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Investigation of transient responses of nanoscale transistors by deterministic solution of the time-dependent BTE

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Abstract

In this work, the transient characteristics of nanoscale field-effect transistors (FETs) have been investigated using a deterministic solver based on the time-dependent multi-subband Boltzmann transport equation (BTE). The response to a step signal superimposed on the gate or drain electrode is simulated. The transient process can be understood as a combination of electrostatic and transport relaxation. The extracted transient relaxation time for the drain current, which is unrelated to the direct-current (DC) shift, is important for transient device modeling.

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References

  1. Jin, S., et al.: Theoretical study of carrier transport in Silicon nanowire transistors based on the multisubband Boltzmann transport equation. IEEE Trans. Electron. Devices 55(11), 2886 (2008)

    Article  Google Scholar 

  2. Jin, S., et al.: Simulation of Silicon Nanowire Transistor Using Boltzmann Transport Equation Under Relaxation Time Approximation. IEEE Trans. Electron. Devices 55(3), 727 (2008)

    Article  Google Scholar 

  3. Scaldaferri, S., et al.: Direct solution of the Boltzmann transport equation and Poisson-Schrödinger equation for nanoscale MOSFETs. IEEE Trans. Electron Devices 54(11), 2901 (2007)

    Article  Google Scholar 

  4. Gnani, E., et al.: Quasi-ballistic transport in nanowire field-effect transistors. IEEE Trans. Electron Devices 55(11), 2918 (2008)

    Article  Google Scholar 

  5. Palestri, P., et al.: Understanding quasi-ballistic transport in nano- MOSFETs: Part I-scattering in the channel and in the drain. IEEE Trans. Electron Devices 52(12), 2727 (2005)

    Article  Google Scholar 

  6. Fischetti, M.V., et al.: Theoretical study of some physical aspects of electronic transport in MOSFETs at the 10-nm gate length. IEEE Trans. Electron Devices 54(9), 2116 (2007)

    Article  Google Scholar 

  7. Delaurens, F., Mustieles, F.J.: A deterministic particle method for solving kinetic transport equations: the semiconductor Botzmann equation case. SIMA J. Appl. Math. 52, 973 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Filbet, F., Russo, G.: High order numerical methods for the space non-homogeneous Boltzmann equation. J. Comput. Phys. 186, 457 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Fatemi, E., Odeh, F.: Upwind finite difference solution of Boltzmann equation applied to electron transport in semiconductor devices. J. Comput. Phys. 108, 209 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Majorana, A., Pidatella, R.M.: A finite difference scheme solving the Boltzmann-Poisson system for semiconductor devices. J. Comput. Phys. 174, 649 (2001)

    Article  MATH  Google Scholar 

  11. Jungemann, C., et al.: Stable discretization of the Boltzmann equation based on spherical harmonics, box integration, and a maximum entropy dissipation principle. J. Appl. Phys. 100(2), 024502 (2006)

    Article  Google Scholar 

  12. Ventura, D., et al.: Multidimensional spherical harmonics expansion of Boltzmann equation for transport in semiconductors. Appl. Math. Lett. 5, 85 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pham, A.T. et al.: Deterministic multisubband device simulations for strained double gate PMOSFETs including magnetotransport. Proc. Int. Electron Device Meeting Tech. Dig. (2008)

  14. Ruic, D., Jungemann, C.: A self-consistent solution of the Poisson, Schrödinger and Boltzmann equations by a full Newton-Raphson approach for nanoscale semiconductor devices. Proc. Int. Conf. Simul. Semicond. Processes Devices 356 (2013)

  15. Ruic, D., Jungemann, C.: Numerical aspects of noise simulation in MOSFETs by a Langevin-Boltzmann solver. J. Comput. Electronics 14(1), 21–36 (2015)

    Article  Google Scholar 

  16. Lu, T., et al.: A finite volume method for the multi subband Boltzmann equation with realistic 2D scattering in double gate MOSFETs. Commun. Comput. Phys. 10(2), 305 (2011)

    Article  Google Scholar 

  17. Zhao, K. et al.: Impact of Back biasing in Ultra Short Channel UTBB SOI nMOSFETs. Proc. Int. Conf. Simul. Semicond. Processes Devices 288 (2013)

  18. Liu, G., et al.: Simulation study of quasi-ballistic transport in asymmetric DG-MOSFET by directly solving boltzmann transport equation. IEEE Trans. Nanotechnology 12(2), 168 (2013)

    Article  Google Scholar 

  19. Lu, T. et al.: Multi subband deterministic simulation of an ultra-thin double gate MOSFET with 2D electron gas. Proc. 13th Int. Workshop Comput. Electron (2009)

  20. Smirnov, S.: Physical Modeling of Electron Transport in Strained Silicon and Silicon-Germanium. PhD thesis, Fakultät für Elektrotechnik und Informationstechnik, von, Wien, Österreich, (2003)

  21. Abdallah, Ben N., C’aceres, M.J., Carrillo, J.A., Vecil, F.: A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs. J. Comput. Phys. 228, 6553–6571 (2009)

  22. http://www.itrs.net/

  23. Lundstrom, M.S.: Elementary scattering theory of the Si MOSFET. IEEE Electron Device Lett. 18(7), 361 (1997)

    Article  Google Scholar 

  24. Rahman, A., Lundstrom, M.S.: A compact scattering model for the nanoscale double-gate MOSFET. IEEE Trans. Electron. Devices 49(3), 481 (2002)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Fundamental Basic Research Program of China under Grant 2011CBA00604 and the National Natural Science Foundation of China under Grants 91230107, 91434201, and 61404005.

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Correspondence to Kai Zhao.

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Di, S., Zhao, K., Lu, T. et al. Investigation of transient responses of nanoscale transistors by deterministic solution of the time-dependent BTE. J Comput Electron 15, 770–777 (2016). https://doi.org/10.1007/s10825-016-0818-1

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  • DOI: https://doi.org/10.1007/s10825-016-0818-1

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