transmitted, absorbed, and reflected are approximately 0.90, 0.05, and 0.05, respectively. However, at 0.55 mm, the respective fractions have shifted to about 0.50, 0.48, and 0.02.
21.9 COLOR
color
Transparent materials appear colored as a consequence of specific wavelength ranges of light that are selectively absorbed; the color discerned is a result of the combination of wavelengths that are transmitted. If absorption is uniform for all visible wavelengths, the material appears colorless; examples include high-purity inorganic glasses and high-purity and single-crystal diamonds and sapphire. Usually, any selective absorption is by electron excitation. One such situation involves semiconducting materials that have band gaps within the range of photon energies for visible light (1.8 to 3.1 eV). Thus, the fraction of the visible light having energies greater than Eg is selectively absorbed by valence bandconduction band electron transitions. Of course, some of this absorbed radiation is reemitted as the excited electrons drop back into their original, lower-lying energy states. It is not necessary that this reemission occur at the same frequency as that of the absorption. As a result, the color depends on the frequency distribution of both transmitted and reemitted light beams.
Reflected 1.0 Fraction of radiant energy 0.8 0.6 0.4 0.2 0 0.2 Transmitted visible Absorbed
Figure 21.8 The variation with wavelength of the fractions of incident light transmitted, absorbed, and reflected through a green glass. (From W. D. Kingery, H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics, 2nd edition. Copyright 1976 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)
0.3
0.4
0.5
0.6
0.7
0.8
1.0
1.5
2.0
2.5
3.0
Wavelength ( m)
1496T_c21_W57-W85
3/1/06
15:22
Page W70
W70 Chapter 21 / Optical Properties For example, cadmium sulfide (CdS) has a band gap of about 2.4 eV; hence, it absorbs photons having energies greater than about 2.4 eV, which correspond to the blue and violet portions of the visible spectrum; some of this energy is reradiated as light having other wavelengths. Nonabsorbed visible light consists of photons having energies between about 1.8 and 2.4 eV. Cadmium sulfide takes on a yellow-orange color because of the composition of the transmitted beam. With insulator ceramics, specific impurities also introduce electron levels within the forbidden band gap, as discussed above. Photons having energies less than the band gap may be emitted as a consequence of electron decay processes involving impurity atoms or ions as demonstrated in Figures 21.6b and 21.6c. Again, the color of the material is a function of the distribution of wavelengths that is found in the transmitted beam. For example, high-purity and single-crystal aluminum oxide or sapphire is colorless. Ruby, which has a brilliant red color, is simply sapphire to which has been added 0.5 to 2% of chromium oxide (Cr2O3). The Cr3+ ion substitutes for the Al3+ ion in the Al2O3 crystal structure and, furthermore, introduces impurity levels within the wide energy band gap of the sapphire. Light radiation is absorbed by valence band-conduction band electron transitions, some of which is then reemitted at specific wavelengths as a consequence of electron transitions to and from these impurity levels. The transmittance as a function of wavelength for sapphire and ruby is presented in Figure 21.9. For the sapphire, transmittance is relatively constant with wavelength over the visible spectrum, which accounts for the colorlessness of this material. However, strong absorption peaks (or minima) occur for the ruby, one in the blue-violet region (at about 0.4 mm), and the other for yellow-green light (at about 0.6 mm). That nonabsorbed or transmitted light mixed with reemitted light imparts to ruby its deep-red color. Inorganic glasses are colored by incorporating transition or rare earth ions while the glass is still in the molten state. Representative colorion pairs include Cu2 , blue-green; Co2 , blue-violet; Cr3 , green; Mn2 , yellow; and Mn3 , purple. These colored glasses are also used as glazes, decorative coatings on ceramic ware.
Concept Check 21.6
Compare those factors that determine the characteristic colors of metals and transparent nonmetals.
[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]
Transmittance (%)
Figure 21.9 Transmission of light radiation as a function of wavelength for sapphire (single-crystal aluminum oxide) and ruby (aluminum oxide containing some chromium oxide). The sapphire appears colorless, while the ruby has a red tint due to selective absorption over specific wavelength ranges. (Adapted from The Optical Properties of Materials, by A. Javan. Copyright 1967 by Scientific American, Inc. All rights reserved.)
