The ultimate in real-time ellipsometry: Multichannel Mueller matrix spectroscopy

A review of the techniques and applications of multichannel ellipsometry in the dual-rotating-compensator configuration is given. This ellipsometric approach has been established as the ultimate in real-time, single-spot optical measurement, as it determines the entire 16-element Mueller matrix of a sample over a wide spectral range (up to 1.7-5.3 eV) from raw data collected over a single optical period of 0.25 s. The sequence of optical elements for this ellipsometer is denoted PC_1rSC_2rA, where P, S, and A represent the polarizer, sample, and analyzer. C_1r and C_2r represent two MgF₂ rotating compensators, either biplates or monoplates that rotate synchronously at frequencies of ω₁ = 5ω and ω₂ = 3ω, where π/ω is the fundamental optical period. Previous high-speed Mueller matrix measurements with this instrument have been performed on uniform, weakly anisotropic samples such as (110) Si, in which case one can extract the bulk isotropic and near-surface anisotropic optical responses simultaneously. In such an application, the instrument is operated at its precision/accuracy limits. Here, ex situ results on a strongly anisotropic, locally biaxial film are presented that demonstrate instrument capabilities for real-time analysis of such films during fabrication or modification. In addition, the use of the instrument as a real-time probe to extract surface roughness evolution on three different in-plane scales for an isotropic film surface is demonstrated for the first time.     

Multichannel mueller matrix ellipsometry for simultaneous real-time measurement of bulk isotropic and surface anisotropic complex dielectric functions of semiconductors

We have applied a dual rotating-compensator multichannel ellipsometer to acquire spectra ( approximately 2.0-4.6 eV) in all 16 elements of the Mueller matrix associated with a specularly reflecting surface, in a minimum time of 0.25 s. In this initial study, such results have been collected for the (110) silicon surface at an incidence angle of approximately 70 degrees and have been used to derive spectra in the bulk isotropic dielectric function epsilon (b)= epsilon (1b)-i epsilon (2b) and the surface-induced dielectric function anisotropy Delta epsilon =Delta epsilon (1)-iDelta epsilon (2). Thus, this instrument shows promise for simultaneous real-time measurement of epsilon (b) and Delta epsilon spectra in oblique reflection during the fabrication of semiconductor structures having bulk isotropic components.     

Calculations of the Mueller matrix for scattering of light from two-dimensional surfaces

Abstract

Results are presented of an analysis of the Mueller matrix parameters for the problem of scattering of light from two-dimensional rough surfaces. The Mueller matrix fully describes the polarization properties of the scattered light. It is shown, using symmetry arguments, that for normal incidence it is necessary to measure the Mueller matrix terms in only one plane, thus reducing the amount of data to be analysed. Examples of the form of the Mueller matrix terms are calculated using a simple ray-trace approach.     

Complete determination of the conical Mueller matrix for one-dimensional rough metallic surfaces

We present results of the complete determination of the Mueller matrix for the light scattered by a one-dimensional random rough metallic surface under a conical or out-the-plane of incidence geometry. We present and apply a reduced method for its complete determination. This reduced method considers only 16 intensity-polarized measurements instead of the 36 intensity-polarized measurements recently reported. Effects related with the enhanced backscattering were observed.     

Nematic films and radially anisotropic Delaunay surfaces

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoid in addition to other new surfaces.     

Polarization state and Mueller matrix measurements in terahertz-time domain spectroscopy

We derive the complete formulae governing the polarization state measurement in terahertz-time domain spectroscopy (THz-TDS) by using a rotatable THz polarizer. Four Stokes parameters can be uniquely obtained by spectrally-resolved measurement in THz-TDS. Further, we propose a new approach to measure the Mueller matrix of a pure birefringent material, using THz-TDS, by rotating the material under test. Based on the above techniques, we successfully measured the Mueller matrices of a quartz crystal in the frequency domain.     

Mueller matrix determination for one-dimensional rough surfaces: Four reduced measurement equivalent sets

There are several methods for the experimental determination of the Mueller matrix (MM) for a general scattering system. For the case of scattering in the plane-of-incidence, we apply the direct method of Mueller matrix ellipsometry to determine the MM associated to a one-dimensional scattering system. We show the MM for a 1-D surface can be determined with four different measurements from four equivalent sets consisting of four Stokes vector inputs and four analyzers. We show all the possible measurements can be reduced to a single set of four different intensity measurements.     

