Toward perfect antireflection coatings. 3 ... - OSA Publishing

Toward perfect antireflection coatings. 3. Experimental results obtained with the use of Reststrahlen materials J. A. Dobrowolski, Yanen Guo, Tom Tiwald, Penghui Ma, and Daniel Poitras

The equipment and methods used to produce wide-angle antireflection coatings based on Reststrahlen materials are described. The optical constants of the coating materials used in the construction of the multilayers were determined by spectrophotometric ellipsometry and are compared with the literature values. The measured performance of an experimentally produced antireflection coating is compared with the expected calculated performance. The reflectance is low over a wide range of angles, but only in the narrow-wavelength region at which the refractive index of the Reststrahlen material is close to unity. © 2006 Optical Society of America OCIS codes: 310.0310, 310.1210, 310.1860, 310.3840.

1. Introduction

Antireflection (AR) coatings are essential components of optical systems. A book1 and many hundreds of papers and patents have been devoted to this topic. A useful general review of the theory of AR coatings can be found in this special issue of Applied Optics.2 It is desirable for optical components to operate over a wide spectral region and a broad angular range. Recently attention has been focused on socalled perfect mirrors that operate over just such a wide wavelength and angular range. The present paper is a continuation of our efforts at the National Research Council of Canada (NRCC) to determine to what extent it might be possible to produce multilayers that approach the performance of ideal “perfect AR coatings” that would have zero reflection at all wavelengths and angles of incidence. It has been shown that to achieve a low reflectance over a broad range of wavelengths and angles of incidence, a thick layer is required with a refractive index that differs only a little from that of the incidence medium.3,4 A further, equally important requirement is that the layer’s extinction coefficient be zero or very small over the same range of wavelengths. Preliminary experi-

J. A. Dobrowolski ([email protected]), Y. Guo, P. Ma, and D. Poitras are with Institute for Microstructural Sciences, National Research Council of Canada, 1200 Montreal Road, Ottawa, K1A 0R6 Canada. T. Tiwald is with J. A. Woollam Co., Inc., 645 M Street, Suite 102, Lincoln, Nebraska 68508. Received 21 March 2005; accepted 24 June 2005. 0003-6935/06/071555-08$15.00/0 © 2006 Optical Society of America

mental research has shown that such coatings can be produced for solid–solid interfaces.5 In this paper we show that by using Reststrahlen materials, it is possible to produce wide-angle AR coatings for substrate– air interfaces, but only over the narrow range of wavelengths in which the refractive index of the Reststrahlen material is close to unity. In Section 2 calculated results are presented for two different AR coatings based on this principle for the case of a Si–air interface. The optical constants of materials considered for the manufacture of these coatings are discussed in Section 3. In Section 4 the design of a SiO2-based AR coating is reoptimized by using experimentally determined optical constants. Various aspects of the thin-film deposition process are discussed in Section 5. This is followed, in Section 6, by a presentation of the measured results. Finally, some conclusions are drawn in Section 7. 2. Calculated Performance of Antireflection Coatings Based on Reststrahlen Materials

It has been shown in our previous publications3,4 that for an AR coating to be effective over a wide range of angles of incidence, the layer adjacent to the incidence medium must be quite thick and have a refractive index that is only slightly higher than that of the medium and an extinction coefficient that is small over the entire range of wavelengths for which the reflectance of the coating is to be low. Some Reststrahlen materials satisfy these requirements but only over a narrow range of wavelengths. This is because their optical constants are very dispersive in the spectral regions in which their refractive index is close to unity. For this reason an AR coating that is 1 March 2006 兾 Vol. 45, No. 7 兾 APPLIED OPTICS

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Fig. 1. Published optical constants n, k of GeO2 and SiO2. Arrows in the two diagrams indicate the wavelengths at which the refractive indices are equal to unity.

based on a Reststrahlen material can be effective only over a narrow spectral region. There exist, of course, many Reststrahlen materials (see, for example, Ref. 6). Two materials in particular, GeO2 and SiO2, were examined in this study. They happen to be well-known coating materials, and they have Reststrahlen bands that occur at comparatively low wavelengths in the infrared 共⬍10 ␮m兲. This latter point is important for two reasons. First, the shorter the Reststrahlen wavelength, the thinner the overall thickness required for the AR coating. This will reduce the deposition time as well as increase the chances that the coating will be mechanically stable and not break up during or after its fabrication. Second, it is easier to perform accurate optical measurements at shorter wavelengths. Some published optical constants for GeO2 and SiO2 in the 6.0–12.0 ␮m spectral region are shown in Fig. 1.7,8 The arrows in the two diagrams point to the wavelengths at which the refractive indices of the two materials are equal to unity. Note that in both cases the extinction coefficients appear to be low at these wavelengths. The calculated performance of a threelayer AR coating for a silicon substrate based on a GeO2 layer with the above optical constants is depicted in Fig. 2. The average reflectance for unpolarized light, Rav ⫽ 共Rs ⫹ Rp兲兾2, as a function of angle at a wavelength of ␭ ⫽ 9.3 ␮m is shown in Fig. 2(a). The construction parameters of the design are given in the inset. The other two coating materials used in the design were MgF2 and ZnS. In Fig. 2(b) are shown the reflectances Rav for light incident on the AR coated substrate at angles of incidence of 30°, 50°, 60°, 70°, 80°, and 85°. It can be seen from these dia1556

