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Efficient Algorithms for the Green’s Function Formalism

Semiconductor Transport Simulations on CPUs and GPUs
  • Jan Jacob
  • Bodo Krause-Kyora
  • Lothar Wenzel
  • Qing Ruan
  • Darren Schmidt
  • Vivek Amin
  • Jairo Sinova
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 186)

Abstract

We present efficient implementations of the non-equilibrium Green’s function method for numeric simulations of transport in semiconductor nanostructures. The algorithms are implemented on CPUs and GPUs using LabVIEW 2011 64-Bit together with the Multicore Analysis and Sparse Matrix Toolkit and the GPU Analysis Toolkit.

Keywords

Algorithm GPU Green’s function Inversion LabVIEW Simulations 

Notes

Acknowledgments

This work was supported by the Deutsche Forschungsgemeinschaft via GK 1286 and Me916/11-1, the City of Hamburg via the Center of Excellence “Nanospintronics”, the Office of Naval Research via ONR-N00014110780, and the National Science Foundation by NSF-MRSEC DMR-0820414, NSFDMR-1105512, NHARP

References

  1. 1.
    Datta S (1999) Electronic transport in mesoscopic systems. Cambridge University Press, CambridgeGoogle Scholar
  2. 2.
    Datta S, Das B (1990) Appl Phys Lett 56(7):665CrossRefGoogle Scholar
  3. 3.
  4. 4.
  5. 5.
    Intel. Intel Math Kernel Library. http://software.intel.com/en-us/articles/intel-mkl/
  6. 6.
    Jacob J, Lehmann H, Merkt U, Mehl S, Hankiewicz E (2011) DC-biased InAs spin-filter cascades. J Appl Phys 112:013706Google Scholar
  7. 7.
    Jacob J, Meier G, Peters S, Matsuyama T, Merkt U, Cummings AW, Akis R, Ferry DK (2009) Generation of highly spin-polarized currents in cascaded InAs spin filters. J Appl Phys 105:093714CrossRefGoogle Scholar
  8. 8.
    Jacob J, Wenzel L, Schmidt D, Ruan Q, Amin V, Sinova J (2012) Numerical transport simulations in semiconductor nanostructures on CPUs and GPUs. Lecture notes in engineering and computer science: proceedings of the international multiconference of engineers and computer scientists 2012, IMECSGoogle Scholar
  9. 9.
    Koo HC, Kwon JH, Eom J, Chang J, Han SH, Johnson M (2009) Control of spin precession in a spin-injected field effect transistor. Science 325(5947):1515–1518CrossRefGoogle Scholar
  10. 10.
    MAGMA. Magma—matrix algebra on gpu and multicore architectures. http://icl.cs.utk.edu/magma/
  11. 11.
    National instruments (2012) LabVIEW GPU Analysis Toolkit. beta versionGoogle Scholar
  12. 12.
    National instruments (2012) LabVIEW multicore analysis and sparse matrix toolkit. https://decibel.ni.com/content/docs/DOC-12086
  13. 13.
    NVIDIA. CUDA BLAS implementation description. http://developer.nvidia.com/cuBLAS
  14. 14.
    NVIDIA. CUDA version 4.0 datasheet. http://developer.nvidia.com/cuFFT
  15. 15.
    NVIDIA. CUDA version 4.0 datasheet. http://developer.nvidia.com/cuda-toolkit-40
  16. 16.
    NVIDIA. CUDA version 5 RDMA feature. http://developer.nvidia.com/gpudirect
  17. 17.
    NVIDIA (2011) Tesla M2050 GPGPU datasheetGoogle Scholar
  18. 18.
    Oestreich M, Bender M, Hubner J, Hägele D, Rühle WW, Hartmann Th, Klar PJ, Heimbrodt W, Lampalzer M, Volz K, Stolz W (2002) Spin injection, spin transport and spin coherence. Semicond Sci Technol 17(4):285–297CrossRefGoogle Scholar
  19. 19.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1999) Numerical recipes in C, vol 123. Cambridge University Press, Cambridge, p 50Google Scholar
  20. 20.
    Schenk O, Bollhoefer M, Roemer R (2008) SIAM Rev 50:91–112MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Schenk O, Waechter A, Hagemann M (2007) J Comput Optim Appl 36(2–3):321–341MATHCrossRefGoogle Scholar
  22. 22.
    Schenk O, Gärtner K (2004) Journal of Future Generation Computer Systems 20(3):475–487Google Scholar
  23. 23.
    Schmidt G, Ferrand D, Molenkamp LW, Filip AT, van Wees BJ (2000) Fundamental obstacle for electrical spin injection from a ferromagnetic metal into a diffusive semiconductor. Phys Rev B 62(8):R4790–R4793CrossRefGoogle Scholar
  24. 24.
    Usuki T et al (1994) Phys Rev B 50:7615–7625CrossRefGoogle Scholar
  25. 25.
    Wunderlich J, Park B-G, Irvine AC, Zarbo LP, Rozkotov E, Nemec P, Novak V, Sinova J, Jungwirth T (2010) Science 330(6012):1801–1804Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Jan Jacob
    • 1
  • Bodo Krause-Kyora
    • 2
  • Lothar Wenzel
    • 3
  • Qing Ruan
    • 3
  • Darren Schmidt
    • 3
  • Vivek Amin
    • 4
  • Jairo Sinova
    • 4
  1. 1.Institute of Applied PhysicsUniversity of HamburgHamburgGermany
  2. 2.PHYSnet Computing CenterUniversity of HamburgHamburgGermany
  3. 3.National InstrumentsAustinUSA
  4. 4.Physics DepartmentTexas A&M UniversityCollege StationUSA

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