Modern steppers and scanners have a projection lens whose numerical aperture (NA) can be varied so as to optimize the image performance for certain lithographic features. Thus a variable fraction of the aberrations is actually involved in the imaging process. In this letter, we present a concise formula for the NA scaling of the Zernike coefficients. In addition, we apply our results to the Strehl ratio.
Phase Measurement Interferometers (PMI) are widely used during the manufacturing process of high quality lenses. Although they have an excellent reproducibility and sensitivity, the set-up is expensive and the accuracy of the measurement needs to be checked frequently. This paper discusses an alternative lens metrology method that is based on an aerial image measurement. We discuss the Extended Nijboer-Zernike (ENZ) method and its application to aberration measurement of a high-NA optical system of a wafer stepper. ENZ is based on the observation of the through-focus intensity point-spread function of the projection lens. The advantage of ENZ is a simple set-up that is easy to run and maintain and provides good accuracy. Therefore the method is useful during lens assembly in the factory. The mathematical framework of ENZ is shown and the experimental procedure to extract aberrations for a high-NA lens is demonstrated on a high-NA DUV lithographic lens. PMI data is given as reference data. It is shown that ENZ provides an attractive alternative to the interferometer.
This study presents an experimental method to determine the resist parameters at the origin of a general blurring of a projected aerial image. The resist model includes the effects of diffusion in the horizontal plane and image blur that originates from a stochastic variation of the focus parameter. We restrict ourselves to the important case of linear models, where the effects of resist processing and focus noise are described by a convolution operation. These types of models are also known as diffused aerial image models. The used mathematical framework is the so-called extended Nijboer-Zernike (ENZ) theory, which allows us to obtain analytical results. The experimental procedure to extract the model parameters is demonstrated for several 193-nm resists under various conditions of postexposure baking temperatures and baking times. The advantage of our approach is a clear separation between the optical parameters, such as feature size, projection lens aberrations, and the illuminator setting on one hand, and process parameters introducing blur on the other.
Previously, we have given a detailed description of the so-called
Extended Nijboer-Zernike approach and its application to aberration
measurements of the optical projection system in a wafer scanner in the case of a low or medium high-NA system. The Extended Nijboer-Zernike theory provides an analytical description of the through-focus intensity point-spread function in the presence of lens aberrations and defocus. Taking the Extended Nijboer-Zernike description for the electric field components in the case of a high-NA optical system as a starting point, we present an approach to aberration retrieval when the NA is very high. The experimental procedure involves the analysis of a focus-exposure matrix. The differences between aberration retrieval using the low-NA
scalar model and the high-NA full vectorial model are discussed. The
mathematical framework is shown and the experimental procedure to
extract aberrations for a high-NA lens is demonstrated on modern 193
nm wafer scanners.
Through ArF immersion lithography a road towards increased optical resolution at the 193nm wavelength has been opened. According to recently proposed roadmaps, ArF immersion lithography will be used for 65nm and 45nm technology nodes. Consequently, keeping the same 4x optical demagnification factor, the dimensions on mask scale down to wavelength values when entering these nodes. Moreover CD control becomes tighter and approaches values of 2-3nm. At such conditions, topography on mask, its type and materials cannot be ignored anymore while evaluating image formation either for design analysis or OPC adjustments. The objective of this paper is to analyze the influence of mask topography on imaging. The mask topography influences polarization state and diffraction efficiencies, which are determine further image formation. Therefore these parameters and their dependence on mask type, materials and pitches are of the major concern during the analyses. We analyze the process latitude and CD variations through pitch. The complete rigorous analysis shows improved process windows with the increase of feature aspect ratio and at the same time a large through pitch CD deviation compared to the conventional Kirchhoff diffraction model.
The shrinking of the dimensions for each new process generation increases the challenges for lithography significantly. In order to guarantee manufacturability for future process generations, a strong interaction between lithography and design is required. A quantitative measure for the manufacturability is of key importance for driving the improvements in the design for manufacturing process. Aerial image slopes or contrasts in simulated images provide a measure for the sensitivity to process variations, but do not take the statistical process variation into account. This may result in sub-optimal choices in the design for manufacturing process.
This paper discusses the process capability analysis and provides an optimal design with corresponding imaging conditions, taking the statistical fluctuations of exposure dose and focus into account.
