Fundamentals of Optical Coatings by Angus Macleod Thin Film Center Inc.

Introduction characterize the wave. This wavelength is n times the actual wavelength and implies that we have to make the same adjustments to the distance, d, and During the 16th Century, a secret process to produce mirrors of a quality so we introduce the quantity nd known as the optical thickness. When we never before seen was devised in Venice. The mirrors consisted of a glass talk of the thickness of a film in an optical coating, generally we imply the substrate carrying on their rear surface a layer of mercury-tin amalgam. In optical rather than the physical thickness. spite of vigorous attempts it proved impossible to retain the secret and the n governs refraction at a boundary between two materials through technique spread. Mirrors became an important feature of interior design. Snell’s Law: This was the beginning of the modern optical coating industry. Nowadays, optical coatings have penetrated every corner of our modern lives. From the (1) $20 bill in our pocket to the DVD player in our home, optical coatings play a nn0011sinϑϑ= sin critical role. Optical coatings modify the optical properties of surfaces. Most often where ϑ is the angle between the ray and the surface normal. n is also these are the carefully worked surfaces that shape and direct the light rays involved, through the optical thickness, in the change of phase due to in an optical system but they can also be applied to other surfaces, often in a propagation through a material. If the physical thickness is d, then δ, known decorative mode. Their operation relies on interference effects combined as the phase thickness, is given by with the optical properties of their materials. This account is necessarily 2π nd limited to some of the more common coating types. δ = (2) λ Fundamental parameters where λ is the wavelength measured in free space. y characterizes the In free space, the propagation of an electromagnetic wave is independent of amount of light reflected at a boundary between two media. The ratio of the wavelength or frequency. There are two principal parameters that charac- reflected amplitude to the incident amplitude is given by: terize this propagation. Both are exact and are fundamental physical yy− constants. The first is the velocity of light in vacuum, c, of value 299,792,458 m ρ = 01 (3) sec-1, and the second, the permeability of vacuum, µ , of value 4 10-7 N/A2. 0 π× yy01+ Propagation of an electromagnetic wave in an optical material is a little more complicated. The shape of any arbitrary wave changes as it propagates In dielectric materials the electrons are bound. They accept energy making it difficult to assign a velocity to it. Fortunately at normal power from the electric field but then radiate it back and the principal effect is a levels the phenomena are purely linear. That means that we can represent slowing down of the light so that the refractive index, n, is greater than the light as a spectrum of harmonic components that can be treated unity. In metals the free electrons extract energy from the electric field but separately and do not change shape as they propagate. We are so used to this do not return the energy to the wave. The amplitude of the propagating wave process that we scarcely think about it. The spectral components that we use decays exponentially. The decay is usually expressed as exp(-2πkd/λ) where in the thin-film field are infinite, plane, harmonic waves, that is they are a k is dimensionless and known as the extinction coefficient. An extinction harmonic function of time and distance along the direction of propagation coefficient can also be used to characterize the small residual losses in a only. The electric field, magnetic field and direction of propagation in these dielectric material. In an ideal metal the light wave suffers no change in waves are mutually perpendicular and form what is called a right-handed set. phase as it propagates. In a real metal there is a phase change, often quite The orientation of the electric vector is described by the term polarization. small, and this can be associated with a refractive index through equation We will use the simplest form, called linear, or sometimes plane, polarization, (2). A quite small refractive index can be mistakenly taken as an indication where the electric vector is constant in direction. that the light is traveling faster than its speed in free space. We must not In an optical material the light interacts with the electrons so that its forget that we are dealing with an infinite harmonic wave in a steady-state propagation characteristics are altered. We could build our theories of optical condition and that the refractive index is derived from a steady-state phase behavior using the velocity of light, v, and the permeability, µ, associated with difference. A pulse of light is a transient effect with quite different behavior. a harmonic wave, to characterize our materials, but the results are a great deal Provided that the effects are linear, we can conveniently combine the less clumsy if we introduce two related parameters. The first is the refractive cosine and sine representation of a harmonic wave into a complex form, index, the ratio of the velocity of light in free space to the velocity in the known as a complex wave. material, c/v, written as n. The other is the characteristic admittance of the material, written as y and of value 1/(vµ). The characteristic admittance  22π kz   π nz   22π kz   π nz  represents the ratio of the magnetic to the electric field amplitudes of a EEexp −  cosωt −  +−i exp  sin ωt −  λ λ λ λ propagating harmonic wave. In free space, n is unity and y is 0.002654419 S         (siemens). The electrical engineer usually prefers to use the characteristic   2π nikz−  Eexp it () impedance, z, of value 376.73031 Ω (ohm) in free space. =− ω  (4)  λ  There is an enormous simplification in optics because the frequencies    are so high that there is no direct magnetic interaction with the electrons that are responsible for the optical properties of materials. This means that The quantity (n-ik) appearing in the right-hand side of equation (4) is known as the complex refractive index. As long as we stick to linear the permeability, µ, of the material remains at the value of µ0. This implies that y is simply n times the admittance of free space, or n free space units, operations, like addition or subtraction or multiplication by a real constant, and allows us to use the same number for both quantities. Note that y and n there is never any mixing of the real and imaginary parts of expression (4) are only numerically equal and not physically equal. and it is much simpler to use the right-hand side of (4) than either of the The effects we are dealing with are linear and so the frequency of the terms on the left-hand side. y, the characteristic admittance is then equal to wave is constant. This means if it slows down then the wavelength is reduced (n-ik) free space units. All the previous relationships work equally well with in proportion. We avoid problems by using the wavelength in free space to complex arguments.

