Development of Visible Light Imaging Ellipsometer for Quantitative Characterizing of Thin Films and 2D Structured Materials

Abstract

Polarimetry is a powerful optical characterization technique with many important applications in material science, electronic, optoelectronic, and biophotonic applications. In the realm of technological applications, for example, it holds an important place comparable to contact metrology such as atomic force microscope (AFM) and vacuum-based, and destructive, metrology as scanning and transmission electron microscopies (SEM, TEM). The advantages of polarimetry are, as an optical characterization technique, non-destructive, low cost, and high throughput and can work in a wide range of environments, including standard laboratory conditions, vacuum, controlled atmosphere and liquids, and extremely harsh conditions such as in the presence of plasmas. Furthermore, it can measure buried structures and complex grating line shapes, side-wall’s height, inclination, and mean roughness, which presents a considerable challenge for other techniques. In an ellipsometry measurement, an incident beam of known polarization state illuminates the sample surface, and its polarization state after reflection is analyzed to infer the sample information, including important material characteristics such as composition, roughness, and density, among others. In most current commercial instrumentation, these measurements are taken as an average over the illumination spot size of ~ 3 mm in diameter for collimated beams and ~25 to 300 μm for a focused beam. Therefore, the reflected light is superimposed for structured samples with feature sizes smaller than the beam spot size and cannot accurately resolve the features of interest. Besides the reconstruction of structured samples, the combination of ellipsometry with imaging techniques finds applications in multiplexing sensing, bio-imaging, and combinatorial material strategies. The driving goal of this work is to develop and flexible imaging ellipsometer strategy capable of achieving pixel-sized resolution, smaller than the micro-focused limit of current ellipsometry techniques.

In the first part of the thesis, we study the optical properties of perovskite solar cell materials using a commercial, single rotating-compensator multichannel spectroscopic ellipsometer (SE), Model-2000DI, from J. A. Woollam Co.. The Fresnel equations and matrix transfer formalism is used in the companion data analysis software, CompleteEASE (J.A. Woollam Co.), to model the experimental data. The focus of this work is on the characterization of the thin electron transfer layer made of high-quality TiO₂ by the spray pyrolysis deposition method. In particular, we studied two types of TiO₂ films, namely, compact TiO₂ and mesoporous TiO₂, denoted, respectively, as CL and mp, as well as bilayers CL/mp. It is found that these TiO₂ bilayers increase optical transparency, enabling high energy conversion efficiency (ECE). The complex refractive index data of single-layer TiO₂ was determined from the modeling of SE and transmission (T) data on glass and FTO substrates. The retrieved complex refractive index data from the single-layers were then used to model the double-layers TiO₂ (TiO₂-CL/TiO₂-mp) optical response. Our results pave the way used to theoretically optimize advanced perovskite solar cells using 3D transparent conductive electrodes to minimize front-face reflection losses. This optimization relies on a three-dimensional finite-difference time-domain (FTDT) simulation to study the photonic performance and charge generation rates, whereas a finite element method (FEM) simulation allows the modeling of the charge carrier transfer and the solar cell’s electrical characteristics.

The second part of the thesis deals with the development of a spectroscopic rotating polarizer Imaging ellipsometer (RPIE). Combining ellipsometry with imaging techniques, RPIE measures the ellipsometric parameters Ψ and Δ map. The ellipsometer measures the Stokes parameters (vector). The number of Stokes parameters accessible by an ellipsometer differs according to the instrument configuration. An ellipsometer’s general design comprises a polarization state generator, sample, and polarization state detector. In the RPIE, a broad spectral halogen lamp is a light source coupled to the monochromator with a free-spaced multicore round-to-line optical fiber. The monochromator has interfaced with a computer through RS232, which allows scanning of the wavelength during measurement. A line-to-round multicore optical fiber collects output from the monochromator exit. The existing beam from the round side of the optical fiber becomes parallel. The parallel beam passes through a spatial filter, which generates a collimated light source for RPIE. The source arm is composed of a spatial filter and a polarization state generator. A linear polarizer coupled with a hollow shaft stepper motor and a hollow shaft encoder was connected with the stepper motor shaft. The detector arm is composed of an analyzer and a CMOS camera. Another linear polarizer is used as an analyzer, coupled with the hollow shaft of a stepper motor. The reflected beam passes through the analyzer and reaches the camera. A National Instruments© (NI) Data acquisition (DAQ)-based custom-made control system was developed to collect the encoder pulse, which is attached to the continuously rotating motor. The rotating motor controls the camera trigger and image indexing. The camera was configured in external trigger mode. The encoder pulse gets input as the camera’s trigger, and the camera exposure time is set based on the trigger pulse’s period. The stepper motor runs continuously to enable the collection of images, as the Hadamard sums.

