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arxiv: 2504.00214 · v5 · submitted 2025-03-31 · ❄️ cond-mat.mes-hall · physics.app-ph

SEMIDV: A Compact Semiconductor Device Simulator with Quantum Effects

Chien-Ting Tung This is my paper

Pith reviewed 2026-05-22 21:40 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall physics.app-ph
keywords semiconductor device simulationdrift-diffusionlocalization landscape theoryquantum correctionsnanosheet FETballistic transportGAA transistorvelocity overshoot
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The pith

SEMIDV adds quantum corrections to drift-diffusion equations via localization landscape theory for nanosheet FET simulation.

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

The paper introduces SEMIDV, a compact Python-based simulator that solves the Poisson-Drift-Diffusion equations while incorporating quantum effects. Localization landscape theory is used to compute the ground state of the Schrödinger equation directly, supplying efficient quantum corrections inside the classical framework. A separate compact mobility model accounts for ballistic length dependence and velocity overshoot in short channels. These additions are demonstrated on a 6 nm gate-length GAA/RibbonFET and used to propose an ultra-short 4.5 nm device operating at 0.45 V.

Core claim

Localization landscape theory directly solves the ground state of the Schrödinger equation without further approximation, offering an efficient solution for quantum effect modeling in the drift-diffusion framework. A compact mobility model considering ballistic transport is developed to capture the ballistic length dependence of mobility and the velocity overshoot effect in short-channel devices.

What carries the argument

Localization landscape theory, which computes the ground-state solution of the Schrödinger equation to supply quantum corrections inside the Poisson-Drift-Diffusion solver.

If this is right

  • Quantum corrections become available inside standard drift-diffusion solvers without repeated full Schrödinger solutions.
  • Ballistic length dependence and velocity overshoot are captured in mobility for gate lengths below 10 nm.
  • Electrical characteristics of a 6 nm GAA/RibbonFET can be analyzed for the separate influences of quantum confinement and ballistic transport.
  • A functional transistor design is obtained at 4.5 nm gate length and 0.45 V supply within the model's predictions.

Where Pith is reading between the lines

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

  • The approach may allow rapid design-space exploration for sub-5 nm nodes where full quantum solvers remain too slow for routine use.
  • The Python scripting interface could support coupling to circuit-level simulators if performance permits.
  • Direct comparison with atomistic or NEGF results on the same structures would test the range of validity for still shorter channels.

Load-bearing premise

The localization landscape theory together with the ballistic mobility model supplies sufficiently accurate quantum corrections and transport descriptions for 6 nm and 4.5 nm nanosheet FETs without requiring validation against full quantum transport calculations or measured data.

What would settle it

Compare current-voltage and capacitance-voltage curves produced by SEMIDV for the described 6 nm and 4.5 nm GAA devices against results from a full NEGF quantum transport simulator or against fabricated devices at identical dimensions.

Figures

Figures reproduced from arXiv: 2504.00214 by Chien-Ting Tung.

Figure 1
Figure 1. Figure 1: The flow chart of solving physics equations in SEMIDV. A. Poisson Equation Poisson equation governs the band bending in the presence T [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
read the original abstract

In this paper, I present SEMIDV - a compact semiconductor device simulator incorporating quantum effects. SEMIDV solves the Poisson-Drift-Diffusion equations for semiconductor devices and provides a user-friendly Python interface for scripting and data analysis. Localization landscape theory is introduced to provide quantum corrections to the Drift-Diffusion equation. This theory directly solves the ground state of the Schrodinger equation without further approximation, offering an efficient solution for quantum effect modeling. Additionally, a compact mobility model considering ballistic transport is developed to capture the ballistic length dependence of mobility and the velocity overshoot effect in short-channel devices. Finally, a study on a nanosheet FET using SEMIDV is conducted. I analyze the electrical characteristics of a state-of-the-art GAA/RibbonFET with a 6 nm gate length and discuss the effects of velocity overshoot and quantum confinement on currents and capacitances. A design for an ultra-short-channel transistor with a gate length down to 4.5 nm with a Vdd = 0.45 V is proposed to push the boundaries of integrated circuit technology further.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript presents SEMIDV, a compact Python-based simulator solving the Poisson-drift-diffusion equations for semiconductor devices. It incorporates quantum corrections via localization landscape theory, which the abstract claims directly solves the Schrödinger ground state without further approximation, and introduces a compact mobility model accounting for ballistic transport and velocity overshoot. The tool is applied to analyze a GAA nanosheet FET at 6 nm gate length and to propose an ultra-short-channel design at 4.5 nm with Vdd = 0.45 V, discussing effects on currents and capacitances.

