Showing papers by "Xiangzhao Wang published in 2016"

Zernike polynomials as a basis for modal fitting in lateral shearing interferometry: a discrete domain matrix transformation method.

Abstract: A Zernike-polynomials-based wavefront reconstruction method for lateral shearing interferometry is proposed. Shear matrices are calculated using matrix transformation instead of mathematical derivation. Simulation results show that the shear matrices calculated using the proposed method are the same as those obtained from mathematical derivation. The advantage of the proposed method is that high order shear matrices can be obtained easily; thus, wavefront reconstruction can be extended to higher order Zernike terms, and reconstruction accuracy can be improved.

Pixelated source optimization for optical lithography via particle swarm optimization

Abstract: Source optimization is one of the key techniques for achieving higher resolution without increasing the complexity of mask design. An efficient source optimization approach is proposed on the basis of particle swarm optimization. The pixelated sources are encoded into particles, which are evaluated by using the pattern error as the fitness function. Afterward, the optimization is implemented by updating the velocities and positions of these particles. This approach is demonstrated using three mask patterns, including a periodic array of contact holes, a vertical line/space design, and a complicated pattern. The pattern errors are reduced by 69.6%, 51.5%, and 40.3%, respectively. Compared with the source optimization approach via genetic algorithm, the proposed approach leads to faster convergence while improving the image quality at the same time. Compared with the source optimization approach via gradient descent method, the proposed approach does not need the calculation of gradients, and it has a strong adaptation to various lithographic models, fitness functions, and resist models. The robustness of the proposed approach to initial sources is also verified.

General analytical expressions for the impact of polarization aberration on lithographic imaging under linearly polarized illumination

Abstract: With the shrinking of the critical dimension, the impact of polarization aberration on lithographic imaging becomes increasingly prominent. In this paper, the linear relationships between the image placement error and odd Pauli-Zernike polarization aberrations, as well as those between the best focus shift and even Pauli-Zernike polarization aberrations, are established by analyzing the imaging of the alternating phase-shifting mask. The relational expressions of the polarization aberration sensitivities (PAS) and the polarization angle of illumination are obtained based on these linear relationships. Then the expressions for the zero-value points and extremum points of the PAS are derived, and the impact of the polarization angle of illumination on the PAS is analyzed. The derived analytical expressions match the simulation results well; these can be used to analyze the detrimental impact of polarization aberration on lithographic imaging and provide a theoretical basis for exploring polarization aberration measurement and control techniques.

Parallel detection device for multiple field point wave aberrations of lithographic projection objective lens and detection method

Abstract: The invention provides a parallel detection device for multiple field point wave aberrations of a lithographic projection objective lens and a detection method. Spatial light modulators are respectively placed on an object plane and an image plane of a to-be-detected objective lens; the spatial light modulator in the object plane and the spatial light modulator in the image plane are respectively set into an object plane grating group including a plurality of one-dimensional gratings and an image plane grating group including a plurality of two-dimensional gratings through computer programming; the gratings of the object plane grating group and the image plane grating group are conjugated relative to the to-be-detected objective lens; and each pair of conjugated gratings measures the wave aberration of one field point. Periods and grid line directions of the gratings in the object plane and the image plane are controlled through computer programming; change of a shear direction and adjustment of the shear rate are achieved under the premise of not changing or mechanically moving any device; the system flexibility is improved; movement of grid lines of the gratings in the object plane or the image plane is controlled through computer programming to achieve a phase shift; the problem of a pupil position offset or a field point measurement position offset caused by the phase shift generated by mechanical movement of the gratings is overcome; and the measurement accuracy is improved.

Nonsubsampled contourlet transform method for optical fringe pattern analysis in profilometry and interferometry.

Abstract: A method based on a nonsubsampled contourlet transform, which is an overcomplete transform with multiresolution, directionality, and shift-invariance properties, is proposed to extract the fundamental frequency component of an optical fringe pattern in profilometry and interferometry. The nonsubsampled contourlet transform method overcomes the disadvantages of the original contourlet transform method, which lacks the shift-invariance property. Besides, it improves the frequency selectivity. A strategy is developed to automatically determine the optimal decomposition scale for removing the background intensity and suppressing the noise of the fringe pattern. The proposed method is precise, effective, and possesses a strong noise immune ability. Simulations and experiments verify the validity, and show the superiorities of the proposed method.

Wavefront aberration measurement method for a hyper-NA lithographic projection lens based on principal component analysis of an aerial image

Abstract: A wavefront aberration measurement method for a hyper-NA lithographic projection lens by use of an aerial image based on principal component analysis is proposed. Aerial images of the hyper-NA lithographic projection lens are expressed accurately by using polarized light and a vector imaging model, as well as by considering the polarization properties. As a result, the wavefront aberrations of the hyper-NA lithographic projection lens are measured accurately. The lithographic simulator PROLITH is used to validate the accuracies of the wavefront aberration measurement and analyze the impact of the polarization rotation of illumination on the accuracy of the wavefront aberration measurement, as well as the degree of polarized light and the sample interval of aerial images. The result shows that the proposed method can retrieve 33 terms of Zernike coefficients (Z5-Z37) with a maximum error of less than 0.00085λ.

Pixel-based mask optimization via particle swarm optimization algorithm for inverse lithography

Abstract: An efficient pixel-based mask optimization method via particle swarm optimization (PSO) algorithm for inverse lithography is proposed. Because of the simplicity of principles, the ease of implementation and the efficiency of convergence, PSO has been widely used in many fields. In this study, PSO is used to solve the inverse problem of mask optimization. The pixel-based mask patterns are transformed into frequency space using discrete cosine transformation and the frequency components are encoded into particles. The pattern fidelity is adopted as the fitness function to evaluate these particles. The mask optimization method is implemented by updating the velocities and positions of these particles. Simulation results show that the image fidelity has been efficiently improved after using the proposed method.

Point diffraction interference wave aberration measurement instrument and optical system wave aberration detection method

Abstract: The invention provides a point diffraction interference wave aberration measurement instrument and an optical system wave aberration detection method. The point diffraction interference wave aberration measurement instrument is composed of a light source, a light splitter, a first light intensity and polarization regulator, a phase shifter, a second light intensity and polarization regulator, an ideal wave-front generation unit, an object space precise regulating table, a measured optical system, an image space wave-front detection unit, an image space precise regulating table and a data processing unit. The point diffraction interference wave aberration measurement instrument is characterized in that the center distance between the first output end and the second output end of the ideal wave-front generation unit is less than the diameter of the isoplanatic region of the measured optical system and greater than a result which is obtained through dividing the diameter of the image point dispersion spots of the measured optical system by the magnification times of the measured optical system. The measurement instruction has advantages that the detection steps are easy, the measurement process has average effect, and system error calibration and elimination of complete numerical aperture can be realized.

Wave aberration measurement instrument of point diffraction interference and detection method of wave aberration of optical system

Abstract: The invention discloses a wave aberration measurement instrument of point diffraction interference and a second detection method of a wave aberration of an optical system. The measurement instrument is composed of a light source, an optical splitter, a first light intensity and polarization state regulator, a phase shifter, a second light intensity and polarization state regulator, an ideal wavefront and point light source generation unit, an object space precise adjusting table, the tested optical system, an image space wavefront detection unit, an image space precise adjusting table and a data processing unit. The measurement instrument provided by the invention only needs to generate a channel of standard spherical wave output on an object surface of the tested optical system, so that system complexity is reduced and an optical energy utilization rate is increased; and the measurement instrument also reduces precision requirements and operational complexity of the system.