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Fig. 2. Calculated performance of an AR coating based on GeO2. (a) Angular variation of the average reflectance at a wavelength of 9.3 ␮m. Inset shows the construction parameters of the coating. (b) Average spectral reflectance for light incident at 30°, 50°, 60°, 70°, 80°, and 85°.

grams that at the design wavelength for all angles less than 83°, the calculated value of Rav is less than 0.05. Similar data for a three-layer AR coating for a silicon substrate based on a SiO2 layer with optical constants from Palik’s book8 are given in Fig. 3. As in the GeO2 design, this system also used MgF2 and ZnS layers. The calculated Rav of this system is, if anything, a little lower, and this occurs at a shorter wavelength ␭ ⫽ 7.2 ␮m. 3. Determination of the Coating Materials’ Optical Constants

At this point in the project, the films of the various materials that were needed for the above designs were deposited onto Si substrates by using the same deposition parameters and geometry that were later used in the manufacture of the final AR coating. The experimentally achieved optical constants were measured on an IR–variable angle of incidence spectroscopic ellipsometer (IR–VASE) (J. A. Woollam Co., Lincoln, Nebraska). This instrument is capable of making measurements in the 2–33 ␮m spectral region at angles of incidence ranging from 30° to 90°. The following procedure was used. To begin with, the ellipsometric measurements were performed on silicon substrates coated with single layers of ZnS, MgF2, Al2O3, and GeO2 and with the multilayer MgF2–Al2O3 stack that is described in Section 5. The thicknesses of the single layers were approxi-

calculated from k共␭兲 by using the above equation. Employing techniques described in Refs. 10 and 11, a computer program optimizes these parameter values to obtain the minimum mean-squared error MSE between the experimental data and the data generated from the model. The program uses the following biased MSE equation (Ref. 10):

MSE2 ⫽

1 2N ⫺ M ⫹

⫽

Fig. 3. Calculated performance of an AR coating based on SiO2. (a) Angular variation of the average reflectance at a wavelength of 7.2 ␮m. The construction parameters of the coating are shown in the inset. (b) Average spectral reflectance for light incident at 30°, 50°, 60°, 70°, 80°, and 85°.

mately the same as those needed for the multilayer AR structures. To simplify the data analysis, we suppressed backsurface reflections by abrading the second surface of the silicon substrates prior to measurement. In the calculations the silicon substrate was represented by a Sellmeier dispersion model to account for the effect of electronic transitions at shorter wavelengths.9 The Sellmeier values were fixed during data analysis. For the single layers of GeO2 and SiO2 on the silicon samples, it was important to determine the k共␭兲 values as accurately and with as much detail as the measurement allowed. This was especially true in the spectral region where n ⬇ 1. Therefore n共␭兲 values were explicitly calculated from k共␭兲 by numerically calculating the Kramers–Kronig integral at each measured wavelength, using the following equation:

n共␻兲 ⫽ 冑␧⬁ ⫹

2 P ␲

冕

␻max

␻min

␻⬘k共␻⬘兲 ␻⬘2 ⫺ ␻2

d␻⬘.

(1)

In the equation, ␻ and ␻⬘ have units of wave number, with ␻min ⫽ 300 cm⫺1 and ␻max ⫽ 5000 cm⫺1. The quantity ␧⬁ accounts for the offset created by electronic transitions in the UV spectral region. During the analysis, the film thickness, k共␭兲 and ␧⬁ are allowed to vary at every wavelength, and n共␭兲 is