Significance. If the central claims on accuracy and efficiency hold after correction, SEMIDV could provide a lightweight framework for including quantum confinement and ballistic effects in short-channel device modeling, potentially useful for rapid prototyping of nanosheet or GAA transistors. No machine-checked proofs, reproducible code releases, or falsifiable predictions are described that would strengthen the assessment.

major comments (2)
  1. [Abstract] Abstract: the claim that localization landscape theory 'directly solves the ground state of the Schrödinger equation without further approximation' is overstated. The method solves the auxiliary equation Δu + V u = 1 for the landscape function u and approximates the ground state via 1/u; the approximation error is potential-dependent and is neither quantified nor bounded for the 6 nm and 4.5 nm nanosheet FETs. This directly undercuts the assertion that quantum corrections are obtained without further approximation.
  2. [Abstract] Abstract and results on nanosheet FET: no numerical results, error bars, comparisons to full quantum transport solvers (e.g., NEGF), or experimental data are supplied for the claimed electrical characteristics, velocity overshoot, or quantum confinement effects at 6 nm and 4.5 nm gate lengths. Without such benchmarks the utility and accuracy claims for the mobility model and quantum corrections cannot be assessed.
minor comments (1)
  1. [Abstract] Abstract: 'Schrodinger' should be spelled 'Schrödinger'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that localization landscape theory 'directly solves the ground state of the Schrödinger equation without further approximation' is overstated. The method solves the auxiliary equation Δu + V u = 1 for the landscape function u and approximates the ground state via 1/u; the approximation error is potential-dependent and is neither quantified nor bounded for the 6 nm and 4.5 nm nanosheet FETs. This directly undercuts the assertion that quantum corrections are obtained without further approximation.

    Authors: We agree that the original abstract wording is imprecise and overstated. Localization landscape theory solves the auxiliary equation for the landscape function u and uses 1/u to approximate the ground-state energy and wavefunction; the error is potential-dependent and was not quantified or bounded in the manuscript. We will revise the abstract to state that the method provides an efficient approximation to the ground state of the Schrödinger equation suitable for compact modeling, and we will add a brief clarification of its approximate character in the methods section. revision: yes

  2. Referee: [Abstract] Abstract and results on nanosheet FET: no numerical results, error bars, comparisons to full quantum transport solvers (e.g., NEGF), or experimental data are supplied for the claimed electrical characteristics, velocity overshoot, or quantum confinement effects at 6 nm and 4.5 nm gate lengths. Without such benchmarks the utility and accuracy claims for the mobility model and quantum corrections cannot be assessed.

    Authors: The manuscript presents numerical results for the 6 nm GAA FET and the proposed 4.5 nm design, showing the influence of the included quantum corrections and ballistic mobility model on currents and capacitances. We acknowledge, however, that these results do not include error bars or direct comparisons against NEGF solvers or experimental data. The scope of the work is the development of a lightweight compact simulator rather than exhaustive validation. In revision we will add discussion referencing prior literature on the accuracy of localization landscape theory and the ballistic model, together with an explicit statement of the validation limitations. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper presents SEMIDV as a simulator that incorporates localization landscape theory (an external method) for quantum corrections and develops a separate compact mobility model for ballistic effects. The nanosheet FET analysis is an application of these components rather than a closed predictive loop. No equations or sections exhibit self-definitional reductions, fitted inputs renamed as predictions, load-bearing self-citations, or ansatzes smuggled via citation. The central claims rest on stated external theory and model development with independent content, not on re-deriving inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract; full text would likely reveal additional fitted parameters in the mobility model and domain assumptions about the validity of the localization landscape approach for the specific device geometries.

free parameters (1)
  • Ballistic mobility parameters
    The compact mobility model is developed to capture ballistic length dependence, implying parameters chosen or fitted to match short-channel behavior though exact values are not stated.
axioms (1)
  • domain assumption Localization landscape theory directly solves the Schrödinger ground state without further approximation for quantum corrections to drift-diffusion
    Invoked as the basis for efficient quantum effect modeling in the simulator.

