1. 1 The Science and Engineering of Materials, 4 th ed Donald R. Askeland – Pradeep P. Phulé Chapter 20 – Photonic Materials

2. 2 Objectives of Chapter 20  To present a summary of fundamental principles that have guided applications of optical materials.  To explore two avenues by which we can use the optical properties of materials: emission of photons from materials and interaction of photons with materials.

3. 3 Chapter Outline  20.1 The Electromagnetic Spectrum  20.2 Refraction, Reflection, Absorption, and Transmission  20.3 Selective Absorption, Transmission, or Reflection  20.4 Examples and Use of Emission Phenomena  20.5 Fiber Optic Communication System

4. 4  Light is energy, or radiation, in the form of waves or particles called photons that can be emitted from a material.  The important characteristics of the photons—their energy E, wavelength λ, and frequency ν —are related by the equation Section 20.1 The Electromagnetic Spectrum

5. 5 Figure 20.1 The electromagnetic spectrum of radiation; the bandgaps and cutoff frequencies for some optical materials are also shown. (Source: From Optoelectronics: An Introduction to Materials and Devices, by J. Singh. Copyright © 1996 The McGraw-Hill Companies. Reprinted by permission of The McGraw-Hill Companies.)

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7. 7  Index of refraction - Relates the change in velocity and direction of radiation as it passes through a transparent medium (also known as refractive index).  Dispersion - Frequency dependence of the refractive index.  Reflectivity - The percentage of incident radiation that is reflected.  Linear absorption coefficient - Describes the ability of a material to absorb radiation.  Photoconduction - Production of a voltage due to the stimulation of electrons into the conduction band by light radiation. Section 20.2 Refraction, Reflection, Absorption, and Transmission

8. 8 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.2 (a) Interaction of photons with a material. In addition to reflection, absorption, and transmission, the bream changes direction, or is refracted. The change in direction is given by the index of refraction n. (b) The absorption index (k) as a function of wavelength.

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10. 10 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.3 (a) When a ray of light enters from material 1 into material 2, if the refractive index of material 1 (n 1 ) is greater than that of material 2 (n 2 ), then the ray bends away from the normal and toward the boundary surface. [1, 9] (b) Diagram a light beam in glass fiber for Example 20.1.

11. 11 Optical fibers are commonly made from high-purity silicate glasses. They consist of a core that has refractive index (~ 1.48) that is higher than a region called cladding (refractive index ~ 1.46). This is why even a simple glass fiber in air (refractive index 1.0) can serve as an optical fiber. In designing a fiber optic transmission system, we plan to introduce a beam of photons from a laser into a glass fiber whose index of refraction of is 1.5. Design a system to introduce the beam with a minimum of leakage of the beam from the fiber. Example 20.1 Design of a Fiber Optic System Figure 20.3 (b) Diagram a light beam in glass fiber for Example 20.1.

12. 12 Example 20.1 SOLUTION To prevent leakage of the beam, we need the total internal reflection and thus the angle θ t must be at least 90 o. Suppose that the photons enter at a 60 o angle to the axis of the fiber. From Figure 20.3(b), we find that θ i = 90 - 60 = 30 o. If we let the glass be Material 1 and if the glass fiber is in air (n = 1.0), then Because θ t is less than 90 o, photons escape from the fiber. To prevent transmission, we must introduce the photons at a shallower angle, giving θ t = 90 o.

13. 13 Example 20.1 SOLUTION (Continued) If the angle between the beam and the axis of the fiber is 90 - 41.8 = 48.2 or less, the beam is reflected. If the fiber were immersed in water (n = 1.333), then: In water, the photons would have to be introduced at an angle of less than 90 – 62.7 = 27.3 in order to prevent transmission.