The mean CD value and the CD spread are calculated as a function of the amount of variation in the process variables like focus and exposure dose. Comparing these distribution parameters to the
process specifications yields the so-called process capability index as a quantitative measure for the manufacturability. Another advantage is the possibility to include the effect of mask errors on the manufacturability. Until now, however, this method had only been demonstrated for line space features. In this paper we extend the process capability analysis method for calculating the
manufacturability of arbitrary layouts. The analysis is demonstrated in an evaluation of the manufacturability of various gate layer designs, both conventional as well as litho-driven re-designs.
This study presents an experimental method to determine the resist parameters that are at the origin of a general blurring of the projected aerial image. The resist model includes the effects of diffusion in the horizontal plane and a second cause for image blur that originates from a stochastic variation of the focus parameter. The used mathematical framework is the so-called Extended Nijboer-Zernike (ENZ) theory. The experimental procedure to extract the model parameters is demonstrated for several 193 nm resists under various conditions of post exposure baking temperature and baking time. The advantage of our approach is a clear separation between the optical parameters, such as feature size, projection lens aberrations and the illuminator setting on the one hand and process parameters introducing blur on the other.
A capable process fulfills many requirements on e.g. depth of focus, exposure latitude, and mask error factor. This makes a full optimization complicated. Traditionally only a few parameters are included in the optimization routine, such as the focus-dose process window, while other parameters like the (NA,σ ) illumination conditions are fixed at a specified value. In this paper we present an analytical model for describing the effect of variations in dose, focus and mask CD. We optimize the overall CD distribution, both the target value and the CD variation, taking the statistical variations of focus, dose and mask line width variations into account. The improved CD control is measured quantitatively, using the well-known process capability index (Cpk). The results are compared to traditional optimization schemes and brute force Monte Carlo simulations. Process latitudes can be better optimized while calculating the OPC curve. This is achieved by tuning the mask corrections to the process variations and simultaneously optimizing the global mask bias. Furthermore, the optimization method enables a trade off between mask error and process control. Simulated aerial image data is used to determine the optimum mask bias and illumination condition for different levels of process variation, including mask CD variation. The effect of optimizing the global mask bias is calculated. Finally, the results will be compared to experimental data for a number of illumination settings.
In this paper we show various results of aberration retrieval using the pinhole method in conjunction with the extended Nijboer-Zernike theory. The experiments are performed on modern wafer scanners. Keyboard commanded offsets of the movable lens elements of the imaging tool have been used to introduce astigmatism, coma and spherical aberration in a controlled way. The method is designed to estimate these induced aberrations and we show the experimental results regarding the various types of aberrations created this way.
We give the proof of principle of a new experimental method to determine the aberrations of an optical system in the field. The measurement is based on the observation of the intensity point-spread function of the lens. To analyze and interpret the measurement, use is made of an analytical method, the so-called extended Nijboer-Zernike approach. The new method is applicable to lithographic projection lenses, but also to EUV mirror systems or microscopes such as the objective lens of an optical mask inspection tool. Phase retrieval is demonstrated both analytically and experimentally. The extension of the method to the case of a medium-to-large hole sized test object is presented. Theory and experimental results are given. In addition we present the extension to the case of aberrations comprising both phase and amplitude errors.
In this paper we give the proof of principle of a new experimental method to determine the aberrations of an optical system in the field. The measurement is based on the observation of the intensity point spread function of the lens. To analyze and interpret the measurement, use is made of an analytical method, the so-called extended Nijboer-Zernike approach. The new method is applicable to lithographic projection lenses, but also to EUV mirror systems or microscopes such as the objective lens of an optical mask inspection tool. Phase retrieval is demonstrated both analytically and experimentally. Theory and experimental results are given.
