An Explicit Model for Ultra-thin Gate-All-Around Junctionless Nanowire FETs, Including 2D Quantum Confinement

Danial Shafizade; Farzan Jazaeri; Majid Shalchian

arxiv: 1906.10457 · v1 · pith:6JHJ4ER4new · submitted 2019-06-25 · ⚛️ physics.app-ph · cond-mat.mes-hall

An Explicit Model for Ultra-thin Gate-All-Around Junctionless Nanowire FETs, Including 2D Quantum Confinement

Danial Shafizade , Majid Shalchian , Farzan Jazaeri This is my paper

Pith reviewed 2026-05-25 16:03 UTC · model grok-4.3

classification ⚛️ physics.app-ph cond-mat.mes-hall

keywords junctionless nanowire FETgate-all-aroundquantum confinementexplicit modelPoisson equationperturbation theoryFermi-Dirac statisticsDC characteristics

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The pith

An explicit analytical model for the DC characteristics of ultra-thin junctionless nanowire FETs is obtained by combining parabolic Poisson approximation, first-order perturbation theory, and Fermi-Dirac statistics to include 2D quantum sub

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops an explicit model for the drain current in ultra-thin gate-all-around junctionless nanowire FETs that includes two-dimensional confinement of carriers into discrete sub-bands. The model approximates the electrostatic potential as parabolic, applies first-order perturbation theory to obtain subband energies from the Schrödinger equation, and integrates the resulting density of states with Fermi-Dirac statistics. These steps produce closed-form expressions that describe device operation without numerical iteration. The expressions are shown to hold from deep depletion through accumulation and from the linear to saturation regimes. A reader would care because the closed form supports fast circuit-level analysis of devices where quantum confinement dominates at small scales.

Core claim

Combining a parabolic approximation of the Poisson equation, first-order perturbation theory for the Schrödinger subband energy eigenvalues, and Fermi-Dirac statistics for the confined carrier density produces an explicit solution of the DC current-voltage characteristics in ultra-thin junctionless nanowire FETs that matches TCAD simulations in all regions of operation.

What carries the argument

Parabolic approximation of the Poisson equation combined with first-order perturbation theory for subband energies and Fermi-Dirac statistics for carrier density.

If this is right

Drain current can be calculated directly from closed-form expressions without solving transcendental equations iteratively.
The model remains valid from deep depletion to accumulation and from linear to saturation operation.
Two-dimensional confinement enters the expressions through discrete sub-bands that modify the effective carrier density.
Verification against TCAD simulations confirms the approximations for the targeted ultra-thin geometries.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The closed-form expressions could allow analytical optimization of nanowire radius or doping level for target threshold voltages.
The same sequence of approximations might be applied to other confined structures such as finFETs or nanosheet devices.
Circuit simulators could incorporate the model directly to evaluate large arrays of junctionless nanowires at low computational cost.
Temperature dependence could be added by retaining the explicit Fermi-Dirac integrals already present in the derivation.

Load-bearing premise

The parabolic approximation of the Poisson equation together with first-order perturbation theory remains accurate for the two-dimensional confinement and geometry of ultra-thin junctionless nanowire FETs across all bias regimes.

What would settle it

A direct numerical comparison that shows large deviation between the model's predicted subband energies or current-voltage curves and self-consistent two-dimensional Poisson-Schrödinger solutions at a chosen ultra-thin radius and bias point would falsify the central claim.

read the original abstract

In this paper, we develop an explicit model to predict the DC electrical behavior in ultra-thin surrounding gate junctionless nanowire FET. The proposed model takes into account 2D electrical and geometrical confinements of carrier charge density within few discrete sub-bands. Combining a parabolic approximation of the Poisson equation, first order perturbation theory for the Schrodinger subband energy eigenvalues, and Fermi-Dirac statistics for the confined carrier density leads to an explicit solution of the DC characteristic in ultra-thin junctionless devices. Validity of the model has been verified with technology computer-aided design simulations. The results confirms its validity for all regions of operation, i.e., from deep depletion to accumulation and from linear to saturation. This represents an essential step toward analysis of circuits based on junctionless nanowire devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper gives a usable closed-form model for ultra-thin GAA junctionless nanowires by combining parabolic Poisson, first-order perturbation, and Fermi-Dirac statistics, with claimed TCAD match across regimes.

