A study on the 3-D measurement by using digital projection moiré method

Moiré topography method is a well-known non-contacting 3-D measurement method. Recently, the automatic 3-D measurement technique by moiré topography has been developed in order to apply to the engineering and medical fields. The projection moiré topography is very attractive because of its high measuring speed and high sensitivity. In this paper, using the two-wavelength methods of projection moiré topography was investigated to measure the 3-D shape of an object with 2π-ambiguity problems. Rapid measurement can be accomplished by the synchronization between CCD camera and projector. The experimental results prove that the proposed scheme is capable of finding absolute fringe orders, so that the 2π-ambiguity problems can be effectively overcome so as to treat large step discontinuities in measured objects.     

Low-coherence interferometry based roughness measurement on turbine blade surfaces using wavelet analysis

In this paper, a non-contact optical system, a low-coherence interferometer (LCI), is introduced for the purpose of measuring the surface roughness of turbine blades. The designed system not only possesses a high vertical resolution and is able to acquire the roughness topography, but also it has a large vertical scanning range compared to other commonly used optical systems. The latter characteristic allows us to measure turbine blades surfaces with large curvature without collisions between the lens and the measurement object. After obtaining the surface topography, wavelet analysis is applied to decompose the original surface into multiple bandwidths to conduct a multiscale analysis. The results show that the developed LCI system proofs a good performance not only in obtaining the surface topography in the roughness scale but also in being able to measure surfaces of objects that possess a complex geometry in a large vertical range. Furthermore, the applied biorthogonal wavelet in this study has performed good amplitude and phase properties in extracting the roughness microstructures from the whole surface. Finally, the traditional roughness parameters, such as the mean surface roughness S_a and the Root Mean Square (RMS) roughness S_q, are evaluated in each decomposed subband and their correlations with the scale of each subband are analyzed.     

Three dimensional shape measurement using high-order instantaneous moments based fringe projection method

Fringe projection techniques are popular tools for three-dimensional shape measurement in optical metrology. In these techniques, the information about the shape or the surface profile of an object is usually encoded in the phase of a recorded fringe pattern. The paper presents a high-order instantaneous moments based method for phase estimation in fringe projection. The method employs a piecewise polynomial phase approximation approach and uses high-order instantaneous moments to determine the polynomial phase coefficients to estimate the phase. The method's working is demonstrated using simulation examples and its practical applicability is validated through a shape measurement experiment.     

投影光刻机硅片调焦调平测量模型

成像质量是光学光刻机的最主要指标,硅片调焦调平测量是光刻机控制成像质量的基础.为此建立了硅片调焦调平测量系统单个测量点的测量模型,并根据硅片形貌标准和集成电路尺寸标准,推导了近似运算规则,简化了曝光场高度与测量光斑在光电探测器上的位置之间的数学关系.运用最小二乘法和平面拟合曝光场曲面的方法,推导了基于多个测量点的曝光场高度和倾斜测量的数学模型.该模型能满足调焦调平实时测量和控制的需要,可用于测量精度优于10 nm的高精度调焦调平测量系统,能满足线宽小于100 nm投影步进扫描光刻机的需要.     

From h to p efficiently: Implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations

The spectral/hp element method can be considered as bridging the gap between the – traditionally low-order – finite element method on one side and spectral methods on the other side. Consequently, a major challenge which arises in implementing the spectral/hp element methods is to design algorithms that perform efficiently for both low- and high-order spectral/hp discretisations, as well as discretisations in the intermediate regime. In this paper, we explain how the judicious use of different implementation strategies can be employed to achieve high efficiency across a wide range of polynomial orders. Furthermore, based upon this efficient implementation, we analyse which spectral/hp discretisation (which specific combination of mesh-size h and polynomial order P) minimises the computational cost to solve an elliptic problem up to a predefined level of accuracy. We investigate this question for a set of both smooth and non-smooth problems.     

Formation of dicarboxylic acid-terminated monolayers on silicon wafer surface

Dicarboxylic acid-terminated monolayers on hydroxylated silicon wafer were prepared via the chemisorption of 3-glycidoxypropyldimethylethoxysilane (GPDMES) molecules and subsequent reaction of the epoxy groups with iminodiacetic acid (IDA). The structure and surface composition of the monolayers were characterized by the means of contact-angle measurement, ellipsometric thickness measurement, reflectance FTIR spectroscopy, X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM). Moreover, we found that the dicarboxylic acid-terminated monolayers on silicon wafer exhibit well-defined contact angle titration curve from which the surface acid dissociation constants were determined. The results were compared with the pK_a values reported in the literature for IDA in aqueous solution. Small difference in the surface pK_a values was attributed to variations of the microenvironment of the acid moieties. These experimental findings provide fundamental knowledge at the molecular level for the preparation of bioactive surfaces of controlled reactivity on silicon substrates.     

