528 Optical Properties of Thin Films nonabsorbing substrate is n2 = 1.5, the value for plate glass. The oscillatory nature of the reflected light intensity, caused by interference effects, has a periodicity related to the film thickness and index of refraction. This is the basis for experimentally determining the thickness of transparent films if the index of refraction is known (see Chapter 6). Conversely, the optical proper- ties of the film can be determined at a particular wavelength if its thickness is known. Maxima or minima in the reflected intensity occur at specific fdm thicknesses, for given wavelengths, depending on whether the refractive index of the film is greater or less than that of the substrate. In the former case the reflectivity is enhanced, whereas in the latter case reflectivity is diminished. Optimization of these two effects has led to the development of dielectric mirrors and antireflection coatings, respectively. To quantify the issues related to antireflectivity, Eq. 11-17 reveals that r vanishes when rl + r,exp - is = 0 or when the denominator goes to infinity. The latter is an impossibility, since rl and r2 are less than or equal to 1. The remaining condition can be decomposed into two real transcendental equations: (a) r, + r2cos 6 = 0 and (b) r,sin 6 = 0. Equation @) implies that 6 = 0, f a, +2a, f 3n, etc., but the simultaneous satisfaction of equation (a) requires the selection of 6 = f a, & 3n, f 5a, etc. Under these conditions, r, - r2 = 0 or (no - n,)/(n, + n,) = (n, - n,)/(n, + n2). Therefore, n,= Jnonz. (1 1-20) Since 6 = 4nn,d,/X = a, 3a, 5~, etc, x 3x 5x n,d= - - - , etc. 4’ 4’4 (1 1-21) Equations 11-20 and 11-21 represent the amplitude and phase conditions for zero reflectance, respectively. In the design of a one-layer antireflection coating, the film index of refraction should be the geometric mean of the refractive indices of adjacent media. This is only strictly true for the wave- length X for which the optical thickness of the film is X/4, 3h/4, etc. = 1.23 is optimal for antireflection purposes. Clearly, this is only one consideration among many, including availability, ease of deposition, hardness, and environ- mental stability, which must be taken into account when choosing the film layer. The most widely used AR coating is a X/4-thick film of MgF, with n, = 1.38. It can be used to coat either glass or acrylic substrates. In the absence of an AR coating, glass will exhibit a reflectance of ((1.0 - 1.52)/(1.0 + 1.52))2 = 0.043. Suppose it is desired to reduce the reflectance at a wavelength of 5500 A. Then the film thickness required is X/4n1 or To coat a glass lens (n2 = 1.52), a film with n, = 11 -3 Thin-Film Optics 529 Figure tics. (b) WAVELENGTH (nm) (a) 5 h E4 2 52 Cl w 0 23 0 U w 11111111111111/1111 500 600 700 ' ' I WAVELENGTH (nm) (W 11-1 0. (a) Single (S) and double (0) layer antireflection coating Broadband antireflection coating characteristics. (From Ref. 5). characteris- 5500/4(1.38) = 996 A. Under these conditions the reflectance is given by Eq. 11-18 with r, = (1.0 - 1.38)/(1.0 + 1.38) = -0.160, r, = (1.38 - 1.52)/(1.38 + 1.52) = -0.0483, and 6 = a. Substitution in Eq. 11-18 yields a value of R = 0.0126, indicating an almost fourfold decrease in reflectivity. Greater improvements occur for higher n2 values of the underlying substrate. As an example, for an uncoated glass with n, = 1.75 the reflectance is 0.074. With a quarter-wave-thick MgF, coating, R is reduced to 0.0025. At other wavelengths, but the same optical thickness, R will be different because n, varies with X (Le., dispersion) and because of changes in 6. The reflectance reduction with a single-layer AR coating as a function of wavelength is shown in Fig. 11-10. 530 Optical Properties of Thin Films It is instructive to end the discussion with several observations made by Anders. (Ref. 3) 1. There is a more rapid variation of 6 and hence R with A for a 3x14 film than for a X/4 film. Therefore, R will be less dependent on wavelength with a X/4 coating. 2. It is not always true that films of high refractive index give a high reflectance, whereas those with low refractive index yield AR coatings. The rule is that if the reflected amplitudes rl and r2 are of the same sign, antireflection behavior is observed; if they are of opposite sign, then reflection from the surface is enhanced. 3. For very large amplitude values of f, = - r2, R approaches 100% and the reflection becomes zero only in narrow wavelength bands at X/2, X, 3X/2, . . . . This occurs physically when a film is sandwiched between two media of the same refractive index, Le., cemented film (n, In, /n2), as shown in Fig. 11-9. 