تجزیه و تحلیل حساسیت برای تعیین دقیق پارامترهای PSF

One possible candidate to address future nodes (below 16 nm) is electron beam lithography as sub 10 nm resolution was already demonstrated in PMMA or HSQ resists. If multiple electron beam systems significantly increase the throughput to meet industrial needs, it can be the tool of choice. Nevertheless using a chemically amplified resist (CAR) is mandatory even for systems with a large number of beams. Achieving dense sub 20 nm patterns with CAR is still a challenge as proximity effects degrade the contrast of the aerial image. Bridging, shape rounding or partial development are typical degradation in the desired final pattern shape. Proximity effect correction is needed in order to properly delineate dense features as well as meet the required CD uniformity. Proximity effect correction can only be accurate if a Point Spread Functions (PSF) is precisely determined. In this paper we demonstrate a strategy that allows accurate determination of Point Spread Function parameters. This strategy consists in using sensitivity analysis in order to define conditions where the calibration features and the measured quantities are sensitive enough to the PSF parameters and this without a correlation between the final results.

E-beam lithography is the lithography technique that allows yet the best resolution on isolated structure. With non chemically amplified resists, sub 10 nm patterns were reported [1]. Resolution limits with chemically amplified resist is a bit lower and ceils at 20 nm. However whatever the chemistry of the resist, dense structures or structures surrounded by large patterns have lower resolution capability. One of the origins of this resolution degradation is the contrast loss in the absorbed energy in the resist due to proximity effects. Indeed the local deposited energy is dependent on the surrounding. Due to multiple inelastic collisions of electrons with matter, the energy deposited by a point electron beam spreads around and follows a Point Spread Function. Monte Carlo modeling of the electrons trajectories and energy loss when entering normally in a planar stack was modeled and shows that, depending on the initial beam energy, backscattered electrons are responsible of the absorbed energy at long range [2]. Commonly, the distribution of the absorbed energy is approximated by a sum of Gaussian functions [3]. In the case of thin resists films coated on a bare silicon wafer, and for high energies (above 50 keV), the PSF can be approximated by two Gaussian functions (see Eq. (1)). equation(1) View the MathML sourcePSF(r)=D0π(1+n)1α2e-r2/α2+ηβ2e-r2/β2 Turn MathJax on With α the short range length of scattered incident electrons, β the long range length due to backscattered electrons and η the dimensionless ratio of deposited energy due to the backscattered electrons. D0 is the relative dose. However Monte Carlo simulations allow determining theoretical PSF distributions, not experimental ones. Experimental determination of PSF is possible by comparing theoretical pattern contour with experimental contour of the developed patterns. Hence experimental values of PSF parameters are dependent of the substrate and layers stack on top of it but also of the lithography process, for example the PEB and development steps. Once the values of the PSF parameters are known, one can simulate the absorbed energy in the resist by convoluting the pattern geometry with the PSF. By considering an appropriate resist model, one can predict the final pattern geometry (CD, shape, etc.). Among multiple possibilities, the simplest resist model is a constant threshold model which at first order represents the threshold value of the needed absorbed energy to develop the patterns. Different strategies for PSF determination exist [4], [5], [6] and [7]. Some are based on the comparison of measured CDs of patterns with their simulated CDs, the parameters providing the best match being considered as the ones of the PSF to be estimated. Others are based on indirect reconstruction of the PSF by considering the dose to develop circle of increasing radius. Plotting this dose versus the circle radius allows deducing the PSF. Conversely, the accuracy of such methodology is linked to the sampling size of the generated array of circle and on the accuracy on the dose in the matrix due to the fact that sometimes it is not clear if the pattern begins to develop or not. The goal of this work is to use a sensitivity analysis in order to check if the measurements of a given calibration pattern are sensitive to PSF parameters.

This study points out that sensitivity analysis is a very useful tool when one intends to determine accurately model parameters. Indeed a correlation between parameters occurs in most decreasing the accuracy of the PSF parameter estimation. An accurate experimental determination of α, β and η is possible using the layout used in this study if an appropriate strategy is used. This strategy consists in writing recurrently the layout of Fig. 1 at increasing doses and to measurement the line width CD1 and the width of the horizontal plane. For doses three to ten times the base dose of the resist, α is directly determined from CD1 while a narrow set of {β, η} is determined from CD2 when exposed at the base dose of the resist. Then β is deduced from CD2 for a dose set to ten times the dose to clear and finally η is chosen from the base dose measurements. Accurate calibration of the models is a key to a good proximity correction. We demonstrated that making sensitivity analysis is an inherent part of the calibration process, the test patterns can be chosen in a more relevant manner and the model parameters extracted more accurately. This extremely valuable feature is available in the software tool used for performing this study.