White-light spectral interferometric technique to measure a nonlinear phase function of a thin-film structure

We present a new two-step white-light spectral interferometric technique to measure a nonlinear phase function of a thin-film structure. The technique is based on recording of channeled spectra at the output of a Michelson interferometer and their processing by using a windowed Fourier transform to retrieve the phase functions. First, the phase function including the effect of a thin-film structure is retrieved. Second, the structure is replaced by a reference sample of known phase change on reflection and the corresponding phase function is retrieved. From the two functions, the nonlinear phase function of the thin-film structure is obtained. The feasibility of this simple method is confirmed in processing the experimental data for a SiO₂ thin film on a Si wafer of known optical constants. Four samples of the thin film are used and their thicknesses are determined. The thicknesses obtained are compared with those resulting from reflectometric measurements, and a good agreement is confirmed.     

Spectral interferometry and reflectometry used to measure thin films

A new method for a precise measurement of the oscillatory part of phase change on reflection (interferometric phase) from a thin-film structure is presented. The method, which is based on phase retrieval from the spectral interferograms recorded at the output of a slightly dispersive Michelson interferometer, is combined with reflectometry. The interferometric phase of the thin-film structure is measured precisely using a reference sample of known phase change on reflection. The spectral reflectance of the thin-film structure is also measured in the interferometer. The feasibility of the method is confirmed in processing the experimental data for SiO₂ thin film on a silicon wafer of known optical constants. Four samples of the thin film are used and their thicknesses are determined. We confirm very good agreement between the thicknesses obtained from the interferometric phase and reflectance measurements. PACS  07.60.Ly; 68.55.Jk; 78.20.Bh     

Phase retrieval from the spectral interference signal used to measure thickness of SiO<Subscript>2</Subscript> thin film on silicon wafer

A new method of phase retrieval from the spectral interference signal is presented, which is based on the use of a windowed Fourier transform in the wavelength domain. The phase retrieved by the method is utilized for measuring the thickness of SiO₂ thin film on a silicon wafer. The numerical simulations are performed to demonstrate high precision of the phase retrieval. The feasibility of the method is confirmed in processing experimental data from a slightly dispersive Michelson interferometer with one of the mirrors replaced by SiO₂ thin film on the silicon wafer. We determine the thin-film thickness for four samples provided that the optical constants for all the materials involved in the experiment are known. We confirm very good agreement with the previous results obtained by the fitting of the recorded channelled spectra to the theoretical ones. PACS 07.60.Ly; 42.30.Rx; 68.55.Jk; 78.20.Bh     

Thickness of SiO2 thin film on silicon wafer measured by dispersive white-light spectral interferometry

We present a white-light spectral interferometric technique for measuring the thickness of SiO₂ thin film on a silicon wafer. The technique utilizes a slightly dispersive Michelson interferometer with a cube beam splitter and a fibre-optic spectrometer to record channelled spectra in two configurations. In the first, a standard configuration with two identical metallic mirrors, the recorded channelled spectrum is fitted to the theoretical one to determine the effective thickness of the beam splitter made of BK7 optical glass. In the second configuration one of the mirrors is replaced by SiO₂ thin film on the silicon wafer and the recorded channelled spectrum is fitted to the theoretical one to determine the thin-film thickness. We consider multiple reflection within the thin-film structure, use the optical constants for all the materials involved in the set-up, and confirm very good agreement between theory and experiment. The technique is applied to four samples with various SiO₂ film thicknesses. PACS 07.60.Ly; 68.55.Jk; 78.20     

Dispersion error of a beam splitter cube in white-light spectral interferometry

We revealed that the phase function of a thin-film structure measured by a white-light spectral interferometric technique depends on the path length difference adjusted in a Michelson interferometer. This phenomenon is due to a dispersion error of a beam splitter cube, the effective thickness of which varies with the adjusted path length difference. A technique for eliminating the effect in measurement of the phase function is described. In a first step, the Michelson interferometer with same metallic mirrors is used to measure the effective thickness of the beam splitter cube as a function of the path length difference. In a second step, one of the mirrors of the interferometer is replaced by a thin-film structure and its phase function is measured for the same path length differences as those adjusted in the first step. In both steps, the phase is retrieved from the recorded spectral interferograms by using a windowed Fourier transform applied in the wavelength domain.     

The effect of silicon substrate on thickness of SiO2 thin film analysed by spectral reflectometry and interferometry

Techniques of spectral reflectometry and interferometry are used for measuring small changes in thickness of SiO₂ thin film grown by thermal oxidation on different silicon substrates. A slightly dispersive Michelson interferometer with one of its mirrors replaced by a thin-film structure is used to measure the reflectance and interferometric phase of the thin-film structure at the same time. The experimental data are used to determine precisely the thickness of the SiO₂ thin film on silicon wafers of two crystallographic orientations and different dopant concentrations. We confirmed very good agreement between the experimental data and theory and revealed that the thin-film thickness, which varies with the type of silicon substrate, depends linearly on the wavelength at which minimum in the spectral reflectance occurs. Similar behaviour was revealed for the interferometric phase.     