11.3.3. Absorbing Films The mechanisms by which materials absorb radiation were treated earlier. Absorption effects can be formally incorporated into the Fresnel equations by replacing the refractive index n by the complex refractive index; i.e., N = n - ik. For the case of reflection due to normal incidence of light at an interface between nonabsorbing and absorbing media of refractive indices no and n, - ik, , respectively, no - n, + ik, rl = no + n, - ik, (1 1-22) By evaluating I r, I ,, we have the reflectance formula Eq. 11-6. As an example, consider the reflectance of Al front surface mirrors pro- duced some 15 years apart. Hass (Ref. 15) measured the optical constants of Alto be NA, = 0.76 - i5.5 in 1946 and PIA, = 0.81 - i5.99 in 1961. Substi- tution in Eq. 11-6 with no = 1 yields respective reflectances of 0.909 and 0.9 16. Improved deposition technology including higher and cleaner vacua, purer metal, and higher evaporation rates were probably the cause of the enhanced reflectance. An R value of 0.91 could be achieved with a hypotheti- cal absorption-free material with n = 43. This extremely high value can be thought of as the effective refractive index for aluminum. A frequently asked question regarding thin fdms is, how thick must a metal film (on a transparent substrate) be before it is continuous? By this is meant the 11.4 Multilayer Optical Film Applicatlons 531 thickness at which it can no longer be seen through. A simple estimate can be obtained by arbitrarily assuming that a drop in transmitted intensity by a factor of 1 /e occurs when the film is continuous. Therefore, the use of Eq. 11-3 with I/Zo = 1 /e yields 4 a kd / X = 1, or d = X/4 a k. It is clear that the answer to the question not only depends on the type of metal but also on the wavelength of light used to view it. The critical thickness for A1 films at 5500 is 82 A, whereas for Au films it is 185 A. It is common experience, however, that films that are considerably thicker exhibit some transparency. The reason is that ultrathin films condense in an island structure of discrete clusters rather than as planar, continuous, homogeneous layers assumed in the optical theory. An alternative approach to this problem, which is left to the reader as a lengthy but healthy exercise in the use of complex numbers, is to consider the optical structure no /n, - ik, /n2 corresponding to free-space/metal film/substrate. From Eq. 11-19, T can be calculated for different film thicknesses. By inverting the order of the last two optical components, Le., no /nl /n2 - ik,, we have the case of the back surface or protected mirror. It is commonly believed that the reflection properties of the mirror are unaffected by the protective layer. In reality, the latter actually reduces the reflectance in the visible, and, particularly, in the UV and IR ranges. The remaining case, no /n, - ik, /n2 - ik,, models the optical behavior of an absorbing film on an absorbing substrate. This structure was recently used to determine the real-time kinetics of regrowth of epitaxial Si into an amorphous Si (surface) layer. By bouncing a He-Ne laser beam off the surface and monitoring the reflected beam intensity, the instantaneous position of the epitaxial - amorphous interface could be unfolded from the attenuated periodic signal (Ref. 16). Such a measurement is possible because the optical constants of crystalline and amorphous Si differ. (See Problem 9, p. 543.) 11.4. MULTILAYER OPTICAL FILM APPLICATIONS 11.4.1. Introduction Once the basic principles governing the applications of single dielectric films and their deposition methods were firmly established, extension to multilayer systems was naturally driven by several factors (Ref. 17): 1. By suitable variations in design, it is possible to obtain improved AR 2. Systems with a vast variety of optical filtering properties can be achieved properties over a broader spectral range. 532 Optical Properties of Thin Films ANTI-REFLECTION HIGH-REFLECTIONS BEAMSPLllTERS h h h OR DICHROIC FILTER DICHROIC h h 1 'riii '1 )==@FZING FILTER BEAMSPLllTER h h h Figure 11-11. Typical applications of thin films and film systems in optics. (From Ref. 5). usually with the use of many film layers (sometimes a dozen or more) but with only a very limited number of materials (e.g., MgF, and ZnS). 3. Multilayer optical filters have advantages over other types of filters. The reason is that there is very little absorption loss in dielectric film layers, since they rely on the effects of interference. 4. The principles of design of optical systems applicable to one region of the electromagnetic spectrum (e.g., visible) are also valid in other regions (e.g., UV and IR). Various types of thin-film optical component characteristics are shown in Fig 11-11 where the desired reflectance and transmittance properties are schematically indicated as a function of wavelength. 