Utilization of the cyclic interferometer in polarization phase-shifting technique to determine the thickness of transparent thin-films
TL;DR: In this article, a cyclic interferometric configuration is chosen to maintain the stability of the operation against external vibrations, and a wave plate is inserted into the common paths to introduce an intrinsic phase difference between the orthogonal polarized beams.
Abstract: An alternative polarization phase-shifting technique is proposed to determine the thickness of transparent thin-films. In this study, the cyclic interferometric configuration is chosen to maintain the stability of the operation against external vibrations. The incident light is simply split by a non-polarizing beam splitter cube to generate test and reference beams, which are subsequently polarized by a polarizing beam splitter. Both linearly polarized beams are orthogonal and counter -propagating within the interferometer. A wave plate is inserted into the common paths to introduce an intrinsic phase difference between the orthogonal polarized beams. A transparent thin-film sample, placed in one of the beam tracks, modifies the output signal in terms of the phase retardation in comparison with the reference beam. The proposed phase-shifting technique uses a moving mirror with a set of “fixed” polarizing elements, namely, a quarter-wave retarder and a polarizer, to facilitate phase extraction without rotating any polarizing devices. The measured thicknesses are compared with the measurements of the same films acquired using standard equipment such as the field-emission scanning electron microscope and spectroscopic ellipsometer. Experimental results with the corresponding measured values are in good agreement with commercial measurements. The system can be reliably utilized for non-destructive thickness measurements of transparent thin -films.
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TL;DR: In this article, a modified Sagnac interferometer with a self-referenced polarization and phase-shifting technique for real-time thickness measurement of single and double-layer transparent thin films was presented.
Abstract: This paper describes a modified Sagnac interferometer with a self-referenced polarization and phase-shifting technique for real-time thickness measurement of single- and double-layer transparent thin films. The proposed interferometric setup generated outstanding rotating linearly polarized light with a degree of polarization (DOP) of 99.40%. A beam splitter placed at the interferometer output separated the beam into two identical linearly polarized beams. One of the beams served as a reference, while the other served as a sensing arm. The output linear polarizer set at 45° relative to a reference plane was positioned anterior to the photodetectors to get rotating light intensities for phase shift measurement; hence, the intensities at various polarizations of 0°, 45°, and 90° were automatically acquired without any polarizing device adjustments. These intensities were then transformed into a phase retardation introduced by a sample, and the resulting phase shift was eventually converted into film thickness. The samples were properly prepared, with pure BK7 substrate being deposited by WO3-, Ta2O5-, and WO3/Ta2O5 films of known thicknesses. The thickness measurement obtained from the proposed system yielded reading errors of 1.3%, 0.2%, and 1.3/2.5% for WO3-, Ta2O5-, and WO3/Ta2O5 films, respectively. The mathematical theory was effectively demonstrated and empirically confirmed. The experimental results show that the proposed setup has a lot of potential for real-time, non-destructive thickness assessment of transparent thin films without the need to modify polarizing device orientations.
2 citations
10 Mar 2021
TL;DR: In this article, a non-contact thickness measurement of multi-layer thin films with improving the sensitivity, accuracy, and performance of the measurement techniques is reported, where single and double-layer film thickness measurement using different polarization states were studied.
Abstract: The new scheme of a non-contact thickness measurement of multi-layer thin films with improving the sensitivity, accuracy, and performance of the measurement techniques is reported in this paper. Single- and double-layer film thickness measurement using different polarization states were studied. An alternative architecture using triangular cyclic interferometer with simultaneous measurements of reference and sample arms by splitting the beam at the output of interferometer is mathematically achieved. The polarization phase shift using two steps algorithm is observed, with steps shift of n/2 rad for a double layer sample. This shows that the polarization state has an impact on the thickness measurement of different thin- film materials.
1 citations
TL;DR: In this paper , the Sagnac interferometer was modified with phase shifting approach for the determination of thin-film thickness, and the results showed that the phase-shifting technique using three-polarization settings is more suitable for the thickness measurement of the transparent thin film.
Abstract: This paper presents the comparison of three-, four- and five-step techniques for measuring transparent thin-film thickness of Ta2O5 and WO3 deposited on BK-7 substrates. The Sagnac interferometer was modified with phase shifting approach for the determination of thin-film thickness. The input light beam was split into reference and testing beams. Before the output light reaching the balanced photodetectors, the real-time signal detection was performed to obtain the output intensities of both beams using three-, four-, and five-polarization settings of an analyzer. The thicknesses could then be efficiently translated from the measured intensities. Thicknesses from three-, four- and five-stepping algorithms were compared with ones from the conventional FE-SEM measurement, and it was discovered that the former performed better with less errors. The findings show that the phase-shifting technique using three-polarization settings is more suitable for the thickness measurement of the transparent thin film.