read the letter

The core contribution is an explicit DC model for these ultra-thin JLNWFETs that folds 2D confinement into the carrier density without needing iterative solves. It starts from the parabolic approximation to Poisson, applies first-order perturbation to get the subband shifts, then uses Fermi-Dirac to close the current expression. That combination is a reasonable next step from earlier JL nanowire work and produces something that can be dropped into a circuit simulator without numerical overhead. The abstract reports TCAD agreement from deep depletion through accumulation and into saturation, which is the right set of checks for this kind of compact model. If the full paper shows the comparisons without hidden parameter tuning, that counts as real evidence the approximations hold for the target geometry. The main soft spot is exactly the one flagged in the stress test: once the device enters accumulation the potential curvature near the interface is no longer parabolic and the carrier wavefunctions pull toward the oxide, so the unperturbed infinite-well basis plus first-order correction can drift. The paper asserts validation in that regime, but the strength of the claim rests on how closely the model potential tracks a self-consistent 2-D solution and whether the error stays small enough for circuit use. Without seeing the actual error metrics or the potential plots, it is hard to judge how much margin exists. This is a paper for people who build or use compact models for junctionless nanowire circuits. Device physicists working on quantum-corrected electrostatics will find the derivation straightforward to follow, and circuit designers will appreciate the closed form. It is worth sending to peer review because the method is standard, the target application is clear, and the claimed validation gives referees something concrete to examine. A referee can ask for the detailed error data and the accumulation-regime checks without needing to rewrite the approach.

Referee Report

1 major / 1 minor

Summary. The paper develops an explicit analytical model for the DC characteristics of ultra-thin gate-all-around junctionless nanowire FETs that incorporates 2D quantum confinement. It combines a parabolic approximation to the Poisson equation, first-order perturbation theory applied to the Schrödinger equation for subband energies, and Fermi-Dirac statistics to obtain closed-form expressions for carrier density and current; the model is stated to be valid from deep depletion through accumulation and from linear to saturation regimes, with verification performed against TCAD simulations.

Significance. An explicit, closed-form model for quantum-confined JLNWFETs would be useful for rapid circuit simulation where full numerical TCAD is prohibitive. The approach of deriving an explicit solution from standard physical approximations rather than fitting parameters is a positive feature if the resulting expressions remain quantitatively accurate across bias regimes.

major comments (1)

[Abstract / validation] Abstract and validation section: the central claim that the parabolic Poisson solution plus first-order perturbation remains accurate 'for all regions of operation' (including accumulation) is load-bearing for the utility of the explicit model. In ultra-thin GAA JLNWFETs the potential becomes strongly non-parabolic once surface accumulation begins, and the unperturbed infinite-well basis assumed in perturbation theory is expected to degrade; the manuscript must supply point-wise error metrics (e.g., RMS deviation of model potential or subband energies versus self-consistent 2-D Poisson-Schrödinger solutions) in the accumulation regime to substantiate the TCAD comparison.

minor comments (1)

[Abstract] Abstract: 'The results confirms its validity' contains a subject-verb agreement error and should read 'The results confirm its validity'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment on validation in the accumulation regime below.

read point-by-point responses

Referee: [Abstract / validation] Abstract and validation section: the central claim that the parabolic Poisson solution plus first-order perturbation remains accurate 'for all regions of operation' (including accumulation) is load-bearing for the utility of the explicit model. In ultra-thin GAA JLNWFETs the potential becomes strongly non-parabolic once surface accumulation begins, and the unperturbed infinite-well basis assumed in perturbation theory is expected to degrade; the manuscript must supply point-wise error metrics (e.g., RMS deviation of model potential or subband energies versus self-consistent 2-D Poisson-Schrödinger solutions) in the accumulation regime to substantiate the TCAD comparison.

Authors: We acknowledge the referee's point that the parabolic approximation to Poisson's equation and the use of an unperturbed infinite-well basis in perturbation theory may have reduced accuracy once strong surface accumulation sets in. Our existing TCAD comparisons already show acceptable agreement in accumulation (as plotted in the validation figures), but we agree that explicit quantitative error metrics would strengthen the claim. In the revised manuscript we will add RMS deviation tables (or plots) for both the electrostatic potential and the lowest subband energies, extracted directly from the same TCAD data sets in the accumulation regime. These metrics will be presented alongside the existing I-V and C-V comparisons. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation from physical approximations with external TCAD validation

