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In this paper, a new methodology is presented to derive the aberration state of a lithographic projection system from wafer metrology data. For this purpose, new types of phase-shift gratings (PSGs) are introduced, with special features that give rise to a simple linear relation between the PSG image displacement and the phase aberration function of the imaging system. By using the PSGs as the top grating in a diffraction-based overlay stack, their displacement can be measured as an overlay error using a standard wafer metrology tool. In this way, the overlay error can be used as a measurand based on which the phase aberration function in the exit pupil of the lithographic system can be reconstructed. In practice, the overlay error is measured for a set of different PSG targets, after which this information serves as input to a least-squares optimization problem that, upon solving, provides estimates for the Zernike coefficients describing the aberration state of the lithographic system. In addition to a detailed method description, this paper also deals with the additional complications that arise when the method is implemented experimentally and this leads to a number of model refinements and a required calibration step. Finally, the overall performance of the method is assessed through a number of experiments in which the aberration state of the lithographic system is intentionally detuned and subsequently estimated by the new method. These experiments show a remarkably good agreement, with an error smaller than 5¿¿m¿ , among the requested aberrations, the aberrations measured by the on-tool aberration sensor, and the results of the new wafer-based method.

The judgment of the imaging quality of an optical system can be carried out by examining its through-focus intensity distribution. It has been shown in a previous paper that a scalar-wave analysis of the imaging process according to the extended Nijboer-Zernike theory allows the retrieval of the complex pupil function of the imaging system, including aberrations as well as transmission variations. However, the applicability of the scalar analysis is limited to systems with a numerical aperture (NA) value of the order of 0.60 or less; beyond these values polarization effects become significant. In this scalar retrieval method, the complex pupil function is represented by means of the coefficients of its expansion in a series involving the Zernike polynomials. This representation is highly efficient, in terms of number and magnitude of the required coefficients, and lends itself quite well to matching procedures in the focal region. This distinguishes the method from the retrieval schemes in the literature, which are normally not based on Zernike-type expansions, and rather rely on point-by-point matching procedures. In a previous paper [J. Opt. Soc. Am. A 20, 2281 (2003)] we have incorporated the extended Nijboer-Zernike approach into the Ignatowsky-Richards/Wolf formalism for the vectorial treatment of optical systems with high NA. In the present paper we further develop this approach by defining an appropriate set of functions that describe the energy density distribution in the focal region. Using this more refined analysis, we establish the set of equations that allow the retrieval of aberrations and birefringence from the intensity point-spread function in the focal volume for high-NA systems. It is shown that one needs four analyses of the intensity distribution in the image volume with different states of polarization in the entrance pupil. Only in this way will it be possible to retrieve the "vectorial" pupil function that includes the effects of birefringence induced by the imaging system. A first numerical test example is presented that illustrates the importance of using the vectorial approach and the correct NA value in the aberration retrieval scheme.

We propose a measurement approach that allows the determination of aberrations of a microlens by analyzing the through-focus intensity image it produces when the object is a point source. To simulate image formation by a microlens we apply the extended version of the Nijboer-Zernike diffraction theory (ENZ) that uses the Debye diffraction integral to compute the image point-spread function. Due to the aperture size of the microlens and the finite dimensions of the pixels of the electronic detector the Debye diffraction integral should be adapted according to the Li-Wolf scaling rules to yield correct results. In addition to this we also discuss the experimental requirements posed by this characterization approach and derive from this a suitable experimental setup.

Results are presented of mask imaging using the Extended Nijboer-Zernike (ENZ) theory of diffraction. We show that the efficiency of a mask imaging algorithm, derived from this theory, can be increased. By adjusting the basic Finite Difference Time Domain (FDTD) algorithm, we can calculate the near field of isolated mask structures efficiently, without resorting to periodic domains. In addition, the calculations for the points on the entrance sphere of the imaging system can be done separately with a Fourier transformed Stratton-Chu near-to-far-field transformation. By clever sampling in the radial direction of the entrance pupil, the computational effort is already reduced by at least a factor of 4.

We present concise formulae for the Zernike coefficients of numerical aperture reduced pupils and show how they can be exploited within the framework of the ENZ-formalism to characterize optical systems with scaled and annular pupils.

In this paper we introduce a new mask imaging algorithm that is based on the source point integration method (or Abbe method). The method presented here distinguishes itself from existing methods by exploiting the through-focus imaging feature of the Extended Nijboer-Zernike (ENZ) theory of diffraction. An introduction to ENZ-theory and its application in general imaging is provided after which we describe the mask imaging scheme that can be derived from it. The remainder of the paper is devoted to illustrating the advantages of the new method over existing methods (Hopkins-based). To this extent several simulation results are included that illustrate advantages arising from: the accurate incorporation of isolated structures, the rigorous treatment of the object (mask topography) and the fully vectorial through-focus image formation of the ENZ-based algorithm.