Aberration measurement of projection optics in lithographic tools by use of an alternating phase-shifting mask

As a critical dimension shrinks, the degradation in image quality caused by wavefront aberrations of projection optics in lithographic tools becomes a serious problem. It is necessary to establish a technique for a fast and accurate in situ aberration measurement. We introduce what we believe to be a novel technique for characterizing the aberrations of projection optics by using an alternating phase-shifting mask. The even aberrations, such as spherical aberration and astigmatism, and the odd aberrations, such as coma, are extracted from focus shifts and image displacements of the phase-shifted pattern, respectively. The focus shifts and the image displacements are measured by a transmission image sensor. The simulation results show that, compared with the accuracy of the previous straightforward measurement technique, the accuracy of the coma measurement increases by more than 30% and the accuracy of the spherical-aberration measurement increases by approximately 20%. (c) 2006 Optical Society of America.

Even aberration measurement of lithographic projection system based on optimized phase-shifting marks

In the present paper, we propose a novel method for measuring the even aberrations of lithographic projection optics by use of optimized phase-shifting marks on the test mask. The line/space ratio of the phase-shifting marks is optimized to obtain the maximum sensitivities of Zernike coefficients corresponding to even aberrations. Spherical aberration and astigmatism can be calculated from the focus shifts of phase-shifting gratings oriented at 0 degrees, 45 degrees, 90 degrees and 135 degrees at multiple illumination settings. The PROLITH simulation results show that, the measurement accuracy of spherical aberration and astigmatism obviously increase, after the optimization of the measurement mark. (C) 2008 Elsevier B.V. All rights reserved.

Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses

In this paper, we briefly summarize two typical morphology characteristics of the self-organized void array induced in bulk of fused silica glass by a tightly focused femtosecond laser beam, such as the key role of high numerical aperture in the void array formation and the concentric-circle-like structure indicated by the top view of the void array. By adopting a physical model which combines the nonlinear propagation of femtosecond laser pulses with the spherical aberration effect (SA) at the interface of two mediums of different refractive indices, reasonable agreements between the simulation results and the experimental results are obtained. By comparing the fluence distributions of the case with both SA and nonlinear effects included and the case with only consideration of SA, we suggest that spherical aberration, which results from the refractive index mismatch between air and fused silica glass, is the main reason for the formation of the self-organized void array. (c) 2008 American Institute of Physics.

二次光栅在波前测量中的应用

采用一种特殊的二次光栅用于激光波前测量, 它对非零级衍射光束具有不同的聚焦效应, 其光栅线为圆弧型而非直线。导出了在会聚光束情况下的两平面成像在单一像平面上的距离关系, 实验上实现了二次光栅用于会聚光束的波前测量, 测量得到会聚光束具有较大的散焦(-2.93λ)和球差(1.34λ), 与该透镜引起波前的离焦像差理论理想值(-2.695λ)基本符合。该技术可以实现波前的高空间分辨力和高精度实时测量, 大大减少光学元件数量, 降低装置成本。由于大功率激光束的不稳定性, 其波前变化非常快, 所以该方法的实时性非

Spherical nanometer-sized diamond obtained from detonation

Ultrafine diamond (UFD) was synthesized under high pressure and high temperatures generated by explosive detonation. The structure, composition, surface and thermal stability of UFD were studied by use of XRD, TEM, Raman Spectroscopy, FTIR, etc. The influences of the synthesis conditions and purification conditions on the properties of UFD were analyzed. The UFD had an average size of 4-6 nm, commonly exhibiting a spherical shape. The highest yield was of up to 10 mass% of the explosive. Attempts were made to use UFD as an additive to metal-diamond sintering and as crystallite seeds of CVD diamond films. The results show that UFD can decrease the coefficient of friction of the composite by 30%, and raise the nucleation density in CVD diamond films by 2-3 times.

An Energy-Based Method for Analyzing Instrumented Spherical Indentation Experiments

Using dimensional analysis and finite element calculation, we studied spherical indentation in elastic-plastic solids with work hardening. We report two previously unknown relationships between hardness, reduced modulus, indentation depth, indenter radius, and work of indentation. These relationships, together with the relationship between initial unloading stiffness and reduced modulus, provide an energy-based method for determining contact area, reduced modulus, and hardness of materials from instrumented spherical indentation measurements. This method also provides a means for calibrating the effective radius of imperfectly shaped spherical indenters. Finally, the method is applied to the analysis of instrumented spherical indentation experiments on copper, aluminum, tungsten, and fused silica.

A New Modified Expanding Cavity Model for Characterizing the Spherical Indentation Behaviour of Bulk Metallic Glass with Pile-up

Spherical nanoindentation tests were performed on Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass and pile-ups were observed around the indenter. A new modified expanding cavity model was developed to characterize the indentation deformation behavior of strain-hardening and pressure-dependent materials. By using this model, the representative stress-strain response of this bulk metallic glass to hardness and indentation in the elastic-plastic regime were obtained taking into consideration the effect of pile-up.

