Characterization of a next generation step-and-scan system
Timothy J. Wiltshire, Joseph P. Kirk, et al.
SPIE Advanced Lithography 1998
The GW method is a many-body electronic structure technique capable of generating accurate quasiparticle properties for realistic systems spanning physics, chemistry, and materials science. Despite its power, GW is not routinely applied to study large complex assemblies due to the method's high computational overhead and quartic scaling with particle number. Here, the GW equations are recast, exactly, as Fourier-Laplace time integrals over complex time propagators. The propagators are then "shredded" via energy partitioning and the time integrals approximated in a controlled manner using generalized Gaussian quadrature(s) while discrete variable methods are employed to represent the required propagators in real space. The resulting cubic scaling GW method has a sufficiently small prefactor to outperform standard quartic scaling methods on small systems (≳10 atoms) and offers 2-3 order of magnitude improvement in large systems (≈200-300 atoms). It also represents a substantial improvement over other cubic methods tested for all system sizes studied. The approach can be applied to any theoretical framework containing large sums of terms with energy differences in the denominator.
Timothy J. Wiltshire, Joseph P. Kirk, et al.
SPIE Advanced Lithography 1998
William Hinsberg, Joy Cheng, et al.
SPIE Advanced Lithography 2010
Arnon Amir, Michael Lindenbaum
IEEE Transactions on Pattern Analysis and Machine Intelligence
Jianke Yang, Robin Walters, et al.
ICML 2023