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Recent years have shown a strong increase in the use of statistical lithography error analysis for process tuning and in making technology choices. 1 Simulation has shown it can play an important role in this area by accurately predicting experimental critical dimension (CD) distributions. Earlier statistical lithography simulation work was based on the Response Surface Methodology. The response surface is built by simulating CD dependence on input lithography process variables of interest such as focus, dose, mask CD, resist thickness, etc. The process parameters are then sampled from the Gaussian distribution to generate the distribution of the resulting resist CDs. 2,3 When a large number of input parameters are being considered in order to describe the important experimental variations, the computational runtime is rapidly increased due to the requirements to fully simulate an (N+1)-dimensional response surface, where N is the number of input parameters. The work we present here has improved the speed of statistical lithography simulations through the use of Monte Carlo technique. With this technique, the runtime of the simulations is independent of the number of input parameters. The technique can be used for 1D or 2D simulations. We present results benchmarked with 130 nm process data showing the usefulness, runtime improvements and accuracy of this method. We have also used Variable Threshold Resist model (VTRM) in conjunction with the Monte Carlo technique. VTRM was calibrated against experimental focus-exposure matrices at varying line width and pitch. The use of VTRM greatly improves the accuracy of the statistical results by the virtue of establishing a good fit to the experimental data, which can be quantified by the root mean squares of residuals. VTRM also significantly speeds up the computation, since it uses only aerial image calculation as opposed to full resist modeling. Simulation results produced by using VTRM closely match the experimental results through a range of pitches, mask line widths and various illumination conditions.

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Past work on mask topography has documented the effects of the topography on the aerial image intensity and on the responses of CD through defocus and image placement. Device performance, however, is limited by the statistical CD variation in the poly lines that form the logic and memory gates. We have developed a tool that combines fast, rigorous EMF calculations with Monte Carlo simulation to investigate the impact of mask topography on CD control. We have applied it to study the effects of mask topography on through-pitch CD control in 6% EAPSM, AAPSM, and CPL reticles at 90-nm half-pitch design rules. The effects of the topography can be understood by examining the coefficients of the Fourier expansion of the near-field radiation pattern. The magnitude of the 3D effects is not correlated with the amount of mask topography but with the specific details of the Fourier coefficients that pass through the pupil. The topography mainly distributes the energy more evenly and introduces additional phase information. The best imaging results at tight pitch are obtained when the difference between the magnitudes of the two main Fourier coefficients that pass through the pupil is small and their phase difference is close to π. At larger pitches more diffracted orders will pass through the pupil, and the extra phase information from the additional orders will couple with aberrations in a reticle-dependent way and complicate overall RET choice.