Fast simulation methods and modeling for extreme ultraviolet masks with buried defects

Abstract

To support the successful implementation of extreme ultraviolet ͑EUV͒ lithography for high volume manufacturing, a spectrum of simulation tools is needed. For investigation of new materials and geometries, rigorous but computationally expensive simulations are required. For faster simulations, a new method, rapid absorber defect interaction computation for advanced lithography ͑RADICAL͒, is introduced. RADICAL is a modular program, that uses separate methods to simulate the absorber pattern and defective multilayer. Two different methods are used to simulate the multilayer within RADICAL: ray tracing and single surface approximation ͑SSA͒. Ray tracing can accurately simulate arbitrary multilayer geometries. SSA is only accurate for defects shorter than 4.5 nm on the multilayer surface. With ray tracing, RADICAL is nearly 1000 times faster than finite difference time domain ͑FDTD͒ for simulating line-space patterns over buried defects. RADICAL with SSA is nearly 25,000 times faster than FDTD. The accuracy of RADICAL is shown to be excellent for simulating defects in focus, and for simulating defects smaller than 2.5 nm through focus. The error can be as high as 4 nm in predicting CD change for larger defects out of focus due to the complexities of modeling the phase of buried defects. But this error is predictable and will likely be acceptable for most applications considering the huge speed advantages of RADICAL.A spectrum of simulation and modeling technology computer-aided design ͑CAD͒ tools is needed to successfully implement high volume extreme ultraviolet ͑EUV͒ lithography due to the interactions of buried nonplanar multilayer defects with patterned features. Buried defects in EUV masks are one of the main hurdles in the development of EUV lithography. 1 It is possible that defect-free mask blanks will never be available at a reasonable cost, so defect compensation may be necessary. 2 An example geometry that shows the complexity of a defective multilayer structure is shown in Fig. 1. The defect is on the substrate below the multilayer. The multilayer is grown on top of the defect, burying the defect, using the smoothing model described in Ref. 3. The absorber pattern sits on top of the multilayer. A defect buried in the multilayer affects the deposition of layers above it, which reduces the magnitude and disrupts the phase of reflected light.A detailed understanding of the quantitative scattering within a resonant nonplanar layer, mask diffraction of incident and reflected waves, and reduction of these phenomena by compensation of layouts will all be needed. This will require a spectrum of simulation methods ranging from rigorous detailed point-by-point analysis of electromagnetic simulation of scattering within and among structures, as well as more approximate aggregate methods with sufficient speed to support real-time quantitative design decisions. HistoryThe history of defective EUV mask simulation is extensive and has included several methods, like the ones presented in this work, to accelerate the sim...

Characterization and mitigation of 3D mask effects in extreme ultraviolet lithography

“…Mask defects, especially multilayer defects, are not covered here because they have been addressed in other recent studies (see Refs. [20][21][22][23], for example).…”

Defect-aware reticle floorplanning for EUV masks

“…Although CD impact of buried defects has been extensively studied through experiments and simulations [11,18] for different defect dimensions and optical conditions, the focus has always been on dense parallel line patterns. In this work, we assume that similar results will hold for general layout patterns.…”

“…For example, if a single die has multiple defects, moving the die may not improve yield at all but it could still reduce this cost metric. Another important point is that although we have used a closed form expression to calculate CD impact of a buried defect, it is possible to use a fast simulator such as RADICAL [11] for layout snippets around each buried defect to evaluate the design impact more accurately.…”

“…• To account for defocus, which can have a significant impact on CD [11,18], we scale up the values obtained from the linear model by 3X as a pessimistic approximation based on simulation results from [12], for defocus value of ±75nm.…”

Design-Aware Defect-Avoidance Floorplanning of EUV Masks

“…Estimating the impact of buried defects on wafer has been extensively studied through experimental work (wafer exposure followed by inspection) [25] and lithography simulations [26] for different defect dimensions and optical conditions. These approaches typically study minimum pitch grating patterns and look at printability and CD change caused by these mask defects for different defect height, width and position relative to the absorber pattern.…”