14. 14 Example 20.2 Light Transmission in Polyethylene Suppose a beam of photons in a vacuum strikes a sheet of polyethylene at an angle of 10 o to the normal of the surface of the polymer. Calculate the index of refraction of polyethylene and find the angle between the incident beam and the beam as it passes through the polymer. Example 20.2 SOLUTION The index of refraction is related to the high-frequency dielectric constant. For this material the high-frequency dielectric constant k = 2.3: The angle θ t is:

15. 15 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.4 The linear absorption coefficient relative to wavelength for several metals. Note the sudden decrease in the absorption coefficient for wavelengths greater than the absorption edge.

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17. 17 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.5 Fractions of the original beam that are reflected, absorbed, and transmitted.

18. 18 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.6 Relationships between absorption and the energy gap: (a) metals, (b) Dielectrics and intrinsic semiconductors, and (c) extrinsic semiconductors.

19. 19 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.7 (a) Photoconduction in semiconductors involves the absorption of a stimulus by exciting electrons from the valence band to the conduction band. Rather than dropping back to the valence band to cause emission, the excited electrons carry a charge through an electrical circuit. (b) A solar cell takes advantage of this effect.

20. 20 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.8 Elements of a photonic system for transmitting information involves a laser or LED to generate photons from an electrical signal, optical fibers to transmit the beam of photons efficiently, and an LED receiver to convert the photons back into an electrical signal.

21. 21 Determine the critical energy gaps that provide complete transmission and complete absorption of photons in the visible spectrum. Example 20.3 SOLUTION The visible light spectrum varies from 4  10 -5 cm to 7  10 -5 cm. The minimum E g required to assure that no photons in the visible spectrum are absorbed is: Example 20.3 Determining Critical Energy Gaps

22. 22 Example 20.3 SOLUTION (Continued) The maximum E g below which all of the photons in the visible spectrum are absorbed is: For materials with an intermediate E g, a portion of the photons in the visible spectrum will be absorbed.

23. 23 A material has a reflectivity of 0.15 and an absorption coefficient (α) of 100 cm -1. Design a shield that will permit only 1% of the incident radiation from being transmitted through the material. Example 20.4 SOLUTION The fraction of the incident intensity that will be transmitted is: Example 20.4 Design of a Radiation Shield The material should have a thickness of 0.0428 cm in order to transmit 1% of the incident radiation.

24. 24  Unusual optical behavior is observed when photons are selectively absorbed, transmitted, or reflected. Section 20.3 Selective Absorption, Transmission, or Reflection

25. 25 Design an aircraft that cannot be detected by radar. Example 20.5 SOLUTION 1.We might make the aircraft from materials that are transparent to radar. Many polymers, polymer-matrix composites, and ceramics satisfy this requirement. 2.We might design the aircraft so that the radar signal is reflected at severe angles from the source. 3.The internal structure of the aircraft also can be made to absorb the radar. For example, use of a honeycomb material in the wings may cause the radar waves to be repeatedly reflected within the material. 4.We might make the aircraft less visible by selecting materials that have electronic transitions of the same energy as the radar. Example 20.5 Design of a ‘‘Stealthy’’ Aircraft

26. 26  X-rays - Electromagnetic radiation in the wavelength range ~ 1 to 100 Å.  Continuous spectrum - Radiation emitted from a material having all wavelengths longer than a critical short wavelength limit.  Luminescence - Conversion of radiation to visible light.  Fluorescence - Emission of light obtained typically within ~ 10 -8 seconds.  Phosphorescence - Emission of radiation from a material after the stimulus is removed. Section 20.4 Examples and Use of Emission Phenomena

27. 27  Light-emitting diodes (LEDs) - Electronic p-n junction devices that convert an electrical signal into visible light.  Electroluminescence - Use of an applied electrical signal to stimulate photons from a material.  Laser - The acronym stands for light amplification by stimulated emission of radiation. A beam of monochromatic coherent radiation produced by the controlled emission of photons.  Thermal emission - Emission of photons from a material due to excitation of the material by heat. Section 20.4 (Continued)

28. 28 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.9 When an accelerated electron strikes and interacts with a material, its energy may be reduced in a series of steps. In the process, several photons of different energies E 1 to E 5 are emitted, each with a unique wavelength.

