Distributed NEGF Algorithms for the Simulation of Nanoelectronic Devices with Scattering

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

Date of this Version



Stephen Cauley, Mathieu Luisier, Venkataramanan Balakrishnan, Gerhard Klimeck, and Cheng-Kok Koh. Distributed non-equilibrium Green’s function algorithms for the simulation of nanoelectronic devices with scattering. Journal of Applied Physics 110, 043713 (2011); doi: http://dx.doi.org/10.1063/1.3624612


arXiv:1103.5782v1 [cond-mat.mes-hall] 29 Mar 2011

Copyright (2011) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Applied Physics 110, 043713 (2011) and may be found at http://dx.doi.org/10.1063/1.3624612. The following article has been submitted to/accepted by Journal of Applied Physics. Copyright (2011) Stephen Cauley, Mathieu Luisier, Venkataramanan Balakrishnan, Gerhard Klimeck, Cheng-Kok Koh. This article is distributed under a Creative Commons Attribution 4.0 Unported License.


Through the Non-Equilibrium Green’s Function (NEGF) formalism, quantum- scale device simulation can be performed with the inclusion of electron-phonon scattering. However, 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 critical when simulating realistically sized devices due to the aforementioned computational burdens. First, we consider de- termining a distributed compact representation for the retarded Green’s function matrix GR. 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 char- acteristics for the device. Specifically, matrix products between the distributed rep- resentation for the semiseparable matrix GR and the self-energy scattering terms in Σ< produce the less-than Green’s function G


Nanoscience and Nanotechnology