Tingwen Xing

Dynamic compensation for the lithographic object lens

The nominal design residual aberrations are very small for the lithographic object lens. The RMS wavefront error is in a few milliwaves, and the distortion is in a few nanometers. However, The manufacturing-induced aberrations are inevitable and usually many times larger than the design residual level. One method to reduce the manufacturing-induced aberrations is making a few lens adjustable after the object lens is assembled. Dynamic compensation can correct element metrology and assembly errors effectively, especially for the low order Zernike aberrations. We introduce a dynamic compensation method in this paper. This technique is based on the simulated imaging performance using Zernike sensitivity, which is the simulated results of wavefront aberration change by lens element position change. We can select the potential moving lens by this technique. This method can find the optimum combination of moving lens position where the lithographic object lens imaging performance is improved remarkably.

Two-dimension lateral shearing interferometry for microscope objective wavefront metrology

Lateral shearing interferometry was an attractive technique to measure the wavefront aberration of high numerical aperture microscope objective lens. A two-dimension lateral shearing interferometer based on chessboard grating was designed for microscope objective wavefront metrology. By positioning the chessboard grating at the Talbot distance of the objective focal plane, the wavefront was divided and sheared in two-dimension. By applying two-dimensional Fourier transform method and differential Zernike polynomial fitting, Zernike coefficients of the wavefront were obtained. A 10x, NA0.25 microscope objective was measured at 632.8nm wavelength, the results showed that the wavefront of the objective was 0.755λ PV, 0.172λ RMS, the repeatability(3σ) of RMS at random grating position was 2.3mλ, the repeatability(3σ) of Z5 to Z36 at random grating position were better than 17mλ.

Design and location deviation of the computer generated holograms used for aspheric surface testing

Computer generated holograms (CGHs) are widely used in aspheric surface testing and metrology. The primary role of the CGHs is to generate any desired wavefronts to realize phase compensation. In order to eliminate alignment errors of CGH and the tested aspheric, this paper designs a new layout of CGH that has the advantages of high alignment accuracy and simple experimental operation. And further the influence of the location deviation of CGH and the tested aspheric mirror to the entire system is discussed; it shows that the error introduced by the CGH and the tested aspheric mirror tilting around the x-axis or y-axis as well as the tested aspheric mirror moving along the x-axis or y-axis direction is large. Then the CGH design principle and design process are reviewed. Finally, a CGH is designed for measurement of an aspheric mirror (diameter=226mm, F-number =2.2). Interferometric test results of an aspheric mirror show that the whole test system obtains the demanded high accuracy.

Illumination optimization in optical projective lithography

As lithography still pushing toward to lower K1 imaging, traditional illumination source shapes may perform marginally in resolving complex layouts, freeform source shapes are expected to achieve better image quality. Illumination optimization as one of inverse lithography techniques attempts to synthesize the input source which leads to the desired output wafer pattern by inverting the forward model from mask to wafer. Usually, inverse lithography problem could be solved by standard numerical methods. Recently, a set of gradient-based numerical methods have been developed to solve the mask optimization problem based on Hopkins approach. In this study, the same method is also applied to resolve the illumination optimization but based on Abbe imaging formulation for partially coherent illumination. Firstly we state a pixel-based source representation, and analyze the constraint condition for source intensity. Secondly, we propose an objective function which includes three aspects: image fidelity, source smoothness and discretization penalty. Image fidelity is to ensure that the image is as close to the given mask as possible. Source smoothness and discretization penalty are to decrease the source complexity. All of the three items could be described mathematically. Thirdly, we describe the detailed optimization flow, and present the advantages of using Abbe imaging formulation as calculation mode of light intensity. Finally, some simulations were done with initial conventional illumination for 90nm isolated, dense and elbow features separately. As a result, we get irregular dipole source shapes for isolated and dense pattern, and irregular quadrupole for elbow pattern. The results also show that our method could provide great improvements in both image fidelity and source complexity.

