Simulating Transport in Nanodevices Using the Usuki Method

  • Richard Akis
  • Matthew Gilbert
  • Gil Speyer
  • Aron Cummings
  • David Ferry
Chapter

Abstract

To calculate the conductance of mesoscopic structures such as quantum wires and dots at low temperature and bias, one typically employs the Landauer–Büttiker formalism, which relates quantum mechanical transmission probability to conductance. In this chapter, we discuss a numerically stable method to solve this transmission problem, the Usuki method, which is closely related to both the scattering matrix approach and recursive Green’s functions. It has a major advantage over the latter in that the electron density can be obtained far more efficiently. Various applications of this approach are presented: transport through open quantum dots, the study of spin filtering effects in quantum wire structures, computing the conductance of molecules and the application of the method to study MOSFETS. The extensions to the basic method required for each case are also discussed, the most extensive of which are required for the MOSFET problem, where inelastic scattering effects play a crucial role.

Keywords

Nanostructures Quantum dots Quantum wires Molecular electronics MOSFETs Spin-Hall Effect 

Notes

Acknowledgements

We would like to thank the financial support from the Office of Naval Research, the Department of Energy and Intel Corporation. The experiments of Prof. Jonathan Bird and colleagues at ASU and at the University of Buffalo were the inspiration for much of the simulation work we have done over the years. The group of Prof. Yuichi Ochiai at Chiba University provided similar inspiration. At ASU, we have also had fruitful collaborations with the groups of Prof. Dragica Vasileska, Prof. Ying-Chen Lai, Prof. Otto Sankey, and Prof. Stephen Goodnick. The team of Roland Brunner and his adviser Prof. Friedemar Kuchar at the University of Leoben helped illuminate the correspondence between our quantum simulations and the classical behavior in quantum dots. Our thanks also go out to Jan Jacob and his advisors Prof. Meier and Prof. Matsuyama at the University of Hamburg for the collaborative work that they initiated on the spin Hall effect.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Richard Akis
    • 1
  • Matthew Gilbert
  • Gil Speyer
  • Aron Cummings
  • David Ferry
  1. 1.Department of Electrical, Computer, and Energy EngineeringArizona State UniversityTempeUSA

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