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Determination of Refractive Index, Thickness, and the Optical Losses of Thin Films from Prism-Film Coupling Measurements Julien Cardin, Dominique Leduc

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Determination of Refractive Index, Thickness, and the Optical Losses of Thin Films from Prism-Film Coupling Measurements Julien Cardin, Dominique Leduc Determination of refractive index, thickness, and the optical losses of thin films from prism-film coupling measurements Julien Cardin, Dominique Leduc To cite this version: Julien Cardin, Dominique Leduc. Determination of refractive index, thickness, and the optical losses of thin films from prism-film coupling measurements. Applied optics, Optical Society of America, 2008, 47 (7), pp.894-900. 10.1364/AO.47.000894. hal-00932923 HAL Id: hal-00932923 https://hal.archives-ouvertes.fr/hal-00932923 Submitted on 18 Jan 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Determination of refractive index, thickness, and the optical losses of thin films from prism–film coupling measurements Julien Cardin1,* and Dominique Leduc2 1SIFCOM, CNRS UMR 6176, ENSICAEN, 6 Boulevard du Maréchal-Juin, F-14050 Caen Cedex, France 2Université de Nantes, Nantes Atlantique Universités, IREENA, EA1770, Faculté des Sciences et des Techniques, 2 rue de la Houssinière–BP 9208, Nantes F-44000, France *Corresponding author: [email protected] Received 4 September 2007; revised 17 December 2007; accepted 3 January 2008; posted 11 January 2008 (Doc. ID 87215); published 28 February 2008 We present a method of analysis of prism–film coupler spectroscopy based on the use of transfer matrix and genetic algorithm, which allows the simultaneous determination of refractive index, thickness, and optical losses of the measured layer. © 2008 Optical Society of America OCIS codes: 130.3130, 120.3940, 160.4760, 300.1030. 1. Introduction scopy has been developed to characterize thin films. Transparent thin films find wide applications in Full-accuracy index and thickness measurements optics: coating, sensors, integrated components for are obtained, for nonbirefringent films [10] and in telecommunications, solar cell, etc. For all these ap- the absence of nonlinear effects [11], once film thick- plications, it is necessary to perform an accurate ness exceeds a certain minimum threshold value 300 characterization of the optical properties, which in- (typically nm, depending on the film/substrate clude refractive index and optical losses. The optical type) [12,13]. This technique is based on a selective losses of a thin film have three different origins: sur- excitation, through an evanescent field, of guided face scattering due to the surface roughness, volume modes of a film. The total reflection at the upper scattering due to volume defects such as inhomo- boundary of the film is frustrated by the presence geneity, and volume absorption due to intrinsic of the prism and allows the light to go back into absorption [1,2]. From a practical point of view, this the prism. Since this reflected light carries informa- characteristic is of particular importance since it can tion on the film, it can be used to determine the para- severely degrade or modify the performances of a meters of the film. Classically, this method was component. restricted to the determination of the thickness Several techniques exist which allow the charac- and the refractive index of the films. The scope of this terization of the optical parameters of thin films. paper is to present a method of analysis, which al- For example, the measurement of reflection and lows retrieving the optical losses also from classical – transmission coefficients [3–6] and the spectroscopic prism film coupler measurements, for films of negli- ellipsometry [7–9] lead to refractive index, thickness, gible roughness. and extinction factor measurement. 2. Prism–Film Coupler Angular Reflectivity On the other hand, since the 1970s, a prism–film coupler based method, also called m-lines spectro- In m-lines devices, the sample is pressed against a face of a prism in such a way that it is separated from the prism by a thin air gap with a thickness about a 0003-6935/08/070894-07$15.00/0 quarter of wavelength of the measurement light. The © 2008 Optical Society of America prism and the film are mounted onto a rotating stage 894 APPLIED OPTICS / Vol. 47, No. 7 / 1 March 2008 that varies the incidence angle. The incoming light is 1 cos ϕj iγj sin ϕj Mj ; 1 refracted inside the prism and reaches the interface iγj sin ϕj cos ϕj between the prism