A Parallel Implementation of Electron-Phonon Scattering in Nanoelectronic Devices up to 95k Cores

A quantum transport approach based on the Non-equilibrium Green's Function formalism and the tight-binding method has been developed to investigate the performances of atomistically resolved nanoelectronic devices in the presence of electron-phonon scattering. The model is integrated into a quad-level parallel environment (bias, momentum, energy, and spatial domain decomposition) that scales almost perfectly up to 220k cores in the ballistic limit of electron transport. In this case, the momentum and energy points form a quasi-embarrassingly parallel problem. The novelty in this paper is the inclusion of scattering self-energies that couple all the momenta and several energies together, requiring substantial inter-processor communication. An efficient parallel implementation of electron-phonon scattering is therefore proposed and applied to a realistically extended transistor structure. A good scaling of the simulation walltime up to 95,256 cores and a sustained performance of 142 TFlop/s are reported on the Cray-XT5 Jaguar.

[1]  J. Szmelter.  Incompressible flow and the finite element method , 2001 .

[2]  J. C. Slater,et al.  Simplified LCAO Method for the Periodic Potential Problem , 1954 .

[3]  Aatto Laaksonen,et al.  Computer Simulations Studies of Solid–Liquid Phase Transitions in Solid Water Nano Particles , 2008 .

[4]  Fabio Beltram,et al.  Empirical spds^* tight-binding calculation for cubic semiconductors : general method and material parameters , 1998 .

[5]  Arvind Kumar,et al.  Silicon CMOS devices beyond scaling , 2006, IBM J. Res. Dev..

[6]  Jack J. Dongarra,et al.  Basic Linear Algebra Subprograms Technical (Blast) Forum Standard (1) , 2002, Int. J. High Perform. Comput. Appl..

[7]  M. Luisier,et al.  Atomistic full-band simulations of silicon nanowire transistors: Effects of electron-phonon scattering , 2009 .

[8]  A. Di Carlo,et al.  Theory of heat dissipation in molecular electronics , 2007 .

[9]  Yoshihiro Asai,et al.  Nonequilibrium phonon effects on transport properties through atomic and molecular bridge junctions , 2008 .

[10]  Olaf Schenk,et al.  Solving unsymmetric sparse systems of linear equations with PARDISO , 2002, Future Gener. Comput. Syst..

[11]  Gerhard Klimeck,et al.  Single and multiband modeling of quantum electron transport through layered semiconductor devices , 1997 .

[12]  Qin Zhang,et al.  Low-subthreshold-swing tunnel transistors , 2006, IEEE Electron Device Letters.

[13]  G. V. Chester,et al.  Solid State Physics , 2000 .

[14]  W. Fichtner,et al.  Numerical methods for semiconductor device simulation , 1983, IEEE Transactions on Electron Devices.

[15]  John N. Shadid,et al.  Official Aztec user''s guide: version 2.1 , 1999 .

[16]  William R. Frensley,et al.  Boundary conditions for open quantum systems driven far from equilibrium , 1990 .

[17]  S. Datta,et al.  Silicon nano-transistors and breaking the 10 nm physical gate length barrier , 2003, 61st Device Research Conference. Conference Digest (Cat. No.03TH8663).

[18]  M. Anantram,et al.  Two-dimensional quantum mechanical modeling of nanotransistors , 2001, cond-mat/0111290.

[19]  Gerhard Klimeck,et al.  A multi-level parallel simulation approach to electron transport in nano-scale transistors , 2008, 2008 SC - International Conference for High Performance Computing, Networking, Storage and Analysis.

[20]  Jack Dongarra,et al.  Preface: Basic Linear Algebra Subprograms Technical (Blast) Forum Standard , 2002 .

[21]  Gerhard Klimeck,et al.  Valence band effective-mass expressions in the sp 3 d 5 s * empirical tight-binding model applied to a Si and Ge parametrization , 2004 .

[22]  Antti-Pekka Jauho,et al.  Inelastic transport theory from first principles: Methodology and application to nanoscale devices , 2006, cond-mat/0611562.

[23]  T. Boykin,et al.  Diagonal parameter shifts due to nearest-neighbor displacements in empirical tight-binding theory , 2002 .

[24]  M. Luisier,et al.  Atomistic Simulation of Nanowire Transistors , 2008 .

[25]  Anthony Skjellum,et al.  A High-Performance, Portable Implementation of the MPI Message Passing Interface Standard , 1996, Parallel Comput..

[26]  Peide D. Ye,et al.  Fundamentals of III-V Semiconductor MOSFETs , 2010 .

[27]  Daehyun Kim,et al.  30-nm InAs Pseudomorphic HEMTs on an InP Substrate With a Current-Gain Cutoff Frequency of 628 GHz , 2008, IEEE Electron Device Letters.

[28]  W. Fichtner,et al.  Atomistic simulation of nanowires in the sp3d5s* tight-binding formalism: From boundary conditions to strain calculations , 2006 .

[29]  James Demmel,et al.  SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems , 2003, TOMS.

[30]  A. Khakifirooz,et al.  MOSFET performance scaling: Limitations and future options , 2008, 2008 IEEE International Electron Devices Meeting.

[31]  Patrick R. Amestoy,et al.  Multifrontal parallel distributed symmetric and unsymmetric solvers , 2000 .

[32]  Gerhard Klimeck,et al.  Atomistic Modeling of Realistically Extended Semiconductor Devices with NEMO and OMEN , 2010, Computing in Science & Engineering.

[33]  H. Dai,et al.  Room-temperature all-semiconducting sub-10-nm graphene nanoribbon field-effect transistors. , 2008, Physical review letters.

[34]  Donggun Park,et al.  Investigation of nanowire size dependency on TSNWFET , 2007, 2007 IEEE International Electron Devices Meeting.

[35]  David E. Miller,et al.  Quantum Statistical Mechanics , 2002 .

[36]  M. Lundstrom.  On the mobility versus drain current relation for a nanoscale MOSFET , 2001, IEEE Electron Device Letters.

[37]  H.-S.P. Wong,et al.  Extreme scaling with ultra-thin Si channel MOSFETs , 2002, Digest. International Electron Devices Meeting,.

[38]  J. Appenzeller,et al.  Band-to-band tunneling in carbon nanotube field-effect transistors. , 2004, Physical review letters.

[39]  Gerhard Klimeck,et al.  Numerical strategies towards peta-scale simulations of nanoelectronics devices , 2010, Parallel Comput..

[40]  Andreas Schenk,et al.  A Parallel Sparse Linear Solver for Nearest-Neighbor Tight-Binding Problems , 2008, Euro-Par.

[41]  Timothy A. Davis,et al.  A column pre-ordering strategy for the unsymmetric-pattern multifrontal method , 2004, TOMS.

[42]  R. Sani,et al.  Incompressible Flow and the Finite Element Method, Volume 1, Advection-Diffusion and Isothermal Laminar Flow , 1998 .

[43]  Olaf Schenk,et al.  Solving unsymmetric sparse systems of linear equations with PARDISO , 2004, Future Gener. Comput. Syst..