Dispersive white-light spectral interferometry including the effect of thin-film for distance measurement

A spectral-domain white-light interferometric technique is used for measuring distances in a Michelson interferometer with a mirror represented by a thin-film structure (TFS) on a substrate. A fibre-optic spectrometer is employed for recording spectral interferograms that include wide wavelength range effects of dispersion in a cube beam splitter and multiple reflection within the TFS. Knowing the effective thickness of the beam splitter, its dispersion and parameters of the TFS and substrate, the positions of the second interferometer mirror are determined precisely by a least-squares fitting of the theoretical spectral interferograms to the recorded ones. We apply the technique to the beam splitter made of BK7 optical glass and to a uniform SiO₂ thin film on a silicon wafer. We compare the results of the processing that include and do not include the effect of the TFS.     

Maxima of the spectral reflectance ratio of polarized waves used to measure the thickness of a nonabsorbing thin film

A simple method to determine the thickness of a nonabsorbing thin film on an absorbing substrate from maxima of the ratio between the spectral reflectances of p- and s-polarized components reflected from the thin-film structure is presented. The spectral reflectance ratio, which can be measured in a simple polarimetry configuration at a fixed angle of incidence, consists of maxima whose number and positions depend on the thickness of a thin film. An approximative linear relation between the thin-film thickness and a wavelength of the maximum of the reflectance ratio for a specific angle of incidence is revealed, provided that the wavelength-dependent refractive index of the thin film is known and the substrate is weakly absorbing. The relation permits the calculation of the thickness from the measured spectral reflectance ratio by using one maximum only, as is demonstrated theoretically for a SiO₂ thin film on a Si substrate. The application of this method is demonstrated experimentally for the same thin-film structure with different thicknesses of the SiO₂ thin film. The results are compared with those given by the algebraic fitting method, and very good agreement is confirmed.     

Deposited metamaterial thin film with negative refractive index and permeability in the visible regime

Thin films are fabricated from arrays of silver nanorods with thicknesses of 160?nm and 200?nm, to function as a metamaterial. The negative refractive index and negative permeability are retrieved from measured reflection and transmission coefficients using walk-off interferometer in the visible regime. A negative-index-material thin film with negative permittivity or (and) permeability can be produced by glancing angle deposition.     

Measurement of absolute phase Shift on reflection of thin films using white-light spectral interferometry

A novel method to measure the absolute phase shift on reflection of thin film is presented utilizing a white-light interferometer in spectral domain. By applying Fourier transformation to the recorded spectral interference signal, we retrieve the spectral phase function Ф, which is induced by three parts： the path length difference in air L, the effective thickness of slightly dispersive cube beam splitter Teff and the nonlinear phase function due to multi-reflection of the thin film structure. We utilize the fact that the overall optical path difference （OPD） is linearly dependent on the refractive index of the beam splitter to determine both L and Teff. The spectral phase shift on reflection of thin film structure can be obtained by subtracting these two parts from Ф. We show theoretically and experimentally that our new method can provide a simple and fast solution in calculating the absolute spectral phase function of optical thin films, while still maintaining high accuracy.     

System for measuring optical admittance of a thin film stack

A new method based on the polarization interferometer structure has been applied to measure the optical admittance, the refractive index and thickness of a thin film. The structure is a vibration insensitive optical system. There is one Twyman-Green interferometer part to induce a phase difference and one Fizeau interferometer part to induce the interference in the system. The intensities coming from four different polarizers were measured at the same time to prevent mechanical vibration influence. Using the polarization interferometer, the optical admittance, the refractive index and thickness of a single layer of Ta₂O₅ thin film has been measured. The measurement results were compared with the results obtained by ellipsometer. The results meet reasonable values in both refractive index and thickness.     

关于热生长SiO2薄膜厚度的测量

在半导体硅器件的研究工作中,需要准确地测量和控制SiO₂薄膜的厚度。由于干涉原理,SiO₂薄膜在白光照射下呈现颜色。但薄膜厚度与颜色相应的单色光的波长并不成简单的函数关系。本文叙述了用干涉显微镜测量热生长SiO₂薄膜厚度的方法。由测量结果得到SiO₂薄膜的折射率以及SiO₂和硅界面及空气和硅界面反射相移之差。并且测量了一组标准样品的薄膜厚度,列出了薄膜厚度与干涉颜色的对应关系。所得结果与从Rollet数据所推算的结果大致符合。样品厚度还包括了Rollet数据中所未包括的范围(3300—4200?)。     

Multilayer thin-film inspection through measurements of reflection coefficients

A vibration-insensitive interferometer is described to measure the thickness, refraction index and surface profile of thin-film stack at normal incidence. By satisfying the continuous boundary conditions of electric and magnetic fields at interfaces in a multilayer film stack, the reflection coefficient phase of the thin-film stack can be distinguished from the phase of spatial path difference, thus thickness and refraction index can be extracted. The experiment results showed that the measurement precision is significantly increased after the phase analysis was added into the reflectance analysis.     

