A new all-oxide design for broadband antireflection coatings with significantly reduced impact of deposition errors to the final reflectance is presented. Computational manufacturing including re-optimization during deposition has been used in the design work to account for maximum insensibility of the design with respect to deposition errors typical for plasma ion assisted deposition PIAD. Repeated deposition runs with the deducted monitoring and re-optimization strategy verify the validity of the simulations and the stability of the derived design solution.
©2010 Optical Society of America
Antireflection coatings are widely used in optical systems and make up more than 50% of optical coatings production today . In the case of specifications restricted to normal incidence of light and negligible absorption, the best theoretical performance requires two coating materials with maximum contrast in refractive index . For non-absorbing and dispersion free materials a series of optimal design solutions for antireflection coatings is well known . Additionally, the average residual reflectance of these coatings could be calculated by an empirical equation , which also predicts a minimum value of the achievable average reflectance which depends on the optical constants of the selected materials and the required bandwidth. In the refractive index profiles of these designs, one can easily recognize a sequence of more or less similar arrangements of high index layers, called clusters. While an increasing number of clusters will only slightly reduce the average residual reflection, the impact of depositions errors can be assumed to scale linear with total physical thickness as long as no error compensation mechanisms are active during deposition. This will restrict the maximum number of clusters in practice. Also, stability of designs may be improved by incorporation a third material.
In practical application of antireflection coatings, it is usually not only required to minimize reflectance, but also to maximize transmittance. For this reason, the selection of the high index material is commonly restricted to materials with a negligible extinction coefficient in the required spectral range. Furthermore, durability of the coating against temperature and air humidity often favours PIAD deposition techniques, which restricts the possibility of including metal fluorides as low refractive index material. For this reason, only designs based on oxide layer materials that are known to result in dense and homogeneous coatings are included into this work. Nevertheless the developed method is not restricted to a certain class of coating materials but can be applied to a wide range of optical coatings. The experimental setup is outlined in section 2.
In practice, deviations in layer thicknesses and optical constants will result in an increased reflectance of the deposited antireflection coating. For this reason, selection of a sufficient coating design has not only to take the theoretical performance into account, but also requires additional knowledge of their sensitivity to deposition errors. For these investigations computational manufacturing is an efficient approach . Thereby an exact modelling of all error sources as well as application of identical data processing routines during deposition and simulation are required. To completely reflect the capabilities of our broadband optical monitoring system OptiMon [6,7], an adapted approach to computational manufacturing was developed and recently published . Now, support for re-optimization of the design during deposition has been added to the software of the broadband optical monitoring system and computational manufacturing module.
Initial work on error compensation in optical coatings by re-optimization was presented in the 70’s and 80’s of the last century [9,10]. Thereby several approaches are possible and even some kind of self compensation of deposition errors could occur . The refinement of layer thicknesses of remaining layers against a target specification  seems to optimally address the requirements in a wide range of applications and is also used in our approach (Fig. 1 ). For refinement, the recently implemented automation mechanism in the OptiLayer design software  is used. This automatically results in a large variety of supported target definitions. Often, the target for estimation of production yield and refinement are different.
Obviously, the success of re-optimization strongly depends on the accuracy of the modelled layer thicknesses and optical constants. Furthermore, errors in the first few layers of an antireflection coating will result in an insufficient adaption of the coating to the refractive index of the substrate. It is therefore likely that errors in these layers cannot be compensated by adapting the layer thicknesses of remaining layers, these errors must be minimized from the very beginning of deposition.
The impact of systematic measurement errors on the precision of the calculated optical constants of dielectric thin films  and the effect of accumulation of errors in the film thicknesses in the case of broadband optical monitoring have also been studied . In the case of antireflection coatings broadband optical monitoring often seems to be the most efficient method [8,16]. Obviously, the reproducibility of optical constants for the layer materials has to be quite good, because antireflection coatings are known to be sensitive to refractive index errors .