The impact of polarization on grating performance of the lateral shearing interferometer

With the development of modern precision optical systems, optical detecting system requires the accuracy of wavefront aberration to arrive to sub-nanometer level. When the incident field with polarization information, the polarization information will have a significant impact on the accuracy of measurement results by interacting with polarization-sensitive optical components in the lateral shearing interferometer. We propose the integrated interferometer wavefront sensor (IIWS) system, which is based on the traditional lateral shearing interferometer. This wavefront is sheared by a two-dimension diffraction grating in our system, the two-dimension diffraction grating is the key element to analysis the metrology performance. When using a different grating period and shearing direction, the wavefront shearing and phase shifting with polarization information will produce different error, moreover the impact will vary in the different diffraction orders. In this paper, calculation is based on the finite difference time domain (FDTD) algorithm. When calculation of different polarization state distribution of the incident field, the interaction analysis of shearing phase shifted grating and incidence light play an important role in error analysis. Finally we can get the effect of polarization for grating performance.

Design of twin computer-generated hologram for absolute testing of aspheric surfaces

Testing of aspheric surfaces by means of computer-generated holograms（CGHs）is well known. To perform an absolute test of rotationally symmetric aspheric surfaces, a specially designed computer-generated hologram (CGH) that reconstructs an aspherical wave as well as a spherical auxiliary wave. Since both phase functions have the same symmetry and their pattern is simultaneously encoded, we call this type of multiplex hologram a Twin-CGH. The spherical wave is used for calibration. The design principle of Twin-CGH is introduced in this paper. We mathematically analyze the Twin-CGH constructed by taking the phase corresponding to the linear combination of two weighted phase functions. We show that this Twin-CGH may be written as a new linear combination for the original phase functions with new weights. Then we absolutely test aspheric surfaces by Twin-CGH.

Aberration functions expanding in Zernike polynomial for lithographic lens

For characteristic of a lithographic lens, wide field, a series of coefficients of Zernike polynomial cannot express the characteristic of aberration of the whole system．In this paper, we relate coefficient of Zernike polynomial to field coordinates by introducing double Zernike polynomial to represent field dependent aberrations of lithographic lens. The new aberration function is a sum of some four dimensions polynomial, which consist of fringe Zernike of pupil coordinates and field coordinates. We emulate the manufacturing error of lithographic lens by code V, a software of optical design, and fit a set of double Zernike polynomial coefficients by using single Zernike coefficients of a lot of field points to represent the global aberration of lithographic lens.

Source optimization using simulated annealing algorithm

As lithography still pushing toward to lower kU00100b35 imaging, traditional illumination source shapes may perform marginally in resolving complex layouts, freeform source shapes are expected to achieve better image quality. Illumination optimization as one of inverse lithography techniques attempts to synthesize the input source which leads to the desired output wafer pattern by inverting the forward model from mask to wafer. This paper proposes a method to optimize illumination by using simulated annealing algorithms (SA). A synthesis of the NILS values at multi-critical mask locations over a focus range is chose as the merit function. The advantage of the SA algorithm is that it can identify optimum source solutions without any additional apriori knowledge about lithographic processes. The results show that our method can provide great improvements in both image quality and DOF.

Spherical aberrations and manufacturing errors in eliminating the substrate errors of a computer-generated hologram (withdrawn)

This paper [ Opt. Eng. 52 (9), 091723 (2013)] was removed from the SPIE Digital Library on 24 July 2013 by the publisher upon verifying that a significant portion of Section 4 of the paper was taken directly from the following previously published paper without attribution: Ping Zhou and James H. Burge, “Optimal design of computer-generated holograms to minimize sensitivity to fabrication errors,” Optics Express 15 (23), 15410 (2007). The citation is provided here so that interested readers can access the information from the original source.

Error analysis for aspheric surface testing system

Computer-generated holograms (CGHs) are commonly used in optical interferometry for producing reference wavefronts with desired shapes. Uncertainties from the computer generated hologram (CGH) manufacturing processes produce errors in the finished hologram and the generated reference wavefront. CGH errors compromise the accuracy of the interferometric measurements. Although errors in the CGHs may be introduced during either the design or the fabrication process, fabrication uncertainties are mostly responsible for the degradation of the quality of CGHs. To specify and verify detection accuracy of aspheric surface testing system, alignment errors and fabrication errors of the CGHs will be analyzed. Methods are discussed for measuring the fabrication errors in the CGH substrate, duty cycle, etching depth, and effect of surface roughness. An example analysis of the wavefront errors from fabrication nonuniformities for a phase CGH is given.