28 2005 Winter News Bulletin The power per unit area carried by a harmonic wave is given by the product of the electric (E) and magnetic (H) fields. This fluctuates at twice The 8th International Symposium on the frequency of the wave and it is the mean rate that we detect and measure. The mean rate is called the irradiance. The product is a non-linear SPUTTERING & PLASMA operation but fortunately we can write a form of product using the complex quantities that gives directly the mean. This expression is: PROCESSES

1 ∗ Irradiance= Re  EH  (5) June 8-10, 2005 2   Kanazawa, Japan For a harmonic wave, since H = yE, the irradiance is proportional to the square of the electric field amplitude. The expression, (3), is essential for calculations, but when a measure- ment is made it usually concerns the ratio of reflected to incident irradiance. Symposium • Poster Session This is known as reflectance, R, and, through (5), is given by Industrial Exhibition

∗ 2 Scope of the Symposium:  yy01−  yy01−  yy01− (6) R =    = yy yy yy • Fundamentals of Sputtering and Plasma  01+  01+  01+ Processes where we include the possibility that y might be complex. A similar quantity, • Sputtering Processes transmittance, T, measures the ratio of transmitted irradiance to incident • Plasma Processes irradiance. • Plasma Induced Process Technologies Some typical values of optical constants are shown in Table 1. Although the exponential decay is characterized by k the actual absorption losses are • Thin Films better expressed by the product nk. • Micro and Nano Technologies Material nk Material nk Don’t miss the great opportunity • to find solutions for your needs. MgF2 1.38 0 Al2O3 1.673 0 • to discuss sputtering and plasma processes face to SiO2 1.46 0 Ag 0.051 2.96 face with your colleagues. Ta2O5 2.14 0 Al 0.70 5.663 http://issp2005.org/ TiO2 2.35 0 Glass 1.52 0 Table 1. Some typical optical constants at λ=510nm. Note that they do depend to an extent on deposition conditions as well as wavelength. The glass is a typical crown glass.