In section 3 the design approach is described and one solution with low sensitivity to deposition errors is presented. For reference, a design based on the optimal two cluster solution  was additionally investigated. For identification of a stable design solution a large set of different designs with up to 20 layers and 3 materials has been investigated by computational manufacturing. Obviously, the initial number of 20 virtual deposition runs for this simulation is too small to exactly predict the production yield , but should be sufficient to identify candidate designs with an acceptable production yield. In extension to former simulations, not only a sufficient design and monitoring strategy can be deducted by computational manufacturing, but also the impact of re-optimization procedures is included. Details on the simulation results are reported in section 4. Finally, the selected design was deposited several times and the observed performance will be outlined in section 5.
2. Experimental setup
All deposition experiments were performed in a Leybold Syrus pro 1100 deposition plant. For evaporation of SiO2, the electron beam gun HPE10 and for high refractive index materials Nb2O5 and Ta2O5 the electron beam gun HPE6 was used. During deposition the layers were densified with an advanced plasma source (Leybold APSpro). Thereby, the selected deposition parameters (deposition rate, gas flows, bias voltage, …) result in coatings without any relevant shift after cooling and venting . Corresponding shift measurements did not yield a detectable shift, so that a shift – if it occurs – is below 0.1% in absolute value. For monitoring of the layer thickness, either the originally equipped quartz crystal monitoring system QW/TW12 or the in situ broadband optical monitoring system OptiMon was used. Broadband optical monitoring is thereby always performed directly on the moving substrate that is to be overcoated.
Ex situ layer characterization has been performed by transmission/reflection measurements at nearly normal incidence using a Perkin Elmer Lambda 950 scanning spectrophotometer equipped with the VN-measurement attachment for absolute measurements. The measured spectra have been analyzed in terms of the oscillator model using advanced LCalc software . Calculated parameters for the optical constants of all coating materials and random errors for quartz crystal monitoring and our broadband optical monitoring version are published in .
3. Design selection
In this study, we use planar substrates of BK7, widely used also for lenses, prisms and other optical components. To minimize the impact of uncertainties caused by measurements with oblique angle of incidence , in this study, photometric data are only specified for normal incidence of light. In the spectral range 400…680 nm a maximum reflectance of less than 0.4% was required. For 380…400 nm and 680…700 nm, a maximum reflectance of 1% was allowed. Additionally, optical losses in the spectral range 400…700 nm were restricted to be below 1%.
In the first step a set of 100 random designs with minimal reflectance in the required spectral region was generated. Thereby, the maximum number of layers was restricted to 20 to exclude solutions with more than 3 clusters . Up to 3 different coating materials (SiO2, Nb2O5 and Ta2O5) were included into design. Next, all designs violating the specification or containing layers with geometrical thickness below a practically proofed limit of 5 nm were excluded. The remaining designs seem to represent themselves derivations of the well known 2 or 3 cluster antireflection designs . Often, designs with a stepwise graded high refractive index layer have been observed (for an example see Fig. 2 ). This kind of design modification will result in reduced absorption losses, while advantages caused by high contrast in refractive index are still accessible. Furthermore, the different dispersion for both high refractive index materials seems to reduce the required number of very thin layers. This is consistent with a replacement of thin layers and fractions of surrounding material by a layer of intermediate refractive index using Herpin’s symmetric layer approach . A further substitution of the resulting index steps by gradient index layers has been already discussed  and was successfully used for preparation of omnidirectional antireflection coatings .
For reference, a two material design (Nb2O5 and SiO2) based on the optimal 2 cluster design for dispersion and absorption free materials  has been included. The corresponding 14 layer solution was used as initial design. Next, the absorption and dispersion free optical constants has been replaced by calculated values from single layers  and finally a refinement of layer thicknesses was used to minimize the reflectance of the coating. Thereby, the thin SiO2 layer in the last cluster has disappeared, because the refractive index of the substrate is close to that of the low index material . In Fig. 3 the final refractive index profile at the design wavelength of 600 nm is shown. By the way, the physical thickness of only 4.0 nm for the first layer is below the limit outlined earlier.
4. Simulation results and choice of monitoring strategy
The qualified random designs as well as the reference design were investigated by computational manufacturing. Thereby, at least 20 deposition runs have been simulated for layer termination by quartz crystal monitoring and broadband optical monitoring. At this stage, only the same monitoring strategy for all layers and no re-optimization by thickness refinement of remaining layers was included in computational manufacturing.
