Distributed non-equilibrium Green’s function algorithms for the simulation of nanoelectronic devices with scattering

Cauley, Stephen; Luisier, Mathieu; Balakrishnan, Venkataramanan; Klimeck, Gerhard; Koh, Cheng-Kok

doi:10.1063/1.3624612

Title: Distributed non-equilibrium Green’s function algorithms for the simulation of nanoelectronic devices with scattering

Journal Article · Wed Aug 24 00:00:00 EDT 2011 · Journal of Applied Physics

DOI:https://doi.org/10.1063/1.3624612· OSTI ID:1564771

Cauley, Stephen ^[1]; Luisier, Mathieu ^[2]; Balakrishnan, Venkataramanan ^[2]; Klimeck, Gerhard ^[2]; Koh, Cheng-Kok ^[2]

Massachusetts General Hospital, Boston, MA (United States)
Purdue Univ., West Lafayette, IN (United States)

Through the non-equilibrium Green’s function (NEGF) formalism, quantum-scale device simulation can be performed with the inclusion of electron-phonon scattering. Yet, the simulation of realistically sized devices under the NEGF formalism typically requires prohibitive amounts of memory and computation time. Two of the most demanding computational problems for NEGF simulation involve mathematical operations with structured matrices called semiseparable matrices. In this work, we present parallel approaches for these computational problems which allow for efficient distribution of both memory and computation based upon the underlying device structure. This is vital when simulating realistically sized devices due to the aforementioned computational burdens. First, we consider determining a distributed compact representation for the retarded Green’s function matrix G^R. This compact representation is exact and allows for any entry in the matrix to be generated through the inherent semiseparable structure. The second parallel operation allows for the computation of electron density and current characteristics for the device. Specifically, matrix products between the distributed representation for the semiseparable matrix G^R and the self-energy scattering terms in Σ^< produce the less-than Green’s function G^<. As an illustration of the computational efficiency of our approach, we stably generate the mobility for nanowires with cross-sectional sizes as large as 4.5 nm, assuming an atomistic model with scattering.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1564771

Journal Information:: Journal of Applied Physics, Vol. 110, Issue 4; ISSN 0021-8979

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 16 works

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