Aberration measurement of projection optics in lithographic tools based on two-beam interference theory

The degradation of image quality caused by aberrations of projection optics in lithographic tools is a serious problem in optical lithography. We propose what we believe to be a novel technique for measuring aberrations of projection optics based on two-beam interference theory. By utilizing the partial coherent imaging theory, a novel model that accurately characterizes the relative image displacement of a fine grating pattern to a large pattern induced by aberrations is derived. Both even and odd aberrations are extracted independently from the relative image displacements of the printed patterns by two-beam interference imaging of the zeroth and positive first orders. The simulation results show that by using this technique we can measure the aberrations present in the lithographic tool with higher accuracy. (c) 2006 Optical Society of America.

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.

Measurement technique for in situ characterizing aberrations of projection optics in lithographic tools

As the feature size decreases, degradation of image quality caused by wavefront aberrations of projection optics in lithographic tools has become a serious problem in the low-k1 process. We propose a novel measurement technique for in situ characterizing aberrations of projection optics in lithographic tools. Considering the impact of the partial coherence illumination, we introduce a novel algorithm that accurately describes the pattern displacement and focus shift induced by aberrations. Employing the algorithm, the measurement condition is extended from three-beam interference to two-, three-, and hybrid-beam interferences. The experiments are performed to measure the aberrations of projection optics in an ArF scanner. (C) 2006 Optical Society of America.

Coma measurement of projection optics in lithographic tools based on relative image displacements at multiple illumination settings

In this paper, we propose a novel method for measuring the coma aberrations of lithographic projection optics based on relative image displacements at multiple illumination settings. The measurement accuracy of coma can be improved because the phase-shifting gratings are more sensitive to the aberrations than the binary gratings used in the TAMIS technique, and the impact of distortion on displacements of aerial image can be eliminated when the relative image displacements are measured. The PROLITH simulation results show that, the measurement accuracy of coma increases by more than 25% under conventional illumination, and the measurement accuracy of primary coma increases by more than 20% under annular illumination, compared with the TAMIS technique. (c) 2007 Optical Society of America.

One-dimensional improvement and two-dimensional and 3-dimensional treatments for stable oscillation condition, mode structure and power output in high-speed-flow lasers

For high-speed-flow lasers, the one-dimensional and first-order approximate treatment in[1] under approximation of geometrical optics is improved still within the scope of approx-imation of geometrical optics. The strict accurate results are obtained, and what is more,two- and three-dimensional treatments are done. Thus for two- and three-dimensional cases, thestable oscillation condition, the formulae of power output and analytical expression of modesunder approximation of geometrical optics (in terms of gain function) are derived. Accord-ing to the present theory, one-and two-dimensional calculations for the typical case of Gerry'sexperiment are presented. All the results coincide well with the experiment and are better thanthe results obtained in [1].In addition, the applicable scope of Lee's stable oscillation condition given by [1] is ex-panded; the condition for the approximation of gcometrical optics to be applied to mode con-structure in optical cavity is obtained for the first time and the difference between thiscondition and that for free space is also pointed out in the present work.

Enhanced dispersive wave generation by using chirped pulses in a microstructured fiber

A theoretical investigation on the nonlinear pulse propagation and dispersive wave generation in the anomalous dispersion region of a microstructured fiber is presented. By simulating the dispersive wave generation under different conditions. it is found that the generation mechanism of the dispersive wave is mainly due to the pulse trapping across the zero-dispersion wavelength. By varying the initial pulse chirp, the output spectrum can be broadened and the intensity of the dispersive wave can be obviously enhanced. In particular, there exists an optimal positive chirp which maximizes the intensity of the dispersive wave. This effect can be explained by the energy transfer from the Raman soliton to the dispersive wave due to the effect of the pulse trapping and the effect of the higher-order dispersion. From the phase aspect, the explanation of this effect is also included. (C) 2004 Elsevier B.V. All rights reserved.

Self-similarity limits of genomic signatures

It is shown that metric representation of DNA sequences is one-to-one. By using the metric representation method, suppression of nucleotide strings in the DNA sequences is determined. For a DNA sequence, an optimal string length to display genomic signature in chaos game representation is obtained by eliminating effects of the finite sequence. The optimal string length is further shown as a self-similarity limit in computing information dimension. By using the method, self-similarity limits of bacteria complete genomic signatures are further determined.