In the RPIE configuration, the measurement of four sums per optical cycle enables the calculation of the Fourier coefficients and the instrument calibration which was performed using conventional strategies. The main modules developed include i) a LabVIEW DAQ-based custom controller system to control the monochromator, stepper motor, and camera; ii) a LabVIEW program to collect calibration and measurement data; and iii) a MATLAB code integrated with the LabVIEW program for data reduction. A USAF1951 imaging target was used as a test-sample to determine the instrument’s resolution. The standard Si/SiO₂ and imaging target measurement by the RPIE was compared with the commercial J. A. Woollam Co. ellipsometer, Model-2000DI. Details of design, calibration, measurement, and technological challenges are provided.

The final part of the thesis reports on the development of spectroscopic rotating compensator imaging ellipsometry (RCIE). While the RPIE’s optical configuration is simpler, and its optical components are fairly achromatic, it suffers some shortcomings as i) it cannot measure the S₃ component of the stokes parameter and ii) is susceptible of source polarization errors. Therefore, measurement errors increase for Δ~0º or 180º, and the measurement range of the Δ becomes half (0º ≤ Δ ≤ 180º) of the full range (-180º ≤ Δ ≤ 180º). On the other hand, the RCIE configuration can measure S₃, which allows us to measure the full range of Ψ and Δ. Moreover, this configuration enables the measurement of the wavelength-dependent degree of polarization, which facilitates the determination of the depolarization of the spectrum.

The polarization state generator of the RCIE design is improved by using a fixed polarizer as the first element after the light source collimation system followed by a compensator as a rotating component to modulate the polarization incident on the sample. Therefore, the configuration of the RCIE is fixed polarizer - rotating compensator – sample - fixed analyzer - detector. Since the polarizer and analyzer are static, this design eliminates i) residual source polarization and ii) detector polarization sensitivity as sources of systematic errors. Measuring five Hadamard sums per optical cycle allows the calculation of four Fourier coefficients (corresponding to the 2ω and 4ω frequency components, where ω is the rotation frequency of the compensator). The RCIE can measure accurate ∆ values near 0º and ∓180º (when the reflected becomes linearly polarized, such as transparent substrates) and can also measure ∆ over its entire range -180º < ∆ ≤ 180º.

In RCIE, the polarizer and analyzer connectors couple two hollow shaft stepper motors while the compensator holder is attached to a hollow shaft of the zero cogging continuously rotating dc motor. The dc motor encoder triggers the camera through a USB NI DAQ device, enabling the collection of five Hadamard sums in every optical cycle. We developed a custom LabVIEW program to control the monochromator, two stepper motors, continuous rotating dc motor, NI DAQ, and camera. A MATLAB code was integrated with the LabVIEW program to perform data reduction. A standard USAF1951 imaging target was used as a sample to determine the achieved lateral resolution. The standard Si/SiO₂ and imaging target measurement by the RCIE was compared with the commercial J. A. Woollam Co. ellipsometer, Model-2000DI. Details of design, calibration, measurement, and technological challenges are provided for the RCIE.

In the final chapter of the thesis, Conclusions and Future Work, we provide a perspective of the capabilities and strengths of the work done. This includes considerations on i) Mueller matrix ellipsometry (MME) that can provide all 16 elements of a 4 x 4 Mueller matrix, and ii) strategies for the reconstruction of complex nanostructure profiles such as rigorous coupled-wave analysis (RCWA), widely to simulate and reconstruct 1D nanomaterials, and the FDTD method.
 

Date of Award	21 Mar 2023
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Juan Antonio ZAPIEN (Supervisor)