Yu-Faye Chao

Photoelastic modulated imaging ellipsometry by stroboscopic illumination technique

A novel stroboscopic illumination technique is applied in a photoelastic modulated (PEM) ellipsometry to conquer the slow imaging processing of charge-coupled device camera system and form a fast imaging ellipsometry. The synchronized ultrastable short pulse is used to freeze the intensity variation of the PEM modulated signal. The temporal phase is calibrated with respect to the time reference of PEM. The laser diode is modulated by a programable pulse generator for triggering four short pulses at their specific temporal phase angle. The two-dimensional (2D) ellipsometric parameters can be deduced from those recorded four images. Therefore, the 2D thickness profile of a patterned sample can be measured; a static patterned SiO2 thin film on silicon substrate and the drainage behavior of matching oil on silicon wafer were studied by this imaging ellipsometry.

Calibrations of phase modulation amplitude of photoelastic modulator

A multiple harmonic intensity ratio technique is proposed for calibrating the modulation amplitude (Δ0) of a photoelastic modulator (PEM). A data acquisition system is utilized to investigate the frequency response of this technique. Δ0 determined by this technique is independent of frequency, which is proved using the reflection and transmission setups. In addition to confirm our calibration using the digitized oscilloscope waveform, we also obtain a set of ellipsometric parameters under various values of Δ0 before and after calibration. We also introduce a correction factor to correct the effect caused by the shift of the modulation amplitude in the process of etching. An optical thick film is used to calibrate Δ0 using PEM ellipsometry, and its refractive index and extinction coefficient are also obtained in etching. Finally, we suggest the use of the traces of the ellipsometric parameters under various thicknesses for monitoring instead of calculating the thickness in real time.

The ellipsometric measurements of a curved surface

A three-intensity imaging ellipsometric technique is proposed to investigate the surface topography as well as the refractive index profile (RIP) of a lens. The azimuth deviation of polarizer caused by the tilting of a SiO2 thin film on Si substrate was investigated after a careful calibration on the azimuth position of polarizer of the water-surface. The azimuth deviation of polarizer is proved to be the local surface normal; thus we can determine not only the radius of curvature of a Plano-Convex lens from the measurement, but also its incident-angle-corrected RIP.

Index Profile of Radial Gradient Index Lens Measured by Imaging Ellipsometric Technique

A simple three-intensity imaging ellipsometric technique is proposed for measurement of the refractive index profile (RIP) of a radial gradient index (GRIN) lens. According to our numerical analysis, the improved ellipsometric parameters measured by this method are valid as long as the azimuth deviation of the polarizer is less than 3°. A BK7 glass and a radial GRIN lens were measured. A fairly flat refractive index surface profile was obtained for the glass within a 0.3% error. The on-axis refractive index of the radial GRIN lens and its RIP are well fitted to the specifications provided by the manufacturer. Instead of the refracted-ray method, we provide a reflective and nondestructive measurement technique for measurement of the gradient index of a flat surface.

Determination of optical parameters of a twisted-nematic liquid crystal by phase-sensitive optical heterodyne interferometric ellipsometry

What is believed to be a novel phase-sensitive optical heterodyne interferometric ellipsometer is set up to characterize a twisted-nematic liquid crystal (TN-LC) by the elliptical parameters of the output polarization state. This ellipsometer presents the advantages of both polarized optical heterodyne interferometry and optical photometry, which introduce a polarization modulation that is capable of performing with high-sensitivity on phase detection in real time. The twist angle phi and the untwisted phase retardation gamma of TN-LC are measured precisely. The experimental results verify that a TN-LC can be treated as identical to an elliptical retarder.

A three-intensity technique for polarizer-sample-analyser photometric ellipsometry and polarimetry

This work presents a novel three-intensity-measurement technique to determine the ellipsometric parameters and in a polarizer-sample-analyser photometric ellipsometer. This technique can be employed to correct the azimuthal misalignment of the analyser with respect to the plane of incidence. By performing two sets of measurements with this technique with the polarizers azimuth at and , respectively, we can simultaneously determine the azimuthal deviation of the polarizer and further improve the ellipsometric measurements. Applying this technique in the transmission mode allows us to obtain the phase retardation and the optical axis of a waveplate at the same time.

Analytical solutions of the azimuthal deviation of a polarizer and an analyzer by polarizer-sample-analyzer ellipsometry

The analytical solutions of the azimuthal deviation of a polarizer and an analyzer were obtained by polarizer-sample-analyzer ellipsometry with a three-intensity measurement technique. By performing two sets of this three-intensity measurement with the polarizers azimuth set at 45 degrees and at -45 degrees , we were able to obtain a set of ellipsometric parameters free from the azimuthal deviations of the polarizer and the analyzer.

Azimuth Alignment in Photoelastic Modulation Ellipsometry at a Fixed Incident Angle

A high intensity ratio technique is proposed to align all the azimuthal angles of a photoelastic modulation ellipsometric system in a fixed incident angle. This technique is used to determine the azimuthal orientations of the polarizer, the photoelastic modulator and the analyzer to the incident plane. Two pre-designed testing samples and two probing wavelengths for a thin film are introduced to locate the incident plane by the intensity ratio technique in a polarizer-sample-analyzer ellipsometric setup. Then, the azimuth of the photoelastic modulator is directly obtained from two DC radiances separated by 45°. In addition to azimuth deviation, the ellipsometric parameter Ψ can also be determined from the same measurement for determining the incident angle on-line.

An error evaluation technique for the angle of incidence in a rotating element ellipsometer using a quartz crystal

The error in the angle of incidence for a rotating element ellipsometer is evaluated using a uniaxial quartz crystal. At a fixed angle of incidence with respect to the surface of reflection, the ratio of reflectance in the parallel to that in the perpendicular electromagnetic field is measured by rotating the quartz crystal through a full cycle. We determine the deviation in the angle of incidence by comparing the experimentally measured reflectance ratio to its calculated value.

ELLIPSOMETRIC MEASUREMENTS AND ITS ALIGNMENT - USING THE INTENSITY RATIO TECHNIQUE

Using first-order treatment on azimuth errors of the polarizer (P) and analyzer (A) with respect to the plane of incidence (POI), we construct two intensity ratios around a certain configuration, such as P=±π/4 and A=0 as compared to A=π/2. These expressions can be used not only to align the azimuths of the polarizer and analyzer to the POI, but also to obtain the ellipsometric parameter ψ without locating the minimum intensity. BK7 glass and SiO2/Si thin film are ultilized to evaluate this technique.