Accurate,high-order representation of complex three-dimensional surfaces via Fourier continuation analysis

We present a new method for construction of high-order parametrizations of surfaces: starting from point clouds, the method we propose can be used to produce full surface parametrizations (by sets of local charts, each one representing a large surface patch – which, typically, contains thousands of the points in the original point-cloud) for complex surfaces of scientific and engineering relevance. The proposed approach accurately renders both smooth and non-smooth portions of a surface: it yields super-algebraically convergent Fourier series approximations to a given surface up to and including all points of geometric singularity, such as corners, edges, conical points, etc. In view of their C^∞ smoothness (except at true geometric singularities) and their properties of high-order approximation, the surfaces produced by this method are suitable for use in conjunction with high-order numerical methods for boundary value problems in domains with complex boundaries, including PDE solvers, integral equation solvers, etc. Our approach is based on a very simple concept: use of Fourier analysis to continue smooth portions of a piecewise smooth function into new functions which, defined on larger domains, are both smooth and periodic. The “continuation functions” arising from a function f converge super-algebraically to f in its domain of definition as discretizations are refined. We demonstrate the capabilities of the proposed approach for a number of surfaces of engineering relevance.     

Residual stress and strain in CdZnTe wafer examined by X-ray diffraction methods

A non-destructive method based on X-ray diffraction was developed to measure the stress and strain in CdZnTe single crystal near the surface. From the experimental results and calculations, the residual stresses in CdZnTe single crystal were determined to be σ₁=30 MPa, σ₂=14 MPa, and τ₁₂=-4 MPa, respectively. The residual stress derived from the measurement strain in CdZnTe was thought to be composed of the thermal stress, the misfit stress, and the mechanical stress. The distributions of non-uniform strain in a CdZnTe wafer are about 3.9%, while the distributions of uniform strain in the CdZnTe wafer are 0.5%, much smaller than those of the non-uniform strain. PACS 02.10.Xm; 71.55.Gs; 61.10.Nz; 68.35.Gy; 81.40.Jj     

Transformation of phase to (x,y,z)-coordinates for the calibration of a fringe projection profilometer

In this work we present a phase to (x,y,z)-coordinates transformation method for the calibration of a fringe projection profilometer. Our technique is divided in two parts: (1) phase to z transformation (for axial calibration) based on the typical polynomial fitting which uses a flat plane placed at several z positions to measure the phase of the projected fringes. (2) Phase to x and y transformation (for transverse calibration) based on the use of a crossed gratings pattern and a Fourier phase measurement method to determine x and y coordinates at several z positions. As will be shown the use of the crossed gratings pattern and the Fourier phase measurement method for transverse calibration is advantageous in several aspects: an unique image can give us x and y information at once. It provides x and y coordinates at each pixel in the image avoiding the use of interpolation methods. We present some experimental results and explain the viability of the proposed technique.     

调制激光致硅晶圆载流子辐射扫描成像试验研究

建立了调制激光诱发硅晶圆少数载流子密度波一维模型, 仿真分析了少数载流子输运参数对调制激光诱发载流子辐射信号频域响应的影响. 利用调制激光诱发载流子辐射扫描成像系统对含有表面划痕的硅晶圆进行了扫描成像试验研究. 通过少数载流子密度波模型与多参数拟合方法反求得到了扫描区域的输运参数二维分布图. 该方法得到的少数载流子寿命与利用传统光电导方法测量的少数载流子寿命结果相符; 分析了划痕对载流子输运参数造成的影响, 与光电导方法比较, 该方法可以测量不同位置的全部载流子输运参数且分辨率高.     

In situ roughness monitoring of sputtered Pt thin film under dynamic turbulence using adaptive optics

A new optical monitoring system for rapid and in situ surface roughness measurement of Pt film on silicon is developed in this study. The in-process measurement is achieved by combining an optical probe of laser-scattering phenomena and adaptive optics for aberration correction. Platinum (Pt) thin film is selected due to the extensive utilization in semiconductor industry and excellent chemical inertness. The aim of this study was to demonstrate the necessity for adaptive optics (AO) compensation in regions containing room-temperature turbulences. Measurement results of eight Pt films (roughness ranging from 58 to 83 nm) sputtered on top of P-type silicon wafer demonstrate excellent correlation between the peak power and average roughness with a correlation coefficient (R²) of 0.9962 and a trend equation for predicting the surface roughness of Pt thin films is obtained as y = 9E07x^−3.783. Roughness average (Ra) of Pt thin films (x) of can be directly determined from the peak power (y) using the proposed method under dynamic disturbance. Furthermore, the proposed AO-assisted system is in good agreement with stylus method and less than 1.1% error values are obtained for the aforementioned average sample roughness.     

