On the Reliability of Reverse Engineering Results

On the reliability of reverse engineering results Tatiana V. Amotchkina,1,5,* Michael K. Trubetskov,1,2 Vladimir Pervak,3 Boris Romanov,4 and Alexander V. Tikhonravov1 1Research Computing Center, Moscow State University, Leninskie Gory, 119991, Moscow, Russia 2Max Planck Institute of Quantum Optics, Hans-Kopfermann-Str. 1, 85748 Garching, Germany 3Ludwig-Maximilians-Universität München, Am Coulombwall 1, 85748 Garching, Germany 4Leybold Optics GmbH, Siemensstrasse 88, 63755 Alzenau, Germany 5QUEST. Centre for Quantum Engineering and Space-Time Research, Welfengarten 1, 30167 Hannover, Germany *Corresponding author: [email protected] Received 3 May 2012; revised 27 June 2012; accepted 27 June 2012; posted 28 June 2012 (Doc. ID 167892); published 30 July 2012 Determination of actual parameters of manufactured optical coatings (reverse engineering of optical coatings) provides feedback to the design-production chain and thus plays an important role in raising the quality of optical coatings production. In this paper, the reliability of reverse engineering results obtained using different types of experimental data is investigated. Considered experimental data in- clude offline normal incidence transmittance data, offline ellipsometric data, and online transmittance monitoring data recorded during depositions of all coating layers. Experimental data are obtained for special test quarter-wave mirrors with intentional errors in some layers. These mirrors were produced by a well-calibrated magnetron-sputtering process. The intentional errors are several times higher than estimated errors of layer thickness monitoring, and the reliability of their detection is used as a measure of reliability of reverse engineering results. It is demonstrated that the most reliable results are provided by online transmittance data. © 2012 Optical Society of America OCIS codes: 310.6805, 310.3840, 310.1620, 310.1860, 310.6860. 1. Introduction From a mathematical point of view, reverse engi- Reliable determination of actual optical parameters neering is a typical ill-posed inverse problem, and of layers of deposited multilayer coatings (so-called specific numerical algorithms are required to solve reverse engineering of optical coatings [1,2]) plays a this problem [5]. The complexity of this problem is key role in advancing the quality of optical coatings connected with the ambiguity and instability of production. Reverse engineering results provide feed- the problem solution [6–8]. back to the design-production chain because they One of the most popular approaches to reverse en- can be used for adjusting deposition parameters, re- gineering is based on the postproduction analysis of calibrating monitoring systems, and improving con- normal incidence or quasi-normal incidence transmit- trol of thicknesses of individual layers [1,3]. These tance (T) and/or reflectance (R) data related to a pro- results may also be useful in the course of establish- duced coating sample. This approach is simple from ing adequate levels of simulation parameters in cases an experimental point of view. Normal incidence when computational manufacturing is incorporated transmittance and quasi-normal incidence reflectance into the design-production chain [4]. can be measured with a sufficient accuracy using any UV-visible–near-IR dispersive or Fourier-transform spectrophotometer. However, this approach is quite 1559-128X/12/225543-09$15.00/0 complicated from a mathematical point of view be- © 2012 Optical Society of America cause many unknown parameters are found from a 1 August 2012 / Vol. 51, No. 22 / APPLIED OPTICS 5543 single R or/and T data array. In order to determine were quarter-wave mirrors (QWM) with intention- layer parameters reliably, one should apply a se- ally imposed errors on thicknesses of several layers. quence of physically meaningful models of optical con- We knew these errors with a high accuracy because stants and thickness errors [8]. There are situations the mirrors were produced using well-calibrated when it is not possible in principle to find layer para- time monitoring control [19]. In our disposal we meters from single R or/and T data arrays. As an ex- had several sets of measurement data, namely, mul- ample of such a situation, the reverse engineering of tiscan transmittance measurements recorded in the dispersive mirrors working in broadband spectral course of the deposition process, quasi-normal R and ranges can be considered. In this case, reflectance data T data related to produced samples, and ellipso- are not informative, and other spectral characteristics metric data taken for the samples. We used two re- (group delay or group delay dispersion) should be verse engineering software tools in our research. measured [8]. These