Mueller matrix for characterization of one-dimensional rough perfectly reflecting surfaces in a conical configuration

Theoretical results of the use of a Mueller matrix to characterize a one-dimensional rough perfectly reflecting, single-scattering surface in a conical configuration are presented. The conical Mueller matrix (CMM) is derived from the known Mueller matrix of this kind of surface in the plane of incidence [the plane Mueller matrix (PMM)]. The key argument is that, as the PMM is considered to be a Mueller-Jones matrix, an appropriate rotation of the complex amplitude matrix provides the conic Mueller matrix.     

Scattering by rough surfaces in a conical configuration: experimental Mueller matrix

A simple method for measuring the Mueller matrix associated with rough surfaces in a conical configuration is presented. I present result of experimental measurements of the Mueller matrix for the angular distribution of the light scattered by a one-dimensional gold-coated randomly rough surface in a conical configuration. Effects related to the phenomenon of enhanced backscattering are reported.     

Multichannel Raman spectroscopy of unroughened noble metal and non-noble metal films and tunnel junctions

We demonstrate that multichannel optical detectors provide the capability of observing Raman Scattering from molecular monolayers in solid-air and solid-solid interfaces in the absence of the conditions considered essential for surface enhanced Raman scattering. We present spectra of adsorbates on smooth Ag films, air-oxidized smooth Al films and Al gratings. Finally, we demonstrate a new configuration for surface enhanced Raman scattering which need not involve noble metals. Raman scattering from a doped Al/AlOx/Sn tunnel junction provides a specific example of such a configuration.     

光谱型椭偏仪对各向异性液晶层的测量

探讨了利用普通光谱型椭偏仪对各向异性液晶层进行综合性测量的可行性. 并利用法国Jobin Yvon公司的UVISEL SPME(Spectroscopic Phase Modulated Ellipsometer)光谱型椭偏仪测量了光学各向异性液晶层的折射率n_o和n_e及液晶层厚d，进一步利用椭偏仪在透射方式下测量了平行排列液晶层的光延迟特性Δnd，二者取得了很好的一致性，说明利用光谱型椭偏仪可以实现对光学单轴性液晶层及其他材料的测量，测厚精度为纳米量级. 关键词： 光谱型椭偏仪 各向异性 折射率 相位延迟     

Mueller matrix polarimetry for improved liver fibrosis diagnosis

An experimental Mueller matrix polarimeter is used to quantify human liver fibrosis by measuring retardance and depolarization of thin biopsies. The former parameter is sensitive to fibrillar collagen, the latter is specifically sensitive to fibrillar collagen around blood vessels, which is not significant for liver fibrosis diagnosis. By using depolarization like a filter, retardance distribution enables distinguishing between disease stages and limits the high degree of observer discrepancy.     

Least-squares analysis of the Mueller matrix

In a single-mode fiber excited by light with a fixed polarization state, the output polarizations obtained at two different optical frequencies are related by a Mueller matrix. We examine least-squares procedures for estimating this matrix from repeated measurements of the output Stokes vector for a random set of input polarization states. We then apply these methods to the determination of polarization mode dispersion and polarization-dependent loss in an optical fiber. We find that a relatively simple formalism leads to results that are comparable with those of far more involved techniques.     

Fluorescence spectroscopy of ultrathin molecular organic films on surfaces

We review our recent experiments by linear optical spectroscopy in the visible spectral range on interface controlled monolayers and thin films of π-conjugated organic molecules on well-defined surfaces. In particular, cw fluorescence and fluorescence excitation spectroscopy are considered. We discuss two interesting aspects: the possibility to prepare interface controlled films with non-bulk like structures, and consequently different and possibly superior optical properties, and the use of optical spectroscopy as an analytical tool to investigate properties of interfacial organic films.     

