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Three-dimensional quantum-corrected Monte Carlo device simulator of n-FinFETs

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Abstract

The effective potential approach was successfully incorporated as a quantum correction to a Monte Carlo device simulator of n-FinFETs to take into account the electron quantum confinement. The electron line density calculated by the effective potential approach agrees very well with the one calculated by a 2D Schrödinger–Poisson solver. Next, the results for the drain current as a function of the gate and drain voltage obtained by the semiclassical and by the quantum-corrected Monte Carlo device simulator were compared. The quantum-corrected Monte Carlo device simulator properly models volume inversion, which reduces the impact of surface roughness scattering, thus improving the electron drift velocity. Additionally, the quantum correction allows the modeling of the reduction of electron density in the n-FinFETs channel due to the quantum-mechanical size quantization effect. This, in turn, leads to a reduction of the drain current.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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References

  1. Moore, G.E.: Progress in digital integrated electronics. In: Electron Devices Meeting, Washington, DC, vol. 21, pp. 11–13 (1975). https://doi.org/10.1109/N-SSC.2006.4804410

  2. Thompson, S.E., Chau, R.S., Ghani, T., Mistry, K., Tyagi, S., Bohr, M.T.: In search of “Forever,’’ continued transistor scaling one new material at a time. IEEE Trans. Semicond. Manuf. 18(1), 26–36 (2005). https://doi.org/10.1109/TSM.2004.841816

    Article  Google Scholar 

  3. Maurya, R.K., Bhowmick, B.: Review of FinFET devices and perspective on circuit design challenges. SILICON 14(11), 5783–5791 (2022). https://doi.org/10.1007/s12633-021-01366-z

    Article  CAS  Google Scholar 

  4. Rossetto, A.C., Camargo, V.V., Both, T.H., Vasileska, D., Wirth, G.I.: Statistical analysis of the impact of charge traps in p-type MOSFETs via particle-based Monte Carlo device simulations. J. Comput. Electron. 19, 648–657 (2020). https://doi.org/10.1007/s10825-020-01478-6

    Article  CAS  Google Scholar 

  5. Camargo, V.V., Rossetto, A.C., Vasileska, D., Wirth, G.I.: 3-D Monte Carlo device simulator for variability modeling of p-MOSFETs. J. Comput. Electron. 19, 668–676 (2020). https://doi.org/10.1007/s10825-020-01461-1

    Article  CAS  Google Scholar 

  6. Furtado, G.F., Camargo, V.V.D.A., Vasileska, D., Wirth, G.I.: 3-D TCAD Monte Carlo device simulator State-of-the-art FinFET simulation. J. Integr. Circuits Syst. 16(2), 1–10 (2021). https://doi.org/10.29292/jics.v16i2.476

    Article  Google Scholar 

  7. Furtado, G.F., Camargo, V.V.A., Vasileska, D., Wirth, G.I.: Correlation of HCD and percolation paths in FinFETs: study of RDF and MGG impacts through 3-D particle-based simulation. IEEE Trans. Device Mater. Reliab. 22(3), 381–386 (2022). https://doi.org/10.1109/TDMR.2022.3178900

    Article  CAS  Google Scholar 

  8. Furtado, G.F., Camargo, V.V.A., Vasileska, D., Wirth, G.I.: Evaluating the ballistic transport in nFinFETs: a carrier centric perspective. IEEE Trans. Nanotechnol. 21, 311–319 (2022). https://doi.org/10.1109/TNANO.2022.3186147

    Article  ADS  CAS  Google Scholar 

  9. Colinge, J.-P.: FinFETs and Other Multi-gate Transistors. Springer, New York (2008)

    Book  Google Scholar 

  10. Colinge, J.-P., Alderman, J.C., Xiong, W., Cleavelin, C.R.: Quantum-mechanical effects in trigate SOI MOSFETs. IEEE Trans. Electron Devices 53(5), 1131–1136 (2006). https://doi.org/10.1109/TED.2006.871872

    Article  ADS  CAS  Google Scholar 

  11. Ferry, D.K.: The onset of quantization in ultra-submicron semiconductor devices. Superlattices Microstruct. 27(2), 61–66 (2000). https://doi.org/10.1006/spmi.1999.0800

    Article  ADS  Google Scholar 

  12. Ferry, D., Akis, R., Vasileska, D.: Quantum effects in mosfets: use of an effective potential in 3d Monte Carlo simulation of ultra-short channel devices. In: International Electron Devices Meeting 2000. Technical Digest. IEDM (Cat. No. 00CH37138). IEEE, pp. 287–290 (2000)