90
Violet Blue
Green
Orange Red
80
Yellow Sapphire
70
60
Ruby
50 40 0.3
0.4
0.5
0.6 Wavelength,
0.7 ( m)
0.8
0.9
1.0
1496T_c21_W57-W85
3/1/06
15:22
Page W71
21.10 Opacity and Translucency in Insulators W71
21.10 OPACITY AND TRANSLUCENCY IN INSULATORS
The extent of translucency and opacity for inherently transparent dielectric materials depends to a great degree on their internal reflectance and transmittance characteristics. Many dielectric materials that are intrinsically transparent may be made translucent or even opaque because of interior reflection and refraction. A transmitted light beam is deflected in direction and appears diffuse as a result of multiple scattering events. Opacity results when the scattering is so extensive that virtually none of the incident beam is transmitted, undeflected, to the back surface. This internal scattering may result from several different sources. Polycrystalline specimens in which the index of refraction is anisotropic normally appear translucent. Both reflection and refraction occur at grain boundaries, which causes a diversion in the incident beam.This results from a slight difference in index of refraction n between adjacent grains that do not have the same crystallographic orientation. Scattering of light also occurs in two-phase materials in which one phase is finely dispersed within the other. Again, the beam dispersion occurs across phase boundaries when there is a difference in the refractive index for the two phases; the greater this difference, the more efficient is the scattering. Glassceramics (Section 13.3), which may consist of both crystalline and residual glass phases, will appear highly transparent if the sizes of the crystallites are smaller than the wavelength of visible light, and when the indices of refraction of the two phases are nearly identical (which is possible by adjustment of composition). As a consequence of fabrication or processing, many ceramic pieces contain some residual porosity in the form of finely dispersed pores. These pores also effectively scatter light radiation. Figure 21.10 demonstrates the difference in optical transmission characteristics of single-crystal, fully dense polycrystalline, and porous ( 5% porosity) aluminum oxide specimens. Whereas the single crystal is totally transparent, polycrystalline and porous materials are, respectively, translucent and opaque. For intrinsic polymers (without additives and impurities), the degree of translucency is influenced primarily by the extent of crystallinity. Some scattering of visible light occurs at the boundaries crystalline between and amorphous regions, again as a result of different indices of refraction. For highly crystalline specimens, this degree of scattering is extensive, which leads to translucency, and, in some instances, even opacity. Highly amorphous polymers are completely transparent.
Figure 21.10 Photograph showing the light transmittance of three aluminum oxide specimens. From left to right: single-crystal material (sapphire), which is transparent; a polycrystalline and fully dense (nonporous) material, which is translucent; and a polycrystalline material that contains approximately 5% porosity, which is opaque. (Specimen preparation, P. A. Lessing; photography by S. Tanner.)
1496T_c21_W57-W85
3/1/06
15:22
Page W72
W72 Chapter 21 / Optical Properties
Applications of Optical Phenomena
21.11 LUMINESCENCE
luminescence
fluorescence phosphorescence
Some materials are capable of absorbing energy and then reemitting visible light in a phenomenon called luminescence. Photons of emitted light are generated from electron transitions in the solid. Energy is absorbed when an electron is promoted to an excited energy state; visible light is emitted when it falls back to a lower energy state if 1.8 eV 6 hn 6 3.1 eV. The absorbed energy may be supplied as higherenergy electromagnetic radiation (causing valence bandconduction band transitions, Figure 21.6a) such as ultraviolet light, or other sources such as high energy electrons, or by heat, mechanical, or chemical energy. Furthermore, luminescence is classified according to the magnitude of the delay time between absorption and reemission events. If reemission occurs for times much less than one second, the phenomenon is termed fluorescence; for longer times, it is called phosphorescence. A number of materials can be made to fluoresce or phosphoresce; these include some sulfides, oxides, tungstates, and a few organic materials. Ordinarily, pure materials do not display these phenomena, and to induce them, impurities in controlled concentrations must be added. Luminescence has a number of commercial applications. Fluorescent lamps consist of a glass housing, coated on the inside with specially prepared tungstates or silicates. Ultraviolet light is generated within the tube from a mercury glow discharge, which causes the coating to fluoresce and emit white light. The picture viewed on a television screen (cathode ray tube screen) is the product of luminescence.The inside of the screen is coated with a material that fluoresces as an electron beam inside the picture tube very rapidly traverses the screen. Detection of x-rays and g-rays is also possible; certain phosphors emit visible light or glow when introduced into a beam of the radiation that is otherwise invisible.
21.12 PHOTOCONDUCTIVITY
The conductivity of semiconducting materials depends on the number of free electrons in the conduction band and also the number of holes in the valence band, according to Equation 18.13. Thermal energy associated with lattice vibrations can promote electron excitations in which free electrons and/or holes are created, as described in Section 18.6. Additional charge carriers may be generated as a consequence of photon-induced electron transitions in which light is absorbed; the attendant increase in conductivity is called photoconductivity. Thus, when a specimen of a photoconductive material is illuminated, the conductivity increases. This phenomenon is utilized in photographic light meters. A photoinduced current is measured, and its magnitude is a direct function of the intensity of the incident light radiation, or the rate at which the photons of light strike the photoconductive material. Of course, visible light radiation must induce electronic transitions in the photoconductive material; cadmium sulfide is commonly utilized in light meters. Sunlight may be directly converted into electrical energy in solar cells, which also employ semiconductors. The operation of these devices is, in a sense, the reverse of that for the light-emitting diode. A pn junction is used in which photoexcited electrons and holes are drawn away from the junction, in opposite directions, and become part of an external current.