Simple coatings Usually the most important properties controlled by coatings are reflectance and/or transmittance. The simplest coating is probably a single metallic layer. Aluminum and silver have very high values of k. This has two implica- tions. These simple coatings present very high reflectance, over 90%, and a quite thin layer, 100nm or so, has such small transmittance that it appears like bulk metal. Front surface mirrors of aluminum combine the high reflectance of the metal with the dimensional stability and surface optical quality of the underlying substrate, usually glass. The metal layer can quite easily be damaged and so it is normally protected. Architectural mirrors place the metal layer behind the glass but for high optical quality imaging it must be in front and it is usually protected by a thin dielectric layer, (silica being preferred). The protecting layer tends to reduce the metallic reflectance and this reduction is least with low-index protecting layers. More complicated coatings may be constructed entirely from dielectric materials, when they are known as all-dielectric, or they may also include one or more metal and dielectric layers, when they are know as metal-dielectric. Because n does not vary appreciably with wavelength the phase thickness, δ, of a dielectric layer reduces with increasing wavelength. The interference properties weaken with increasing wavelength. All-dielectric coatings, therefore, are most suited to a high reflectance at shorter and high transmittance at longer wavelengths. Over its useful region, the extinction coefficient for a metal is roughly proportional to wavelength. This large dispersion is a problem in that it complicates the design of metal-based coatings but it does mean that metal-based coatings become stronger in their effect, that is they tend to reflect, as we move to longer and longer wavelengths. Metal-dielectric coatings, therefore, perform best in applica- continued on page 31

2005 Winter News Bulletin 29 2 Fundamentals of Optical Coatings y2 continued from page 29 y − f 0 y R = sub (8) y 2 tions where transmittance is required at shorter and reflectance at longer y + f wavelengths. We find when we are forced to achieve the opposite perform- 0 ysub ance that quite difficult and complicated designs are necessary. As an example, the heat-reflecting and luminous light-transmitting coatings round where y0 is the admittance of the incident medium. A half-wave film can be the outer surface of the envelopes of incandescent floodlights must be of represented by a double application of the quarter-wave rule. This returns dielectric material to withstand the very high temperatures and a coating of the admittance to ysub with the obvious result. one hundred or so layers is not unusual. The quarter-wave rule is particularly simple and yet completely accurate. Calculation of properties at other wavelengths or for other thicknesses is rather more difficult and involved. The model is essentially an elaboration of the style of the quarter-wave rule but now for any serious calculations a computer is used. Nevertheless, knowledge of the quarter- wave rule and some appreciation of interference phenomena go a long way towards understanding the performance of a wide range of optical coatings. An immediate consequence of (8) is that the reflectance will be zero if yf is given by √(y0ysub). For glass of admittance 1.52 in air of admittance 1.00, this implies a quarter-wave film of admittance 1.233. Unfortunately, we have difficulty creating a sufficiently rugged film of this low value admittance to serve as a general-purpose antireflection coating. Magnesium fluoride, with index around 1.38, is mostly used. The minimum reflectance is then 1.26%, as shown in Figure 2. Figure 1. The interference fringes as a function of layer thickness in wavelengths resulting from a dielectric thin film over a dielectric substrate. Note that the addition of each quarter wave results in the addition of a fringe extremum.

Dielectric coatings are often constructed from a series of quarter-wave layers. Let us imagine a dielectric substrate surface. Let us apply a film of a different dielectric material to this surface. In the steady state condition achieved by our infinite harmonic waves there will be an infinite number of beams reflected back and forth between the two surfaces of the film giving rise to a multiple-beam interference condition. Let the film be exceedingly thin so that although it still exists, nevertheless the reflectance of the surface is unperturbed. Because the film still exists the multiple-beam effect also exists. When two beams of light of identical wavelength interfere their Figure 2. Theoretical performance of a single-layer antireflection coating consisting combination takes account of their phase difference. This is often expressed of a quarter wave of magnesium fluoride on glass. The film is a quarter wave at a as a path difference. Because of the repeat cycle of the light, one wavelength wavelength of 510 nm. long, a change in the path difference of one wavelength, or any whole number of wavelengths, makes no difference whatsoever to the interference. Two quarter-wave films of admittance 1.70 next to the glass and 1.38 Now let us increase the thickness of our vanishingly thin film so that it is next to the air will, however, give virtually zero reflectance at a specified now one half wave thick. δ for this film is π. This imposes a double traversal wavelength as shown in Figure 3. Here, however, the inexorable rule of of the film between each of the combining beams, (in other words a full interference coatings, as implied in Figure 1, applies itself. The greater the wave). The interference condition is unaffected and, therefore, the total thickness of the coating the greater the number of fringes in any given reflectance is exactly the same as that of the uncoated substrate. The same interval. Since we now have two quarter waves, the coating characteristic is true of a layer one full wave thick and so on. Half-wave layers are reflectance curve is narrower. sometimes called absentee layers because of this property. A similar argument shows us that the thicknesses midway between the half-wave points, quarter-wave layers, with δ of π/2, will yield a maximum interference effect so that the reflectance of the dielectric substrate will either be increased or decreased to a maximum extent. The quarter and half-wave condition can be expressed in terms of the concept of surface admittance and its transformation. A simple material surface presents its characteristic admittance to the light in the incident medium. A thin film can be considered to transform this surface admittance to a new value. In the case of a quarter-wave layer this transformation is known as the “Quarter-wave rule.” If the surface of the substrate has admittance ysub and the characteristic admittance of the film is yf, then the transformed admittance will be given as: Figure 3. Theoretical performance of a two-layer antireflection coating consisting of 2 a quarter wave of admittance 1.70 next to glass followed by a quarter wave of y f (7) admittance 1.38 next to the air incident medium. Again the layers are quarter waves ysub → at a wavelength of 510nm. ysub so that the reflectance of a quarter-wave film on a substrate will become continued on page 32