  13. Ramey, S.M., Ferry, D.K.: Modeling of quantum effects in ultrasmall FD-SOI MOSFETs with effective potentials and three-dimensional Monte Carlo. Phys. B: Condensed Matter 314(1), 350–353 (2002). https://doi.org/10.1016/S0921-4526(01)01385-0. Proceedings of the Twelfth International Conference on Nonequilib rium Carrier Dynamics in Semiconductors

  14. Vasileska, D., Knezevic, I., Akis, R., Ahmed, S., Ferry, D.: The role of quantization effects on the operation of 50 nm MOSFETs, 250 nm FIBMOS devices and narrow-width SOI device structures. J. Comput. Electron. 1, 453–465 (2002). https://doi.org/10.1023/A:1022980703489

    Article  Google Scholar 

  15. Han, W., Wang, Z.M.: Toward Quantum FinFET. Springer, Switzerland (2013)

    Book  Google Scholar 

  16. Colinge, J.-P., Greer, J.C., Greer, J.: Nanowire Transistors: Physics of Devices and Materials in One Dimension. Cambridge University Press, Cambridge (2016)

    Book  Google Scholar 

  17. Wettstein, A., Schenk, A., Fichtner, W.: Quantum device-simulation with the density-gradient model on unstructured grids. IEEE Trans. Electron Devices 48(2), 279–284 (2001). https://doi.org/10.1109/16.902727

    Article  ADS  Google Scholar 

  18. Ancona, M.G., Iafrate, G.J.: Quantum correction to the equation of state of an electron gas in a semiconductor. Phys. Rev. B 39, 9536–9540 (1989). https://doi.org/10.1103/PhysRevB.39.9536

    Article  ADS  CAS  Google Scholar 

  19. Ancona, M.G.: Finite-difference schemes for the density-gradient equations. J. Comput. Electron. 1, 435–443 (2002). https://doi.org/10.1023/A:1020732515391

    Article  CAS  Google Scholar 

  20. A.U. Manual: Silvaco tcad. Santa Clara, CA, USA (2010)

  21. S.D.M.C.U. Guide: Sentaurus Device Monte Carlo User Guide. Synopsys (2013)

  22. Bohm, D.: A suggested interpretation of the quantum theory in terms of “hidden’’ variables I. Phys. Rev. 85, 166–179 (1952). https://doi.org/10.1103/PhysRev.85.166

    Article  ADS  MathSciNet  CAS  Google Scholar 

  23. Kriman, A.M., Zhou, J., Ferry, D.K.: Statistical properties of hard-wall potentials. Phys. Lett. A 138(1), 8–12 (1989). https://doi.org/10.1016/0375-9601(89)90794-9

    Article  ADS  Google Scholar 

  24. Iannaccone, G., Curatola, G., Fiori, G.: Effective Bohm Quantum Potential for device simulators based on drift-diffusion and energy transport. In: Wachutka, G., Schrag, G. (eds.) Simulation of Semiconductor Processes and Devices 2004, pp. 275–278. Springer, Vienna (2004). https://doi.org/10.1007/978-3-7091-0624-2_64

  25. Ferry, D., Ramey, S., Shifren, L., Akis, R.: The effective potential in device modeling: the good, the bad and the ugly. J. Comput. Electron. 1, 59–65 (2002). https://doi.org/10.1023/A:1020763710906

    Article  CAS  Google Scholar 

  26. Soares, C.S., Baikadi, P.K.R., Rossetto, A.C.J., Pavanello, M.A., Vasileska, D., Wirth, G.I.: Modeling Quantum Confinement in Multi-Gate Transistors with Effective Potential. In: 2022 36th Symposium on Microelectronics Technology (SBMICRO), pp. 1–4 ( 2022). https://doi.org/10.1109/SBMICRO55822.2022.9881047

  27. Ando, T., Fowler, A.B., Stern, F.: Electronic properties of two-dimensional systems. Rev. Mod. Phys. 54, 437–672 (1982). https://doi.org/10.1103/RevModPhys.54.437

    Article  ADS  CAS  Google Scholar 

  28. Soffer, S.B.: Statistical model for the size effect in electrical conduction. J. Appl. Phys. 38(4), 1710–1715 (1967)

    Article  ADS  CAS  Google Scholar 

  29. Lee, J.W., Jang, D., Mouis, M., Kim, G.T., Chiarella, T., Hoffmann, T., Ghibaudo, G.: Mobility analysis of surface roughness scattering in finfet devices. Solid-State Electron. 62(1), 195–201 (2011). https://doi.org/10.1016/j.sse.2011.04.020