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Works this paper leans on

32 extracted references · 32 canonical work pages

  1. [1]

    Introduction of synopsys sentaurus TCAD simulation,

    Y.-C. Wu, Y.-R. Jhan, Y.-C. Wu, and Y.-R. Jhan, "Introduction of synopsys sentaurus TCAD simulation," 3D TCAD Simulation for CMOS Nanoeletronic Devices, pp. 1-17, 2018

    work page 2018

  2. [2]

    Victory TCAD Solution

    Silvaco, "Victory TCAD Solution." [Online]. Available: https://silvaco.com/tcad/

    work page

  3. [3]

    PISCES -2ET and its Application Subsystems,

    Z. Yu et al. , "PISCES -2ET and its Application Subsystems," Integrated Circuits laboratory, 1994

    work page 1994

  4. [4]

    DEVSIM: A TCAD semiconductor device simulator,

    J. E. Sanchez, "DEVSIM: A TCAD semiconductor device simulator," Journal of Open Source Software, vol. 7, no. 70, p. 3898, 2022

    work page 2022

  5. [5]

    Genius semiconductor device simulator,

    Cogenda, "Genius semiconductor device simulator," 2016. [Online]. Available: https://github.com/cogenda/Genius-TCAD- Open

    work page 2016

  6. [6]

    Large -signal analysis of a silicon Read diode oscillator,

    D. L. Scharfetter and H. K. Gummel, "Large -signal analysis of a silicon Read diode oscillator," IEEE Transactions on Electron Devices, vol. 16, no. 1, pp. 64 -77, 1969, doi: 10.1109/T - ED.1969.16566

    work page doi:10.1109/t 1969

  7. [7]

    Iterative scheme for 1 -and 2 -dimensional dc - transistor simulation,

    J. W. Slotboom, "Iterative scheme for 1 -and 2 -dimensional dc - transistor simulation," Electronics Letters, vol. 5, no. 26, pp. 677 - 678, 1969

    work page 1969

  8. [8]

    A physics -based analytical/numerical solution to the Boltzmann transport equation for use in device simulation,

    N. Goldsman, L. Henrickson, and J. Frey, "A physics -based analytical/numerical solution to the Boltzmann transport equation for use in device simulation," Solid-State Electronics, vol. 34, no. 4, pp. 389 -396, 1991/04/01/ 1991, doi: https://doi.org/10.1016/0038-1101(91)90169-Y

    work page doi:10.1016/0038-1101(91)90169-y 1991

  9. [9]

    Monte Carlo methods for solving the Boltzmann transport equation,

    J.-P. M. Péraud, C. D. Landon, and N. G. Hadjiconstantinou, "Monte Carlo methods for solving the Boltzmann transport equation," Annual Review of Heat Transfer, vol. 17, 2014

    work page 2014

  10. [10]

    Nanoscale device modeling: the Green’s function method,

    S. Datta, "Nanoscale device modeling: the Green’s function method," Superlattices and Microstructures, vol. 28, no. 4, pp. 253-278, 2000/10/01/ 2000, doi: https://doi.org/10.1006/spmi.2000.0920

    work page doi:10.1006/spmi.2000.0920 2000

  11. [11]

    A Matlab 1D -Poisson-NEGF simulator for 2D FET,

    C.-T. Tung, "A Matlab 1D -Poisson-NEGF simulator for 2D FET," Mar 2024. [Online]. Available: https://nanohub.org/resources/38684

    work page 2024

  12. [12]

    A simple model for quantisation effects in heavily -doped silicon MOSFETs at inversion conditions,

    M. J. Van Dort, P. H. Woerlee, and A. J. Walker, "A simple model for quantisation effects in heavily -doped silicon MOSFETs at inversion conditions," Solid-State Electronics, vol. 37, no. 3, pp. 411-414, 1994

    work page 1994

  13. [13]