11.4.2. AR Coatings Antireflection coatings constitute the overwhelming majority of all optical coatings produced. They are used on the lenses of virtually all optical equipment, including cameras, microscopes, binoculars, range finders, tele- scopes, and on opthalmic glasses. Because of the reflection at each air-glass interface, intolerably large light losses can rapidly mount in complex lens 11.4 Multilayer Optical Film Applications 533 systems. Neglecting absorption effects, the transmission of an optical system is given by T = (1 - Rl)(l - R2)(1 - R3). . . , (1 1-23) where the Ri are the reflectances (Eq. 11-5) at the individual optical inter- faces. For example, in a system with uncoated lenses consisting of 20 interfaces, each with R = 0.05, the value of T = (0.95)20 = 0.358. If, how- ever, R is reduced to 0.01 by means of AR coatings, then T = 0.818. The measured transmission is actually somewhat higher than these estimates be- cause light is backreflected at internal air-glass interfaces. The improvement is impressive indeed. In addition to enhancing light transmission, AR coatings reduce glare. The so-called veiling glare causes a reduction in image contrast by illuminating regions of the image that should normally be dark. Lastly, since lens surfaces fortuitously act as mirrors in addition to refractors, spurious ghost images are frequently generated. These are also reduced through the use of AR coatings. Other optical systems that derive benefit from the use of such coatings to maximize the capture of light include solar cells, infrared detectors, and magneto-optical devices. In the case of the double-layer coating where the indices of refraction vary successively as no (= l)/n, /n2 /n3 from free space to the substrate, the complex reflectivity amplitude is given by rl + r2e-iSl + r3ei(h+h) + r r r e-ihz 1 + rlr2e-'4 + r r e-i(4+*d + r r e-% ( 1 1-24) by analogy with Eq. 11-17. For normal incidence the indicated r for each of the three interfaces is given by 123 r= 13 23 ni-, - n, 47rn,d1 4?rn2d2 , a,=- A' r. = and 6, = -* ' ni-l + ni A where d, and d2 are the thicknesses of the coating layers. Zero reflectance at one wavelength will obtain when the condition n2 = n, &/no is fulfilled. Once film n, has been selected, this condition serves to specify the optimal value of n,. The improvement of a double-layer AR coating relative to the single-film coating is shown in Fig. 11-loa. Interestingly, although the double layer results in a considerable reflectance reduction at wavelengths centered about 5500 A, the response is worse at the spectral extremes due to the high curvature of the R vs. A dependence. Greater care is required in controlling the film thickness in bilayer coatings than in single layers. In the latter a film thickness error simply means that the reflectance minimum is shifted to another wavelength. In contrast, an error in double-layer thicknesses can not only 534 Optical Properties of Thin Films eliminate reflection minima but even increase reflectance. Multilayer film thicknesses must be even more stringently controlled. The extension of the analysis to a multilayer stack of dielectric films of various thicknesses and n values is straightforward, though cumbersome. Exact formulas exist for three and more layers. Modem broadband AR coatings generally consist of three to seven film layers. An example of the reflectance characteristics of such a multilayer coating is shown in Fig. 11-lob. 11.4.3. Multilayer Dlelectric Stacks Since the high reflectance of a single h/4 film is due to the constructive interference of the beams reflected at both surfaces, the effect can be enhanced by phase agreement in the reflected beams from multiple film layers. What is required is a stack of alternating high (H) and low (L) index h/4 films. Next to the substrate is the usual high index layer so that the stacking order is HLHLHLHL . . For z layers it has been calculated that the maximum reflectance is given by (Refs. 4, 17) (11-25) where nH , nL , and n, are the high, low, and substrate indices. An expansion of Eq. 11-18 for n, > n2 shows that the z layers are equivalent to a single layer whose effective refractive index is equal to dm. The spectral characteristics of such a multilayer stack are shown in Fig. 11-12 for the case of a variable number of alternating layers of ZnS and MgF, . Also shown is a portion of the microstructure of a multifilm stack composed of these materials. It is clear that the magnitude of the reflectance increases with the number of layers. The number of sideband oscillations outside the high-re- flectance zone also increases with number of layers. The spectral width of the high reflectance zone is a function of the ratio of the refractive indices of the involved films, and there are a couple of practical ways to extend it. One is to select materials with nH and nL that are higher and lower, respectively, than those of ZnS and MgF, . Another is to broaden the basis of design to include several wavelengths. In such a case the dielectric stack would be composed of staggered layer thicknesses so that consecutive