Studying surfaces and thin films using Mössbauer spectroscopy

Using a series of bi-layer samples, we show how Conversion Electron Mössbauer Spectroscopy (CEMS) and X-ray Backscatter Mössbauer Spectroscopy (XBS) can be done with the same experimental set up. The penetration depths of the K and L conversion electrons are measured as 51(6) and 330(240) nm, respectively, with relative contributions of 88(9) and 12(9)%. The penetration depth of the Fe-K _α X-ray signal is determined to be 3.6(2) μm. As a demonstration we show data on surface damage effects in electropolished TRIP steels, and by comparing CEMS and XBS Mössbauer patterns we estimate the thickness of a damaged layer (created by sanding) to be 550(50) nm.     

Decomposition algorithm of an experimental Mueller matrix

This study deals with the interpretation of experimental Mueller matrices. The understanding of such a matrix is not straightforward in the case, in particular, of a strongly depolarizing medium, which is therefore disturbed and where relevant pieces of information are often distributed among its various elements. As a result, information data need to be extracted by a decomposition of any Mueller matrix into simple elements to uncouple the existing polarimetric effects. This led us to develop an algorithm in order to characterize any depolarizing, or not, polarimetric system. In addition to differentiating the experimental noise from the intrinsic depolarization of the optical system under study, this algorithm proved to: (i) separate depolarization from birefringence and dichroism and (ii) characterize the isotropic or anisotropic nature of the depolarization. At last, this algorithm was validated through the study of several optical systems with different polarimetric properties.     

Characteristic properties of the conical Mueller matrix

We present results of mathematical relations existing between the Mueller matrix obtained for an in-plane of incidence scattering geometry (plane Mueller matrix, PMM) and the Mueller matrix obtained for an out-the-plane of incidence scattering geometry (conical Mueller matrix, CMM), for light scattered from a rough surface. We obtain a similarity relation between the CMM and the PMM for one- (1-D) and for two-dimensional (2-D) surfaces. This similarity relation implies that the PMM and the CMM have the same determinant, trace and eigenvalues for 1-D and 2-D surfaces, respectively. We can say that measurements made in the conical geometry are “Similarity Equivalent” to those in the in-plane geometry for both kind of surfaces, respectively.     

Optimization of a snapshot Mueller matrix polarimeter

We report on the optimization of a snapshot Mueller matrix polarimeter performed by using singular-value decomposition. The snapshot technique relies on wavelength polarization coding by four wave plates. The statistical noise on Mueller components is minimized through adjustment of the thickness of each plate. The spectrometer response and its cutoff frequency were considered to find the optimal configurations described here.     

Electron-energy-loss spectroscopy of C60 monolayer films on active and inactive surfaces

The characteristics of interaction between C₆₀ molecules and Si(1 1 1)-7×7, Ag/Si(1 1 1)-√3×√3 R30° and layered material MoS₂ surfaces have been investigated using electron-energy-loss spectroscopy (EELS). The EEL spectrum of C₆₀/Si(1 1 1)-7×7 shows a new peak at loss energy of 2.7 eV. This indicates the existence of charge transfer from the substrate to C₆₀ molecules. The EEL spectrum of a C₆₀ monolayer film grown on a cleaved surface of MoS₂ is almost the same as that of bulk C₆₀. The EEL spectrum of a C₆₀ monolayer film on an Ag/Si(1 1 1) surface is quite different from that on a clean Si(1 1 1)-7×7 surface, although the films on those substrates have the same epitaxial arrangement. Furthermore, intensities of energy-loss peaks of C₆₀/Ag/Si(1 1 1) are slightly smaller than those of C₆₀/MoS₂ in spite of having the same loss-energy. This suggests that the interaction between C₆₀ molecules and the Ag/Si(1 1 1) surface is stronger than that between C₆₀ molecules and the MoS₂ surface.     

MathCAD在椭圆偏振仪测定薄膜光学常数中的应用

薄膜光学常数决定薄膜的光学性能。通过对椭圆偏振仪测试原理的分析,得到求解薄膜光学常数超越方程的数值算法简化公式,并利用MathCAD的“Solve Block”模块开发了基于Windows系统的椭圆偏振测量薄膜光学常数的计算程序,该程序可用于单层有吸收薄膜或无吸收薄膜折射率和厚度的计算。实际应用结果表明,该计算具有数值准确、精度高、运算速度快、适应性好,对系统无特殊要求等优点,可用于薄膜制备过程的在线检测。