photoconductivity
1496T_c21_W57-W85
3/10/06
07:14
Page W73
21.12 Photoconductivity W73
MATERIALS OF IMPORTANCE
Light-Emitting Diodes
I
electroluminescence lightemitting diode (LED)
n Section 18.15 we discussed semiconductor p-n junctions, and how they may be used as diodes or as rectifiers of an electric current.1 Furthermore, in some situations, when a forward-biased potential of relatively high magnitude is applied across a p-n junction diode, visible light (or infrared radiation) will be emitted. This conversion of electrical energy into light energy is termed electroluminescence, and the device that produces it is termed a light-emitting diode (LED). The forward-biased potential attracts electrons on the n-side toward the junction, where some of them pass into (or are injected into) the p-side (Figure 21.11a). Here, the electrons are minority charge carriers, and as such, they recombine with, or are annihilated by the holes in the region near the junction, according to Equation 21.17, where the energy is in the form of photons of light (Figure 21.11b). An analogous process occurs on the p-sidei.e., holes travel to the junction, and recombine with the majority electrons on the n-side. The elemental semiconductors, silicon and germanium, are not suitable for LEDs due to the detailed natures of their band structures. Rather, some of the III-V semiconducting compounds such as gallium arsenide (GaAs), indium phosphide (InP), and alloys composed of these materials (i.e., GaAsxP1 x, where x is a small number less than unity) are frequently used. Furthermore, the wavelength (i.e., color) of the emitted radiation is related to the band gap of the semiconductor (which is normally the same for both n- and p-sides of the diode). For example, red, orange, and yellow colors are possible for the GaAsInP system. And, blue and green LEDs have been developed using (Ga,In)N semiconducting alloys. Thus, with this comple-
ment of colors, full-color displays are possible using LEDs. Several important applications for semiconductor LEDs include digital clocks and illuminated watch displays, optical mice (computer input devices), and film scanners. Electronic remote controls (for televisions, DVD players, etc.) also employ LEDs that emit an infrared beam; this beam transmits coded signals that are picked up by detectors in the receiving devices. In addition, LEDs are now being used for light sources. They are more energy efficient than incandescent lights, generate very little heat, and have much longer lifetimes (since there is no filament that can burn out). Most new traffic control signals use LEDs instead of incandescent lights. We noted in Section 18.17 that some polymeric materials may be semiconductors (both
Injection of electron into p-side p-side
+ + + + + + + +
n-side
+
+
+
Battery (a ) Recombination (annihilation of electron) p-side
+ + + + + + + + +
n-side
+
Photon emitted
Battery (b)
1
Schematic diagrams showing electron and hole distributions on both sides of the junction, with no applied electric potential, as well as for both forward and reverse biases are presented in Figure 18.21. In addition, Figure 18.22 shows the current-versusvoltage behavior for a p-n junction.
Figure 21.11 Schematic diagram of a forward-biased semiconductor p-n junction showing (a) the injection of an electron from the n-side into the p-side, and (b) the emission of a photon of light as this electron recombines with a hole.
1496T_c21_W57-W85
3/1/06
15:22
Page W74
W74 Chapter 21 / Optical Properties n- and p-type). As a consequence, light-emitting diodes made of polymers are possible, of which there are two types: (1) organic light-emitting diodes (or OLEDs), which have relatively low molecular weights; and (2) the high molecular-weight polymer light-emitting diodes (or PLEDs). For these LED types, amorphous polymers are used in the form of thin layers that are sandwiched together with electrical contacts (anodes and cathodes). In order for the light to be emitted from the LED, one of the contacts must be transparent. Figure 21.12 is a schematic illustration that shows the components and configuration of an OLED. A wide variety of colors is possible using OLEDs and PLEDs, and, in fact, more than a single color may be produced from each device (such is not possible with semiconductor LEDs)thus, combining colors makes it possible to generate white light. Although the semiconductor LEDs currently have longer lifetimes than these organic emitters, OLEDs/PLEDs have distinct advantages. In addition to generating multiple colors, they are easier to fabricate (by printing onto their substrates with an ink jet printer), are relatively inexpensive, have slimmer profiles, and can be patterned to give high-resolution and full-color images. OLED displays are currently being marketed for use on digital cameras, cell phones, and car audio components. Potential applications include larger displays for televisions, computers, and bill boards. In addition, using the right combination of materials, these displays can also be flexible. Can you imagine having a computer monitor or television that can be rolled up like a projection screen, or a lighting fixture that is wrapped around an architectural column or is mounted on a room wall to make ever-changing wallpaper?
210V DC Metal cathode Electron transport (n-type) layer Organic emitters Hole injection and transport (p-type) layer Anode
Glass substrate
Light output
Figure 21.12 Schematic diagram that shows the components and configuration of an organic light-emitting diode (OLED). (Reproduced by arrangement with Silicon Chip magazine.)
Photograph showing a very large light-emitting diode video display located at the corner of Broadway and 43rd Street in New York City. ( Stephen Chemin/Getty Images News and Sports Services.)