    Macroscopic physics of the silicon inversion layer,

    M. G. Ancona and H. F. Tiersten, "Macroscopic physics of the silicon inversion layer," Physical Review B, vol. 35, no. 15, p. 7959, 1987

    work page 1987

  14. [14]

    Quantum correction to the equation of state of an electron gas in a semiconductor,

    M. G. Ancona and G. J. Iafrate, "Quantum correction to the equation of state of an electron gas in a semiconductor," Physical Review B, vol. 39, no. 13, p. 9536, 1989

    work page 1989

  15. [15]

    Density -gradient theory: a macroscopic approach to quantum confinement and tunneling in semiconductor devices,

    M. G. Ancona, "Density -gradient theory: a macroscopic approach to quantum confinement and tunneling in semiconductor devices," Journal of Computational Electronics, vol. 10, no. 1, pp. 65 -97, 2011/06/01 2011, doi: 10.1007/s10825-011-0356-9

    work page doi:10.1007/s10825-011-0356-9 2011

  16. [16]

    Kinetic Velocity Model to Account for Ballistic Effects in the Drift-Diffusion Transport Approach,

    O. Penzin, L. Smith, A. Erlebach, M. Choi, and K. H. Lee, "Kinetic Velocity Model to Account for Ballistic Effects in the Drift-Diffusion Transport Approach," IEEE Transactions on Electron Devices, vol. 64, no. 11, pp. 4599 -4606, 2017, doi: 10.1109/TED.2017.2751968

    work page doi:10.1109/ted.2017.2751968 2017

  17. [17]

    Distributive Quasi -Ballistic Drift Diffusion Model Including Effects of Stress and High Driving Field,

    R. Kotlyar, R. Rios, C. E. Weber, T. D. Linton, M. Armstrong, and K. Kuhn, "Distributive Quasi -Ballistic Drift Diffusion Model Including Effects of Stress and High Driving Field," IEEE Transactions on Electron Devices, vol. 62, no. 3, pp. 743 -750, 2015, doi: 10.1109/TED.2015.2392717

    work page doi:10.1109/ted.2015.2392717 2015

  18. [18]

    Extending drift-diffusion paradigm into the era of FinFETs and nanowires,

    C. Munkang, V. Moroz, L. Smith, and H. Joanne, "Extending drift-diffusion paradigm into the era of FinFETs and nanowires," in 2015 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD) , 9-11 Sept. 2015 2015, pp. 242 - 245, doi: 10.1109/SISPAD.2015.7292304

    work page doi:10.1109/sispad.2015.7292304 2015

  19. [19]

    Localization landscape theory of disorder in semiconductors. I. Theory and modeling,

    M. Filoche, M. Piccardo, Y.-R. Wu, C.-K. Li, C. Weisbuch, and S. Mayboroda, "Localization landscape theory of disorder in semiconductors. I. Theory and modeling," Physical Review B, vol. 95, no. 14, p. 144204, 2017

    work page 2017

  20. [20]

    A self -consistent iterative scheme for one - dimensional steady state transistor calculations,

    H. K. Gummel, "A self -consistent iterative scheme for one - dimensional steady state transistor calculations," IEEE Transactions on Electron Devices, vol. 11, no. 10, pp. 455 -465, 1964, doi: 10.1109/T-ED.1964.15364

    work page doi:10.1109/t-ed.1964.15364 1964

  21. [21]

    A unified mobility model for device simulation—I. Model equations and concentration dependence,

    D. B. M. Klaassen, "A unified mobility model for device simulation—I. Model equations and concentration dependence," Solid-State Electronics, vol. 35, no. 7, pp. 953 -959, 1992/07/01/ 1992, doi: https://doi.org/10.1016/0038-1101(92)90325-7

    work page doi:10.1016/0038-1101(92)90325-7 1992

  22. [22]

    A physically based mobility model for numerical simulation of nonplanar devices,

    C. Lombardi, S. Manzini, A. Saporito, and M. Vanzi, "A physically based mobility model for numerical simulation of nonplanar devices," IEEE Transactions on Computer -Aided Design of Integrated Circuits and Systems, vol. 7, no. 11, pp. 1164-1171, 1988, doi: 10.1109/43.9186

    work page doi:10.1109/43.9186 1988

  23. [23]