Nanopolishing of silicon wafers using ultrafine-dispersed diamonds

In the present study, two new methods are proposed for the polishing of silicon wafers using ultrafine-dispersed diamonds (UDDs). The first proposed polishing method uses a polishing tool with an ultrafine abrasive material made through the electrophoretic deposition of UDDs onto a brass rod. Dry polishing tests showed that the surface roughness of the silicon wafer was reduced from R_a=107 to 4 nm after polishing for 30 min. The second method uses a new polishing pad with self-generating porosity. By polishing with the new pad in combination with the polycrystalline UDD in a water suspension, it is possible to achieve the specified surface roughness of the silicon wafer much faster than when using a conventional pad made of foamed polyurethane. The tests showed that the surface roughness of the silicon wafer was reduced from R_a=107 to 2 nm after polishing for 90 min.     

光刻机硅片表面不平度原位检测技术

随着光刻特征尺寸的不断减小,硅片表面不平度对光刻性能的影响越来越显著.该文提出了一种新的硅片表面不平度的原位检测技术本文在分析特殊测试标记成像规律的基础上,讨论了测试标记的对准位置偏移量与硅片表面起伏高度的变化规律,提出了一种新的硅片表面不平度原位检测技术.实验表明,该技术可实现硅片表面不平度及硅片表面形貌的高准确度原位测量.该技术考虑了光刻机承片台吸附力的非均匀性对硅片表面不平度的影响,更真实反映曝光工作状态下的硅片表面不平度大小.与现有的原位检测方法相比,硅片表面不平度的测量空间分辨率提高了1.67%倍,可实现硅片表面形貌的原位检测.     

基于B样条的TERS形貌成像背景扣除方法

在针尖增强拉曼光谱(TERS)形貌成像过程中，由于针尖与扫描台无法绝对平行、样品电子密度骤变处针尖快速升降以及扫描控制系统响应时间特性差等综合原因的影响，往往使形貌图中带有倾斜或边界面卷曲的成像背景。成像背景对样品形貌的识别和分析带来十分不利的影响，而背景扣除就是解决该问题的重要手段，也是形貌成像预处理的重要组成部分。背景扣除的原理一般是通过拟合背景的方法来扣除成像中的背景。传统的背景扣除方法是利用多项式拟合的方法对成像进行逐行的基线校正，但是该方法在处理形貌成像时常常会由于过拟合而造成样品形貌的失真，同时容易在图片上留下明显的线条纹理。针对传统方法的缺点，本文提出采用B样条曲面拟合方法，直接对样品形貌图进行曲面背景拟合，发挥B样条低阶光滑的优点，能够有效克服传统方法的缺陷。在实验中，同时利用传统方法和该方法对金单晶和合成金片的形貌图进行背景扣除，实验结果表明，两种方法都能够扣除样品形貌图中的成像背景，但与传统方法相比，所提出的方法不会造成样品形貌的失真，且不会留下线条纹理，获得了更加良好的背景扣除效果，为进一步分析样品形貌特征提供了更准确可靠的信息，是一种更加有效的TERS形貌成像背景扣除算法。     

基于体视显微镜的三维显微表面测量系统

将条纹投影轮廓测量术和体视显微镜相结合，搭建了一套能够对微小器件的表面三维形貌进行测量的系统。该系统由一台Greenough型的体视显微镜，一台DMD投影仪，一个CCD相机和一个机械平移台组成。在利用相移算法和降级去包裹算法得到被表面形貌调制过的无歧义相位后，通过相位和高度的映射关系，得到高度值，从而能够对微小器件的表面形貌进行重建。在标定时，通过精密的机械平移台将陶瓷标定板置于不同的高度，对其进行相位测量，得到多组相对应的相位和高度值，再对每个像素点进行多项式拟合来确定相位和高度的映射关系。实验测量了标定的最后一个平面以及微型的球栅阵列，平面测量结果显示测量误差在10 μm以内，从微型球栅阵列的三维重建结果可以清晰地看到排列的球形结构。实验结果证明了该系统对于平面和复杂的三维结构都能够进行精确的测量。     

Physical spherical phase compensation in reflection digital holographic microscopy