1496T_c21_W57-W85
3/1/06
15:22
Page W75
21.13 Lasers W75
Concept Check 21.7
Is the semiconductor zinc selenide (ZnSe), which has a band gap of 2.58 eV, photoconductive when exposed to visible light radiation? Why or why not?
[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]
21.13 LASERS
All the radiative electron transitions heretofore discussed are spontaneous; that is, an electron falls from a high energy state to a lower one without any external provocation. These transition events occur independently of one another and at random times, producing radiation that is incoherent; that is, the light waves are out of phase with one another. With lasers, however, coherent light is generated by electron transitions initiated by an external stimulus; in fact, laser is just the acronym for light amplification by stimulated emission of radiation. Although there are several different varieties of laser, the principles of operation are explained using the solid-state ruby laser. Ruby is simply a single crystal of Al2O3 (sapphire) to which has been added on the order of 0.05% Cr3 ions. As previously explained (Section 21.9), these ions impart to ruby its characteristic red color; more important, they provide electron states that are essential for the laser to function. The ruby laser is in the form of a rod, the ends of which are flat, parallel, and highly polished. Both ends are silvered such that one is totally reflecting and the other partially transmitting. The ruby is illuminated with light from a xenon flash lamp (Figure 21.13). Before this exposure, virtually all the Cr3 ions are in their ground states; that is, electrons fill the lowest energy levels, as represented schematically in Figure 21.14. However, photons of wavelength 0.56 mm from the xenon lamp excite electrons from the Cr3 ions into higher energy states. These electrons can decay back into their ground state by two different paths. Some fall back directly; associated photon emissions are not part of the laser beam. Other electrons decay into a metastable intermediate state (path EM, Figure 24.14), where they may reside for up to 3 ms (milliseconds) before spontaneous emission (path MG). In terms of electronic processes, 3 ms is a relatively long time, which means that a large number of these metastable states may become occupied. This situation is indicated in Figure 21.15b. The initial spontaneous photon emission by a few of these electrons is the stimulus that triggers an avalanche of emissions from the remaining electrons in
Figure 21.13 Schematic diagram of the ruby laser and xenon flash lamp. (From R. M. Rose, L. A. Shepard, and J. Wulff, The Structure and Properties of Materials, Vol. 4, Electronic Properties. Copyright 1966 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)
laser
Flash lamp
Ruby Coherent beam
Power source
1496T_c21_W57-W85
3/1/06
15:22
Page W76
W76 Chapter 21 / Optical Properties
Excited state E
Figure 21.14 Schematic energy diagram for the ruby laser, showing electron excitation and decay paths.
Spontaneous decay (nonradiative, phonon emission) Electron excitation Energy M
Metastable state
Spontaneous and stimulated emission
Incident photon (xenon lamp) Ground state (Cr3+)
Laser photon G
the metastable state (Figure 21.15c). Of the photons directed parallel to the long axis of the ruby rod, some are transmitted through the partially silvered end; others, incident to the totally silvered end, are reflected. Photons that are not emitted in this axial direction are lost. The light beam repeatedly travels back
Fully silvered Partially silvered
(a)
(b)
(c)
Figure 21.15 Schematic representations of the stimulated emission and light amplification for a ruby laser. (a) The chromium ions before excitation. (b) Electrons in some chromium ions are excited into higher energy states by the xenon light flash. (c) Emission from metastable electron states is initiated or stimulated by photons that are spontaneously emitted. (d) Upon reflection from the silvered ends, the photons continue to stimulate emissions as they traverse the rod length. (e) The coherent and intense beam is finally emitted through the partially silvered end. (From R. M. Rose, L. A. Shepard, and J. Wulff, The Structure and Properties of Materials, Vol. 4, Electronic Properties. Copyright 1966 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)
(Just before next reflection)
(At midcrystal) (d)
(After reflection)
(e) Excited Cr atom Cr atom in ground state
1496T_c21_W57-W85
3/1/06
15:22
Page W77
21.13 Lasers W77 and forth along the rod length, and its intensity increases as more emissions are stimulated. Ultimately, a high intensity, coherent, and highly collimated laser light beam of short duration is transmitted through the partially silvered end of the rod (Figure 21.15e). This monochromatic red beam has a wavelength of 0.6943 mm. Semiconducting materials such as gallium arsenide may also be used as lasers that are employed in compact disk players and in the modern telecommunications industry. One requirement of these semiconducting materials is that the wavelength
Partially reflecting mirror
Fully reflecting mirror Photon emission
Conduction band
Eg + + + + + + Valence band (a) +
Excited electrons Holes + + + + + + + (d) + + + + +
+
Recombined excited electron and hole + + + + (b) + + + + + + + + + + (e) + + +
New excited electron
+
+
+
+
+ (c)
+
+
+
+
+
+ (f )
+
+
+
+
New hole
Figure 21.16 For the semiconductor laser, schematic representations of the stimulated recombination of excited electrons in the conduction band with holes in the valence band that gives rise to a laser beam. (a) One excited electron recombines with a hole; the energy associated with this recombination is emitted as a photon of light. (b) The photon emitted in (a) stimulates the recombination of another excited electron and hole resulting in the emission of another photon of light. (c) The two photons emitted in (a) and (b), having the same wavelength and being in phase with one another, are reflected by the fully reflecting mirror, back into the laser semiconductor. In addition, new excited electrons and new holes are generated by a current that passes through the semiconductor. (d) and (e) In proceeding through the semiconductor, more excited electronhole recombinations are stimulated, which give rise to additional photons of light that also become part of the monochromatic and coherent laser beam. ( f ) Some portion of this laser beam escapes through the partially reflecting mirror at one end of the semiconducting material. (Adapted from Photonic Materials, by J. M. Rowell. Copyright 1986 by Scientific American, Inc. All rights reserved.)