冉

N

兺

i⫽1

冋冉

⌿imod ⫺ ⌿iexp

⌬imod ⫺ ⌬imod exp ␴⌿, i

exp ␴⌿, i

冊册

冊

2

2

1 ␹2, 2N ⫺ M

(2)

where N is the number of 共⌿, ⌬兲 pairs, M is the numexp ber of variable parameters in the model, and ␴⌿, ⌬ is the standard experimental deviation calculated during data acquisition. The resulting analysis involved approximately 1170 free parameters 共k at ⬃1163兲 wavelengths, plus thickness and ␧⬁ values). These parameters were simultaneously fit to approximately twice as many data points 共⌿ and ⌬ at each of the ⬃1163 wavelengths). It is practically impossible to look at twoparameter correlation matrices with ⬃1170 ⫻ 1170 elements. However, a survey of the first 30 elements indicated that the largest correlation, 0.89, existed between thickness and ␧⬁ and was within acceptable limits. The other correlations were extremely small, i.e., less than |0.1|. A useful figure of merit (FOM) is the product of the standard 90% confidence limit (SCL) multiplied by the MSE.12 For these analyses, the FOMs for the thickness and ␧⬁ were less than 1% and were less than 10% for the k共␭兲 fit parameters. This brute-force approach is computationally intensive, and finding starting values that provide numerical convergence can be difficult. Therefore ellipsometric data analyses typically model n共␭兲 and k共␭兲 by using a summation of Lorentzian, Gaussian, or other oscillator functions (Refs. 10 and 11). However, during preliminary fits to the data it was found that these oscillator models tend to obscure subtle details in n共␭兲 and k共␭兲, especially when k共␭兲 is near zero. By tying n共␭兲 and k共␭兲 together via the Kramers–Kronig integral, it was possible to guarantee that the optical constants have a physical significance, despite the large number of free parameters. The results of these measurements are shown in Fig. 4 (the presence in these diagrams of the optical constants of Al2O3 will be explained later). In Fig. 5 the measured values of the optical constants of GeO2 and SiO2 are compared with values from the literature. At first glance the agreement between the two sets of curves appears reasonable. Although the two extinction coefficient curves for GeO2 are in good agreement, the two refractive-index curves are horizontally displaced with respect to each other at values of n close to unity. This means that the inter1 March 2006 兾 Vol. 45, No. 7 兾 APPLIED OPTICS

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Fig. 4. Measured optical constants of the Si substrate and of the GeO2, SiO2, ZnS, MgF2, and Al2O3 layers.

cepts of the curves with the line n ⫽ 1.0 occur at the significantly different wavelengths 9.3 and 9.7 ␮m. This has two serious consequences. First, the design wavelengths at which the optimum performance is obtained are different. Second, in the AR coating that is based on the optical constants found in the literature, the extinction coefficient at the design wavelength is equal to 0.016; however, the corresponding extinction coefficient for the experimentally produced layer is 0.104. This is a difference that should lead to a significantly worse performance. A quick exploratory experiment in which a GeO2-based AR coating was constructed and whose Rav was measured for various angles of incidence confirmed this conclusion. As a result it was decided to concentrate efforts on the manufacture of an AR coating based on SiO2. 4. Further Calculations on the SiO2-Based Antireflection Coating

The layer system of Fig. 3 was reoptimized by using the measured optical constants depicted in Fig. 4. Next the sensitivity of this solution to experimental errors was investigated. To determine the sensitivity of this system to thickness errors, we calculated the angular variation of the average reflectance Rav for 50 systems in which the thicknesses of the layers underwent random perturbations with a 20% deviation from a Gaussian distribution. In Fig. 6(a) are shown the calculated upper and lower boundaries within which one would expect the Rav of 66% of experimentally produced AR coatings with such thickness errors to lie. Clearly, the system is quite insensitive to thickness errors, and thickness control should not be critical. Thickness uniformity should also not be an 1558


Fig. 5. Comparison of measured optical constants of GeO2 and SiO2 with values from the literature: (a) refractive indices and (b) extinction coefficients.

issue. In Figs. 6(b) and 6(c) are shown the effects on Rav of a change of ⫾0.2 in the refractive indices of ZnS and MgF2. Once again, even such large changes in the refractive indices of the ZnS and MgF2 layers have little effect on the Rav versus the angle-ofincidence curves. It follows from the above calculations that the errors in the optical constants of the layer closest to air will be the most critical.3–5 5. Deposition Issues

Deposition equipment available in the laboratory included a Balzers BAK-760 system equipped for thermal and electron-beam-gun (e-gun) evaporation with or without ion assist, a Veeco-IonTech Spector dualion-beam sputtering system, and a NRCC-designed dual-ac magnetron sputtering system. Processes and targets were unavailable in the last two systems for the deposition of MgF2 and ZnS layers, but all the systems were capable of depositing SiO2 layers. The properties of SiO2 layers produced by the three systems were measured and found to be rather similar. For this reason it was decided to deposit the whole AR coating in the Balzers BAK-760 system by using e-gun evaporation for all the materials. A problem posed by this design is that the metric thickness of the SiO2 layer needed to be of the order of 5 ␮m. It would have had to be appreciably thicker if the AR coating were required to be effective up to, say, 88°. Such layer thicknesses require long deposition times and venting of the system for refilling of the crucibles. Another problem with such designs is that they call for MgF2 layers that have a metric thickness of