Reflection configured digital holographic microscopy (DHM) can perform accurate optical topography measurements of reflecting objects, such as MEMs, MOEMs, and semiconductor wafer. It can provide non-destructive quantitative measurements of surface roughness and geometric pattern characterization with nanometric axial resolution in real-time. However, the measurement results may be affected by an additional phase curvature introduced by the microscope objective (MO) used in DHM. It needs to be removed either by numerical compensation or by physical compensation.We present a method of physical spherical phase compensation for reflection DHM in the Michelson configuration. In the object arm, collimated light is used for illumination. Due to the use of the MO, the object wavefront may have a spherical phase curvature. In the reference arm, a lens and mirror combination is used to generate a spherical recording reference wave in order to physically compensate the spherical phase curvature of the object wavefront. By controlling the position of the mirror and the sample stage, the compensation process has been demonstrated. The relative positions of the test specimen and the reference mirror must be fixed for the physical spherical phase to be totally compensated. A numerical plane reference wave is preferred for the numerical reconstruction of the phase introduced by the test specimen. Experimental results on wafer pattern recognition are also given.     

基于谱域相位分辨光学相干层析的纳米级表面形貌成像

提出了一种基于谱域相位分辨光学相干层析的纳米级表面形貌成像方法,由干涉光谱计算样品相邻两点的相位差,得到样品表面相位差分图,经过积分,重建样品表面形貌的定量分布.当相邻两点相位差的绝对值小于π,不产生相位包裹,避免了目前的干涉法相位解包裹存在的问题,将干涉法相邻两点相位差绝对值的限制条件由目前的π扩大到2π,提高了干涉法表面形貌成像的适用范围.参考面和样品置于同一平台之上,消除环境干扰及系统振动的影响,噪声幅度小于0.3 nm.通过对光学分辨率片及表面粗糙度标准样板的表面形貌成像,对本方法进行了验证,系统的轴向分辨率优于1 nm.     

A Monte Carlo method for simulating fractal surfaces

A Monte Carlo method is presented for simulating rough surfaces with the fractal behavior. The simulation is based on power-law size distribution of asperity diameter and self-affine property of roughness on surfaces. A probability model based on random number for asperity sizes is developed to generate the surfaces. By iteration, this method can be used to simulate surfaces that exhibit the aforementioned properties. The results indicate that the variation of the surface topography is related to the effects of scaling constant G and the fractal dimension D of the profile of rough surface. The larger value of D or smaller value of G signifies the smoother surface topography. This method may have the potential in prediction of the transport properties (such as friction, wear, lubrication, permeability and thermal or electrical conductivity, etc.) on rough surfaces.     

Geometric conservation law and applications to high-order finite difference schemes with stationary grids

The geometric conservation law (GCL) includes the volume conservation law (VCL) and the surface conservation law (SCL). Though the VCL is widely discussed for time-depending grids, in the cases of stationary grids the SCL also works as a very important role for high-order accurate numerical simulations. The SCL is usually not satisfied on discretized grid meshes because of discretization errors, and the violation of the SCL can lead to numerical instabilities especially when high-order schemes are applied. In order to fulfill the SCL in high-order finite difference schemes, a conservative metric method (CMM) is presented. This method is achieved by computing grid metric derivatives through a conservative form with the same scheme applied for fluxes. The CMM is proven to be a sufficient condition for the SCL, and can ensure the SCL for interior schemes as well as boundary and near boundary schemes. Though the first-level difference operators δ₃ have no effects on the SCL, no extra errors can be introduced as δ₃ = δ₂. The generally used high-order finite difference schemes are categorized as central schemes (CS) and upwind schemes (UPW) based on the difference operator δ₁ which are used to solve the governing equations. The CMM can be applied to CS and is difficult to be satisfied by UPW. Thus, it is critical to select the difference operator δ₁ to reduce the SCL-related errors. Numerical tests based on WCNS-E-5 show that the SCL plays a very important role in ensuring free-stream conservation, suppressing numerical oscillations, and enhancing the robustness of the high-order scheme in complex grids.     

Measurement of small angle based on a (1 0 0) silicon wafer and heterodyne interferometer

In this paper, a new optical material application and a heterodyne interferometer are proposed for measuring small angles. In the proposed interferometer, the optical material is a (1 0 0) silicon wafer applied to compose a new architecture of small angle sensor. The small angle measurement used the phase difference which is dependent on the incident angle at the silicon wafer surface to deduce the angular variation. The proposed architecture is simple and uses the common path method to compare test and reference signals; thus, small angles can be easily and accurately measured by estimating the phase difference. The experimental results demonstrate the feasibility of this method. The angular resolution and sensitivity levels superior to 7 × 10^?5° (1.3 × 10^?6 rad) and 150 (deg/deg), respectively, were attainable in a dynamic range of 0.45°.