1496T_c21_W57-W85
3/10/06
07:14
Page W78
W78 Chapter 21 / Optical Properties l associated with the band gap energy Eg must correspond to visible light. That is, from a modification of Equation 21.3, namely l hc Eg (21.20)
l must lie between 0.4 and 0.7 mm. A voltage applied to the material excites electrons from the valence band, across the band gap, and into the conduction band; correspondingly, holes are created in the valence band. This process is demonstrated in Figure 21.16a, which shows the energy band scheme over some region of the semiconducting material, along with several holes and excited electrons. Subsequently, a few of these excited electrons and holes spontaneously recombine. For each recombination event, a photon of light having a wavelength given by Equation 21.20 is emitted (Figure 21.16a). One such photon will stimulate the recombination of other excited electronhole pairs, Figure 21.16bf, and the production of additional photons that have the same wavelength and are all in phase with one another and with the original photon; thus, a monochromatic and coherent beam results. As with the ruby laser (Figure 21.15), one end of the semiconductor laser is totally reflecting; at this end, the beam is reflected back into the material so that additional recombinations will be stimulated. The other end of the laser is partially reflecting, which allows for some of the beam to escape. Furthermore, with this type of laser, a continuous beam is produced inasmuch as a constant applied voltage ensures that there is always a steady source of holes and excited electrons. The semiconductor laser is composed of several layers of semiconducting materials that have different compositions and are sandwiched between a heat sink and a metal conductor; a typical arrangement is represented schematically in Figure 21.17. The compositions of the layers are chosen so as to confine both the excited electrons and holes as well as the laser beam to within the central gallium arsenide layer. A variety of other substances may be used for lasers, including some gases and glasses. Table 21.2 lists several common lasers and their characteristics. Laser
Forward-bias voltage
Metal Silicon dioxide Heavily p-doped gallium arsenide p-Doped gallium aluminum arsenide Gallium arsenide n-Doped gallium aluminum arsenide Heavily n-doped gallium arsenide Laser beam
Figure 21.17 Schematic diagram showing the layered cross section of a GaAs semiconducting laser. Holes, excited electrons, and the laser beam are confined to the GaAs layer by the adjacent n- and p-type GaAlAs layers. (Adapted from Photonic Materials, by J. M. Rowell. Copyright 1986 by Scientific American, Inc. All rights reserved.)
Metal
Heat sink
1496T_c21_W57-W85
3/1/06
15:22
Page W79
21.14 Optical Fibers in Communications W79 Table 21.2 Characteristics and Applications of Several Types of Lasers
Laser HeNe CO2 Argon HeCd Dye Ruby NdYAG NdGlass Diode
a
Type Gas Gas Gas ion Metal vapor Liquid Solid state Solid state Solid state Semiconductor
Common Wavelengths ( m) 0.6328, 1.15, 3.39 9.6, 10.6 0.488, 0.5145 0.441, 0.325 0.38 1.0 0.694 1.06 1.06 0.33 40
Max. Output Power ( W )a 0.00050.05 (CW) 500 15,000 (CW) 0.005 20 (CW) 0.050.1 0.01 (CW) 1 106 (P) (P) 1000 (CW) 2 108 (P) 5 1014 (P) 0.6 (CW) 100 (P)
Applications Line-of sight communications, recording/ playback of holograms Heat treating, welding, cutting, scribing, marking Surgery, distance measurements, holography Light shows, spectroscopy Spectroscopy, pollution detection Pulsed holography, hole piercing Welding, hole piercing, cutting Pulse welding, hole piercing Bar-code reading, CDs and DVDs, optical communications
CW denotes continuous; P denotes pulsed.
applications are diverse. Since laser beams may be focused to produce localized heating, they are used in some surgical procedures and for cutting, welding, and machining metals. Lasers are also used as light sources for optical communication systems. Furthermore, because the beam is highly coherent, they may be utilized for making very precise distance measurements.
