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.
Similar content being viewed by others
Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
Code availability
Not applicable.
References
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
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
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
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
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
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
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
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
Colinge, J.-P.: FinFETs and Other Multi-gate Transistors. Springer, New York (2008)
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
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
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)
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
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
Han, W., Wang, Z.M.: Toward Quantum FinFET. Springer, Switzerland (2013)
Colinge, J.-P., Greer, J.C., Greer, J.: Nanowire Transistors: Physics of Devices and Materials in One Dimension. Cambridge University Press, Cambridge (2016)
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
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
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
A.U. Manual: Silvaco tcad. Santa Clara, CA, USA (2010)
S.D.M.C.U. Guide: Sentaurus Device Monte Carlo User Guide. Synopsys (2013)
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
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
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
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
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
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
Soffer, S.B.: Statistical model for the size effect in electrical conduction. J. Appl. Phys. 38(4), 1710–1715 (1967)
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
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)
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
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
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)
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
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
Bufler, F., Schenk, A., Fichtner, W.: Efficient Monte Carlo device modeling. IEEE Trans. Electron Devices 47(10), 1891–1897 (2000)
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)
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
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)
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)
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
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)
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)
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.
Author information
Authors and Affiliations
Contributions
All authors whose names appear on the submission 1) made substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data; or the creation of new software used in the work; 2) drafted the work or revised it critically for important intellectual content; 3) approved the version to be published; and 4) agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.
Corresponding author
Ethics declarations
Conflict of interest
Not applicable.
Ethics approval
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10825-024-02145-w