Aberrations, aberrations, here there everywhere but how do we collect useful data that can be incorporated into our simulators? Over the past year there have no less than 18 papers published in the literature discussing how to measure aberrations to answering the question if Zernikes are really enough. The ability to accurately measure a Zernike coefficient in a timely cost effective manner can be priceless to device manufacturers. Exposure tool and lens manufacturers are reluctant to provide this information for a host of reasons, however, device manufacturers can use this data to better utilize each tool depending on the level and the type of semiconductors they produce. Dirksen et al. first discussed the ring test as an effective method of determining lens aberrations in a step and repeat system, later in a scanning system. The method is based on two elements; the linear response to the ring test to aberrations and the use of multiple imaging conditions. The authors have been working to further enhance the capability on the test on the first small field 157 nm exposure system at International SEMATECH. This data was generated and analyzed through previously discussed methods for Z5 through Z25 and correlated back to PMI data. Since no 157nm interferemetric systems exist the lens system PMI data was collected at 248nm. Correlation studies have isolated the possible existence of birefringence in the lens systems via the 3-foil aberration which was not seen at 248nm. Imaging experiments have been conducted for various geometry's and structures for critical dimensions ranging from 0.13micrometers down to 0.10micrometers with binary and 0.07micrometers with alternating phase shift mask. The authors will review the results of these experiments and the correlation to imaging data and PMI data.
KEYWORDS: Monochromatic aberrations, Spherical lenses, Sodium, Interferometry, 3D modeling, Scanners, Deep ultraviolet, Data modeling, Scanning electron microscopy, Optical lithography
The aberration ring test is used to determine the low and high order lens aberrations. The method is based on two key elements: the linear response of ART to aberrations and the use of multiple imaging conditions. Once the model parameters are determined by means of simulations, the Zernike coefficients are solved from a set of linear equations. The Zernike coefficients thus obtained are correlated to interferometric lens data and to line width measurements.
The aberration monitor allows independent determination of spherical, coma, astigmatism and three point in a single experiment using existing equipment. The monitor consists of a circular phase object, with a diameter of approximately (lambda) /NA and a phase depth of (lambda) /2. Due to the relative large diameter, the image prints as a narrow ring into the resist. Without aberrations its contours are concentric circles. Aberrations deform the ring in a characteristic way. A detailed analysis of the ring shape through focus identifies the aberrations of the projection lens. A linear aberration model is compared with simulations. Experimental results of various aberrations are shown and ar correlated to line width measurements and interferometric lens data.
Processes such as chemical mechanical polishing and spin coating can result in the asymmetric deformation of alignment marks. In this paper, the effects of such asymmetric mark deformations on the accuracy of the stepper alignment system are investigate. An advanced phase grating alignment system is presented which is more robust against the above mentioned process-induced alignment deviations. The potential of the new alignment system will be illustrated with result of both numerical simulations and experimental measurements. Various process modules that are known to cause mark deformations have been investigated.
The effects of resist spinning, aluminum sputtering and chemical mechanical polishing on the observed alignment position in ASML wafer steppers are presented. Vector maps of the process induced alignment shifts are shown for various processing conditions. The deposition experiments are compared with simulations and a specially designed alignment system modeling program.
The standard ASML alignment system in combination with modified marks is used to determine the primary imaging parameters of the stepper: focus and exposure dose. The method uses a standard chromium on glass reticle. The paper discusses system calibration and feedforward process control in production. A lens qualification at the specified resolution and swing curves are shown. The exposure dose measurements are compared with dose to clear measurements. The theory for optimizing the mark layout is presented.
A new latent image metrology technique is discussed that determines best focus with a precision of (sigma) equals 20 nm. This technique uses the existing alignment system of an ASM-L wafer stepper and requires no hardware or software modifications. The user just needs a standard chrome reticle. It can operate for machine setup at the factory, but also in-process for fully automatic self calibration of focus and tilt. A typical measurement takes a few minutes.
Step and scan projection printers overcome the most stringent restriction of step and repeat cameras: the trade off between the resolving power of the lithographic lens and its image field. In a scanning projection printer the reticle and wafer both have to be moved with a constant velocity, keeping their speed ratio equal to the reduction of the lens. The length of the circuit is now reticle limited. An additional extension consists in stitching several lanes together in order to lengthen the dimension perpendicular to the scan direction. However, lens aberrations, mechanical vibrations as well as synchronization errors of the stages, deteriorate the image transfer. The aim of this article is the classification and treatment of these scan- induced deteriorations. So-called contrast transfer curves are calculated offering the possibility of gaining quantitative values of the disturbance amplitudes for permissible contrast drops. Additionally, exposure-defocus (ED) trees are constructed as an evaluation criterion of the scan-induced image degradation.
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