Coma measurement by use of an alternating phase-shifting mask mark with a specific phase width

The correlation between the coma sensitivity of the alternating phase-shifting mask (Alt-PSM) mark and the mark's structure is studied based on the Hopkins theory of partially coherent imaging and positive resist optical lithography (PROLITH) simulation. It is found that an optimized Alt-PSM mark with its phase width being two-thirds its pitch has a higher sensitivity to coma than Alt-PSM marks with the same pitch and the different phase widths. The pitch of the Alt-PSM mark is also optimized by PROLITH simulation, and the structure of p - 1.92 lambda/NA and pw = 2p/3 proves to be with the highest sensitivity. The optimized Alt-PSM mark is used as a measurement mark to retrieve coma aberration from the projection optics in lithographic tools. In comparison with an ordinary Alt-PSM mark with its phase width being a half its pitch, the measurement accuracies of Z(7) and Z(14) apparently increase. (C) 2009 Optical Society of America

水-岩土反应的力学与环境效应研究

The research on mechanical effects of water-rock and soil interaction on deformation and failure of rocks and soils involves three aspects of mechanics, physics and chemistry. It is the cross between geochemistry and rock mechanics and soil mechanics. To sum up, the mechanical effects of water-rock and soil interaction is related to many complex processes. Research in this respect has been being an important forward field and has broad prospects. In connection with the mechanism of the effects of the chemical action of water-rock on deformation and failure of rocks and soils, the research significance, the present state, the developments in this research domain are summarized. Author prospects the future of this research. The research of the subject should be possessed of important position in studying engineering geology and will lead directly to a new understand on geological hazard and control research. In order to investigation the macroscopic mechanics effects of chemical kinetics of water-rock interaction on the deformation and failure, calcic rock, red sandstone and grey granite reacting chemically with different aqueous solution at atmospheric temperature and atmospheric pressure are uniaxially compressed. The quantitative results concerning the changes of uniaxially compressive strength and elastic modulus under different conditions are obtained. It is found that the mechanical effects of water on rock is closely related to the chemical action of water-rock or the chemical damage in rock, and the intensity of chemical damage is direct ratio to the intensity of chemical action in water-rock system. It is also found that the hydrochemical action on rock is time-dependent through the test. The mechanism of permeation and hydrochemical action resulting in failure of loaded rock mass or propagation of fractures in rocks would be a key question in rock fracture mechanics. In this paper, the fracture mechanical effects of chemical action of water-rock and their time- and chemical environment-dependent behavior in grey granite, green granite, grey sandstone and red sandstone are analyzed by testing K_(IC) and COD of rock under different conditions. It is found that: ①the fracture mechanical effect of chemical action of water-rock is outstanding and time-dependent, and high differences exist in the influence of different aqueous solution, different rocks, different immersion ways and different velocity of cycle flow on the fracture mechanical effects in rock. ②the mechanical effects of water-rock interaction on propagation of fractures is consistent with the mechanical effects on the peak strength of rock. ③the intensity of the mechanical fracture effects increases as the intensity of chemical action of water-rock increases. ④iron and calcium ion bearing mineral or cement in rock are some key ion or chemical composition, and especially iron ion-bearing mineral resulting in chemical action of water-rock to be provided with both positive and negative mechanical effects on rock. Through the above two tests, we suggest that primary factors influencing chemical damage in rock consist of the chemical property of rock and aqueous solution, the structure or homogeneity of rocks, the flow velocity of aqueous solution passing through rock, and cause of formation or evolution of rock. The paper explores the mechanism on the mechanical effects of water-rock interaction on rock by using the theory of chemistry and rock fracture mechanics with chemical damage proposed by author, the modeling method and the energy point of view. In this paper, the concept of absorbed suction between soil grains caused by capillary response is given and expounded, and the relation and basic distinction among this absorbed suction, surface tension and capillary pressure of the soil are analyzed and established. The law of absorbed suction change and the primary factors affecting it are approached. We hold that the structure suction are changeable along with the change of the saturation state in unsaturated soils. In view of this, the concept of intrinsic structure suction and variable structure suction are given and expounded, and this paper points out: What we should study is variable structure suction when studying the effective stress. By IIIy κHH's theory of structure strength of soils, the computer method for variable structure suction is analyzed, the measure method for variable structure suction is discussed, and it reach the conclusions: ①Besides saturation state, variable structure suction is affected by grain composition and packing patter of grains. ②The internal relations are present between structure parameter N in computing structure suction and structure parameter D in computing absorbed suction. We think that some problems exit in available principle of effective stress and shear strength theory for unsaturated soil. Based on the variable structure suction and absorbed suction, the classification of saturation in soil and a principle of narrow sense effective stress are proposed for unsaturated soils. Based on generalized suction, the generalized effective stress formula and a principle of generalized effective stress are proposed for unsaturated soils. The experience parameter χ in Bishop's effective stress formula is defined, and the principal factors influencing effective stress or χ. The primary factor affecting the effective stress in unsaturated soils, and the principle classifying unsaturated soils and its mechanics methods analyzing unsaturated soils are discussed, and this paper points out: The theory on studying unsaturated soil mechanics should adopt the micromechanics method, then raise it to macromechanics and to applying. Researching the mechanical effects of chemical action of water-soil on soil is of great importance to geoenvironmental hazard control. The texture of soil and the fabric of soil mass are set forth. The tests on physical and mechanical property are performed to investigate the mechanism of the positive and negative mechanical effects of different chemical property of aqueous solution. The test results make clear that the plastic limit, liquid limit and plasticity index are changed, and there exists both positive and negative effects on specimens in this test. Based on analyzing the mechanism of the mechanical effects of water-soil interaction on soil, author thinks that hydrochemical actions being provided with mechanical effects on soil comprise three kinds of dissolution, sedimentation or crystallization. The significance of these tests lie in which it is recognized for us that we may improve, adjust and control the quality of soils, and may achieve the goal geological hazard control and prevention.The present and the significance of the research on environmental effects of water-rock and soil interaction. Various living example on geoenvironmental hazard in this field are enumerated. Following above thinking, we have approached such ideals that: ①changing the intensity and distribution of source and sink in groundwater flow system can be used to control the water-rock and soil interaction. ②the chemical action of water-rock and soil can be used to ameliorate the physical and mechanical property of rocks and soils. Lastly, the research thinking and the research methods on mechanical effects and environmental effects of water-rock and soil interaction are put forward and detailed.