29. 29 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.10 The continuous and characteristic spectra of radiation emitted from a material. Low-energy stimuli produce a continuous spectrum of low-energy, long-wavelength photons. A more intense, higher energy spectrum is emitted when the stimulus is more powerful until, eventually, characteristic radiation is observed.

30. 30 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.11 Characteristic x-rays are produced when electrons change from one energy level to a lower energy level, as illustrated here for copper. The energy and wavelength of the x-rays are fixed by the energy differences between the energy levels.

31. 31 Design a filter that preferentially absorbs K β x-rays from the nickel spectrum but permits K α x-rays to pass with little absorption. This type of filter is used in x-ray diffraction (XRD) analysis of materials. Example 20.6 Design/Materials Selection for an X-ray Filter

32. 32 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.12 Elements have a selective lack of absorption of certain wavelengths. If a filter is selected with an absorption edge between the K α and K β peaks of an x-ray spectrum, all x-rays except K α are absorbed (for Example 20.6).

33. 33 Example 20.6 SOLUTION When determining a crystal structure or identifying unknown materials using various x-ray diffraction techniques, we prefer to use x-rays of a single wavelength. If both K α and K β characteristic peaks are present and interact with the material, analysis becomes much more difficult. However, we can use the selective absorption, or the existence of the absorption edge, to isolate the K α peak. Table 20-2 includes the information that we need. If a filter material is selected; such that the absorption edge lies between the K α and K β wavelengths, then the K β is almost completely absorbed, whereas the K α is almost completely transmitted. In nickel, K α = 1.660 Å and K β = 1.500 Å. A filter with an absorption edge between these characteristic peaks will work. Cobalt, with an absorption edge of 1.608 Å, would be our choice. Figure 20-12 shows how this filtering process occurs.

34. 34 Design a filter to transmit at least 95% of the energy of a beam composed of zinc K α x-rays, using aluminum as the shielding material. (The aluminum has a linear absorption coefficient of 108 cm -1.) Assume no loss to reflection. Example 20.7 SOLUTION The final intensity will therefore be 0.95I 0. Example 20.7 Design of an X-ray Filter We would like to roll the aluminum to a thickness of 0.00047 cm or less. The filter could be thicker if a material were selected that has a lower linear absorption coefficient for zinc K α x-rays.

35. 35 Suppose an electron accelerated at 5000 V strikes a copper target. Will K α, K β, or L α x-rays be emitted from the copper target? Example 20.8 SOLUTION The electron must possess enough energy to excite an electron to a higher level, or its wavelength must be less than that corresponding to the energy difference between the shells: Example 20.8 Generation of X-rays for XRD For copper, K α is 1.542 Å, K β is 1.392 Å, and L α is 13.357 Å. Therefore, the L α peak may be produced, but K α and K β will not.

36. 36 The micrograph in Figure 20.13 was obtained using a scanning electron microscope at a magnification of 1000. The beam of electrons in the SEM was directed at the three different phases, creating x-rays and producing the characteristic peaks. From the energy spectra, determine the probable identity of each phase. Assume each region represents a different phase. Example 20.9 Energy Dispersive X-ray Analysis (EDXA)

37. 37 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.13 Scanning electron micrograph of a multiple-phase material. The energy distribution of emitted radiation from the three phases marked A, B, and C is shown. The identity of each phase is determined in Example 20.9.

38. 38 Example 20.9 SOLUTION All three phases have an energy peak of about 1.5 keV = 1500 eV, which corresponds to a wavelength of: In a similar manner, energies and wavelengths can be found for the other peaks. The identity of the elements in each phase can be found, as summarized in the table.

