Yanqiu Li

Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry

Least-squares (LS)-based integration computes the function values by solving a set of integration equations (IEs) in LS sense, and is widely used in wavefront reconstruction and other fields where the measured data forms a slope. It is considered that the applications of IEs with smaller truncation errors (TEs) will improve the reconstruction accuracy. This paper proposes a general method based on the Taylor theorem to derive all kinds of IEs, and finds that an IE with a smaller TE has a higher-order TE. Three specific IEs with higher-order TEs in the Southwell geometry are deduced using this method, and three LS-based integration algorithms corresponding to these three IEs are formulated. A series of simulations demonstrate the validity of applying IEs with higher-order TEs in improving reconstruction accuracy. In addition, the IEs with higher-order TEs in the Hudgin and Fried geometries are also deduced using the proposed method, and the performances of these IEs in wavefront reconstruction are presented.

Approach to characterize manufacture tolerances of two-dimensional cross-phase grating

Abstract. Two-dimensional cross-phase grating (CPG), diffracting the incident wave into (+1,+1), (+1,−1), (−1,−1), and (−1,+1) orders diffraction light, is used as a wavefront shearing element in cross-phase grating lateral shearing interferometer. However, the manufacture errors always exist, and they produce unwanted diffraction orders in the process of CPG manufacture. The appearance of the unwanted orders will increase the background noise of the interferogram and may affect the accuracy of the interferogram analysis. So, it is necessary to analyze the influences of manufacture errors and to determine the manufacture tolerances to remove the effect. A method based on Fourier transform analysis is presented to characterize manufacture tolerances of CPG. In this method, first, the normalized intensity distribution produced by CPG with manufacture errors in the far field is obtained. In addition, relative intensity of other unwanted orders to (+1,−1) order diffraction light of the four replicas is calculated, respectively. According to the relative intensity, the influences due to different types of manufacture errors can be evaluated, and the manufacture tolerances can also be determined. Using the proposed method, the manufacture tolerances of CPG at 632.8 nm are determined. Experimental evaluation of the proposed method using the manufactured CPG at 632.8 nm is also carried out.

Grouping design method with real ray tracing model for extreme ultraviolet lithographic objective

Abstract. Choosing an adequate initial design for optimization plays an important role in obtaining high-quality extreme ultraviolet (EUV) lithographic objectives. A grouping design method with real ray tracing model is developed to acquire initial configurations of high numerical aperture (NA) objective for EUV lithography. In this method, the objective system is first divided into three mirror groups. The initial parameters of each mirror group are then determined by real ray calculation under design constraints. Finally, the three mirror groups are connected directly into a feasible initial system. Due to real ray calculation, the discrepancy of the ray path induced by paraxial approximation and the exhaustive search of variables is avoided in a high-NA objective design. In addition, the incidence angles on reflective mirrors can be controlled in the design of each group, which makes the initial configuration suited to further optimization and compatible multilayer design. An NA 0.33 six-mirror EUV lithographic objective is designed as an example to implement this method.

Misalignment effects of cross-phase grating lateral shearing interferometer and its alignment technique

Abstract. To realize in-situ wavefront aberration measurement of hypernumerical aperture projection optics, a hypernumerical aperture cross-phase grating lateral shearing interferometer (HNA-CPGLSI) is proposed. To achieve high-wavefront measurement accuracy, accurate alignment of HNA-CPGLSI is essential. Misalignments of HNA-CPGLSI include collimation optics, cross-phase grating, and CCD. Misalignment of collimation optics mainly produces defocus aberration. After the CPGLSI formed by cross-phase grating and CCD is accurately aligned, the alignment of collimation optics is easy to achieve by measuring and controlling the defocus aberration. So the misalignments effects analysis and alignment of CPGLSI formed by cross-phase grating and CCD are focused. Using wave interference theory and wavefront reconstruction technique, a method to analyze the sensitivity relationship between cross-phase grating or CCD and measured aberrations is built. Misalignment effects of CPGLSI on wavefront measurement accuracy are evaluated. An experimental study on CPGLSI is also carried out. The results show that the measurement accuracy of CPGLSI after accurate alignment can reach to 3.0 mλ (1.9 nm, λ=632.8  nm) root mean square (RMS) and repeatability can reach to 0.20 mλ (0.13 nm, λ=632.8  nm) RMS.

Automatic figure errors balancing method for catoptric and catadioptric lenses

Abstract. For high performance imaging and focusing applications, figure errors can degrade the performance of lenses, especially in catoptric and catadioptric lenses. An automatic figure errors balancing method is proposed. By using geometrical optics, the linear relationships between the figure errors and wavefront error (WFE) of lens for three kinds of optical surfaces are established and verified. The WFE sensitivity to figure errors based on this linear relationship is analyzed before clocking optimization to improve the efficiency of optimization. The clocking procedure indirectly optimizes the rotation angle of individual WFE map induced by figure error and performs a 360-deg tour to determine which the best position is. Using this method, the optimal combination of rotation angle of components would be acquired fleetly, especially for optical system included an optical component which figure errors is remarkable influence on WFE. The method is implemented on two manufactured optical systems: a Schwarzschild projection lens and a collimator lens. Simulation experiment proves our method can greatly reduce the aberration caused by figure errors. Compared with conventional randomly assembling method, WFE of the projection lens can be reduced by 40% and WFE of the collimator lens can be reduced by 51%.

