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Open AccessFeature PaperArticle

Analysis of an Approximated Model for the Depletion Region Width of Planar Junctionless Transistors

by Arian Nowbahari 1,‡, Avisek Roy 2,†,‡, Muhammad Nadeem Akram 2,†,‡ and Luca Marchetti 2,*,†,‡
1
Department of Electronics and Telecommunications, Polytechnic University of Turin, 10129 Torino, Italy
2
Department of Microsystems, IMS, University of South Eastern Norway, 3184 Borre, Norway
*
Author to whom correspondence should be addressed.
Current address: Raveien 215, 3184 Borre, Norway.
These authors contributed equally to this work.
Electronics 2019, 8(12), 1436; https://doi.org/10.3390/electronics8121436
Received: 1 September 2019 / Revised: 23 October 2019 / Accepted: 21 November 2019 / Published: 1 December 2019
(This article belongs to the Special Issue Advanced Technologies in Nanoelectronics)
In this paper, we investigate the accuracy of the approximated analytical model currently utilized, by many researchers, to describe the depletion region width in planar junctionless transistors (PJLT). The proposed analysis was supported by numerical simulations performed in COMSOL Multiphysics software. By comparing the numerical results and the approximated analytical model of the depletion region width, we calculated that the model introduces a maximum RMS error equal to 90 % of the donor concentration in the substrate. The maximum error is achieved when the gate voltage approaches the threshold voltage ( V t h ) or when it approaches the flat band voltage ( V F B ) of the transistor. From these results, we concluded that this model cannot be used to determine accurately the flat-band and the threshold voltage of the transistor, although it represents a straightforward method to estimate the depletion region width in PJLT. By using the approximated analytical model, we extracted an analytical formula, which describes the electron concentration at the ideal boundary of the depletion region. This formula approximates the numerical data extracted from COMSOL with a relative error lower than 1 % . The proposed formula is in our opinion, as useful as the formula of the approximated analytical model because it allows for estimating the position of the depletion region also when the drain and source terminals are not grounded. We concluded that the analytical formula proposed at the end of this work could be useful to determine the position of the depletion region boundary in numerical simulations and in graphical representations provided by COMSOL Multiphysics software. View Full-Text
Keywords: junctionless transistor; depletion region; electron concentration; COMSOL junctionless transistor; depletion region; electron concentration; COMSOL
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Nowbahari, A.; Roy, A.; Nadeem Akram, M.; Marchetti, L. Analysis of an Approximated Model for the Depletion Region Width of Planar Junctionless Transistors. Electronics 2019, 8, 1436.

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