These simulations clearly indicate a low sensitivity to deposition errors for the particular 3 materials design (Fig. 2) presented in the previous section. In Fig. 4 , the expected reflectance (20 simulation runs) for complete process control by broadband optical monitoring is shown. In these simulations, already 18 deposition runs out of 20 result in a reflectance below the specified limit. In the simulation of further 100 deposition runs, additional 84 successful experiments have been observed. This is close to the initial estimation and in good accordance to the predicted fast convergence of the simulated production yields for the extreme cases of yields close to 0% and 100% . Assuming quartz crystal monitoring, a number of only 36 successful deposition runs out of 100 indicates a significantly lower yield and also confirms the advantages of broadband optical monitoring when being applied to antireflection coatings [8,16].
General advantages of computational manufacturing against real deposition experiments are not only given by higher speed and reduced costs, but also by granting access to simulated data for optical constants and layer thicknesses of the resulting coating. Investigation of these data have shown that even when only random errors with Gaussian distribution are taken into account, the average thickness for layers is often different to the design value. This could result from the strongly nonlinear character of the equations required for calculation the optical behaviour of multilayer coatings. Additionally, broadband optical monitoring can result in correlated thickness errors. In Fig. 5 such a correlation between layer thickness in the first and third layer is outlined. For both layers, an overshot in physical thicknesses is predicted, but absolute values of random errors in the first layer seem to be significantly amplified by a factor of 3.8 in the third layer. For example, an overshot in layer thickness of 0.35 nm in the first layer seems to implicate an additional overshot of 1.7 nm in the third layer. To interrupt this propagation, a hybrid monitoring strategy seems promising. Initially accumulated data from simulated deposition runs completely controlled either by quartz crystal monitoring or broadband optical monitoring can be used to deduct a hybrid monitoring strategy minimizing thickness errors for individual layers. It turns out, that only layers 3, 4, 13 and 14 should be terminated by quartz crystal monitoring. For all other layers, the expected thickness error for broadband optical monitoring is smaller.
However, in the computational manufacturing experiment for this design only 43 deposition runs out of 100 have been successful when a hybrid monitoring strategy is applied. This value is very close to the results observed for pure quartz crystal monitoring and significantly lower than observed in the case of broadband optical monitoring. This strongly indicates some built-in self compensation mechanism for deposition errors when broadband optical monitoring is used, which is in agreement to . Further investigations on terminating only one layer by quartz crystal monitoring indicate that the self compensation of deposition errors mainly occurs in layer 14.
Based on various simulation runs for different monitoring strategies, termination of all layers using broadband optical monitoring has finally been selected for investigation of the impact of re-optimization to the final result. For this reason, the optional adaption of layer thicknesses of remaining layers has been enabled in different layers and simulated by computational manufacturing. Thereby the initial 7 layers have been excluded because the observed deviations between measured and theoretical transmittance commonly remains below the estimated accuracy of in situ measurements. In layers 10, 12 and 13 the re-optimization shows no relevant effect. Attempting to compensate errors directly after completing layers 8, 9 and 11 will result in a significant drop down of the production yield close to values observed for quartz crystal monitoring. On the contrary, adapting the thickness of the last layer after termination of the previous layer will result in a rise of the expected production yield close to 100%. In Fig. 6 , the calculated reflectance for 20 simulation runs is shown. All coatings have a reflectance below the specified value. For additional 200 simulation runs, the performance was only 3 times slightly outside the specification. In accordance to  layer 14 can be identified as a key point to apply error compensation using re-optimization.
The result of our simulations thus favours exclusively broadband optical monitoring of the design shown in Fig. 2 with allotted re-design of the last layer in order to suffice the formulated AR-specification. In the next section, experimental results for this design, monitoring strategy and re-optimization approach will be outlined.
