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Micromachines
Volume 13
Issue 4
10.3390/mi13040533
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Article

Analysis of the Reformulated Source to Drain Tunneling Probability for Improving the Accuracy of a Multisubband Ensemble Monte Carlo Simulator

by
Jose Luis Padilla
1,2,*,
Cristina Medina-Bailon
1,2,
Antonio Palomares
3,
Luca Donetti
1,2,
Carlos Navarro
1,2,
Carlos Sampedro
1,2 and
Francisco Gamiz
1,2
1
Nanoelectronics Research Group, Departamento de Electrónica y Tecnología de Computadores, Universidad de Granada, 18071 Granada, Spain
2
Centro de Investigación en Tecnologías de la Información y las Comunicaciones, Universidad de Granada, 18071 Granada, Spain
3
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
*
Author to whom correspondence should be addressed.
Micromachines 2022, 13(4), 533; https://doi.org/10.3390/mi13040533
Submission received: 23 December 2021 / Revised: 22 March 2022 / Accepted: 25 March 2022 / Published: 28 March 2022
(This article belongs to the Special Issue Emerging CMOS Devices)
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Abstract

As an attempt to improve the description of the tunneling current that arises in ultrascaled nanoelectronic devices when charge carriers succeed in traversing the potential barrier between source and drain, an alternative and more accurate non-local formulation of the tunneling probability was suggested. This improvement of the probability computation might result of particular interest in the context of Monte Carlo simulations where the utilization of the conventional Wentzel-Kramers-Brillouin (WKB) approximation tends to overestimate the number of particles experiencing this type of direct tunneling. However, in light of the reformulated expression for the tunneling probability, it becomes of paramount importance to assess the type of potentials for which it behaves adequately. We demonstrate that, for ensuring boundedness, the top of the potential barrier cannot feature a plateau, but rather has to behave quadratically as one approaches its maximum. Moreover, we show that monotonicity of the reformulated tunneling probability is not guaranteed by boundedness and requires an additional constraint regarding the derivative of the prefactor that modifies the traditional WKB tunneling probability.
Keywords: direct source-to-drain tunneling; tunneling probability; multi-subband ensemble Monte Carlo direct source-to-drain tunneling; tunneling probability; multi-subband ensemble Monte Carlo

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MDPI and ACS Style

Padilla, J.L.; Medina-Bailon, C.; Palomares, A.; Donetti, L.; Navarro, C.; Sampedro, C.; Gamiz, F. Analysis of the Reformulated Source to Drain Tunneling Probability for Improving the Accuracy of a Multisubband Ensemble Monte Carlo Simulator. Micromachines 2022, 13, 533. https://doi.org/10.3390/mi13040533

AMA Style

Padilla JL, Medina-Bailon C, Palomares A, Donetti L, Navarro C, Sampedro C, Gamiz F. Analysis of the Reformulated Source to Drain Tunneling Probability for Improving the Accuracy of a Multisubband Ensemble Monte Carlo Simulator. Micromachines. 2022; 13(4):533. https://doi.org/10.3390/mi13040533

Chicago/Turabian Style

Padilla, Jose Luis, Cristina Medina-Bailon, Antonio Palomares, Luca Donetti, Carlos Navarro, Carlos Sampedro, and Francisco Gamiz. 2022. "Analysis of the Reformulated Source to Drain Tunneling Probability for Improving the Accuracy of a Multisubband Ensemble Monte Carlo Simulator" Micromachines 13, no. 4: 533. https://doi.org/10.3390/mi13040533

APA Style

Padilla, J. L., Medina-Bailon, C., Palomares, A., Donetti, L., Navarro, C., Sampedro, C., & Gamiz, F. (2022). Analysis of the Reformulated Source to Drain Tunneling Probability for Improving the Accuracy of a Multisubband Ensemble Monte Carlo Simulator. Micromachines, 13(4), 533. https://doi.org/10.3390/mi13040533

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