maxima would overlap. In this way 15 layers of ZnS and Na,AIF, with different optical thicknesses can be used to span the visible range. By similar methods dielectric mirrors are designed to operate in the infrared or ultraviolet with very small residual 11.4 Multilayer Optical Film Applications 535 . "" Y 90- 00 - v s 70- 40- 20 - os 11 11 I I 11 1 11 I I 11, I 0 10 20 30 40 50 60 70 00 90 100 110 120 130 140 150 160 1701 PHASE THICKNESS 16/21 I I1 I I 1 I I 1 5000 1000 000 600 460 400 300 250 230 WAVELENGTH (nm) (4 (b) Figure 11-12. (a) Spectral characteristics of multilayer stacks formed of alternating h/4 layers of ZnS and MgF, 0: glass (n, = 1.52) as a function of 2 ?rnd/h. Normally incident light with h = 4600 A assumed. Number of layers in each stack is indicated. (From Ref. 18). (b) Transmission electron micrograph of a replica of the ZnS/MgF, multilayer cross section. (Courtesy of K. H. Guenther). absorption. In reducing the difference between nH and nL, a narrow-band reflection filter, the minus filter of Fig. 11-1 1, can be generated. Multilayer dielectric interference systems are ideally suited as reflection coatings for fully reflecting and partially transmitting laser mirrors. Negligible absorption means that reflectances of almost 100% can be achieved. Typical 536 Optical Properties of Thin Films material combinations have included ZnS-ThF, , Ti0,-SiO, , and other oxide combinations in either broad or narrow spectral-band mirror configurations. Much attention must be paid to substrates employed where low light scattering and good film adhesion are critical requirements. 11.4.4. Cold Light and Heat Mirrors There are two noteworthy practical variants of dielectric mirrors-cold light and heat mirrors. The cold light mirror spectral characteristics are shown in Fig. 11-13. It has high reflectivity for visible light but a high transmission for IR radiation. These characteristics are particularly suited to motion picture or slide projectors in order to avoid overheating the photographic emulsion. Intense light sources (e.g., carbon arc, xenon lamps) emit IR radiation in addition to visible light and the heat generated by the former must be dissipated. A cold mirror is thus placed at 45" in front of the light source. The heating infrared radiation passes through it while the nonheating visible light reflects off to illuminate the object. Metals cannot be used because they are good reflectors of the IR. Interference films are required and these must have low absorption in the IR. In addition the first film on the glass should be material having high reflectance in the visible and transmitting in the IR (e.g., Ge or Si). A few alternating X/4 amplifying film layers on top of this help achieve the high reflectance over a suitably wide visible bandwidth. Heat or dark mirrors have characteristics that are inverse to those of cold mirrors (Fig. 11-14). There are two approaches to achieving high visual transmittance simultaneously with high IR reflectance. The first is to employ COLD MIRROR 0.4 0.5 0.6 0.7 0.8 0.9 1.0 WAVELENGTH IN MICRONS Spectral characteristics of a cold light mirror. (From Ref. 19 0 Figure 11-13. burin Publishing Co. Inc.). 11.4 Multllayer Optical Film Appllcalions 537 HOT MIRROR WAVELENGTH IN MICRONS Figure 11-14. Spectral characteristics of a heat or dark mirror. (From Ref. 19 0 Laurin Publishing Co. Inc.). interference phenomena in an all-dielectric film stack. The second makes use of the properties of transparent conducting films. Consider the application to a low-pressure sodium vapor lamp, which consists of a Na-filled discharge tube within an evacuated glass envelope. For optimum Na pressure, the discharge tube must be kept at a temperature of about 260 "C. The necessary power for this is supplied by the gas discharge. However, the tube loses heat through radiation of energy in the far IR. Therefore, to conserve energy the inside of the envelope is coated so as to enable the (cold) yellow light to emerge while reflecting the IR back to the discharge tube. In another energy-saving application, home window panes coated with heat mirrors would reflect heat back into the house in the winter. In the summer the window could be reversed so that the coating could reflect the IR from the sun and help provide interior cooling. 11.4.5. Photothermal Coatings The direct conversion of solar radiation into energy for heating or cooling applications is a vital component of energy supply and conservation strategies. Coatings play an important role in photothermal conversion, and it is appropri- ate to briefly consider them because of their outward resemblance to the above mirrors. They differ because the substrate is usually a heat-absorbing metal panel. In addition, they are designed for optimal response to the spectral characteristics of sunlight. The situation can be modeled by noting that A + R = 1, where A is the coating absorbance. Strong absorption of sunlight in the range of 0.3-2.0 pm is required to heat the substrate. However, a portion of the heat will be lost by reradiation from the surface, reducing the [...]