For the reference design based on the optimal 2 cluster solution for dispersion and absorption free materials a significantly lower stability has been observed. In the case of quartz crystal monitoring only 3 simulated deposition runs out of 20 are below the specified reflectance. For this design, even broadband optical monitoring with default settings doesn’t provide a good performance (Fig. 7 ) and always result in a significant overshot in layer thickness for the second layer. When the averaged spectra are processed by the full triangular algorithm , the calculated layer thicknesses becomes very close to the exact value. This clearly demonstrates the higher stability of the triangular algorithm in comparison to the widely used sequential algorithm for termination. Nevertheless, layer deposition termination with optical monitoring is a real-time task, which needs to make use of a time sequential re-engineering algorithm. In our case the simulations show, that this leads to significant deposition errors in the first five layers of the design from Fig. 3.
Some additional analysis to the design shows that during deposition of the second layer the expected transmittance has only a low sensitivity to current thickness. In Fig. 8 , theoretical transmittance values for intermediate layer thicknesses of 30 nm (solid line) and 40 nm (dashed line) for the second layer are shown. Changes in the spectra are very small and below the noise level of the broadband optical monitoring system. Nevertheless, a fine tuning of re-engineering parameters has been used to significantly improve the accuracy for termination in the initial five layers, while in the other layers only a small decrease in accuracy has been observed. But even this modification has resulted in an only slightly improved performance of the final coatings.
Already at this stage it is clear, that the presented simulator (Fig. 1) with re-design option appears to be a powerful tool for design and monitoring strategy selection.
5. Performance of the deposited antireflection coatings
The selected design (refer to Fig. 2 for refractive index profile) has been deposited 7 times using broadband optical monitoring with enabled re-optimization in layer 14. During this series of deposition experiments not only material for both electron beam guns has been refilled but also the cathode of the plasma source was replaced because the end of lifetime has been reached. Nevertheless, only small variations of the optical performance close to measurement accuracy of the Perkin Elmer Lambda 950 spectrometer have been observed for all deposited coatings and measured reflectance remains below the specified limit for all samples (Fig. 9 ). Only in 3 deposition runs the thickness of the last layer has been modified by up to 2 nm. Otherwise, deviation between theoretical and measured transmittance was below the noise level of the broadband optical monitoring system. In this case, no significant deposition error could be detected and finally no re-optimization was required.
In Fig. 10 the measured reflectance of the uncoated substrate and substrate with antireflection coating on either one or both sides is shown. In the spectral range 400…680 nm a substrate with antireflection coating deposited on both sides has an average reflectance of only 0.43% and the maximum reflectance of 0.89%. In the spectral range 380…700 nm the average reflectance is 0.47% and the maximum reflectance is 1.48%.
6. Conclusions and outlook
A new all-oxide design for broadband antireflection coatings with significant reduced impact of deposition errors to reflectance of the resulting coating has been deducted by computational manufacturing and successfully deposited by PIAD using our broadband optical monitoring system with re-optimization during deposition. Thus, the main results of this study may be expressed in two major points:
Firstly, we demonstrate the function and benefit of an automated re-optimization routine, which is incorporated into the computational manufacturing module as well as into the real monitoring process during deposition. In our solution, support for compensation of previous deposition errors is performed through adaption of thicknesses of remaining layers using automation capabilities of the OptiLayer software. Now, feasible designs, adapted monitoring strategies and re-optimization solutions can be deducted for a large variety of specifications by computational manufacturing.
Secondly, we demonstrate a novel all-oxide broadband antireflection design, which has been derived from previously published design ideas making explicit use of the mentioned computational manufacturing procedure to comply with feasibility considerations. The proposed design shows a modified cluster structure in comparison to “optimal” antireflection coating designs, but with a reduced required number of very thin layers and total number of layers by incorporating a third deposition material. Furthermore, this design avoids insensitive layers for broadband optical monitoring and seems to provide a built-in mechanism for compensation of deposition errors in layer 14. The same layer has been proofed by simulations to be the best choice for error compensation by thickness adaptation. The gap between theoretical and experimental performance of the broadband antireflection coating has been reduced to a value commonly not accessible by PIAD. Future research on antireflection coatings will also address mixtures of materials to possible include layers either with tailored refractive index or refractive index gradient into design.
