White-light Spectral Interferometer Research Articles

Simultaneous film thickness and refractive index measurement using a constrained fitting method in a white light spectral interferometer.

Film is widely used in optoelectronic and semiconductor industries. The accurate measurement of the film thickness and refractive index, as well as the surface topography of the top and bottom surfaces are necessary to ensure its processing quality. Multiple measurement methods were developed; however, they are limited by the requirements of a known dispersion model and initial values of thickness and refractive index. Further, their systems are rarely compatible with surface topography measurement methods. We propose a constrained nonlinear fitting method to simultaneously measure the thickness and refractive index of film in a simple white-light spectral interferometer. The nonlinear phase extracted by the spectral phase-shifting is fitted with the theoretical nonlinear phase obtained by multiple reflection model. The constraints of nonlinear fitting are obtained by the interferometric signal of vertical scanning, reconstructed by the integration of the white-light spectral signal to avoid local minima. The proposed method does not require a priori knowledge of the dispersion model and initial values of thickness and refractive index, and its system is compatible with the vertical scanning interferometry (VSI) method to reconstruct the surface topography of the top and bottom surfaces of film. Three SiO2 films with different thicknesses are measured, and the results show that the measured refractive index is within the theoretical value range of wavelength bandwidth and the measured thicknesses are closely aligned with the values provided by the commercial instrument. The measurement repeatability of refractive index reaches 10-3. Measurements on a polymer film demonstrate that this method is feasible for measuring the film without a priori information.

Accuracy improvement of a white-light spectral interferometer using a line-by-line spectral calibration method

Smile distortion caused by aberration of the optical system is the key factor that affects the spectral calibration of a white-light spectral interferometer. To improve the accuracy of surface metrology, this paper proposes a novel calibration approach based on a line-by-line method. An acousto-optic tunable filter (AOTF) is adopted for the wavelength scanning process during calibration. By fitting sufficient calibration data, a more accurate relationship between wavelength and pixel position can be obtained. The simulation results show that the accuracy of surface metrology has different sensitivities to the coefficients of the calibration equation, and that the effect of smile distortion becomes more severe as the optical path difference increases. The presence of smile distortion is confirmed in the calibration experiment of a home-built white-light spectral interferometer. Subsequently, a silicon wafer and a standard step of 1.806 ± 0.011 μm are tested using the calibrated metrology system. The measurement results demonstrate that the line-by-line calibration method performs well in correcting spectral distortion and can improve the measurement accuracy of surface profile.

Analysis of the synchronous phase-shifting method in a white-light spectral interferometer.

For white-light spectral interferometry, the phase information is usually retrieved via the Fourier transform method and the temporal phase-shifting method. In comparison, the synchronous phase-shifting method can be used to synchronously acquire interferometric signals with good accuracy and reduced noise. Therefore, it has potential for online measurement and is suitable for application in precision industries and for ultrahigh-speed measurement. In this work, a white-light spectral interferometer for synchronous phase shifting based on polarization interference was built, and the two-step phase-shifting algorithm was used to retrieve phase information. A variety of spectral interferometric signals were simulated based on the mathematical model of the two-step phase-shifting algorithm to illustrate the effects of differences in intensity and envelope shape, random noise, and phase-shift error on measurement of the absolute distance. Measurements of the absolute distance were conducted, and they indicated that the system had high accuracy.

Nonlinear phase error analysis of equivalent thickness in a white-light spectral interferometer

Abstract A white light spectral interferometry based on a Linnik type system was established to accurately measure the thin film thickness through transparent medium. In practical work, the equivalent thickness of a beam splitter and the mismatch of the objective lens introduce nonlinear phase errors. Adding a transparent medium also increases the equivalent thickness. The simulation results show that the equivalent thickness has a significant effect on thin film thickness measurements. Therefore, it is necessary to perform wavelength correction to provide a constant equivalent thickness for beam splitters. In the experiments, some pieces of cover glasses as the transparent medium were added to the measured beam and then a standard thin film thickness of 1052.2±0.9 nm was tested through the transparent medium. The results demonstrate that our system has a nanometer-level accuracy for thin film thickness measurement through transparent medium with optical path compensation.

Rapid measurement of large step heights using a microscopic white-light spectral interferometer

A method for rapid measurement of large step heights is proposed. Owing to elimination of mechanical scanning processes, this method possesses a greatly reduced measurement time. The theory underlying the proposed method is described in detail. The single-shot spectral interferometric signal is recorded using a Linnik microscopic white-light spectral interferometer and phase information is retrieved using a windowed Fourier transform. The proposed method was used to measure a 10.083(±0.022) μm step height standard. The mean measured height and standard deviation obtained from ten measurements were 10.0827 μm and 2.1 nm, respectively, and the experimental results agreed well with the calibrated value.

Film thickness measurement based on nonlinear phase analysis using a Linnik microscopic white-light spectral interferometer.

