Massively-parallel FDTD simulations to address mask electromagnetic effects in Hyper-NA immersion lithography

Abstract

In the Hyper-NA immersion lithography regime, the electromagnetic response of the reticle is known to deviate in a complicated manner from the idealized Thin-Mask-like behavior. Already, this is driving certain RET choices, such as the use of polarized illumination and the customization of reticle film stacks. Unfortunately, full 3-D electromagnetic mask simulations are computationally intensive. And while OPC-compatible mask electromagnetic field (EMF) models can offer a reasonable tradeoff between speed and accuracy for full-chip OPC applications, full understanding of these complex physical effects demands higher accuracy. Our paper describes recent advances in leveraging High Performance Computing as a critical step towards lithographic modeling of the full manufacturing process. In this paper, highly accurate full 3-D electromagnetic simulation of very large mask layouts are conducted in parallel with reasonable turnaround time, using a Blue-Gene/L supercomputer and a Finite-Difference Time-Domain (FDTD) code developed internally within IBM. A 3-D simulation of a large 2-D layout spanning 5μm × 5μm at the wafer plane (and thus (20μm × 20μm × 0.5μm at the mask) results in a simulation with roughly 12.5GB of memory (grid size of lOnm at the mask, single-precision computation, about 30 bytes/grid point). FDTD is flexible and easily parallelizable to enable full simulations of such large layout in approximately an hour using one BlueGene/L "midplane" containing 512 dual-processor nodes with 256MB of memory per processor. Our scaling studies on BlueGene/L demonstrate that simulations up to 100pm × 100pm at the mask can be computed in a few hours. Finally, we will show that the use of a subcell technique permits accurate simulation of features smaller than the grid discretization, thus improving on the tradeoff between computational complexity and simulation accuracy. We demonstrate the correlation of the real and quadrature components that comprise the Boundary Layer representation of the EMF behavior of a mask blank to intensity measurements of the mask diffraction patterns by an Aerial Image Measurement System (AIMS) with polarized illumination. We also discuss how this model can become a powerful tool for the assessment of the impact to the lithographic process of a mask blank.