Honggang Gu

Calibration of misalignment errors in composite waveplates using Mueller matrix ellipsometry

Composite waveplates consisting of two or more single waveplates are widely used in optical instruments, such as ellipsometry, polarimetry, cryptography, and photoelasticity. Accurate calibration of the misalignment errors in composite waveplates is of great importance (to minimize or correct the spurious artifacts in the final collected spectral data of these instruments induced by the misalignment errors). In this paper, we choose the fast axis azimuth and the rotary angle of composite waveplates as the detected characteristic parameters to calibrate the misalignment errors in composite waveplates. We first derive a general analytical model to describe the relationship between the mislignment errors and the characteristic parameters, and then propose an inverse approach to the calibration of the misalignment errors in composite waveplates. An experimental device based on the dual rotating-compensator Mueller matrix ellipsometry principle is set up to measure the characteristic parameters of composite waveplates. Both numerical simulations and experiments on an MgF(2)-MgF(2)-quartz triplate demonstrate the correctness and efficiency of the proposed approach. It is expected that the proposed approach can be readily extended to calibrate the misalignment errors in more complex composite waveplates.

Optimal broadband Mueller matrix ellipsometer using multi-waveplates with flexibly oriented axes

Accurate measurement of the Mueller matrix over a broad band is highly desirable for the characterization of nanostructures and nanomaterials. In this paper, we propose a general composite waveplate (GCW) that consists of multiple waveplates with flexibly oriented axes as a polarization modulating component in the Mueller matrix ellipsometer (MME). Although it is a common practice to make achromatic retarders by combining multiple waveplates, the novelty of the GCW is that both the retardances and azimuths of fast axes of the single-waveplates in the GCW are flexible parameters to be optimized, which is different from the conventional design where single-waveplates are usually arranged in symmetrical layout or with their fast axes parallel or perpendicular to each other. Consequently, the GCW can provide many more flexibilities to adapt to the optimization of the MME over a broad band. A quartz triplate, as a concrete example of the GCW, is designed and used in a house-made MME. The experimental results on the air demonstrate that the house-made MME using the optimally designed quartz triplates has an accuracy better than 0.2% and a precision better than 0.1% in the Mueller matrix measurement over a broad spectral range of 200~1000 nm. The house-made MME exhibits high measurement repeatability better than 0.004 nm in testing a series of standard SiO2/Si samples with nominal oxide layer thicknesses ranging from 2 nm to 1000 nm.

Accurate alignment of optical axes of a biplate using a spectroscopic Mueller matrix ellipsometer

The biplate that consists of two single wave plates made from birefringent materials with their fast axes oriented perpendicular to each other is one of the most commonly used retarders in many optical systems. The internal alignment of the optical axes of the two single wave plates is a key procedure in the fabrication and application of a biplate to reduce the spurious artifacts of oscillations in polarization properties due to the misalignment error and to improve the accuracy and precision of the systems using such biplates. In this paper, we propose a method to accurately align the axes of an arbitrary biplate by minimizing the oscillations in the characteristic parameter spectra of the biplate detected by a spectroscopic Mueller matrix ellipsometer (MME). We derived analytical relations between the characteristic parameters and the misalignment error in the biplate, which helps us to analyze the sensitivity of the characteristic parameters to the misalignment error and to evaluate the alignment accuracy quantitatively. Experimental results performed on a house-developed MME demonstrate that the alignment accuracy of the proposed method is better than 0.01° in aligning the optical axes of a quartz biplate.

A facile and environment-friendly method for fabrication of polymer brush

A novel environment-friendly system is proposed to fabricate polymer brush, which has the advantages including non-toxic and inexpensive initiator (eosin Y), visible-light exposure (λ = 515 nm), water medium and ambient environment. The experimental results from UV-Vis spectroscopy, AFM-based single molecule force spectroscopy (SMFS) and other measurements indicate that a polymer brush with a living nature is fabricated via free radical polymerization. This polymer brush may find applications in coatings, bio-interfaces and so forth.

Characterization of curved surface layer by Mueller matrix ellipsometry

The authors apply Mueller matrix ellipsometry to characterize the curved surface layers, by utilizing the noticeable anisotropy observed from the measured data. The authors demonstrate that this anisotropy is introduced by the curved surface shape as well as the misalignment between the illumination spot and the surface vertex. An optical model is proposed to expound the anisotropy, and is applied to evaluate the curved thin thermal oxide layer on a silicon sphere crown. After incorporating the proposed optical model in the parameter extraction, the experimental results show that not only will the accuracy of the oxide layer thickness measurement at an arbitrary location on the surface be improved, the curvature radius as well as the position of detection can also be determined directly.

