Fast EMF solver for rigorous lithography simulations.   

Support from modeling and simulation is necessary to push the limits of traditional optical lithography. A specific requirement for lithography modeling and simulation is the need for very efficient electromagnetic field (EMF) solvers that allow the simulation of large 3D computational domains (ITRS roadmap).

JCMsuite is a finite-element package for accurate and fast simulations of electromagnetic problems. Due to the good convergence properties of FEM it is especially well suited for the accurate simulation of nanostructures, as it is necessary in photomask simulations or optical metrology of semiconductor nanostructures. Comparably large 3D computational domains can be handled at moderate computational effort. The solver has been compared and benchmarked with RCWA and FDTD-based EMF simulators for 2D and 3D computational domain problems in the field of lithography. Due to the good convergence properties of the used methods, JCMsuite could outperform the competing methods in these benchmarks.

Figure 1 shows results for structures which include 45-degree angles in the x-y-mask-plane. These structures are favourable from the electronic design point of view, but they are critical for optical simulators relying on x-y-structured meshes. From top to bottom, Figure 1 shows a schematics of the layout, an electromagnetic near-field solution, the aerial image intensity distribution, and the resist topography after etch. The resist topography has been simulated using the resist simulator of Dr.LiTHO. Dr.LiTHO is a comprehensive simulation environment for photolithography, developed at the Fraunhofer IISB, Erlangen, Germany. In a joint effort of Fraunhofer IISB and JCMwave an interface has been developed which allows to perform rigorous electromagnetic field (EMF) simulations with the simulator JCMsuite and subsequent aerial imaging and resist simulations with the simulator Dr.LiTHO.

Fig. 1: Lithography simulation workflow for a test sample: Design layout, near field simulation, aerial image, resist topography.


 Figure 2 shows rigorous simulation results for relatively large 3D mask structures (test structures). From top to bottom Figure 2 shows the layout (red regions correspond to material / chromium and green regions correspond to blank), the electromagnetic near field intensity distribution, and the aerial image at best focus. The computational domain has a size of 10 microns by 10 microns and a height of about one wavelength (193nm). Computations have been performed on a standard workstation. Accuracies in the 0.1 percent regime (which are necessary for process window optimization) can be reached with a computational effort of roughly 15 minutes of computation time and 30GB of RAM consumption.

Fig. 2: Simulation results of a 10 micron by 10 micron test mask: layout, near field intensity distribution, aerial image.

Benchmark of rigorous methods for electromagnetic field simulations -Benchmark FEM vs. RCWA, interface to Dr.LiTHO.

Benchmark of FEM, waveguide, and FDTD algorithms for rigorous mask simulation.

Rigorous simulation of 3D masks - Comparison to experimental results.

3D simulations of periodic patterns - Process window optimization for alternating phase-shift contact-hole masks.