21.14 OPTICAL FIBERS IN COMMUNICATIONS
The communications field has recently experienced a revolution with the development of optical fiber technology; at present, virtually all telecommunications are transmitted via this medium rather than through copper wires. Signal transmission through a metallic wire conductor is electronic (i.e., by electrons), whereas using optically transparent fibers, signal transmission is photonic, meaning that it uses photons of electromagnetic or light radiation. Use of fiber-optic systems has improved speed of transmission, information density, and transmission distance, with a reduction in error rate; furthermore, there is no electromagnetic interference with fiber optics. With regard to speed, optical fibers can transmit, in one second, information equivalent to three episodes of your favorite television program. Or relative to information density, two small optical fibers can transmit the equivalent of 24,000 telephone calls simultaneously. Furthermore, it would require 30,000 kg (33 tons) of copper to transmit the same amount of information as only 0.1 kg (1 lbm) 4 of optical fiber material. The present treatment will center on the characteristics of optical fibers; however, it is thought worthwhile to first briefly discuss the components and operation of the transmission system. A schematic diagram showing these components is presented in Figure 21.18. The information (i.e., telephone conversation) in electronic form must first be digitized into bits, that is, 1s and 0s; this is accomplished in the encoder. It is next necessary to convert this electrical signal into an optical (photonic) one, which takes place in the electrical-to-optical converter (Figure 21.18). This converter is normally a semiconductor laser, as described in the previous
1496T_c21_W57-W85
3/1/06
15:22
Page W80
W80 Chapter 21 / Optical Properties
Fiber optic cable
Input signal Encoder
Electrical/ Optical Converter
Repeater
Optical/ Electrical Converter
Output Decoder signal
Figure 21.18 Schematic diagram showing the components of an optical fiber communications system.
section, which emits monochromatic and coherent light. The wavelength normally lies between 0.78 and 1.6 mm, which is in the infrared region of the electromagnetic spectrum; absorption losses are low within this range of wavelengths. The output from this laser converter is in the form of pulses of light; a binary 1 is represented by a high-power pulse (Figure 21.19a), whereas a 0 corresponds to a low-power pulse (or the absence of one), Figure 21.19b. These photonic pulse signals are then fed into and carried through the fiber-optical cable (sometimes called a waveguide) to the receiving end. For long transmissions, repeaters may be required; these are devices that amplify and regenerate the signal. Finally, at the receiving end the photonic signal is reconverted to an electronic one, and is then decoded (undigitized). The heart of this communication system is the optical fiber. It must guide these light pulses over long distances without significant signal power loss (i.e., attenuation) and pulse distortion. Fiber components are the core, cladding, and coating; these are represented in the cross-section profile, Figure 21.20. The signal passes through the core, whereas the surrounding cladding constrains the light rays to travel within the core; the outer coating protects core and cladding from damage that might result from abrasion and external pressures. High-purity silica glass is used as the fiber material; fiber diameters normally range between about 5 and 100 mm. The fibers are relatively flaw free and, thus, remarkably strong; during production the continuous fibers are tested to ensure that they meet minimum strength standards. Containment of the light to within the fiber core is made possible by total internal reflection; that is, any light rays traveling at oblique angles to the fiber axis are reflected back into the core. Internal reflection is accomplished by varying the index of refraction of the core and cladding glass materials. In this regard, two design types are employed. With one type (termed step-index), the index of refraction
Figure 21.19 Digital encoding scheme for optical communications. (a) A high-power pulse of photons corresponds to a one in the binary format. (b) A lowpower photon pulse represents a zero.
Intensity
Time (a)
Intensity
Time (b)
1496T_c21_W57-W85
3/1/06
15:22
Page W81
21.14 Optical Fibers in Communications W81
Figure 21.20 Schematic cross section of an optical fiber.
Coating Cladding Core
of the cladding is slightly lower than that of the core. The index profile and the manner of internal reflection are shown in Figures 21.21b and 21.21d. For this design, the output pulse will be broader than the input one (Figures 21.21c and e), a phenomenon that is undesirable since it limits the rate of transmission. Pulse broadening results because various light rays, although being injected at approximately the same instant, arrive at the output at different times; they traverse different trajectories and, thus, have a variety of path lengths. Pulse broadening is largely avoided by utilization of the other or graded-index design. Here, impurities such as boron oxide (B2O3) or germanium dioxide (GeO2) are added to the silica glass such that the index of refraction is made to vary parabolically across the cross section (Figure 21.22b). Thus, the velocity of light within the core varies with radial position, being greater at the periphery than at the center. Consequently, light rays that traverse longer path lengths through the outer periphery of the core travel faster in this lower-index material, and arrive at the output at approximately the same time as undeviated rays that pass through the center portion of the core. Exceptionally pure and high-quality fibers are fabricated using advanced and sophisticated processing techniques, which will not be discussed here. Impurities and other defects that absorb, scatter, and thus attenuate the light beam must be eliminated. The presence of copper, iron, and vanadium is especially detrimental; their concentrations are reduced to on the order of several parts per billion. Likewise, water and hydroxyl contaminant contents are extremely low. Uniformity of fiber cross-sectional dimensions and core roundness are critical; tolerances of these parameters to within a micrometer over 1 km (0.6 mile) of length are possible. In addition, bubbles within the glass and surface defects have been virtually eliminated. The attenuation of light in this glass material is imperceptibly small. For
Input impulse Cladding Core Radial position Output impulse
Intensity
Index of refraction (a) (b)
Intensity Time (c) (d) Time (e)
Figure 21.21 Step-index optical fiber design. (a) Fiber cross section. (b) Fiber radial index of refraction profile. (c) Input light pulse. (d) Internal reflection of light rays. (e) Output light pulse. (Adapted from S. R. Nagel, IEEE Communications Magazine, Vol. 25, No. 4, p. 34, 1987.)
