Nested dissection solver for transport in 3D nano-electronic devices
Pages 708 - 720
Abstract
The hierarchical Schur complement method (HSC) and the HSC-extension have significantly accelerated the evaluation of the retarded Green's function, particularly the lesser Green's function, for two-dimensional nanoscale devices. In this work, the HSC-extension is applied to determine the solution of non-equilibrium Green's functions on three-dimensional nanoscale devices. The operation count for the HSC-extension is analyzed for a cuboid device. When a cubic device is discretized with $$N \times N \times N$$N N N grid points, the state-of-the-art recursive Green function (RGF) algorithm takes $$\mathscr {O}(N^7)$$O(N7) operations, whereas the HSC-extension only requires $$\mathscr {O}(N^6)$$O(N6) operations. Operation counts and runtimes are also studied for three-dimensional nanoscale devices of practical interest: a graphene-boron nitride-graphene multilayer system, a silicon nanowire, and a DNA molecule. The numerical experiments indicate that the cost for the HSC-extension is proportional to the solution of one linear system (or one LU-factorization) and that the runtime speed-ups over RGF exceed three orders of magnitude when simulating realistic devices, such as a graphene-boron nitride-graphene multilayer system with 40,000 atoms.
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Published: 01 June 2016
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