full rationale

The paper derives an explicit DC model by starting from the parabolic approximation to Poisson's equation, applying first-order perturbation theory to the Schrödinger subband eigenvalues, and using Fermi-Dirac statistics for confined carrier density. These steps produce closed-form expressions for the device characteristics that are then compared to independent TCAD simulations across depletion, accumulation, linear, and saturation regimes. No quoted equations or steps reduce a claimed prediction to a fitted parameter by construction, invoke load-bearing self-citations, or rename known results; the central claim rests on standard physical approximations whose accuracy is assessed externally rather than by re-deriving the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Insufficient information in the provided abstract to identify specific free parameters, axioms, or invented entities; the model invokes standard physical approximations whose detailed assumptions cannot be audited from the abstract alone.

pith-pipeline@v0.9.0 · 5680 in / 1168 out tokens · 54055 ms · 2026-05-25T16:03:03.885878+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Nanowire Transistors Without Junctio ns,

Jean-Pierre Colinge, Chi-Woo Lee, Aryan Afzalian, Nima Dehdashti Akhavan, Ran Y an, Isabelle Ferain, Pedram Razavi, Brendan O ’Neill, Alan Blake, Mary White, Anne-Marie Kelleher, Brendan McCar thy, and Richard Murphy, “Nanowire Transistors Without Junctio ns,” Nature Nanotechnology, vol. 5, pp. 225–229, February 2010

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Charge-based Modeling of Junctionless Double-Gate Field -Effect Tran- sistors,

J. Sallese, N. Chevillon, C. Lallement, B. Iniguez, and F . Pregaldiny, “Charge-based Modeling of Junctionless Double-Gate Field -Effect Tran- sistors,” IEEE Transactions on Electron Devices , vol. 58, no. 8, pp. 2628–2637, Aug 2011

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Compact Modeli ng of the Threshold V oltage in Silicon Nanowire MOSFET including 2D-quantum Conﬁnement Effects,

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A Self-Consistent Compact Model of Ballistic Nanowire MOSFET With Rectangular Cross Section,

T. Numata, S. Uno, J. Hattori, G. Mil’nikov, Y . Kamakura, N. Mori, and K. Nakazato, “A Self-Consistent Compact Model of Ballistic Nanowire MOSFET With Rectangular Cross Section,” IEEE Transactions on Electron Devices, vol. 60, no. 2, pp. 856–862, Feb 2013

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Analytical Compact Model for Quantization i n Undoped Double-Gate Metal Oxide Semiconductor Field Effect Transi stors and Its Impact on Quasi-Ballistic Current,

M. Ferrier, R. Clerc, G. Pananakakis, G. Ghibaudo, F. Boe uf, and T. Skotnicki, “Analytical Compact Model for Quantization i n Undoped Double-Gate Metal Oxide Semiconductor Field Effect Transi stors and Its Impact on Quasi-Ballistic Current,” Japanese Journal of Applied Physics, vol. 45, no. 4B, pp. 3088–3096, apr 2006

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Analytic Drain Current Model for IIIV Cylindrical Nanowir e Transis- tors,

E. G. Marin, F. G. Ruiz, V . Schmidt, A. Godoy, H. Riel, and F . Gmiz, “Analytic Drain Current Model for IIIV Cylindrical Nanowir e Transis- tors,” Journal of Applied Physics , vol. 118, no. 4, p. 044502, 2015

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Trans-capacita nce modeling in junctionless symmetric double-gate mosfets,

F. Jazaeri, L. Barbut, and J. Sallese, “Trans-capacita nce modeling in junctionless symmetric double-gate mosfets,” IEEE Transactions on Electron Devices, vol. 60, no. 12, pp. 4034–4040, Dec 2013

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Trans-capac itance modeling in junctionless gate-all-around nanowire fets,

F. Jazaeri, L. Barbut, and J.-M. Sallese, “Trans-capac itance modeling in junctionless gate-all-around nanowire fets,” Solid- State Electronics , vol. 96, pp. 34 – 37, 2014. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0038110114000707

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An alytical model for ultra-thin body junctionless symmetric double gate mos fets in subthreshold regime,

F. Jazaeri, L. Barbut, A. Koukab, and J.-M. Sallese, “An alytical model for ultra-thin body junctionless symmetric double gate mos fets in subthreshold regime,” Solid-State Electronics , vol. 82, pp. 103 – 110, 2013

work page 2013