tools were OptiRE module of OptiLayer soft- Another approach to reverse engineering is based ware ver. 8.85 [12] and Woollam WVASE32 ver. on the analysis of multiangle R and T measurements 3.770 [10]. taken for a produced multilayer coating [9]. In [9]we In Section 2, we describe in detail our experimen- demonstrated that simultaneous analysis of reflec- tal samples and measurement data. In Section 3,we tance and transmittance data taken at different an- obtain reverse engineering results on the basis of gles of incidence (AOI) and for different polarization analysis of different sets of measurement data and states increased the reliability of reverse engineering find that data sets provide reliable results. Our final results. conclusions are presented in Section 4. Spectral ellipsometric data are used mainly for optical characterization of single thin films [10,11]. 2. Experimental Samples and Measurement Data Numerical algorithms for reverse engineering of For our study, we produced six experimental sam- multilayer optical coatings on the basis of spectral ples. Two samples were the samples of single ellipsometry are provided by several commercial Ta2O5 and Si2O2 films on Suprasil substrates of software packages (see, for example, [10,12]). It is 6.35 mm thickness. Geometrical thicknesses of the known that in some cases, ellipsometric data sig- films were about 290 and 400 nm, respectively. We nificantly reduce ambiguity and provide unique used these samples to verify consistency of character- solutions to reverse engineering problems. In [13], el- ization results obtained from different measurement lipsometric data were used for characterization of di- data sets. gitized rugate coatings with the help of a general Four samples were the test samples of 15 layer regularization approach [5]. In [14] it was proved QWM with a central wavelength of 600 nm. We used that three layer structures “dielectric film–ultrathin tantalum pentoxide as a high index material (odd metal-dielectric composite film–dielectric film” can layers) and silicon dioxide as a low index material be reliably characterized on the basis of ellipsometric (even layers). In the course of the deposition of test data. Authors of [6] used ellipsometric measure- samples, intentional errors were imposed on thick- ments in combination with photometric measure- nesses of several layers. We used these samples to ments to reduce instability in the course of reverse check the reliability of reverse engineering results engineering of hybrid antireflection coatings. obtained on the basis of analysis of different mea- In recent years, reverse engineering algorithms surement data sets. based on multiscan measurements have been elabo- The experimental samples were produced with rated [4,15–17]. These multiscan measurements are magnetron-sputtering plant (HELIOS, Leybold typically transmittance or reflectance data recorded Optics GmbH). This plant was equipped with two in-situ during the deposition process. Such multiscan proprietary TwinMags magnetrons and a plasma data sets can be provided by broadband monitoring source for plasma/ion assisting. The system was (BBM) systems [2,3,18]. Using multiscan data allows pumped by turbo-molecular pumps to 1 · 10−6 m one to involve more input information in solving bar before the sputtering. Argon and oxygen were reverse engineering problems and to reduce the used for both magnetrons. The cathode power for ambiguity of its solution. Si (purity 99.999%) and Ta (purity 99.8%) targets In this paper, we investigated the reliability of re- were 4500 and 2500 W, respectively. The power ap- verse engineering results obtained on the basis of plied to the Ta cathode was not constant because analysis of different experimental data sets. At the it operated in the oxygen control mode that guaran- current state of art, this question has not been stu- teed stable film properties. The gas pressure was 1 · died systematically. The primary goal of our paper 10−3 m bar during the sputtering process. Oxygen was to reveal measurement data sets that are suffi- was fed near the targets to oxidize the sputtering cient for providing reliable reverse engineering films. The distance from targets to the substrates results. Our secondary goal was to demonstrate ex- was 100 mm. The deposition rates were approxi- amples of data sets that may give wrong reverse mately 0.5 nm ∕ s for both materials. engineering results. In total, we performed four deposition runs. In As experimental basis, we produced samples of the first and second deposition runs, we produced single layers and multilayer stacks. These stacks samples of single Ta2O5 and SiO2 films. 5544 APPLIED OPTICS / Vol. 51, No. 22 / 1 August 2012 In the third deposition run, we deposited two of the

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