    A Unified Analytical Model for Bulk and Surface Mobility in Si n - and p-Channel MOSFET's,

    S. Reggiani, M. Valdinoci, L. Colalongo, and G. Baccarani, "A Unified Analytical Model for Bulk and Surface Mobility in Si n - and p-Channel MOSFET's," in 29th European Solid -State Device Research Conference, 13-15 Sept. 1999 1999, vol. 1, pp. 240-243

    work page 1999

  24. [24]

    Y. S. Chauhan et al. , FinFET/ GAA Modeling for IC Simulation and Design (Second Edition). Academic Press, 2024

    work page 2024

  25. [25]

    Compact Models and the Physics of Nanoscale FETs,

    M. S. Lundstrom and D. A. Antoniadis, "Compact Models and the Physics of Nanoscale FETs," IEEE Transactions on Electron Devices, vol. 61, no. 2, pp. 225 -233, 2014, doi: 10.1109/TED.2013.2283253

    work page doi:10.1109/ted.2013.2283253 2014

  26. [26]

    Carrier mobilities in silicon empirically related to doping and field,

    D. M. Caughey and R. E. Thomas, "Carrier mobilities in silicon empirically related to doping and field," Proceedings of the IEEE, vol. 55, no. 12, pp. 2192 -2193, 1967, doi: 10.1109/PROC.1967.6123

    work page doi:10.1109/proc.1967.6123 1967

  27. [27]

    Simulation of nanoscale MOSFETs using modified drift-diffusion and hydrodynamic models and comparison with Monte Carlo results,

    R. Granzner et al. , "Simulation of nanoscale MOSFETs using modified drift-diffusion and hydrodynamic models and comparison with Monte Carlo results," Microelectronic Engineering, vol. 83, no. 2, pp. 241 -246, 2006/02/01/ 2006, doi: https://doi.org/10.1016/j.mee.2005.08.003

    work page doi:10.1016/j.mee.2005.08.003 2006

  28. [28]

    Monte Carlo simulation of a 30 nm dual-gate MOSFET: how short can Si go?,

    Frank, Laux, and Fischetti, "Monte Carlo simulation of a 30 nm dual-gate MOSFET: how short can Si go?," in 1992 International Technical Digest on Electron Devices Meeting , 13 -16 Dec. 1992 1992, pp. 553-556, doi: 10.1109/IEDM.1992.307422

    work page doi:10.1109/iedm.1992.307422 1992

  29. [29]

    Silicon RibbonFET CMOS at 6nm Gate Length,

    A. Agrawal et al. , "Silicon RibbonFET CMOS at 6nm Gate Length," in 2024 IEEE International Electron Devices Meeting (IEDM), 7 -11 Dec. 2024 2024, pp. 1 -4, doi: 10.1109/IEDM50854.2024.10873367

    work page doi:10.1109/iedm50854.2024.10873367 2024

  30. [30]

    Screening in Ultrashort (5 nm) Channel MoS2 Transistors: A Full -Band Quantum Transport Study,

    V. Mishra et al., "Screening in Ultrashort (5 nm) Channel MoS2 Transistors: A Full -Band Quantum Transport Study," IEEE Transactions on Electron Devices, vol. 62, no. 8, pp. 2457 -2463, 2015, doi: 10.1109/TED.2015.2444353

    work page doi:10.1109/ted.2015.2444353 2015

  31. [31]

    Demonstration of High Transconductance Gate - All-Around Transistors Using Negative Capacitance ‘Super High - K’ Gate Stack,

    J. H. Park et al., "Demonstration of High Transconductance Gate - All-Around Transistors Using Negative Capacitance ‘Super High - K’ Gate Stack," IEEE Electron Device Letters, vol. 46, no. 4, pp. 533-536, 2025, doi: 10.1109/LED.2025.3541547

    work page doi:10.1109/led.2025.3541547 2025

  32. [32]

    International Roadmap for Devices and Systems (IRDS ™) 2023 Update

    "International Roadmap for Devices and Systems (IRDS ™) 2023 Update." [Online]. Available: https://irds.ieee.org/editions/2023

    work page 2023