Nondestructive analysis of lithographic patterns with natural line edge roughness from Mueller matrix ellipsometric data
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Keywords:
Ellipsometry
Mueller calculus
Line (geometry)
Matrix (chemical analysis)
Surface roughness of part was vital to its application.40Cr material was irradiated by large scale pulse electron beam with orthogonal experiment and the surface roughness was checked.The results indicate that the surface roughness of 40Cr is changed by different electron beam parameters.Surface roughness of part increases or decreases in terms of electron beam parameter.The samples with high and low surface roughness are tested with electron beam respectively.The results show that the surface roughness decreases with irradiation numbers increasing in high original surface roughness,contrary surface roughness increases with irradiation numbers increasing in low original surface roughness.It is analysed that the surface roughness is influenced in two opposite sidedness when it is modified on the surface with pulsed electron beam.
Electron beam processing
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We develop the method for determining the Mueller matrix elements using standard photometric ellipsometer. Small ellipsometer design changes give an opportunity to completely determine all elements of the Mueller matrix. It is shown how the values of Mueller matrix elements can be obtained from the measurements at different azimuthal positions of optical units.
Mueller calculus
Ellipsometry
Matrix (chemical analysis)
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Ellipsometry is an optical technique used for studies of thin films and surfaces. The technique is based on measurement and analysis of the changes in the state of polarization that occur when polarized light is reflected on a sample surface.The multichannel Mueller matrix ellipsometer is a new system that is about to enter the commercial market. It can measure the full 4x4 Mueller matrix of a sample.The Laboratory of Applied Optics at the Department of Physics, Chemistry and Biology at Linkopings University has purchased one such multichannel Mueller matrix ellipsometer, called RC2, from J.A. Woollam Co., Inc.This project has the objective to investigate potentials and limitations of this new ellipsometer. This is done by comparing measurements carried out on RC2 with similar measurements made on a different, well known ellipsometer system, the VASE ellipsometer.A study of the theoretical background of ellipsometry has been made including a description of the Jones formalism of describing optical properties as well as the Stokes/ Mueller formalism.A short theoretical description of the RC2 principles, in order to better understand the new ellipsometer is also given.Measurements have been made on samples of varying complexity, including isotropic and anisotropic samples with in-plane anisotropy and out-of-plane anisotropy.On samples with no depolarization there should be no difference between the two ellipsometers. As can be seen in the experimental results there is some difference, but very little. Both for the isotropic samples, where Δ and ψ have been measured, and anisotropic, where the full Mueller matrix has been measured, we find a good match between VASE and RC2.When the samples are depolarizing, we expect to see a difference in the Mueller matrix. We do notice a significant difference in the measurements on tilted nanometer rods of TiO2, which has an advanced nano-structure in the upper layer. We can thus conclude that samples with depolarizing properties reveal this when measured with the new RC2 ellipsometer.
Mueller calculus
Ellipsometry
Stokes parameters
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Mueller calculus
Ellipsometry
Polarizer
Matrix (chemical analysis)
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Mueller calculus
Ellipsometry
Chirality
Dichroism
Matrix (chemical analysis)
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Mueller calculus
Ellipsometry
Reflection
Matrix (chemical analysis)
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Optical Constants are the fundamental thermophysical properties of materials, and spectroscopic ellipsometry (SE) has been widely applied to measure the optical constants of solids. During the ellipsometric measurements, the surface micro-roughness is one key issue, which will induce some derivation of the optical constants from the true values. The roughness layer (RL) model based on the effective medium approximation has been routinely employed to consider the effects of the surface micro-roughness, yet the accuracy of the RL model remains unverified. In this work, the SE parameters of aluminum rough surfaces with 1D micro-structure at different incident angles are calculated with the rigorous coupled wave analysis (RCWA) method. The optical constants are then derived from the SE parameters to simulate the experimental optical constants determination process by SE. By comparing the optical constants derived from the SE parameters with the true values, the effects of micro-roughness and incident angle are analyzed. The results show that the relative errors of the optical constants increase with the surface micro-roughness, and the RL model could reduce the influence of the roughness effectively. Moreover, the relative errors decrease significantly with increasing incident angle. It concludes that the accuracy of the optical constants determined by SE could be improved by reducing the surface roughness and performing the SE measurements at large incident angles.
Ellipsometry
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Mueller calculus
Ellipsometry
Matrix (chemical analysis)
Matrix method
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The object of ellipsometry is to determine the complex ratio ρ (ρ=tanifi exp(i&) ) of the reflected or transmitted polarization state parameters. Ellipsometry has traditionally been used as a tool for measuring the optical constants (n,k) of a surface, or when given the optical constants of the substrate, to determine some property such as the thickness of a thin film. The operation of a Photo Elastic Modulator (PEM) type ellipsometer is described in Mueller matrix terms. The phase shift (6) between orthogonal polarization components and the relative amplitude ratio (tan b) is contained in the Mueller matrix elements and can be obtained via combinations of measlired matrix elements using no mechanical motion. Polarization modulation ellipsometry offers a fast automatic means for obtaining the Mueller matrix for an optical component or system. A computer controlled implementation is described along with simple algorithms to extract the ellipsometric constants. Experimental results for a low phase shift "standard" reflector are given.
Ellipsometry
Matrix (chemical analysis)
Matrix algebra
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To accurately determine the thickness of ultrathin films, the influence of roughness on ellipsometric measurements must be examined Although ellipsometry has been applied to study roughness, quantitative relationship of Si surface roughness measured by ellipsometry and atomic force microscopy is not available. This leads to difficulties in estimating the influence of roughness on oxide thickness measurements. Here we first establish the correlation of roughness measured by these two techniques. Based on such a relationship, we can explain the discrepancy of oxide thickness measured by ellipsometry and surface sensitive techniques.
Ellipsometry
Silicon oxide
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