Measurement of the dielectric constant of thin films by terahertz time-domain spectroscopic ellipsometry

We present a reflection-type terahertz time-domain spectroscopic ellipsometry (THz-TDSE) technique for measuring the complex dielectric constants of thin-film materials without replacement of the sample. THz-TDSE provides complex dielectric constants from the ratio of the complex amplitude reflection coefficients between p- and s-polarized THz waves. The measured dielectric constants of doped GaAs thin films show good agreement with predictions of the Drude model, even though the film thickness is of the order of a tenth of the penetration depth of the THz waves. In addition, we demonstrate the measurements of soft-phonon dispersion in SrTiO(3) thin films deposited on a Pt layer. The obtained dielectric constants agree well with the predictions of a generalized harmonic oscillator model.     

Measurement of mechanical deformation of dielectric fibres by a light scattering method

This paper describes an experimental method to detect quantitative changes of both refractive index and diameter of unclad dielectric fibres, such as fused silica fibre and nylon 6 fibre, due to tensile stress. The technique employed here is based on the variation in the position of a fringe in back-scattered light, which is generated when a laser beam is incident at a right angle to the axis of the fibre. This procedure makes it possible to measure refractive index, diameter and ellipticity to within an accuracy of 0.048%, 2.6% and 0.05%, respectively.     

Measurement of the normal thermal diffusivity of a dielectric film by a pulsed photoacoustic method

A method of determining the thermal diffusivity of a thin film of a transparent dielectric in the direction normal to the surface has been developed. It is based on excitation of reflecting dynamic gratings. The effectiveness of the method is checked experimentally with the example of a thermally oxidized submicron SiO₂ film on a silicon substrate. The temperature dependence of in the range 290–420 K is measured. The possibilities of setting up thermal measurements of films tens of nanometers thick and its problems are discussed.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 793–797, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

An iterative method for scattering from rough dielectric or conducting interfaces

Abstract

We introduces an iterative method for scattering a two-dimensional scalar wave from a rough interface between two media. The method is applicable to the case of electromagnetic scattering from a rough metallic or dielectric surface that varies only in one dimension. The first iteration is equivalent to the Kirchhoff approximation, and the series converges in one step for a flat surface. We discuss the conditions for convergence, and find that they are similar to those which Meecham showed to be necessary in the Dirichlet case.     

An iterative method for scattering from rough dielectric or conducting interfaces

We introduces an iterative method for scattering a two-dimensional scalar wave from a rough interface between two media. The method is applicable to the case of electromagnetic scattering from a rough metallic or dielectric surface that varies only in one dimension. The first iteration is equivalent to the Kirchhoff approximation, and the series converges in one step for a flat surface. We discuss the conditions for convergence, and find that they are similar to those which Meecham showed to be necessary in the Dirichlet case.     

Transverse magnetic scattering of two incident plane waves by a dielectric coated cylindrical reflector

Scattering characteristics of two plane waves are investigated for a circular cylinder covered by a dielectric substance. Fields are assumed to be transverse magnetic (TM) and represented in an exponential series form. The diffracted radiations are found by applying the boundary conditions to the wave functions. The wave transformation method and the orthogonality of the exponential functions are respectively employed to obtain an infinite series in the solution. Numerical results are evaluated by reducing the infinite series to a finite number of terms and comparing estimates with the single plane wave scattering situation.     

椭偏光散射分析类金刚石薄膜的散射特性

 基于光学薄膜反射椭偏法的测量原理,对光学薄膜散射椭偏特性进行了研究。给出了光学薄膜散射逆问题的解决方法,并对不同脉冲频率下采用脉冲真空电弧离子镀技术沉积的类金刚石薄膜的散射特性进行了研究。分析了光学薄膜界面的相关特性以及膜层中局部缺陷对散射光椭偏特性的影响。结果表明:随着脉冲频率的增加,所沉积的类金刚石薄膜的相关性变差,且薄膜中的局部缺陷引起的体散射越明显。     

Effect of surface roughness on ellipsometry of aluminum

Controlled surface roughness experiments have been performed on aluminum to determine the effect on ellipsometric parameters. To help characterize the surfaces SEM, light scattering, photo electron emission, surface potential difference and water contact angle measurements were made. Comparison of experimental results with recent theory is also presented.     

脉冲激光入射下介质薄膜双频互相关散射截面及功率展宽

结合特殊的镀金聚酯薄膜表面的粗糙度和半球反射率,依据基尔霍夫近似及粗糙面脉冲散射互相关函数,数值计算了脉冲激光（1.06 μm）在不同入射角照射下该材料薄膜双频互相关散射截面随相干带宽频差和散射角的变化情况。并给出δ脉冲和高斯脉冲波入射下,其散射功率随时间和散射角的波形分布。计算结果表明：该薄膜材料激光双频互相关散射截面在镜反射方向有最大的散射峰值,在非镜反射方向上,其散射值随相干带宽频差的增大迅速减小,当窄脉冲垂直入射时,粗糙面散射功率展宽现象明显。     

脉冲激光入射下介质薄膜双频互相关散射截面及功率展宽

 结合特殊的镀金聚酯薄膜表面的粗糙度和半球反射率,依据基尔霍夫近似及粗糙面脉冲散射互相关函数,数值计算了脉冲激光（1.06 μm）在不同入射角照射下该材料薄膜双频互相关散射截面随相干带宽频差和散射角的变化情况。并给出δ脉冲和高斯脉冲波入射下,其散射功率随时间和散射角的波形分布。计算结果表明：该薄膜材料激光双频互相关散射截面在镜反射方向有最大的散射峰值,在非镜反射方向上,其散射值随相干带宽频差的增大迅速减小,当窄脉冲垂直入射时,粗糙面散射功率展宽现象明显。     