2005 Winter News Bulletin 31 Fundamentals of Optical Coatings continued from page 31

The coating is not broad enough to cover the visible region that stretches roughly from 400nm to 700nm. Early in the history of optical coatings, however, it was discovered that a half-wave layer of high admittance inserted between the two quarter waves of the two-layer coating could broaden the characteristic. The half wave is an absentee where the two layers yield low reflectance but perturbs the performance elsewhere in a favorable manner. Most modern antireflection coatings are related to this three-layer coating. Figure 6. Transmittance performance of a quarter-wave stack showing some of the various types of filter that can be produced from this simple structure. Ripple is the major remaining problem. The major problem that is obvious in Figure 6 is the interference fringes that we usually call “Ripple.” Ripple can be greatly reduced by tuning the outermost layers of the system so that they form a matching or antire- flecting structure between the outside media and the quarter-wave core of the coating. If we place two quarter-wave stacks together we arrive at a structure like:

Air | HLHLHLH HLHLHLH | Glass (10)

At the wavelength for which the layers are quarter waves the central HH Figure 4. The quarter-half-quarter coating. Here we are including dispersion. We use layer is a half wave and, therefore, an absentee. Then we see that the Al2O3 next to the glass, MgF2 next to the air and a half wave of Ta2O5 in between. The surrounding LL combination must also be an absentee. A similar argument flattening effect of the added half-wave layer is pronounced. can be applied right through the structure and the whole coating is an High-reflectance coatings consisting of metal layers are the only option absentee at the reference wavelength. The reflectance and transmittance for mirrors to be used over a very wide range of wavelengths. For a much are therefore the values of the uncoated substrate. The absentee condition narrower range, however, it is possible to build a high reflectance coating involves many layers so that the high transmittance fringe is narrow and is from a series of quarter wave layer of alternate high and low admittance. A surrounded by high reflectance regions typical of the quarter-wave stacks. In shorthand notation where we represent quarter waves by capital letters is a fact, the structure is a simple narrow-band filter. The width of the pass band useful way of expressing the design. We call the wavelength for which the will be reduced if the number of layers is increased and vice versa. We call the central half-wave layer a cavity and the entire structure is a single-cavity layers are quarter waves, the “Reference wavelength” and denote it by λ0. filter. In the same way that we couple tuned electrical circuits together to Air | HLHLHLHLHLHLHLHLHLHLH | Glass (9) give more rectangular response we can couple cavities.

Here we represent a high-admittance layer by H and a low-admittance by L. Air | HLHLHLH HLHLHLH L HLHLHLH HLHLHLH | Glass (11) Figure 5 shows a typical curve. Note that at the half-wave points we have the reflectance of the uncoated substrate. and

Air | HLHLHLH HLHLHLH L HLHLHLH HLHLHLH L HLHLHLH HLHLHLH | Glass (12) represent two and three-cavity filters. The L layers in between the cavity structures are known as coupling layers. They are necessary to avoid creating unwanted cavities from their surrounding H layers. Figure 7 shows how the edge steepness increases with the number of cavities.

