ABSTRACT
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.
- R. Chau, et al., "Silicon Nano-Transistors and Breaking the 10nm Physical Gate Length Barrier", Conference Digest of 61st Device Research Conference, Salt Lake City, Utah 123-126 (2003).Google Scholar
- D. A. Antoniadis and A. Khakifirooz, "MOSFET performance scaling: Limitations and future options", IEEE International Electron Devices Meeting 2008, Technical Digest, 253256 (2008).Google ScholarCross Ref
- W. Haensch et al., "Silicon CMOS devices beyond scaling", IBM J. Res. & Dev. 50, 339-361 (2006). Google ScholarDigital Library
- B. Doris et al., "Extreme scaling with ultra-thin Si channel MOSFETs", IEDM Tech. Dig. 2002, 267-270 (2002).Google ScholarCross Ref
- S. D. Suk et al., "Investigation of nanowire size dependency on TSNWFET", IEDM Tech. Dig. 2007, 891-894 (2007).Google Scholar
- Y. Q. Wu, W. K. Wang, O. Koybasi, D. N. Zakharov, E. A. Stach, S. Nakahara, J. C. M. Hwang and P. D. Ye, "0.8-V Supply Voltage Deep-Submicrometer Inversion-Mode In0.75Ga0.25As MOSFET", IEEE Elec. Dev. Lett. 30, 700-702 (2009).Google ScholarCross Ref
- X. Wang, Y. Ouyang, X. Li, H. Wang, J. Guo, H. Dai, "Room Temperature All Semiconducting sub-10nm Graphene Nanoribbon Field-Effect Transistors", Phys. Rev. Lett. 100, 206803 (2008).Google Scholar
- J. Appenzeller, Y.-M. Lin, J. Knoch, and P. Avouris, "Band-to-band tunneling in carbon nanotube field-effect transistors," Phys. Rev. Lett. 93, 196805 (2004).Google Scholar
- See the Modeling & Simulation Section of the ITRS at http://www.itrs.net/Links/2009ITRS/Home2009.htmGoogle Scholar
- M. Luisier, G. Klimeck, A. Schenk, and W. Fichtner, "Atomistic Simulation of Nanowires in the sp3d5s* Tight-Binding Formalism: from Boundary Conditions to Strain Calculations, Phys. Rev. B, 74, 205323 (2006).Google Scholar
- M. Luisier and A. Schenk, "Atomistic Simulation of Nanowire Transistors", J. of Computational and Theoretical Nanoscience 5, 1-15 (2008).Google ScholarCross Ref
- S. Datta, "Electronic Transport in Mesoscopic Systems", Cambridge University Press (1995).Google Scholar
- W. R. Frensley, "Boundary conditions for open quantum systems driven far from equilibrium", Rev. Mod. Phys. 62, 745-791 (1990).Google Scholar
- J. C. Slater and G. F. Koster, "Simplified LCAO Method for the Periodic Potential Problem", Phys. Rev. 94, 1498-1524 (1954).Google ScholarCross Ref
- J. M. Jancu, R. Scholz, F. Beltram, and F. Bassani, "Empirical spds* tight-binding calculation for cubic semiconductors: General method and material parameters, Phys. Rev. B 57, 6493-6507 (1998).Google ScholarCross Ref
- T. B. Boykin, G. Klimeck, and F. Oyafuso, "Valence band effective-mass expressions in the sp3d5s* empirical tight-binding model applied to a Si and Ge parametrization", Phys. Rev. B 69, 115201 (2004).Google ScholarCross Ref
- T. B. Boykin, G. Klimeck, R. Chris Bowen, and F. Oyafuso, "Diagonal parameter shifts due to nearest-neighbor displacements in empirical tight-binding theory", Phys. Rev. B 66, 125207 (2002).Google Scholar
- M. Luisier and G. Klimeck, "A multi-level parallel simulation approach to electron transport in nano-scale transistors", Proceedings of the 2008 ACM/IEEE Conference on Supercomputing, article 12 (2008). Google ScholarDigital Library
- M. Luisier and G. Klimeck, "Numerical strategies towards peta-scale simulations of nanoelectronics devices", Parallel Computing 36, 117-128 (2010). Google ScholarDigital Library
- M. Luisier, A. Schenk, W. Fichtner, T. B. Boykin, and G. Klimeck, "A parallel sparse linear solver for nearest-neighbor tight-binding problems", Proc. of the 14th international Euro-Par conference on Parallel Processing, 790-800 (2008). Google ScholarDigital Library
- D. H. Kim and J. A. del Alamo, "30-nm InAs Pseudomorphic HEMTs on an InP Substrate With a Current-Gain Cutoff Frequency of 628 GHz", IEEE Elec. Dev. Lett. 29, 830-833 (2008).Google ScholarCross Ref
- G. Klimeck and M. Luisier, "Atomistic Modeling of Realistically Extended Semiconductor Devices with NEMO and OMEN", Computing in Science & Engineering 12, 28-35 (2010). Google ScholarDigital Library
- S. Oktyabrsky and P. Ye, "Fundamentals of III-V Semiconductor MOSFETs", Springer (2009). Google ScholarDigital Library
- Q. Zhang, W. Zhao, and A. C. Seabaugh, "Low-subthreshold-swing transistors", IEEE Elec. Dev. Lett. 27, 297-300 (2006).Google ScholarCross Ref