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TL;DR: In this paper, a new calculation following traditional methods is proposed for deducing optical constants and thickness from the fringe pattern of the transmission spectrum of a thin transparent dielectric film surrounded by nonabsorbing media.
Abstract: A new calculation following traditional methods is proposed for deducing optical constants and thickness from the fringe pattern of the transmission spectrum of a thin transparent dielectric film surrounded by non-absorbing media. The particular interest of this method, apart from its easiness, is that it makes a directly programmable calculation possible; the accuracy is of the same order as for the iteration method.
1,499 citations
"Utilization of the cyclic interfero..." refers background in this paper
...Film thickness determination The transmitted light T under various conditions can be carefully examined [22]....
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TL;DR: A cyclic interferometers can be used for both lateral and radial shearing, and the working of a polarization phase shifting cyclic shear interferometer is demonstrated.
Abstract: A cyclic interferometer can be used for both lateral and radial shearing. Being common-path this interferometer is quite stable. The use of a cyclic shear interferometer for phase shifting interferometry is discussed. The phase shifting is provided here by polarization techniques. Some useful cyclic phase shifting interferometer arrangements are discussed, and the working of a polarization phase shifting cyclic shear interferometer is demonstrated.
112 citations
TL;DR: In this article, the dielectric function of amorphous tantalum oxide was obtained by line shape analysis of the experimental ellipsometric data over the range from E=0.03 to 8.5 eV (40 μm-145 nm).
Abstract: Amorphous tantalum oxide thin films were deposited by reactive rf magnetron sputtering onto [001] silicon substrates. Growth temperature, oxygen partial pressure, and total gas pressure have been varied to obtain thin films with different densities. The thin films were analyzed by glancing angle-of-incidence x-ray diffraction, atomic force microscopy, and variable angle-of-incidence spectroscopic ellipsometry in the near infrared to vacuum ultraviolet spectral region for photon energies from E=1 to 8.5 eV, and in the infrared region from E=0.03 to 1 eV. We present the dielectric function of amorphous tantalum oxide obtained by line shape analysis of the experimental ellipsometric data over the range from E=0.03 to 8.5 eV (40 μm–145 nm). In the infrared spectral region the ellipsometric data were analyzed using Lorentzian line shapes for each absorption mode observed in the spectra. Amorphous tantalum oxide optical properties in the near infrared to vacuum ultraviolet spectral region were extracted by usin...
83 citations
"Utilization of the cyclic interfero..." refers methods in this paper
...Spectroscopic ellipsometry (SE) and FE-SEM analysis The values obtained from the VASE for the WO3 thin-film and the Tauc–Lorentz oscillator [25] were used to plot the fitting curves of the ellipsometric parameters for different deposition times....
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TL;DR: In this paper, an achromatic phase shifting arrangement based on polarization components is described, in which the phase shifting is obtained by rotating a polarizer and these components can be used in a polarization interferometer to introduce variable phase shift independent of wavelength.
63 citations
TL;DR: A method by which the frequency shift equals 4N times the rotation rate, where N is the number of rotating components available, and a higher heterodyne frequency is possible than with the previously described techniques is described.
Abstract: Twyman-Green. This Letter describes a method by which the frequency shift equals 4N times the rotation rate, where N is the number of rotating components available. The advantage of this method over previously described methods is that a higher heterodyne frequency is possible than with the previously described techniques. Let the light entering an interferometer, shown in Fig. 1, be separated into two orthogonal linear polarizations using, for example, a polarization beam splitter P. Each component travels a separate path through the interferometer cavity seeing a different optical phase retardation. Upon recombination the light passes through the frequency shifter and onto a detector plane, where the temporally varying optical signal has a phase equal to the net phase difference between the two paths inside the interferometer. The frequency shifter, which we shall describe using Jones calculus 3 and the complex wave representation of light, consists of a stationary quarterwave plate (QS) followed by a series of rotating halfwave plates (Hr) separated by stationary halfwave plates (HS), followed by a stationary linear polarizer (LS). The following analysis demonstrates a frequency shift of eight times the rotation rate of the halfwave plates. We begin by treating the horizontal (X) component, which we represent by
60 citations