Figure 5. A 21-layer quarter-wave stack plotted in terms of layer thickness in quarter waves, that is inversely proportional to wavelength. The layers in this stack have admittances 1.46 and 2.14 corresponding to SiO2 and Ta2O5.. Because we have dielectric layers with no loss, the transmittance of the coating is simply the inverse of reflectance. Plotting transmittance against wavelength we recognize basic characteristics that can serve as different types of filters. Long-wave-pass filters, short-wave-pass, notch filters and even broad band-pass filters are possible. If the reflected light is also to Figure 7. Single, two-cavity and three-cavity narrow-band filters using the designs (10) to (12) with materials SiO and Ta O . be collected then we have a special type of beam splitter that separates 2 2 5 wavelength regions and is known as a “Dichroic beam splitter.”

continued on page 42

32 2005 Winter News Bulletin Fundamentals of Optical Coatings Advertiser’s Index continued from page 32 A&N Corporation ...... 6 Ametek, Inc...... 12 Conclusion APX Scientific Instruments, Inc...... 35 These are just some examples of simple optical coatings. They are AVEM International...... 38 typical of some of the building blocks that are used as the starting structures for more complex and higher-performance designs. For example C&C General, LLC ...... 21 the designs of Dense Wavelength Division Multiplexing Filters follow the Coating 2005 ...... 33 kinds of structures used in Figure 7 but frequently have around 200 layers Comdel, Inc...... 10 rather than the 44 or so shown. Because the structures are so complicated Denton Vacuum, LLC...... 3 and accurate calculations are so involved and tedious, computers are Ferrotec (USA) Corporation ...... 18 indispensable in coating design. Fil-Tech, Inc...... 14 Further Reading Filmetrics, Inc...... 7 Huettinger Electronic, Inc...... 19 There are many books dealing with thin-film optical coatings. Three recent ones, still in print, are: Inficon ...... 11 Intelvac ...... 16 Kaiser, N and H K Pulker, eds. Optical Interference Coatings. Optical ISSP 2005 ...... 29 Sciences, ed. W.T. Rhodes. 2003, Springer-Verlag: Berlin, Heidelberg, Maxtek, Inc...... 9 New York. pp 500. MDC Vacuum Products Corporation ...... 22 & 23 Macleod, H A, Thin-Film Optical Filters. Third ed. 2001, Bristol and MKS Instruments, Inc...... 39 Philadelphia: Institute of Physics Publishing. Normandale Community College ...... 29 Willey, Ronald R, Practical Design and Production of Optical Thin Pacific Nanotechnology...... 12 Films. Second ed. Optical Engineering, ed. B. Thompson. 2002, New Pfeiffer Vacuum ...... 17 York, Basel: Marcel Dekker Inc. PHPK Technologies ...... 15 Polycold Systems, Inc...... 2 R.D. Mathis Company ...... 5 Adhesion Promotion Techniques for Society of Vacuum Coaters ...... 30 Coating of Polymer Films System Control Technologies ...... 44 continued from page 37 Telemark ...... 43 Torr International, Inc...... 18