39. 39 Example 20.9 SOLUTION (Continued) Thus, phase A appears to be an aluminum matrix, phase B appears to be a silicon needle (perhaps containing some aluminum), and phase C appears to be an Al-Si-Mn-Fe compound. Actually, this is an aluminum-silicon alloy. The stable phases are aluminum and silicon, with inclusions forming when manganese and iron are present as impurities.

40. 40 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.14 Luminescence occurs when photons have a wavelength in the visible spectrum. (a) In metals, there is no energy gap, so lumine- scence does not occur. (b) Fluorescence occurs when there is an energy gap. (c) Phosphorescence occurs when the photons are emitted over a period of time due to donor traps in the energy gap.

41. 41 Select a phosphor material that will produce a blue image on a television screen. Example 20.10 Design/Materials Selection for a Television Screen Figure 20.1 The electromagnetic spectrum of radiation; the bandgaps and cutoff frequencies for some optical materials are also shown. (Source: From Optoelectronics: An Introduction to Materials and Devices, by J. Singh. Copyright © 1996 The McGraw-Hill Companies. Reprinted by permission of The McGraw-Hill Companies.)

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43. 43 Example 20.10 SOLUTION Photons having energies that correspond to the color blue have wavelengths of about 4.5  10 -5 cm (Figure 20.1). The energy of the emitted photons therefore is: Typical phosphorescent materials for television screens might include CaWO 4, which produces photons with a wavelength of 4.3  10 -5 cm (blue).

44. 44 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.15 Diagram of a light-emitting diode (LED). A forward-bias voltage across the p-n junction produces photons.

45. 45 Figure 20.16 The laser converts a stimulus into a beam of coherent photons. The mirror on one side is 100% reflecting, the mirror on the right transmits partially. (Source: From Optical Materials: An Introduction to Selection and Application, by S. Musikant, p. 201, Fig. 10-1. Copyright © 1985 Marcel Dekker, Inc.)

46. 46 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.17 Creation of a laser beam from a semiconductor: (a) Electrons are excited into the conduction band by an applied voltage. (b) Electron 1 recombines with a hole to produce a photon. The photon stimulates the emission of photon 2 by a second recombination. (c) Photons reflected from the mirrored end stimulate even more photons. (d) A fraction of the photons are emitted as a laser beam, while the rest are reflected to simulate more recombinations.

47. 47 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.18 Schematic cross-section of a GaAs laser. Because the surrounding p- and n-type GaAlAs layers have a higher energy gap and a lower index of refraction than GaAs, the photons are trapped in the active GaAs layer.

48. 48 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.19 Intensity in relation to wavelengths of photons emitted thermally from a material. As the temperature increases, more photons are emitted from the visible spectrum.

49. 49  Generating the Signal - In order to best transmit and process information, the light should be coherent and monochromatic (to minimize dispersion).  Transmitting the Beam - Optical fibers transmit the information.  Receiving the Signal - The job of a receiver in the fiber optic system is to convert the optical signal into an electronic signal.  Processing the Signal - Normally, the received signal is converted immediately into an electronic signal and then processed using conventional silicon-based semiconductor devices.  Photonic bandgap materials - These are structures produced using micromachined silicon or colloidal particles, such that there is a range of frequencies that cannot be transmitted through the structure. Section 20.5 Fiber Optic Communication System

50. 50 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.20 Schematic of a fiber-optic based communication system.

51. 51 Figure 20.21 Different types of optical fibers. (a) A step index glass fiber, in which the index or refrac- tion is slightly different in each glass. (b) The profile of a refractive index in a graded refractive index (GRIN) fiber. (c) The path of rays entering at different angles. [1,5]

52. 52 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.22 Results from an x-ray fluorescence analysis of an unknown metal sample (for Problem 20.41).

53. 53 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.23 X-ray emission spectrum (for Problem 10.42)

54. 54 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 20.24 Intensity of the initial spectrum from a copper x-ray source before filtering (for Problem 20.43).