Theory And Method For In-Situ Lens Aberration Measurement In Optical Lithographic Tools Based On Image Intensity

With the development of lithographic tools, the limit of resolution is being pushed, and the numerical aperture (NA) is incresing. Since lens aberration directly influences the imaging resolution and process window, it is the most important parameter of imaging evaluation. Lens aberration should be monitoring at every manufacture stage, while the measurement precision must reach an exremely high level. Due to the advantage of lower cost, easier implement and less error sources, intensity based techniques have been widely used for in-situ measurement. But in practical applications, intensity based lens aberration measurement technique encounters many technical challenges, which can be categorized as follow:Firstly, lack of analytical model directly leads to lower measurement accuracy of pupil aberration. Secondly, in most intensity based aberration measurement techniques, dozens of mask patterns are needed and through focus image intensities should be monitored, which leads to economic cost and time-consuming measurement. Thirdly, most of the intensity based aberration measurement techniques utilize a simplified linear response model, which can not be used when aberrations are relatively large. Fourthly, with the increasing of numerical aperture, polarization aberration becomes more important, in which intensity based measurement techniques are not widely and efficiently used yet. With the purpuse of solving these problems, this dissertation carries out research on new thoery and method for in-situ measurement of lens aberration in optical lithographic tools based on image intensity. The main contents of this dissertation are as follow:A transport of intensity equation (TIE) based in-situ method of lens aberration measurement for lithographic tools with an analytical aberration model is proposed. The conventional TIE, which can only be used with coherence illumination, is extended to the general case of partially coherent illumination. By investigating the physical characteristic of far field imaging in lithographic tools, an analytical formulation of pupil phase and image field is established, which makes TIE based aberration measurement method realizable. This method requires only a minimum of two intensity measurements at closely spaced planes, and fast Fourier transform (FFT) algorithm is introduced to calculate the aberrations, with the accuracy of aberrations on the order of m?s for the lithographic tools with NA<0.6.A single image based in-situ method of small lens aberration retrieval for lithographic tools with relatively high NA is proposed. By in-depth theoretical derivation, a linear formulation of imaging systems is derived in a matrix form that directly relates the measurement image to the unknown Zernike coefficients, and a test pattern optimization method is proposed. This method only requires to measure one single defocused image of intensity. With the optimized test pattern and least square method, Zernike coefficients can be in-situ extracted. This method overcomes the high cost and time-consuming problem, with a very good accuracy on the order of m?s when the input aberrations are less than 60m?.An iterative method for in-situ mesurement of lens aberrations in lithographic tools is proposed, which can be used in the case when aberrations are relatively large. A quadratic aberration model is established, which is a natural extension of the linear model. By taking into account interactions among individual Zernike coefficients, the basis image terms are defined. In this method, with the help of basis image terms, the Zernike coefficients are determined by solving an inverse problem through an iterative procedure from several through focus images of a specially designed mask pattern. The method still achieves high accuracy of Zernike coefficients and aberrations when the aberration is relatively large (up to 150m?).For the polarization aberration measurement in immersion lithographic tools with hyper-NA, a sensitivity analysis based in-situ measurement method is proposed. By in-depth analysis of polarization characteristic in imaging, a vector imaging model is established, based on which the aberrated image induced by different polarization aberration is researched. Pauli-Zernike polynomials are used to parameterize the polarization aberration, and analytical sensitivity analysis based on binary gratings is proceeded. This method needs to measure three-dimensional distribution of image intensity. Combining the sensitivity matrices of different polarization aberrations, Pauli-Zernike coefficients can be extracted. Using this method, the polarization aberration is measuremed effectively, with the realative error of Jones pupil measurement less than 10-2.The methods in this dissertation propose corresponding solutions for the difficulties of intensity based aberration measurement techniques, which are practicable, low cost, high efficiency and high precision. In summary, these methods provide novel theories and new ways, and greatly enrich the aberration measurement theory in optical lithographic tools.