3. A. Yializis, M.G. Mikhael, R.E. Ellwanger, and E.M. Mount III, “Surface ULVAC Technologies, Inc...... 34 Functionalization of Polymer Films“, 42nd Annual Technical Conference VACUUM COATING Technologies, Inc...... 41 Proceedings of the Society of Vacuum Coaters, p. 469, 1999. Vacuum Research Limited ...... 8 4. A. Yializis, M.G. Mikhael, T.A. Miller, and R.E. Ellwanger, “Use of Functional Acrylate Polymers for Different Web Coating Applications,” Proc. 11th Int. Varian Inc. Vacuum Technologies ...... 27 Conf. on Vacuum Web Coating, p. 138, 1997. VAT, Inc...... 16 5. P. Grπning, O.M. Kuttel, M. Collaud-Coen, G. Dietler, and L. Schlapbach, “Interaction of low-energy ions (<10 eV) with polymethylmethacrylate during plasma treatment,” Appl. Surf. Sci. 89(1), p. 83, 1995. 6. F. Garbassi, M. Morra, E. Occhiello, L. Barino, and R. Scordamaglia, 16. S.A. Pirzada, A. Yializis, W. Decker, and R.E. Ellwanger, “Plasma Treatment of “Dynamics of macromolecules: a challenge for surface analysis,” Surf. Interf. Polymer Films,” 42nd Annual Technical Conference Proceedings of the Anal. 14(10), p.585, 1989. Society of Vacuum Coaters, p. 301, 1999. 7. R.W. Burger and L.J. Gerenser, “Understanding the Formation and Properties 17. M. Geisler, J. Bartella, G. Hoffmann, R. Kukla, R. Ludwig, and D. Wagner, “rf of Metal/Polymer Interfaces via Spectroscopic Studies of Chemical Bonding,” 34th Annual Technical Conference Proceedings of the Society of Vacuum Plasma Tool for Ion-Assisted Large-Scale Web and Sheet Processing,” 44th Coaters, p. 162, 1991. Annual Technical Conference Proceedings of the Society of Vacuum Coaters, p. 482, 2001. 8. F.D. Egitto and L.J. Matienzo, “Plasma modification of polymer surfaces for adhesion improvement,” IBM J. Res. Dev. 38(4), p. 423, 1994. 18. R. Emmerich, M. Kaiser, H. Urban, M. Graf, E. Rauchle, P. Elsner, J. 9. B. Chapman, “Thin Film adhesion,” J. Vac. Sci. Technol., 11(1), p. 106, 1974. Feichtinger, A. Schulz, M. Walker, K.M. Baumgartner, and H. Muegge, “New 10. M. Roehrig and C. Bright, “Vacuum Heat Transfer Models for Web microwave plasma sources for large scale applications up to atmospheric Substrates: Review of Theory and Experimental Heat Transfer Data,” 43rd pressure,” Proc. IEEE 29th Int. Conf. on Plasma Sciences, p. 320, 2002. Annual Technical Conference Proceedings of the Society of Vacuum Coaters, p. 335, 2000. 19. I.V. Svadkovski and A.P. Dostanko, “Ion sources for ion beam assisted thin film deposition,” Symposium Ion-Solid Interactions for Materials Modification 11. A. Yializis, R.E. Ellwanger, and J. Harvey, “Barrier Degradation in Aluminum Metallized Polypropylene Films,” 40th Annual Technical Conference and Processing, p. 635, 1996. Proceedings of the Society of Vacuum Coaters, p. 371, 1997. 20. A. Shabalin, M. Amann, M. Kishinevsky, K. Nauman, and C. Quinn, “Industrial 12. W. Decker and B. Henry, “Basic Principles of Thin Film Barrier Coatings,” Ion Sources and Their Application for DLC Coating,” 42nd Annual Technical 45th Annual Technical Conference Proceedings of the Society of Vacuum Conference Proceedings of the Society of Vacuum Coaters, p. 338, 1999. Coaters, p. 492, 2002. 13. H. Kersten, R. Wiese, D. Gorbov, A. Kapitov, F. Scholze, and H. Neumann, 21. D. Burtner, R. Blacker, J. Keem, D. Siegfried, and E. Wahlin, “Linear Anode- “Characterization of a broad beam ion source by determination of the energy Layer Ion Sources with 340- and 1500-mm Beams,” 46th Annual Technical flux,” Surf. Coat. Technol. 173-174, p. 918, 2003. Conference Proceedings of the Society of Vacuum Coaters, p. 263, 2003. 14. D.J. McClure, D.S. Dunn, and A.J. Ouderkirk, “Adhesion Promotion 22. S. Schiller, U. Heisig, Chr. Korndörfer, and J. Strümpfel, “Stabilization of the Technique for Coatings on PET, PEN and PI,” 43rd Annual Technical Reactive Magnetron Discharge with Close Target-to-Substrate Coupling,” Conference Proceedings of the Society of Vacuum Coaters, p. 342, 2000. Proc. 3rd Int. Conf. on Vacuum Web Coating, p. 155, 1989. 15. V. Cassio, “Plasma Pre-Treatment in Aluminum Web Coating: A Converter Experience,” 42nd Annual Technical Conference Proceedings of the Society 23. Patent No.: EP 0867 036 B1. of Vacuum Coaters, p. 465, 1999. 24. T. Linz (Advanced Energy Industries GmbH), private communication.

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