JSTS:Journal of Semiconductor Technology and Science

The Institute of Electronics and Information Engineers (대한전자공학회)
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Transient Simulation of Graphene Sheets using a Deterministic Boltzmann Equation Solver

  • Hong, Sung-Min (School of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology)
  • Received : 2016.08.25
  • Accepted : 2016.10.26
  • Published : 2017.04.30
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Abstract

Transient simulation capability with an implicit time derivation method is a missing feature in deterministic Boltzmann equation solvers. The H-transformation, which is critical for the stable simulation of nanoscale devices, introduces difficulties for the transient simulation. In this work, the transient simulation of graphene sheets is reported. It is shown that simulation of homogeneous systems can be done without abandoning the H-transformation, as much as a specially designed discretization method is employed. The AC mobility and step response of the graphene sheet on the $SiO_2$ substrate are simulated.

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References

  1. S.-M. Hong, A.-T. Pham, and C. Jungemann, Deterministic Solvers for the Boltzmann Transport Equation, Springer Verlag Wien/New York, 2011.
  2. S.-M. Hong and C. Jungemann, "A fully coupled scheme for a Boltzmann-Poisson equation solver based on a spherical harmonics expansion," Journal of Computational Electronics, vol. 8, pp. 225- 241, 2009. https://doi.org/10.1007/s10825-009-0294-y
  3. C. Jungemann, "A deterministic approach to RF noise in silicon devices based on the Langevin Boltzmann equation," IEEE Transactions on Electron Devices, vol. 54, pp. 1185-1192, 2007. https://doi.org/10.1109/TED.2007.893210
  4. D. Ruic and C. Jungemann, "Numerical aspects of noise simulation in MOSFETs by a Langevin-Boltzmann solver," Journal of Computational Electronics, vol. 14, pp. 21-36, 2015. https://doi.org/10.1007/s10825-014-0642-4
  5. K. Rupp, C. Jungemann, S.-M. Hong, B. Bina, T. Grasser, and J. Jungel, "A review on recent advances in the spherical harmonics expansion method for semiconductor device simulation," Journal of Computation Electronics, vol. 15, pp. 939-958, 2016. https://doi.org/10.1007/s10825-016-0828-z
  6. M. Dyakonov and M. Shur, "Shallow water analogy for a ballistic field effect transistor: New machanism of plasma wave generation by dc current," Physical Review Letters, vol. 71, pp. 2465-2468, 1993. https://doi.org/10.1103/PhysRevLett.71.2465
  7. S. Bhardwaj, N. K. Nahar, S. Rajan, and J. L. Volakis, "Numerical analysis of terahertz emissions from an ungated HEMT using full-wave hydrodynamic model," IEEE Transactions on Electron Devices, vol. 63, pp. 990-996, 2016. https://doi.org/10.1109/TED.2015.2512912
  8. S. Di, K. Zhao, T. Lu, G. Du, and X. Liu, "Investigation of transient responses of nanoscale transistors by deterministic solution of the time-dependent BTE," Journal of Computational Electronics, vol. 15, pp. 770-777, 2016. https://doi.org/10.1007/s10825-016-0818-1
  9. Y. Cheng, I. M. Gamba, A. Majorana, and C.-W. Shu, "Discontinuous Galerkin solver for the semiconductor Boltzmann equation," International Conference on Simulation of Semiconductor Processes and Devices, pp. 257-260, 2007.
  10. Y. Koseki, V. Ryzhii, T. Otsuji, V. V. Popov, and A. Satou, "Giant plasmon instability in dual-grating-gate graphene field-effect transistor," Physical Review B, vol. 93, p. 245408, 2016. https://doi.org/10.1103/PhysRevB.93.245408
  11. S.-M. Hong, "Transient device simulation using a deterministic Boltzmann equation solver," Asia-Pacific Workshop on Fundamentals and Applications of Advanced Semiconductor Devices, pp. 185-188, 2016.
  12. Y.-M. Lin, K. Jenkins, D. Farmer, A. Valdes-Garcia, P. Avouris, C.-Y. Sung, H.-Y. Chiu, and B. Ek, "Development of graphene FETs for high frequency electronics," International Electron Device Metting, pp. 237-240 , 2009.
  13. M. G. Ancona, "Electron transport in graphene from a diffusion-drift pespective," IEEE Transactions on Electron Devices, vol. 57, pp. 681-689, 2010. https://doi.org/10.1109/TED.2009.2038644
  14. C. Jungemann, A. T. Pham, B. Meinerzhagen, C. Ringhofer, and M. Bollhofer, "Stable discretization of the Boltzmann equation based on spherical harmonics, box integration, and a maximum entropy dissipation principle," Journal of Applied Physics, vol. 100, p. 024502, 2006. https://doi.org/10.1063/1.2212207
  15. A. Gnudi, D. Ventura, G. Baccarani, and F. Odeh, "Two-dimensional MOSFET simulation by means of a multidimensional spherical harmonics expansion of the Boltzmann transport equation," Solid-State Electronics, vol. 36, pp. 575-581, 1993. https://doi.org/10.1016/0038-1101(93)90269-V
  16. S.-M. Hong and S. Cha, "Deterministic Boltzmann equation solver or graphene sheets including self-heating effects," International Conference on Simulation of Semiconductor Processes and Devices, pp. 197-200, 2016.
  17. K. M. Borysenko, J. T. Mullen, E. A. Barry, S. Paul, Y. G. Semenov, J. M. Zavada, M. Buongiorno Nardelli, and K. W. Kim, "First-principles analysis of electron-phonon interactions in graphene," Physical Review B, vol. 81, p. 121412, 2010. https://doi.org/10.1103/PhysRevB.81.121412
  18. R. Rengle, C. Couso, and M. J. Martin, "A Monte Carlo study of electron transport in suspended monolayer graphene," Spanish Conference on Electron Devices, pp. 175-178, 2013.