Fig. 7. Schematic of an AR coating (a) without and (b) with thin Al2O3 layers (see text for discussion).

has to start from the beginning. We also placed thin Al2O3 layers on the substrate and at layer interfaces to improve adhesion between the layers. The transformation of the original layer system into one with thin Al2O3 layers is depicted schematically in Fig. 7. It should be mentioned here that numerical calculations show that the presence of the 0.07 ␮m thick Al2O3 layers in the system has no significant effect on the performance of the AR coating. Finally, Fig. 8 shows the system of masking that

Fig. 6. Calculated effect on the average reflectance Rav of errors in the thicknesses and refractive indices of the SiO2-based AR system.

⬃1.5 ␮m or more. However, layers of MgF2 that are thicker than approximately 0.6 or 1.0 ␮m deposited by normal techniques are known to break up (see, for example, Refs. 13–15). It was reported that MgF2 layers of up to 2.0 ␮m in thickness were produced by ionized-cluster-beam deposition,16 but this technique is not always available. MgF2 layers, because of their low refractive index, would be ideal for use in many different types of infrared coating designs if only they could be produced in thicker layers by more or less conventional deposition techniques. In our laboratory we have produced thicker layers of MgF2 by depositing the coating material at rates of the order of ˚ 兾s onto a substrate at ambient temperature and 35 A through the simultaneous use of thin Al2O3 layers. We divided the MgF2 layer into two or three parts of equal thickness and separated them with 0.07 ␮m thick layers of Al2O3. It is well known that Al2O3 layers deposited even onto cold substrates have an amorphous like structure. We believe that the Al2O3 layers interrupt the column growth in the MgF2 layers and that after each such layer the column growth

Fig. 8. Schematic of the masking used during the deposition process that enabled the evaluation of the finished AR coating as well as of each separate layer. 1 March 2006 兾 Vol. 45, No. 7 兾 APPLIED OPTICS

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was used during deposition of the individual layers onto the silicon substrate; this permitted measurements to be made on the bare substrate, on each individual layer, and on the completed AR coating. The substrate was a 15 cm diameter semiconductorgrade silicon wafer. The coated areas in the form of long strips could be measured readily on the spectrophotometric ellipsometer in the manner described in Section 3, even with radiation incident at quite oblique angles. The optical constants of the materials used in the theoretical calculations were based on these measurements. The comparison of the calculated and measured reflectance spectra of each component of the AR coating provided very useful information on the accuracy of the deposition process. 6. Measurements and Results

The samples were first measured on a Nicolet FT-IR MAGNA-IR 550 Series II spectrophotometer with a Pike Technologies variable-angle specular reflectance accessory. At angles of incidence larger than 60°, these measurements were qualitative at best. The samples were then sent out to be measured on the IR-VASE described in Section 3. This apparatus could also accurately measure the reflectance spectra of the finished AR coatings over the same ranges of angles and wavelengths. The optical constants obtained from the singlelayer samples were then applied to the appropriate multilayer structures. For the AR coating structure (Figs. 7 and 8), reasonable results were obtained by fixing the optical constants and by fitting only the film thicknesses. However, the MSE was ⬃13.5 共MSE ⱕ 10 are typical for good fits to thick multilayer structures), with differences between the modelgenerated and experimental data curves ranging as much as 10° in ⌿ and 40° in ⌬ at some wavelengths. Allowing the MgF2–Al2O3 layer’s ␧⬁ to vary during the fitting lowered the MSE to ⬃9. The new fit reduced the differences in ⌿ and ⌬ curves by a factor or 3, making the generated-data and experimental data curves visibly indistinguishable at full scale. The new fit decreased the MgF2–Al2O3 layer’s ␧⬁ from 1.766 to 1.744. The FOMs for the thicknesses and ε⬁ were less than 1%, and the correlation values were less than |0.5|. Varying the SiO2 or ZnS layer’s optical-constants during analysis of the AR multilayer coating data did not significantly improve the fit. This suggests that only the MgF2–Al2O3 layer’s optical properties changed significantly during deposition on the ZnS film (plus the Al2O3 glue layer) versus direct deposition on the silicon substrate. Given the good fits obtained for the AR coating structure, it was concluded that this level of analysis was sufficient for this proof-of-principle study. More detailed ellipsometric studies of the various film combinations could sort out many of the depositionrelated details for these AR coatings. The measured average reflectance Rav of the manufactured SiO2-based wide-angle AR coating measured at a wavelength ␭ ⫽ 7.27 ␮m is presented in 1560