... also be used as the basis for the design of edge filters, particularly those that require a sharp transmission between the pass and stop portions of the transmittance curves The way to sharpen the transition is to increase the number of layers in the stack Unfortunately, the amplitude and frequency of the sideband oscillations in the passband also increase when this is done Suppression of these oscillations... Fracture Tribology of Films and Coatings Diffusional, Protective, and Thermal Coatings 12. 2 HARD COATING MATERIALS 12. 2.1 Compounds and Properties Hard coating materials can be divided into three categories, depending on the nature of the bonding The first includes the ionic hard oxides of Al, Zr, Ti, etc Next are the covalent hard materials exemplified by the borides, carbides, and nitrides of Al, Si, and... alloy, tool, and stainless steels The multilayer of Fig 12- 6b containing A1203 has many of the same characteristics but is capable of cutting at higher speeds without tool failure Because of its low thermal conductivity, A1203 shields the cemented carbide substrate and enables the generated heat to be diverted to the chip instead Among the reasons for the use of TiN as the outer coating layer are its... hardness of about H, = 850 Hardness is the most often quoted material property of hard coatings Therefore, Section 12. 3 has been specially reserved for an extensive discussion of the concept of hardness, the technique of measurement, and the significance of its magnitude in coatings 2 These compounds have very high melting points and decomposition temperatures For example, the decomposition temperatures of. .. not have the ability to withstand high-temperature oxidation, corrosion, particle erosion, and wear On the other hand, the materials that do possess the environmental resistance either do not qualify as structural materials because of low toughness or, if they do, are prohibitively expensive to fashion in bulk form Before we turn to the main subjects of the chapter, it is worth noting some of the similarities... measure of this fracture susceptibility is given by the thermal shock parameter S, This composite quantity is derivable from heat transfer and thermal stress considerations that are defined respectively by the equations Q = -K(AT/Ax) (12- 1) and CJ = ( E A a A T ) / ( l - v) (12- 2) In the first equation the heat flux Q is given by the product of the thermal conductivity K and the temperature gradient The. .. (See Section 14.2.) Finally, there are the metallic hard compounds consisting of the transition metal borides, carbides, and nitrides Typical mechanical and thermal property values for important representatives of these three groups of hard materials are listed in Table 12- 1 The reader should be aware that these data were gathered from many sources (Refs 1-6) and that there is wide scatter in virtually... processing equipment, and high-purity sources of precursor gases, powders and sputtering targets has facilitated the option of employing coatings Various combinations of the above factors have then resulted in the marriage of coatings to the underlying base materials, each with their particular set of desirable and complementary properties For example, many structural materials with adequate high-temperature... to have thermal expansion coefficients that are higher by approximately a factor of two or more than these hard compounds 5 The thermal conductivity of the hard metallic and covalent compounds is comparable to that of the transition metals and their alloys Good metallic electrical conductors have proportionally higher thermal conductivities Ceramic oxides are the poorest thermal conductors The last... Properties of Thin Films overall conversion efficiency Therefore, a second requirement of the coating surface is a low emittance or high reflectivity in the spectral region of reradiation-2-10 pm Emittance E is defined by the ratio of power emitted by a given surface to that of a blackbody Clearly, higher values of A / E result in desired higher equilibrium temperatures reached by the coating (The similarity . width of the high reflectance zone is a function of the ratio of the refractive indices of the involved films, and there are a couple of practical ways to extend it. One is to select materials. of the reflectance increases with the number of layers. The number of sideband oscillations outside the high-re- flectance zone also increases with number of layers. The spectral width of. case of a variable number of alternating layers of ZnS and MgF, . Also shown is a portion of the microstructure of a multifilm stack composed of these materials. It is clear that the magnitude