Determination of optical constants of a biaxially anisotropic film by standard multiangle monochromatic ellipsometry

Possibilities of standard multiangle monochromatic ellipsometry in the determination of parameters of a uniform biaxially anisotropic layer are studied for the case of an arbitrary orientation of the two principal axes in the plane of incidence of the light beam and perpendicularity of the third axis to the plane of incidence. Using numerical simulation, it has been found that the measurement accuracy that is necessary in the determination of all the three principal components of the dielectric permittivity tensor ε and tilt angle of the axes using only angular dependences of ellipsometric parameters must be no worse than 0.0001°, which is far beyond the accuracy limits provided by present-day ellipsometers. If the tilt angle is known, standard multiangle monochromatic ellipsometry provides the determination of thickness and all three principal components of the dielectric permittivity tensor. This method allows one to determine the layer thickness and tensor component for the axis perpendicular to the plane of incidence, as well as the average value of components for the axes lying in the plane of incidence without involving the data about the tilt angle of the axes. This is demonstrated by an example of experimental data for biaxially anisotropic SiO _x films obtained by oblique deposition of silicon monoxide SiO evaporated in vacuum.     

Raman scattering enhancement by dielectric spheres

Raman scattering experiments were performed on Si(60 nm)/metal/substrate structures with and without silica microspheres (with a diameter between 0.5 and 5 µm) on top. Raman scattering from the thin Si layer exhibits enhancements (~20) due to the dielectric spheres, where the enhancement factors depend on the diameter of the spheres. The interaction between light and dielectric spheres has been simulated by finite difference time domain calculations (FDTD), wherein particularly the electric energy density (ED) distribution in the thin Si layer was of concern. For microspheres with a diameter less than ~3 µm, the transverse ED distribution (perpendicular to the incident light direction) within the Si layer is characterised by a single peak centered on the optical axis. For larger diameters, a multimodal transverse ED distribution develops where the maximum is not centered on the optical axis. Using an ad‐hoc approach for surface enhanced Raman scattering in combination with the FDTD calculations, the experimental Raman observations are well accounted for. Copyright © 2013 John Wiley & Sons, Ltd.     

Low-frequency scattering by rectangular dielectric particles

The field scattered by a homogeneous isotropic dielectric particle illuminated by a low-frequency plane electromagnetic wave is expressed in terms of a single polarizability tensor which is a function of only the geometry of the particle and a material parameter τ representing either the relative permittivity or permeability of the dielectric. The mathematical formulation is specialized to the case of a rectangular parallelepiped and numerical techniques are developed for computing the tensor elements. Specific data are presented for the tensor elements of rectangular parallelepipeds having square cross sections and are compared to the results obtained for spheroids and right circular cylinders of similar dimensions.     

Radiation scattering by finite dielectric cyclinders

The volumetric integral equation formalism (VIEF) is used to determine characteristics of scattering of radiation falling along the axis of dielectric cylinders that scatter the radiation. The spectral dependence of the extinction efficiency factor Q is studied with changes in the length l of the cylinder (300–2200 nm), its width d (100–300 nm), and the refraction index m (1.33–1.65). In the range of angles θ=0–180°, for a cylinder with l=700 nm, d=100 nm, and m=1.33, angular intensity distribution functions i_i and i₂ are calculated for the components of the scattered radiation that are polarized perpendicular and parallel to the plane of observation, respectively. No effect of scattered-radiation depolarization is found. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 2, pp. 256–260, March–April, 1998.     

Mixed polarization in determining the film thickness of a silicon sphere by spectroscopic ellipsometry

The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed, and a method to eliminate this effect is proposed. Based on the simulation result of the SE measurement on a silicon sphere by ray tracking, we find that the sphere makes the parallel incident beam of the SE be divergent after reflection, and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory. By settling an aperture in front of the detector of the SE, we can almost eliminate the error. For the silicon sphere with a diameter of 94 mm used in the Avogadro project, the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method. The principle of the method and the results of the experimental verification are presented.     

Mixed polarization in determining the film thickness of a silicon sphere by spectroscopic ellipsometry

The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed,and a method to eliminate this effect is proposed.Based on the simulation result of the SE measurement on a silicon sphere by ray tracking,we find that the sphere makes the parallel incident beam of the SE be divergent after reflection,and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory.By settling an aperture in front of the detector of the SE,we can almost eliminate the error.For the silicon sphere with a diameter of 94 mm used in the Avogadro project,the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method.The principle of the method and the results of the experimental verification are presented.     

Reflection and scattering of spin waves by surface roughness of a ferromagnet

Abstract

A detailed theory of volume spin wave reflection from the randomly rough surface of a ferromagnet is presented. The contribution to damping of the reflected wave is calculated. This contribution is due to the scattering of the initial volume wave into secondary surface and volume spin waves. The value of damping is proportional to the correlation length and the square of the roughness amplitude. Numerical calculations of the attenuation rate as a function of the angle of incidence and the ratio between the surface anisotropy and the wavenumber are provided. They yield the angle of incidence where the attenuation has a maximum. In analogy to optics, this angle is similar to the Brewster angle. Numerical estimations of damping and a comparison of its value with the ferromagnetic resonance linewidth are also made. Finally, the results of the calculation of the scattering of surface exchange spin waves by surface roughness are presented and discussed.