A Multimoment Finite-Volume Shallow-Water Model On The Yin-Yang Overset Spherical Grid

A numerical model for shallow-water equations has been built and tested on the Yin-Yang overset spherical grid. A high-order multimoment finite-volume method is used for the spatial discretization in which two kinds of so-called moments of the physical field [i.e., the volume integrated average ( VIA) and the point value (PV)] are treated as the model variables and updated separately in time. In the present model, the PV is computed by the semi-implicit semi-Lagrangian formulation, whereas the VIA is predicted in time via a flux-based finite-volume method and is numerically conserved on each component grid. The concept of including an extra moment (i.e., the volume-integrated value) to enforce the numerical conservativeness provides a general methodology and applies to the existing semi-implicit semi-Lagrangian formulations. Based on both VIA and PV, the high-order interpolation reconstruction can only be done over a single grid cell, which then minimizes the overlapping zone between the Yin and Yang components and effectively reduces the numerical errors introduced in the interpolation required to communicate the data between the two components. The present model completely gets around the singularity and grid convergence in the polar regions of the conventional longitude-latitude grid. Being an issue demanding further investigation, the high-order interpolation across the overlapping region of the Yin-Yang grid in the current model does not rigorously guarantee the numerical conservativeness. Nevertheless, these numerical tests show that the global conservation error in the present model is negligibly small. The model has competitive accuracy and efficiency.

Numerical Study Of Pile-Up In Bulk Metallic Glass During Spherical Indentation

Pile-up around indenter is usually observed during instrumented indentation tests on bulk metallic glass. Neglecting the pile-up effect may lead to errors in evaluating hardness, Young's modulus, stress-strain response, etc. Finite element analysis was employed to implement numerical simulation of spherical indentation tests on bulk metallic glass. A new model was proposed to describe the pile-up effect. By using this new model, the contact radius and hardness of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass were obtained under several different indenter loads with pile-up, and the results agree well with the data generated by numerical simulation.

Numerical verification for instrumented spherical indentation techniques in determining the plastic properties of materials

 Instrumented indentation tests have been widely adopted for elastic modulus determination. Recently, a number of indentation-based methods for plastic properties characterization have been proposed, and rigorous verification is absolutely necessary for their wide application. In view of the advantages of spherical indentation compared with conical indentation in determining plastic proper-ties, this study mainly concerns verification of spherical indentation methods. Five convenient and simple models were selected for this purpose, and numerical experiments for a wide range of materials are carried out to identify their accuracy and sensitivity characteristics. The verification results show that four of these five methods can give relatively accurate and stable results within a certain material domain, which is defined as their validity range and has been summarized for each method.

Periodic vortex breakdown in wide spherical gaps

The flow field with vortex breakdown in wide spherical gaps was studied numerically by a finite difference method under the axisymmetric condition. The result shows that the flow bifurcates to periodic motion as the Reynolds number or the eccentricity of the spheres increases. (C) 1997 American Institute of Physics.

Numerical study of bifurcation solutions of spherical Taylor-Couette flow

The steady bifurcation flows in a spherical gap (gap ratio sigma=0.18) with rotating inner and stationary outer spheres are simulated numerically for Re(c1)less than or equal to Re less than or equal to 1 500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775 less than or equal to Re less than or equal to 1 220 and three steady stable flows with 0, 1, or 2 vortices for 1 220

Three-dimensional finite element analysis of composites with coated spherical inclusions

A three-dimensional finite element analysis has been used to determine the internal stresses in a three-phase composite. The stresses have been determined for a variety of interphase properties, the thicknesses of the interphase and the volume fractions of particles. Young's modulus has been calculated from a knowledge of these stresses and the applied deformation. The calculations show that stress distributions in the matrix and the mechanical properties are sensitive to the interphase property in the three-phase composites. The interfacial stresses in the three-dimensional analysis are in agreement with results obtained by an axisymmetric analysis. The predicted bulk modulus in three-dimensional analysis agrees well with the theoretical solution obtained by Qui and Weng, but it presents a great divergence from that in axisymmetric analyses. An investigation indicates that this divergence may be caused by the difference in the unit cell structure between two models. A comparison of the numerically predicted bulk and shear modulus for two-phase composites with the theoretical results indicates that the three-dimensional analysis gives quite satisfactory results.

Parameter-estimation of a spherical top inductively-coupled plasma source with global-model

Using spatially averaged global model, we succeed in obtaining some plasma parameters for a low pressure inductively coupled plasma source of our laboratory. As far as the global balance is concerned, the models can give reasonable results of the parameters, such as the global electron temperature and the ion impacting energy, etc. It is found that the ion flow is hardly affected by the neutral gas pressure. Finally, the magnetic effects are calculated by means of the method. The magnetic field can play an important role to increase plasma density and ion current.

Non-die explosive forming of spherical pressure-vessels

This paper presents a newly developed method of manufacturing spherical pressure vessels based on the technology of non-die explosive forming. Compared with the traditional method, this technology does not need any dies and pressing equipment, so that the cost of the production process can be greatly reduced, especially for vessels of less than 100 m3 capacity.