Wavefront Aberration Measurement Technology Based On Two-dimensional Lateral Shearing Interferometry

With the strong demand of integrated circuit(IC)devices and the continuous progress of lithography technology,IC manufacturing technology has advanced into the nanoscale regime.Modern lithographic tools are the key equipments to manufacture the very large-scale integrated circuits(VLSI).The projection objective is one of the most important subsystems in the lithographic tools.The wavefront aberration of the projection objective directly determines the resolution,imaging contrast,and process window of lithographic tools.The traditional wavefront aberration measurement methods,based on the photoresist pattern and aerial image,can not satisfy the requirement of precision and timeliness of modern high numerical-aperture(NA)lithographic objective measurements.Therefore,a two-dimensional shearing interferometer based on an amplitude chessboard grating and a wavefront reconstruction algorithm is designed to measure the wavefront aberration of high NA objectives.In this dissertation,we focus on the principle of the chessboard grating lateral shearing interferometer(CBGLSI),the interferogram-resolving algorithm,and systematic error attributable to the grating alignment error.The primary contents include the following four parts.The transmission functions and far-field diffraction distributions of different amplitude gratings were derived using Fourier optics theory.The far-field diffraction properties and efficiencies of different amplitude gratings were analyzed.They indicate that chessboard gratings offer better diffraction efficiencies and fewer disturbing diffraction orders than traditional cross-gratings.Subsequently,a CBGLSI with the phase-shifting mode and Fourier transform mode was configured.The CBGLSI can work in the phase-shifting mode and Fourier transform mode.The interference intensity formulae and modulation functions of the phase-shifting mode were deduced.According to the interference intensity formulae and the phase-shifting properties of diffraction grating,the least-square phase-shifting algorithm was designed.The interferogram-resolving process in the phase-shifting mode was provided.Finally,the interference intensity formulae and modulation functions of the Fourier transform mode were deduced.The interferogram-resolving process in the Fourier transform mode was also provided.The phase-shifting shearing interferograms formed by the first-order diffraction and third-order diffraction were simulated.Based on the modulation distribution of the phase-shifting shearing interferograms,the algorithm to determine the shearing region of the ±1-order diffraction was proposed.The wavefront reconstruction method based on the differential Zernike polynomial fitting was developed.The extraction method of the first-order diffraction information in the phase-shifting shearing interferograms was discussed using the periodic extension and Fourier transform filter methods.The spatial-carrier shearing interferogram formed by the first order diffraction was simulated.The ±1-order diffraction information was extracted using two-dimensional Fourier transform and the frequency-domain filtering method.An algorithm to determine the shearing region of the ±1 order diffraction from the intensity distribution was proposed.The algorithms were validated by the simulated shearing interferogram.The feasibilities of the measurement principle and the inteferogram resolving algorithm were validated.Grating manufacturing errors,including the duty-cycle and pattern-deviation errors,were analyzed using the Fourier transform method.The influence of the phase-shifting error was analyzed through the shearing interferometer measurement process simulation.The shear ratio and pupil coordinate errors were analyzed through the wavefront reconstruction process simulation.According to the relation between the spherical pupil and planar detector coordinates,the influence of the distortion of the pupil coordinates was simulated.Finally,the systematic error attributable to the grating alignment errors was deduced through the geometrical ray-tracing method.The CBGLSI experimental setup has been built.The wavefront aberration measurement experiments with different NA objectives and different period gratings have been performed.Our experimental results indicate that the measuring repeatability(3?)of the wavefront aberration was better than 3 m? when the NA of the objective is below 0.4.The experiment validated that the CBGLSI can function in a dual mode: the phase-shifting mode and the Fourier transform mode.The differences of Z5 to Z36 between the two modes are better than 28m?.Subsequently,through experiments with different Talbot distances,we observed that the systematic error became larger as the defocus increased.The major systematic errors are the tetrafoil aberrations.From the experiments with different period gratings,we observed that the coma aberrations were different.The reason is that the tilt angles of the grating were different when the grating is replaced.Furthermore,we performed a systematic error calibration experiment based on the multiple-order method.The correct wavefront aberration can be obtained after the calibration.The systematic error calibration results were consistent with the previous analyses.Finally,several special problems involved in the measurement of wavefront aberration were discussed,and the results suggest that the influences of pupil coordinate distortion and irradiance attenuation at the pupil edge should be considered when wavefront aberration of the high NA objective is measured.