and the sample. As the refractive 2 2 1=2 index of the prism is higher than that of the sample, with phase factor ϕ d n~ k0 β , where d is j j j j for a given range of incidence angles, the light is the thickness of the jth layer, k0 is the wave vector, totally reflected by this interface and then emerges and β is the propagation constant in the direction from the prism. However, for some angles, called parallel to the interface. The transversal component “synchronous angles,” a part of the light is coupled in the direction perpendicular to the interface of the 1 in the waveguide. Depending on refractive indices wave vector is γj djk0 ϕj for TE waves and γj ~ 2 1 of layer and cladding, one obtains guided or leaky k0nj ϕj for TM waves. modes. For both cases, the light coupled inside the The global transfer matrix M of the system formed film is subtracted to the detected light. Thus, a typi- by the two layer stack (air gap + thin film) is the pro- cal m-lines spectrum is made of several absorption- duct of the individual transfer matrices: M M · M and the power reflection coefficient R θ of like peaks, centered around the synchronous angles. a f In classical analysis, the propagation constants of the stack surrounded by the prism and the substrate the guided modes are deduced from the positions of is given by the synchronous angles, and then the refractive 2 index and thickness are determined by solving the m11 m12γ γ m21 m22γ R θ s p s ; 2 modal dispersion equations. A previous paper [14] m11 m12γ γ m21 m22γ s p s on the analysis of m-lines spectroscopy with genetic algorithm was also done in the framework of the where θ is the incidence angle of the incoming wave, modal dispersion equations with the synchronous mij are the elements of M,andγs and γp are, respec- angles as input data. In our case, we are performing tively, the transversal component of the wave vector a fit on the whole recorded spectrum by using the (γj factor) in the substrate and in the prism. transfer matrix theory to simulate the angular reflec- Measurements were performed with two different tivity of the prism–film coupler. kinds of m-lines setups at 632:8 nm and in TE mode: Consider the schematic of the m-lines prism cou- one commercial setup from Metricon Corporation pler in Fig. 1. In our model, the prism positioned [17] in transmission configuration (see Fig. 1(a)) on the top part of the drawing is considered as a non- and one homemade setup in reflection configuration absorbing medium. The optical film is surrounded [18] (see Fig. 1(b)). However, since there is a total in- by a thin air gap and a semi-infinite substrate. ternal reflection on both faces of the prism in the lat- The complex refractive indexes, n~ n ik, including ter device (see Fig. 1(b)), the two cases are identical. extinction factor k, are used for each layer. We cannot The incident wave is first refracted inside the prism, separate the contributions of surface, volume scatter- then reflected by the two layer stack, and finally ing, and volume absorption only from the m-lines refracted in the air before reaching the detector. spectrum. Thus, in our case we consider this extinc- Hence, the global reflectivity of the prism/film cou- pler is T θ R θ T θ , where T θ and T θ tion factor as an effective extinction factor, which a=p p=a a=p p=a represents a priori the three types of contribution are the classical transmittivity of the prism/air to optical losses. The extinction factors of the air diopter: and of the prism were assumed to be zero. 2 2 2 A transfer matrix M , which binds the electromag- pnp nasin θ 2 j T θ a=p tap na cos θ j j ; 3 netic fields at the backplane of the layer to the fields 8 na cos θ 2 < T θ p=a 2 2 2 tpa at its front plane, is associated with both film and air pnp nasin θ j j layers [15,16]: : where tap (respectively, tpa) is the Fresnel transmis- sion coefficient [19] of the air/prism diopter (respec- tively, prism/air), and np and na are the refractive index of prism and air. To analyze real measurements, it is necessary to add a transfer function of the apparatus H θ to the calculated reflectivity: R θ H θ T θ R θ T θ : 4 calc a=p p=a This transfer function contains all the variations of the detected intensity related to the measurement device; it is the ratio of the theoretical and ex- Fig. 1. Prism coupler configuration: (a) transmission configura- perimental reflectivity without the loaded sam- tion, and (b) reflection configuration. ple. H θ is determined by measuring the angular 1 March 2008 / Vol. 47, No.
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