Dependence of wavDependence of wavefront errors on nonuniformity of thin films

In contrast to uncoated substrate, a nonlinear relationship of phase shift with the thicknesses of the thin film makes the calculation of wavefront aberration complicated. A program is compiled to calculate the wavefront aberration of multilayer thin film produced by thickness nonuniformity. The physical thickness and the optical phase change on reflection are considered. As an example, the wavefront aberration of the all-dielectric mirror is presented in ArF excimer lithography system with a typical thickness distribution. In addition, the wavefront errors of the thin film at wavelengths of 193 and 633 nm are compared in the one-piece and two-piece arrangements. Results show that the phase shift upon reflection of the thin film produced by thickness nonuniformity is very sensitive to the incident angle, wavelength, and polarization.     

用迈克尔逊干涉仪测量全息干板膜厚度

全息干板膜的厚度是全息干板的重要参数之一。使用迈克尔逊干涉仪和白光光源对2种全息干板膜厚度进行测量，并对测量结果误差进行分析，给出了测量误差与膜厚及折射率之间的关系以及此方法的适用范围。研究结果表明：在膜厚从8μm增至41μm的过程中，测量结果的绝对误差≤2μm且变化很小，相对误差则从14.1%降到了2.2%。随着膜厚的增加，相对误差明显降低；折射率n也参与了误差传递，其值与测量误差呈类似反比关系；当n值在1.5附近时，为保证测量的准确性，所测膜厚≥40μm。最后指出，迈克尔逊干涉仪在测量全息干板膜等较厚的薄膜时，具有测量范围大，结果较准确等优点。     

Reflectometry technique for studying metal nanolayers on a substrate

A new noncontact technique is proposed for determining the parameters of nanosized metal coatings (absorption coefficients, refractive indices, and thicknesses). It is based on processing the measured angular dependence of the energy reflection coefficient of a polarized laser beam reflected by a thin-film structure surface. Features of determining the parameters of films on silicon substrates have been considered.     

Thin film characterization by laser interferometry combined with SIMS

Thin film properties of technologically important materials (Si, GaAs, SiO₂, WSi_x) have been measured by using a novel technique that combines secondary ion mass spectrometry (SIMS) and laser interferometry.The simultaneous measurement of optical phase and reflectance as well as SIMS species during ion sputtering yielded optical constants, sputtering rates and composition of thin films with high depth resolution. A model based on the principle of multiple reflection within a multilayer structure, which considered also transformation of the film composition in depth and time during sputtering, was fitted to the reflectance and phase data. This model was applied to reveal the transformation of silicon by sputtering with O ₂ ⁺ ions. Special attention was paid to the preequilibrium phase of the sputter process (amorphization, oxidation, and volume expansion). To demonstrate the analytical potential of our method the multilayer system WSi_x/poly-Si/SiO₂/Si was investigated. The physical parameters and the stoichiometry of tungsten suicide were determined for annealed as well as deposited films. A highly sensitive technique that makes use of a Fabry-Perot etalon integrated with a Michelson type interferometer is proposed. This two-stage interferometer has the potential to profile a sample surface with subangstroem resolution.     

A new technique to measure the phase characteristics of laser mirrors based on semiconductor heterostructures

A reflection interferometer based on a thin metal film is proposed to measure the phase of the reflection spectrum of laser mirrors. The device is applied to the study of the phase characteristics of the all-semiconductor mirror which combines the functions of the saturable absorber and the dispersion compensator (all-in-one) in the Nd³⁺:KGd(WO₄)₂ laser operating in the ultrashort-pulse regime. The method provides improvement of spectral resolutions and an increase in the accuracy in the measurement of the phase characteristics.     

Full X-ray pattern analysis of vacuum deposited pentacene thin films

Pentacene thin films with thicknesses ranging from 10 nm to 180 nm are investigated by specular X-ray diffraction in the reflectivity regime and in the wide angular regime. The results of the reflectivity measurements show a clear shift of the 001 reflection of the thin film phase depending on the layer thickness. It is shown that this shift can be explained by the dynamical scattering theory. The wide angular regime measurements show the 00L of the thin film phase. Williams-Hall plots are used to extract information on the crystallite size and mean micro strain of the thin film phase. The crystallite size is in good agreement with the results obtained by the reflectivity measurements. From this it can be concluded that the thin film phase crystallites are extended over the entire film thickness down to the substrate. Additionally an increase of the micro strain with increasing film thickness is observed.     

Determination of piezoelectric coefficients of ferroelectric thin films using GaAs:Cr adaptive interferometer

We report on simple interferometric technique for the measurement of piezoelectric coefficients of thin films using GaAs:Cr adaptive photodetectors in the geometry of modified Mach–Zehnder interferometer. The technique needs no special vibroinsulation and automatically adjusts and keeps the operation point of the interferometer. Strong hysteresis effects with a slightly asymmetric form of the hysteresis loop were observed at the dependence of d₃₃ coefficients of the Pb(Zr,Ti)O₃ (PZT) thin film versus DC electric field. The obtained values of d₃₃ coefficients are in agreement with known data.