Fig. 9. Comparison of the calculated and measured average reflectances Rav of a wide-angle SiO2-based AR coating (a) as a function of angle, at the wavelength of 7.27 ␮m. (b) The construction parameters of the manufactured coating are shown in the inset as a function of wavelength, for light incident at 30°, 50°, 60°, 70°, 80°, and 85°.

Fig. 9. In Fig. 9(a) the calculated and measured variations of the average reflectances Rav as a function of the angle of incidence are compared. The agreement between the two curves is good. Also shown for comparison purposes is the average reflectance of a bare substrate. The nominal metric thicknesses of the various layers of the system are shown in the inset. In Fig. 9(b) are shown the calculated and measured spectral reflectance curves Rav for angles of incidence of 30°, 50°, 60°, 70°, 80°, and 85°. The agreement between the two sets of data is very good for all angles at the design wavelength and is quite reasonable across the spectrum for curves for angles up to and including 80°. From the above, one can assume that the optical constants of the materials must be close to those used in the calculations. It is therefore reasonable to use these constants to calculate the expected average transmittances Tav ⫽ 共Ts ⫹ Tp兲兾2 and absorptances Aav ⫽ 共As ⫹ Ap兲兾2 as a function of angle of incidence. The results of these calculations are shown in Fig. 10(a). It can be seen that Tav drops sharply at angles greater than 60°. On the other hand, Aav in-

Fig. 10. Calculated average transmittance Tav and absorptance Aav (a) for the system of Fig. 9 and (b) for a similar system, but in which the SiO2 layer is nonabsorbing. (c) Measured extinction coefficients of materials used in the AR coating of Fig. 9(a).

creases at angles greater than 60°, reaches a peak at ⬃80° and drops off thereafter. Of course, at 90° both Tav and Aav are zero. The optical constants used to obtain the curves shown in Fig. 10(b) were identical to those used to obtain the results in Fig. 10(a), except that the extinction coefficient of SiO2 was deliberately set equal to 0.0. In Fig. 10(c) are shown, once again on an expanded scale, the extinction coefficients of the materials used in the construction of the wide-angle AR coating. The design wavelength is also indicated in this diagram. It follows that even very small extinction coefficients in the Reststrahlen material can materially affect the Tav and Aav values but do not significantly affect the Rav value. 7. Conclusions

A narrow-band, wide-angle AR coating that is based on a layer of a Reststrahlen material was successfully constructed. The results for such coatings depend strongly on the optical constants of the Reststrahlen materials but not on the thicknesses of the individual layers. At high angles of incidence the Aav and especially the Tav values depend critically on the extinc-

tion coefficients of the Reststrahlen material at the design wavelength. An important aspect of this study was the accurate determination of the optical constants of the coating materials used. (A separate paper is currently being prepared in which further details of the deposition parameters and ellipsometric measurements of the infrared optical constants of SiO2 films produced by different deposition processes will be given.) A difficult problem that had to be solved was the deposition of thick MgF2 layers—the technique described in this paper should be of interest for many other thin-film applications in which the use of thick MgF2 layers would be useful. Infrared spectrophotometric ellipsometers are very well adapted for the accurate measurement of reflectances at high angles of incidence. Specifically, the SiO2-based AR coating for a silicon substrate described in this paper had a measured average reflectance for unpolarized light at ␭ ⫽ 7.27 ␮m of less than 3% for all angles smaller than 80°, which is in good agreement with the calculated performance. It is likely that by using a thicker SiO2 layer, with perhaps more layers in the AR system, one could improve upon this performance or extend it to angles of 85° or more. It is likely that there are other Reststrahlen materials with properties that could be used for the construction of similar AR coatings at other wavelengths in the infrared spectral region. Should the extinction coefficient of a Reststrahlen material remain very low beyond the wavelength at which n ⫽ 1.0, a certain amount of tuning of the design wavelength should be possible by depositing a dilute mixture of that material with another, higher-index nonabsorbing material. Furthermore, some fine-tuning of the design wavelength might be possible with subwavelength structuring of the last layer. The authors thank Chun-Ying Song and Frances Lin for their assistance. The subject matter of this paper was first presented at the Topical Meeting on Optical Interference Coatings in Tucson, Arizona, June 28 –July 2 2004.

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