    Article  ADS  CAS  Google Scholar 

  30. Boriçi, M., Watling, J., Wilkins, R., Yang, L., Barker, J.: A non perturbative model of surface roughness scattering for monte carlo simulation of relaxed silicon n-mosfets. J. Comput. Electron. 2, 163–167 (2003)

    Article  Google Scholar 

  31. Watling, J.R., Yang, L., Boriçi, M., Wilkins, R.C.W., Asenov, A., Barker, J.R., Roy, S.: The impact of interface roughness scattering and degeneracy in relaxed and strained si n-channel mosfets. Solid-State Electron. 48(8), 1337–1346 (2004). https://doi.org/10.1016/j.sse.2004.01.015. Strained-Si Heterostructures and Devices

  32. Fuchs, K.: The conductivity of thin metallic films according to the electron theory of metals. Math. Proc. Camb. Philos. Soc. 34(1), 100–108 (1938). https://doi.org/10.1017/S0305004100019952

    Article  ADS  CAS  Google Scholar 

  33. Goodnick, S., Gann, R., Sites, J., Ferry, D.K., Wilmsen, C., Fathy, D., Krivanek, O.: Surface roughness scattering at the si-sio2 interface. J. Vac. Sci. Technol. B Microelectron. Process. Phenom. 1(3), 803–808 (1983)

    Article  ADS  CAS  Google Scholar 

  34. Fischetti, M.V., Laux, S.E.: Monte Carlo analysis of electron transport in small semiconductor devices including band-structure and space-charge effects. Phys. Rev. B 38, 9721–9745 (1988). https://doi.org/10.1103/PhysRevB.38.9721

    Article  ADS  CAS  Google Scholar 

  35. Vasileska, D., Gross, W.J., Ferry, D.K.: Monte Carlo particle-based simulations of deep-submicron n-mosfets with real-space treatment of electron-electron and electron-impurity interactions. Superlattices Microstruct. 27(2), 147–157 (2000). https://doi.org/10.1006/spmi.1999.0806

    Article  ADS  CAS  Google Scholar 

  36. Bufler, F., Schenk, A., Fichtner, W.: Efficient Monte Carlo device modeling. IEEE Trans. Electron Devices 47(10), 1891–1897 (2000)

    Article  ADS  CAS  Google Scholar 

  37. Laux, S., Fischetti, M.: Monte Carlo study of velocity overshoot in switching a 0.1-micron cmos inverter. In: International Electron Devices Meeting. IEDM Technical Digest, pp. 877–880. IEEE (1997)

  38. Bufler, F., Smith, L.: 3D Monte Carlo simulation of FinFET and FDSOI devices with accurate quantum correction. J. Comput. Electron. 12, 651–657 (2013). https://doi.org/10.1007/s10825-013-0518-z

    Article  CAS  Google Scholar 

  39. Bufler, F., Heinz, F., Smith, L.: Efficient 3d Monte Carlo simulation of orientation and stress effects in finfets. In: 2013 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), pp. 172–175. IEEE (2013)

  40. Bufler, F.M., Ritzenthaler, R., Mertens, H., Eneman, G., Mocuta, A., Horiguchi, N.: Performance comparison of n-type si nanowires, nanosheets, and finfets by mc device simulation. IEEE Electron Device Lett. 39(11), 1628–1631 (2018)

    Article  ADS  CAS  Google Scholar 

  41. Vasileska, D., Goodnick, S.M., Klimeck, G.: Computational Electronics: Semiclassical and Quantum Device Modeling and Simulation, 1st edn. CRC Press, Boca Raton (2010). https://doi.org/10.1201/b13776

    Book  Google Scholar 

  42. Wang, J., Polizzi, E., Ghosh, A., Datta, S., Lundstrom, M.: Theoretical investigation of surface roughness scattering in silicon nanowire transistors. Appl. Phys. Lett. 87(4), 043101 (2005)

    Article  ADS  Google Scholar 

  43. Gamiz, F., Fischetti, M.: Monte Carlo simulation of double-gate silicon-on-insulator inversion layers: the role of volume inversion. J. Appl. Phys. 89(10), 5478–5487 (2001)

    Article  ADS  CAS  Google Scholar 

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Funding

This work was supported by CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico—Brasil, and it was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001.

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Soares, C.S., Furtado, G.F., Rossetto, A.C.J. et al. Three-dimensional quantum-corrected Monte Carlo device simulator of n-FinFETs. J Comput Electron (2024). https://doi.org/10.1007/s10825-024-02145-w

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