Clocking-optimization method for figure-error balancing in complex optical systems

Abstract. Figure errors of optical surfaces degrade the performance of optical systems. When predicting the performance and performing system assembly, compensation by clocking of optical components around the optical axis is a conventional but user-dependent method. Commercial optical software cannot optimize this clocking, and existing automatic figure-error balancing methods have limitations. To overcome these limitations, a global and general optimization method based on analyzing the precise relationships between the figure errors and the wavefront error (WFE) is proposed. Using the footprint data of each optical surface, the resulting WFE is calculated. Direct map operation is used for intercepting and rotating the figure-error maps. The simulated annealing algorithm is used to seek the optimal combination of clocking angles for the optical components. This method can be applied to most coaxial optics systems, including dioptric, catoptrics, and catadioptric complex lenses. It is successfully implemented for a catadioptric immersion lithographic optics system with artificial figure errors, and for an experimental lithographic optics system with actual manufacturing figure errors.

Design method of off-axis extreme ultraviolet lithographic objective system with a direct tilt process

Abstract. An off-axis extreme ultraviolet (EUV) lithographic objective can achieve a high numerical aperture (NA) beyond 0.33 with only six mirrors due to the efficient separation of the ray path, which greatly improves the resolution and energy utilization. A method is developed to design an off-axis lithographic objective with six mirrors. The method starts with a coaxial system with ray vignetting caused by increase of the NA. To avoid the ray vignetting, a reasonable range of solution for the tilt angle of each mirror is determined by real ray calculation. A set of optimal solutions for tilt angles of mirrors, which corresponds to the minimal composite root-mean-square wavefront error, is found from the reasonable ranges of solutions by a search program. In this way, an initial off-axis configuration without ray vignetting can be directly obtained and it is suitable for further optimization. To demonstrate the practicability of the method, an off-axis design example is given which shows that the presented method provides an efficient process to get to initial configuration for off-axis EUV lithographic objective with six mirrors.

Improved wavefront reconstruction using difference Zernike polynomials for two double-shearing wavefronts

To realize wavefront reconstruction for two double-shearing wavefronts produced by our studied cross phase grating lateral shearing interferometer(CPGLSI) in x and y directions, improved wavefront reconstruction using difference Zernike polynomials is studied in this paper. Firstly, the x directional double-shearing wavefronts in the x direction produced by shearing of (+1, +1), (-1, +1) orders diffraction beams and that of (+1,-1), (-1,-1) orders diffraction beams are represented respectively by the corresponding difference Zernike polynomials. Then the whole difference wavefront in x direction is represented by the half value of the sum of the above x directional double-shearing wavefronts. Similarly, the double-shearing wavefronts in the y direction produced by shearing of (+1, +1), (+1, -1) orders and that of (-1, +1), (-1,-1) orders are represented respectively by the corresponding difference Zernike polynomials. Then the whole difference wavefront in y direction is also represented by the half value of the sum of the y directional double-shearing wavefronts. Secondly, the least square fitting is used to obtain the whole wavefront. Investigations on reconstruction accuracy and reliability are carried out by numerical experiments, in which influences of different shearing amounts and noises on reconstruction accuracy are evaluated. The simulation results show that the wavefront reconstruction accuracy can all reach to high accuracy corresponding to different shearing amounts and also validate that our wavefront reconstruction technique is robust to noise.

Calibration method to characterize the accuracy of phase-shifting point diffraction interferometer

Characterization of measurement accuracy of the phase-shifting point diffraction interferometer (PS∕PDI) is usually performed by two-pinhole null test. In this procedure, the geometrical coma and detector tilt astigmatism systematic errors are almost one or two magnitude higher than the desired accuracy of PS∕PDI. These errors must be accurately removed from the null test result to achieve high accuracy. Published calibration methods, which can remove the geometrical coma error successfully, have some limitations in calibrating the astigmatism error. In this paper, we propose a method to simultaneously calibrate the geometrical coma and detector tilt astigmatism errors in PS∕PDI null test. Based on the measurement results obtained from two pinhole pairs in orthogonal directions, the method utilizes the orthogonal and rotational symmetry properties of Zernike polynomials over unit circle to calculate the systematic errors introduced in null test of PS∕PDI. The experiment using PS∕PDI operated at visible light is performed to verify the method. The results show that the method is effective in isolating the systematic errors of PS∕PDI and the measurement accuracy of the calibrated PS∕PDI is 0.0088λ  rms  (λ = 632.8  nm).

High numerical aperture Hartmann wavefront sensor with pinhole array extended source

In situ aberration measurement of projection objective is necessary for lithography tool. For 90 nm technology node, aberration measurement accuracy of 1 nm rms is required. In this paper, a high numerical aperture Hartmann wavefront sensor with pinhole array extended source is proposed. The sensor uses source mask with pinhole array on the object plane of projection objective to filter the aberration of illumination optics as well as provide sufficient power required by Hartmann sensor. A coupling objective, which is installed at the confocal position of the projection objective under test, transforms the high numerical aperture spherical waves to plane waves. A null mask, which has similar structure with source mask, can be inserted at the image plane of projection objective. With the null mask installed and source mask uninstalled, the systematic measurement errors mainly caused by coupling objective can be calibrated by the relative measurement process. In this paper, some design considerations of source mask and null mask are presented. Using partial coherent light propagation and Fourier optics theory, the proper spacing and quantity of pinholes on either source mask or null mask are calculated. Finally, measurement accuracy of the sensor is evaluated using three-dimensional electromagnetic simulation of 193nm high numerical aperture converging beam propagation through pinhole with different pinhole parameters. Simulation results show that, measurement accuracy of the sensor is better than 0.5 nm rms in theory after systematic errors calibration.