1496T_c21_W57-W85
3/1/06
15:22
Page W82
W82 Chapter 21 / Optical Properties
Input impulse Cladding Core Radial position Output impulse
Index of refraction (a) (b)
Intensity
Time (c) (d)
Intensity Time (e)
Figure 21.22 Graded-index optical fiber design. (a) Fiber cross section. (b) Fiber radial index of refraction profile. (c) Input light pulse. (d) Internal reflection of a light ray. (e) Output light pulse. (Adapted from S. R. Nagel, IEEE Communications Magazine, Vol. 25, No. 4, p. 34, 1987.)
example, the power loss through a 16-kilometer (10-mile) thickness of optical fiber glass is equivalent to the power loss through a 25-millimeter (1-inch) thickness of ordinary window glass!
SUMMARY
Electromagnetic Radiation Light Interactions with Solids The optical behavior of a solid material is a function of its interactions with electromagnetic radiation having wavelengths within the visible region of the spectrum. Possible interactive phenomena include refraction, reflection, absorption, and transmission of incident light. Optical Properties of Metals Metals appear opaque as a result of the absorption and then reemission of light radiation within a thin outer surface layer. Absorption occurs via the excitation of electrons from occupied energy states to unoccupied ones above the Fermi energy level. Reemission takes place by decay electron transitions in the reverse direction. The perceived color of a metal is determined by the spectral composition of the reflected light. Atomic and Electronic Interactions Refraction Light radiation experiences refraction in transparent materials; that is, its velocity is retarded and the light beam is bent at the interface. Index of refraction is the ratio of the velocity of light in a vacuum to that in the particular medium. The phenomenon of refraction is a consequence of electronic polarization of the atoms or ions, which is induced by the electric field component of the light wave. Reflection When light passes from one transparent medium to another having a different index of refraction, some of it is reflected at the interface.The degree of the reflectance depends on the indices of refraction of both media, as well as the angle of incidence.
1496T_c21_W57-W85
3/1/06
15:22
Page W83
Important Terms and Concepts W83 Absorption Nonmetallic materials are either intrinsically transparent or opaque. Opacity results in relatively narrow-band gap materials as a result of absorption whereby a photons energy is sufficient to promote valence band-conduction band electron transitions. Transparent nonmetals have band gaps greater than about 3 eV. Some light absorption occurs in even transparent materials as a consequence of electronic polarization. Color For wide-band gap insulators that contain impurities, decay processes involving excited electrons to states within the band gap are possible with the emission of photons having energies less than the band gap energy. These materials appear colored, and the color depends on the distribution of wavelength ranges in the transmitted beam. Opacity and Translucency in Insulators Normally transparent materials may be made translucent or even opaque if the incident light beam experiences interior reflection and/or refraction. Translucency and opacity as a result of internal scattering may occur, (1) in polycrystalline materials that have an anisotropic index of refraction, (2) in two-phase materials, (3) in materials containing small pores, and (4) in highly crystalline polymers. Luminescence Photoconductivity Lasers Three other important optical phenomena were discussed: luminescence, photoconductivity, and light amplification by stimulated emission of radiation (lasers). With luminescence, energy is absorbed as a consequence of electron excitations, which is reemitted as visible light. The electrical conductivity of some semiconductors may be enhanced by photoinduced electron transitions, whereby additional free electrons and holes are generated. Coherent and high-intensity light beams are produced in lasers by stimulated electron transitions. Optical Fibers in Communications This chapter concluded with a discussion of the use of optical fibers in our modern telecommunications. Using fiber-optic technology, transmission of information is interference free, rapid, and intense.
I M P O R TA N T T E R M S A N D C O N C E P T S
Absorption Color Electroluminescence Excited state Fluorescence Ground state Index of refraction Laser Light-emitting diode (LED) Luminescence Opaque Phosphorescence Photoconductivity Photon Plancks constant Reflection Refraction Translucent Transmission Transparent
1496T_c21_W57-W85
3/1/06
15:22
Page W84
W84 Chapter 21 / Optical Properties
REFERENCES
Azaroff, L.V., and J. J. Brophy, Electronic Processes in Materials, McGraw-Hill, New York, 1963, Chapter 14. Reprinted by TechBooks, Marietta, OH. Javan, A., The Optical Properties of Materials, Scientific American, Vol. 217, No. 3, September 1967, pp. 238248. Kingery, W. D., H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics, 2nd edition, Wiley, New York, 1976, Chapter 13. Ralls, K. M., T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering, Wiley, New York, 1976, Chapter 27. Rowell, J. M., Photonic Materials, Scientific American, Vol. 255, No. 4, October 1986, pp. 146157.
