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



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


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<. As an illustration of the compu- tational efficiency of our approach, we stably generate the mobility for nanowires with cross-sectional sizes of up to 4.5nm, assuming an atomistic model with scattering.


Nanoscience and Nanotechnology