Numerical simulation of an adaptive optics system with laser propagation in the atmosphere

A comprehensive model of laser propagation in the atmosphere with a complete adaptive optics (AO) system for phase compensation is presented, and a corresponding computer program is compiled. A direct wave-front gradient control method is used to reconstruct the wave-front phase. With the long-exposure Strehl ratio as the evaluation parameter, a numerical simulation of an AO system in a stationary state with the atmospheric propagation of a laser beam was conducted. It was found that for certain conditions the phase screen that describes turbulence in the atmosphere might not be isotropic. Numerical experiments show that the computational results in imaging of lenses by means of the fast Fourier transform (FFT) method agree well with those computed by means of an integration method. However, the computer time required for the FFT method is 1 order of magnitude less than that of the integration method. Phase tailoring of the calculated phase is presented as a means to solve the problem that variance of the calculated residual phase does not correspond to the correction effectiveness of an AO system. It is found for the first time to our knowledge that for a constant delay time of an AO system, when the lateral wind speed exceeds a threshold, the compensation effectiveness of an AO system is better than that of complete phase conjugation. This finding indicates that the better compensation capability of an AO system does not mean better correction effectiveness. (C) 2000 Optical Society of America.

Effects of Noise and Detection Error in a Dynamic Adaptive Optics System

It is well known that noise and detection error can affect the performances of an adaptive optics (AO) system. Effects of noise and detection error on the phase compensation effectiveness in a dynamic AO system are investigated by means of a pure numerical simulation in this paper. A theoretical model for numerically simulating effects of noise and detection error in a static AO system and a corresponding computer program were presented in a previous article. A numerical simulation of effects of noise and detection error is combined with our previous numeral simulation of a dynamic AO system in this paper and a corresponding computer program has been compiled. Effects of detection error, readout noise and photon noise are included and investigated by a numerical simulation for finding the preferred working conditions and the best performances in a practical dynamic AO system. An approximate model is presented as well. Under many practical conditions such approximate model is a good alternative to the more accurate one. A simple algorithm which can be used for reducing the effect of noise is presented as well. When signal to noise ratio is very low, such method can be used to improve the performances of a dynamic AO system.

Cone Effect in Astronomical Adaptive Optics System Investigated by a Pure Numerical Simulation

It is well-known that cone effect or focus anisoplanatism is produced by the limited distance of a laser guide star (LGS) which is created within the Earth atmosphere and consequently located at a finite distance from the observer. In this paper, the cone effect of the LGS for different vertical profiles of the refractive index structure constant Cn2 is numerically investigated by using a revised computer program of atmospheric propagation of optical wave and an adaptive optics (AO) system including dynamic control process. According to the practice, the overall tilt for the tilt-correction mirror is obtained from a natural star and the aberrated wavefront for phase correction of the deformable mirror is obtained from a LGS in our numerical simulation. It is surprisingly found that the effect of altitude of the LGS on the AO phase compensation effectiveness by using the commonly-available vertical profiles of Cn2 and the lateral wind speed in the atmosphere is relatively weak, and the cone effect for some Cn2 profiles is even negligible. It is found that the cone effect does not have obvious relationship with the turbulence strength, however, it depends on the vertical distribution profile of Cn 2 apparently. On the other hand, the cone effect depends on the vertical distribution of the lateral wind speed as well. In comparison to a longer wavelength, the cone effect becomes more obvious in the case of a shorter wavelength. In all cases concerned in this paper, an AO system by using a sodium guide star has almost same phase compensation effectiveness as that by using the astronomical target itself as a beacon. Effect of dynamic control process in an AO system on the cone effect is studied in this paper for the first time within our knowledge.