Measurement errors induced by axis tilt of biplates in dual-rotating compensator Mueller matrix ellipsometers

Dual-rotating compensator Mueller matrix ellipsometer (DRC-MME) has been designed and applied as a powerful tool for the characterization of thin films and nanostructures. The compensators are indispensable optical components and their performances affect the precision and accuracy of DRC-MME significantly. Biplates made of birefringent crystals are commonly used compensators in the DRC-MME, and their optical axes invariably have tilt errors due to imperfect fabrication and improper installation in practice. The axis tilt error between the rotation axis and the light beam will lead to a continuous vibration in the retardance of the rotating biplate, which further results in significant measurement errors in the Mueller matrix. In this paper, we propose a simple but valid formula for the retardance calculation under arbitrary tilt angle and azimuth angle to analyze the axis tilt errors in biplates. We further study the relations between the measurement errors in the Mueller matrix and the biplate axis tilt through simulations and experiments. We find that the axis tilt errors mainly affect the cross-talk from linear polarization to circular polarization and vice versa. In addition, the measurement errors in Mueller matrix increase acceleratively with the axis tilt errors in biplates, and the optimal retardance for reducing these errors is about 80°. This work can be expected to provide some guidences for the selection, installation and commissioning of the biplate compensator in DRC-MME design.

Development of a tomographic Mueller-matrix scatterometer for nanostructure metrology

In this paper, we describe the development of a novel instrument, tentatively called tomographic Mueller-matrix scatterometer (TMS), which enables illuminating sequentially a sample by a plane wave with varying illumination directions and recording, for each illumination, the polarized scattered field along various directions of observation in the form of scattering Mueller matrices. The incidence angle is varied from 0° to 65.6° with the rotation of a flat mirror that changes the position of the focal point of a light beam on the back focal plane of a high numerical aperture objective lens. The scattering Mueller matrices are collected over a wide range of scattering angles (0°-67°) and azimuthal angles (0°-360°). The developed instrument was then applied for the measurement of nanostructures in combination with an inverse scattering problem solving technique. The experiment performed on a periodic nanostructure preliminarily demonstrates the performance of TMS as well as its potential in nanostructure metrology. It is expected that the TMS would be a powerful tool for characterizing the polarized scattered-field distributions and measuring nanostructures in nanomanufacturing.

Optimal design of wide-view-angle waveplate used for polarimetric diagnosis of lithography system

The diagnosis and control of the polarization aberrations is one of the main concerns in a hyper numerical aperture (NA) lithography system. Waveplates are basic and indispensable optical components in the polarimetric diagnosis tools for the immersion lithography system. The retardance of a birefringent waveplate is highly sensitive to the incident angle of the light, which makes the conventional waveplate not suitable to be applied in the polarimetric diagnosis for the immersion lithography system with a hyper NA. In this paper, we propose a method for the optimal design of a wideview- angle waveplate by combining two positive waveplates made from magnesium fluoride (MgF2) and two negative waveplates made from sapphire using the simulated annealing algorithm. Theoretical derivations and numerical simulations are performed and the results demonstrate that the maximum variation in the retardance of the optimally designed wide-view-angle waveplate is less than ± 0.35° for a wide-view-angle range of ± 20°.

Correction of depolarization effect in Mueller matrix ellipsometry with polar decomposition method

Mueller matrix ellipsometry has been demonstrated as a powerful tool for nanostructure metrology in high-volume manufacturing. Many factors may induce depolarization effect in the Mueller matrix measurement, and consequently, may lead to accuracy loss in the nanostructure metrology. In this paper, we propose to apply a Mueller matrix decomposition method for the Mueller matrix measurement to separate the depolarization effect caused by the MME system. The method is based on the polar decomposition by decomposing the measured depolarizing Mueller matrix into a sequence of three matrices corresponding to a diattenuator followed by a retarder and a depolarizer. Since the depolarization effects will be only reflected in the depolarizer matrix, the other two matrices are used to extract the structure parameters of the measured sample. Experiments performed on a one-dimensional silicon grating structure with an in-house developed MME layout have demonstrated that the proposed method achieves a higher accuracy in the nanostructure metrology.

Mueller matrix polarimeter with imperfect compensators: calibration and correction

We propose a method to calibrate the depolarization parameters of the imperfect compensators in dual-rotating compensator Mueller matrix polarimeters, and deduce a set of correction equations for the Mueller matrix calculation.