QUESTIONS AND PROBLEMS
Electromagnetic Radiation 21.1 Visible light having a wavelength of 5 10 7 m appears green. Compute the frequency and energy of a photon of this light. Light Interactions with Solids 21.2 Distinguish between materials that are opaque, translucent, and transparent in terms of their appearance and light transmittance. Atomic and Electronic Interactions 21.3 (a) Briefly describe the phenomenon of electronic polarization by electromagnetic radiation. (b) What are two consequences of electronic polarization in transparent materials? Optical Properties of Metals 21.4 Briefly explain why metals are opaque to electromagnetic radiation having photon energies within the visible region of the spectrum. Refraction 21.5 In ionic materials, how does the size of the component ions affect the extent of electronic polarization? 21.6 Can a material have an index of refraction less than unity? Why or why not? 21.7 Compute the velocity of light in diamond, which has a dielectric constant r of 5.5 (at frequencies within the visible range) and a magnetic susceptibility of 2.17 10 5. 21.8 The indices of refraction of fused silica and a polystyrene within the visible spectrum are 1.458 and 1.60, respectively. For each of these materials determine the fraction of the relative dielectric constant at 60 Hz that is due to electronic polarization, using the data of Table 18.5. Neglect any orientation polarization effects. 21.9 Using the data in Table 21.1, estimate the dielectric constants for silica glass (fused silica), sodalime glass, polytetrafluoroethylene, polyethylene, and polystyrene, and compare these values with those cited in Table 18.5. Briefly explain any discrepancies. 21.10 Briefly describe the phenomenon of dispersion in a transparent medium. Reflection 21.11 It is desired that the reflectivity of light at normal incidence to the surface of a transparent medium be less than 5.0%. Which of the following materials in Table 21.1 are likely candidates: sodalime glass, Pyrex glass, periclase, spinel, polystyrene, and polypropylene? Justify your selections. 21.12 Briefly explain how reflection losses of transparent materials are minimized by thin surface coatings. 21.13 The index of refraction of quartz is anisotropic. Suppose that visible light is passing from one grain to another of different crystallographic orientation and at normal incidence to the grain boundary.
1496T_c21_W57-W85
3/1/06
15:22
Page W85
Design Problem W85 Calculate the reflectivity at the boundary if the indices of refraction for the two grains are 1.544 and 1.553 in the direction of light propagation. Absorption 21.14 Zinc selenide has a band gap of 2.58 eV. Over what range of wavelengths of visible light is it transparent? 21.15 Briefly explain why the magnitude of the absorption coefficient (b in Equation 21.18) depends on the radiation wavelength. 21.16 The fraction of nonreflected radiation that is transmitted through a 5-mm thickness of a transparent material is 0.95. If the thickness is increased to 12 mm, what fraction of light will be transmitted? Transmission 21.17 Derive Equation 21.19, starting from other expressions given in the chapter. 21.18 The transmissivity T of a transparent material 15 mm thick to normally incident light is 0.80. If the index of refraction of this material is 1.5, compute the thickness of material that will yield a transmissivity of 0.70. All reflection losses should be considered. Color 21.19 Briefly explain what determines the characteristic color of (a) a metal and (b) a transparent nonmetal. 21.20 Briefly explain why some transparent materials appear colored while others are colorless. Opacity and Translucency in Insulators 21.21 Briefly describe the three absorption mechanisms in nonmetallic materials. 21.22 Briefly explain why amorphous polymers are transparent, while predominantly crystalline polymers appear opaque or, at best, translucent. Luminescence Photoconductivity Lasers 21.23 (a) In your own words describe briefly the phenomenon of luminescence. (b) What is the distinction between fluorescence and phosphorescence? 21.24 In your own words, briefly describe the phenomenon of photoconductivity. 21.25 Briefly explain the operation of a photographic lightmeter. 21.26 In your own words, describe how a ruby laser operates. 21.27 Compute the difference in energy between metastable and ground electron states for the ruby laser. Optical Fibers in Communications 21.28 At the end of Section 21.14 it was noted that the intensity of light absorbed while passing through a 16-kilometer length of optical fiber glass is equivalent to the light intensity absorbed through for a 25-mm thickness of ordinary window glass. Calculate the absorption coefficient b of the optical fiber glass if the value of b for the window glass is 10 4 mm 1.
DESIGN PROBLEM
Atomic and Electronic Interactions 21.D1 Gallium arsenide (GaAs) and gallium phosphide (GaP) are compound semiconductors that have room-temperature band gap energies of 1.42 and 2.25 eV, respectively, and form solid solutions in all proportions. Furthermore, the band gap of the alloy increases approximately linearly with GaP additions (in mol%). Alloys of these two materials are used for light-emitting diodes wherein light is generated by conduction band-to-valence band electron transitions. Determine the composition of a GaAsGaP alloy that will emit red light having a wavelength of 0.68 mm.