The presented work has been done in the framework of the TACo project. The authors gratefully acknowledge the Federal Ministry of Economics and Technology (BMWi) for financial support in terms of grant 16IN0408. Additionally, the authors want to thank A. V. Tikhonravov and M. K. Trubetskov for providing optimon.dll and fruitful discussions, H. Haase for assistance with sample preparation, and D. Müller for technical assistance during manuscript preparation.
References and Links
1. Market and Research Report Optical Coatings: Technologies and Global Markets, October 2009, SMC030D, BCC Research, Wellesley, MA USA Web: www.bccresearch.com
3. J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, and P. G. Verly, “Optimal single-band normal incidence antireflection coatings,” Appl. Opt. 35(4), 644–658 (1996). [CrossRef] [PubMed]
4. A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, and J. A. Dobrowolski, “Estimation of the average residual reflectance of broadband antireflection coatings,” Appl. Opt. 47(13), C124–C130 (2008). [CrossRef] [PubMed]
6. S. Wilbrandt, O. Stenzel, N. Kaiser, M. K. Trubetskov, and A. V. Tikhonravov, “In situ optical characterization and reengineering of interference coatings,” Appl. Opt. 47(13), C49–C54 (2008). [CrossRef] [PubMed]
7. S. Wilbrandt, O. Stenzel, and N. Kaiser, “All-optical in-situ analysis of PIAD deposition processes,” Proc. SPIE 7101, 71010D (2008). [CrossRef]
8. K. Friedrich, S. Wilbrandt, O. Stenzel, N. Kaiser, and K. H. Hoffmann, “Computational manufacturing of optical interference coatings: method, simulation results, and comparison with experiment,” Appl. Opt. 49(16), 3150–3162 (2010). [CrossRef] [PubMed]
9. J. A. Dobrowolski, “Modern computational methods for optical thin film systems,” Thin Solid Films 34(2), 313–321 (1976). [CrossRef]
11. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Does Broadband Optical Monitoring Provide an Error Self Compensation Mechanism?”, in Optical Interference Coatings Topical Meeting, 2010 OSA Technical Digest Series (Optical Society of America, 2010), Poster TuC3.
14. A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41(13), 2555–2560 (2002). [CrossRef] [PubMed]
15. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the effect of accumulation of thickness errors in optical coating production by broadband optical monitoring,” Appl. Opt. 45(27), 7026–7034 (2006). [CrossRef] [PubMed]
17. B. T. Sullivan, G. A. Clarke, T. Akiyama, N. Osborne, M. Ranger, J. A. Dobrowolski, L. Howe, A. Matsumoto, Y. Song, and K. Kikuchi, “High-rate automated deposition system for the manufacture of complex multilayer coatings,” Appl. Opt. 39(1), 157–167 (2000). [CrossRef]
18. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “On the Reliability of Computational Estimations Used for Choosing the Most Manufacturable Design”, in Optical Interference Coatings Topical Meeting, 2010 OSA Technical Digest Series (Optical Society of America, 2010), Poster TuA3.
19. O. Stenzel, S. Wilbrandt, K. Friedrich, and N. Kaiser, “Realistische Modellierung der NIR/VIS/UV-optischen Konstanten dünner optischer Schichten im Rahmen des Oszillatormodells,” Vakuum in Forschung und Praxis 21(5), 15–23 (2009). [CrossRef]
21. A. Herpin, “Calcul du pouvoir réflecteur d’un système stratifiè quelconque,” C. R. Acad. Sci. 225, 182–183 (1947).
22. S. Wilbrandt, Dissertation “Online-Monitoring inhomogener optischer Schichtsysteme im visuellen Spektralbereich”, (2006)
23. V. Janicki, S. Wilbrandt, O. Stenzel, D. Gäbler, N. Kaiser, A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Hybrid optical coating design for omnidirectional antireflection purposes,” J. Opt. A, Pure Appl. Opt. 7(8), L9–L12 (2005). [CrossRef]
24. A. Shuttleworth, P. Girow, S. McCabe, and J. Bennett, “Real time re-optimisation of optical thin film coating designs during manufacture,” IEE Conf. Publ. 435, 197–201 (1997).
25. A. V. Tikhonravov and M. K. Trubetskov, “On-line characterization and reoptimization of optical coatings,” Proc. SPIE 5250, 406 (2003). [CrossRef]