- T. Frederiksen, M. Paulsson, M. Brandbyge, and A.-P. Jauho, "Inelastic transport theory from first principles: Methodology and application to nanoscale devices", Phys. Rev. B 75 205413 (2007).Google Scholar
- A. Pecchia, G. Romano, and A. Di Carlo, "Theory of heat dissipation in molecular electronics", Phys. Rev. B 75 035401 (2007).Google ScholarCross Ref
- Y. Asai, "Nonequilibrium phonon effects on transport properties through atomic and molecular bridge junctions", Phys. Rev. B 78 045434 (2008).Google ScholarCross Ref
- M. Luisier and G. Klimeck, "Atomistic full-band simulations of silicon nanowire transistors: Effects of electron-phonon scattering", Phys. Rev. B 80, 155430 (2009).Google ScholarCross Ref
- http://www.nccs.gov/computing-resources/jaguar/Google Scholar
- R. Lake, G. Klimeck, R. C. Bowen, and D. Jovanovic, "Single and multiband modeling of quantum electron transport through layered semiconductor devices", J. of Appl. Phys. 81, 7845 (1997).Google ScholarCross Ref
- N. Ashcroft and N. Mermin, "Solid State Physics", Rinehart and Winston (1976).Google Scholar
- P. M. Gresho and R. L. Sani, "Incompressible Flow and the Finite Element Method: Isothermal Laminar Flow", John Wiley and Sons, New York (2000).Google Scholar
- R. E. Bank, D. J. Rose, and W. Fichtner, "Numerical Methods for Semiconductor Device Simulation", IEEE Trans. Electron Dev. 30, 1031 (1983).Google ScholarCross Ref
- W. Gropp, E. Lusk, N. Doss, and A. Skjellum, "A high-performance, portable implementation of the MPI message passing interface standard", Parallel Computing 22, 789 (1996). Google ScholarDigital Library
- J. Dongarra, "Basic Linear Algebra Subprograms Technical Forum Standard", International Journal of High Performance Applications and Supercomputing, 16, 1-111 (2002).Google ScholarDigital Library
- E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, "LAPACK User's Guide", Third Edition, SIAM, Philadelphia (1999). Google ScholarDigital Library
- O. Schenk and K. Gärtner, "Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO, Journal of Future Generation Computer Systems", J. of Future Generation Computer Systems 20, 475 (2004). Google ScholarDigital Library
- X. S. Li and J. W. Demmel "SuperLU_DIST: A Scalable Distributed Memory Sparse Direct Solver for Unsymmetric Linear Systems", ACM Trans. on Math. Software 29, 110 (2003). Google ScholarDigital Library
- P. R. Amestoy, I. S. Duff, and J.-Y. L'Excellent, "Multifrontal parallel distributed symmetric and unsymmetric solvers" Comput. Methods in Appl. Mech. Eng. 184, 501 (2000).Google ScholarCross Ref
- T. A. Davis, "A column pre-ordering strategy for the unsymmetricpattern multifrontal method", ACM Trans. on Math. Software 30, 165 (2004). Google ScholarDigital Library
- R. S. Tuminaro, M. Heroux, S. A. Hutchinson, and J. N. Shadid, "Official Aztec User's Guide: Version 2.1" (1999).Google Scholar
- A. Svizhenko, M. P. Anantram, T. R. Govindan, R. Biegel, and R. Venugopal, "Two-dimensional quantum mechanical modeling of nanotransistors", J. Appl. Phys. 91, 2343-2354 (2002).Google ScholarCross Ref
- M. S. Lundstrom, "On the Mobility Versus Drain Current Relation for a Nanoscale MOSFET", IEEE Elc. Dev. Lett. 22, 293-295 (2001).Google ScholarCross Ref
- L. P. Kadanoff and G. Baym, "Quantum Statistical Mechanics", W. A. Benjamin Inc, New York (1962).Google Scholar
Recommendations
Semiclassical Approximation of Electron-Phonon Scattering Beyond Fermi's Golden Rule
We derive a quantum mechanical correction to the semiclassical Fermi golden rule operator for scattering of electrons in a crystal. This correction takes into account the fact that electron-phonon interaction is not instantaneous in quantum mechanics. The ...
Quantum correction to the semiclassical electron-phonon scattering operator
LSSC'05: Proceedings of the 5th international conference on Large-Scale Scientific ComputingA quantum kinetic equation approach is adopted in order to incorporate quantum effects such as collisional broadening due to finite lifetime of single particle states, and collisional retardation due to finite collision time. A quantum correction to the ...
Electron---phonon dissipation in quantum nanodevices
Microscopic modelling of electronic-phase coherence versus energy dissipation plays a crucial role in the design and optimization of new-generation electronic quantum nanodevices, like quantum-cascade light sources and quantum logic gates; in this ...
Comments