Characterization of Thin Film Parameters Based on Polarization Properties of Vector Beams
Objective Layered thin film characterization is significant for the fabrication of micro/nano structures.It is necessary to accurately measure refractive indices and thicknesses of films for ensuring the performance of micro/nano structures.As ellipsometry has high efficiency without intrusion,it nowadays serves as a metrology workhorse for critical dimension determination of nanostructures by comparing measured phase retardation and intensity variation between s/p-polarized reflected beams with theoretical prediction.However,traditional ellipsometry employs a quasi-plane wave to illuminate the sample,resulting in low spatial resolution and potential interference of the reflected light at the other surface for transparent substrates.Additionally,the illumination and detecting arms should be mechanically rotated to adjust the illumination angle for angle-resolved measurements,which requires high stability and reliability.Thus,it is desirable to develop a metrology system capable of measuring without mechanical movements.To this end,we propose a polarization imaging system with a tightly focused vector beam as the light source.As rays from different positions of the aperture provide angle-resolved illumination,the reflected spot images contain information on multi-angle s/p-polarized reflection coefficients,which can be further employed to retrieve film parameters.Compared with ellipsometry,the spot size is close to the diffraction limit in the proposed method,which significantly improves the spatial resolution,reduces the focal depth,and helps avoid mechanical rotation.Methods A numerical procedure is developed to simulate the reflection of a vector beam on layered films.The amplitude of rays from different positions of the pupil is traced during the reflection based on coordinate system transformation.The angular spectrum theory is adopted to calculate the propagation of focused beams in the free space.By utilizing the proposed numerical method,datasets relating x/y-polarized reflected spot images with different film parameters are created,and a parametric study is performed to examine the sensitivity of reflected spot images to film parameter variation.Meanwhile,we investigate the potential influences of noise on the parameter retrieval accuracy and build an experimental setup to perform the measurement.A linearly polarized plane wave is focused by an objective with a high numerical aperture to generate a tightly focused beam for illumination.The reflected beam is collected by the objective and captured by a camera after being filtered by an analyzer.Film parameters are determined by searching the dataset for spot images that mostly agree with the measured one.Results and Discussions Numerical simulation is first performed to deepen the understanding of the dependence of reflected spot images on film parameters.It is shown that a slight variation in film parameters leads to observable changes in x/y-polarized spot images,which demonstrates the high sensitivity of the method.Independent multiplicative noises are deliberately introduced to examine the system robustness.The errors are respectively less than 0.005 and 1.5 nm for the refractive index and thickness while the noise level is 3％.It indicates that due to the information on multi-angle reflection coefficients included in spot images,the system is highly robust against noise influences,which helps lower the requirement for the detection environment.A bare silicon wafer is employed to calibrate the transmission coefficients of the beam splitter for s/p-polarized beams by comparing experimental measurements and theoretically predicted intensity.Commercial single-layer SiO2 films with thicknesses of 100 nm,200 nm,and 300 nm on silicon substrates are finally measured to validate the system.The discrepancy in thickness measurement between the proposed polarization imaging system and commercial spectroscopic ellipsometry is less than 2 nm.Additionally,variations of thickness and refractive index are less than 0.2 nm and 0.003 in consecutive seven measurements,demonstrating the high stability of the polarization imaging system.Conclusions In response to the demand for ellipsometry with a high spatial resolution,we report a polarization imaging metrology system with a tightly focused vector beam for illumination.An experimental setup capable of measuring the reflected light field distribution in different polarization directions is built.Numerical simulation of the reflected light field is conducted and a dataset of the relationship between film parameters and reflected light field is established to retrieve the film parameters.Simulation results show that the reflected light field is highly sensitive to film parameters,which reveals the information of film parameters.Since it contains information on reflection coefficients of multi-angle rays,the system has high robustness against noise and can be adopted to characterize thin films.The experiment on a commercial single-layer SiO2 film on a silicon substrate is performed.The deviation of film thickness is less than 2 nm,and the measurement uncertainty is less than 0.2 nm.Compared with traditional ellipsometers,our polarization imaging system has higher spatial resolution and smaller focal depth.We believe it can find a broad range of applications in nanostructure characterization.
polarizationvector beamthin film parameterreflectioninverse problem
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