Based on white-light spectral interferometry and the Linnik microscopic interference configuration, the nonlinear phase components of the spectral interferometric signal were analyzed for film thickness measurement. The spectral interferometric signal was obtained using a Linnik microscopic white-light spectral interferometer, which includes the nonlinear phase components associated with the effective thickness, the nonlinear phase error caused by the double-objective lens, and the nonlinear phase of the thin film itself. To determine the influence of the effective thickness, a wavelength-correction method was proposed that converts the effective thickness into a constant value; the nonlinear phase caused by the effective thickness can then be determined and subtracted from the total nonlinear phase. A method for the extraction of the nonlinear phase error caused by the double-objective lens was also proposed. Accurate thickness measurement of a thin film can be achieved by fitting the nonlinear phase of the thin film after removal of the nonlinear phase caused by the effective thickness and by the nonlinear phase error caused by the double-objective lens. The experimental results demonstrated that both the wavelength-correction method and the extraction method for the nonlinear phase error caused by the double-objective lens improve the accuracy of film thickness measurements.

Wavelength correction for thin film measurement in a microscopic white light spectral interferometer

A film measuring method based on a new data model using a home-made microscopic white light spectral interferometer is proposed. It can improve the measuring accuracy of the thin film thickness at different OPDs. The influence of the effective thickness caused by the beam splitter prism in a Michelson interferometric objective is analysed and found not to be negligible while calculating the thin-film thickness. The linear relationship between the effective thickness and the optical path difference (OPD) can be removed by introducing a wavelength correction which made the effective thickness measurement more accurate. Some experiments on the film standard with calibrated film thickness showed that introducing a wavelength correction made the film thickness measurement more accurate at different OPDs.

Initial estimation of thin film thickness measurement based on white light spectral interferometry

White-light interferometry has been extended into the spectral domain for many years. The authors discuss a white light spectral interferometer using a Michelson interferometric objective and spectrometer to measure the film thickness and propose two methods for initial estimation which are based on the frequency of the nonlinear phase and the overall visibility of the spectral signal. Both of the methods are capable of obtaining good, rapid, initial estimates in these measurements: our proposed methods are quicker than the commonly used global algorithms (simulated annealing algorithm and genetic algorithm). In terms of the speed and precision, the proposed methods are suited to in-line, high-speed measurement. In general, when the film thickness is more than 1μm, it is better to use the method based on the nonlinear phase to estimate the initial value, and when the film thickness is <1μm, the method based on overall visibility is more applicable.

Supercontinuum generation from a multiple-ring-holes tellurite microstructured optical fiber pumped by a 2 μm mode-locked picosecond fiber laser

Supercontinuum (SC) generation from a highly nonlinear tellurite microstructured optical fiber with multiple rings of holes was demonstrated by pumping with a 2 μm mode-locked picosecond fiber laser. The chromatic dispersion of the fiber was measured with a homemade white-light spectral interferometer in a wide wavelength range and agreed with the theoretical calculation. Although the pumped wavelength was far from the zero dispersion wavelength, with flat dispersion profile of the fiber in the anomalous dispersion, the SC could be expanded from 650 to 2850 nm with launched pulse energy of several hundred picojoules. Simulations of SC generation agreed with the experimental results.

Group delay dispersion measurement of a dispersive mirror by spectral interferometry: comparison of different signal processing algorithms

We built a dispersive white-light spectral interferometer for precisely measuring the dispersion properties of a multilayer thin-film structure. A novel algorithm with improved robustness to measurement errors is presented by combining a windowed Fourier transformation with wavelet-based differentiation. Compared with previously published algorithms, this method shows substantial resistance to measurement errors. The group delay dispersion properties of bulk materials and a homemade chirped mirror are measured by our apparatus, and the measurement result manifests considerable accuracy and robustness. The technique shows reasonable potential for the characterization of ultrabroadband chirped mirrors.

基于白光频谱干涉测试光学薄膜的光学特性

基于白光频谱干涉测试光学薄膜的光学特性

An Improved Data Processing Method in Differential White Light Spectral Interferometry for the Measurement of Thickness of Ultra-Thin Metallic Foil

The accurate thickness measurement of Ultra-thin rolling metallic foil has an important role in industrial or some special applications. Unfortunately, commercial thickness meters do not provide high precision measurements non-destructively. A new spectral-domain interferometric method for measuring absolute thickness of Ultra-thin metallic foil is proposed here. The thickness is measured by differential white light spectral interferometer. Two differential Michelson Interferometers (MI) are used as basic measuring system to obtain the spectral interference fringes on the spectrometers. The spectral interference between both beams, which shows up a periodic modulation of the source spectrum with the period dependent on the OPD, serves as an illustration of a technique for measuring both OPDs and displacements in a range dependent on the source spectrum width. Therefore, the interference fringes only depend on the OPD due to the thickness of metallic foil and are unrelated to the position of the foils in the system, which is insensitive to the vibration. The spectral interference fringes are resolved over a wide spectral range and the absolute thickness of metallic foil can be calculated by measuring the OPD with a modified extremum method based on the least root mean square (RMS) deviation. The theoretical analysis and preliminary experiments indicate that the technique can measure the thickness of foils in the range of 1μm to 80μm, and it requires less than 50ms within the single measurement. Experimental results are presented.