Optimized quantum drift diffusion model for a resonant tunneling diode
-
Orazio Muscato
,
Vittorio Romano
und
Giorgia Vitanza
Abstract
The main aim of this work is to optimize a Quantum Drift Diffusion model (QDD) (V. Romano, M. Torrisi, and R. Tracinà, “Approximate solutions to the quantum drift-diffusion model of semiconductors,” J. Math. Phys., vol. 48, p. 023501, 2007; A. El Ayyadi and A. Jüngel, “Semiconductor simulations using a coupled quantum drift-diffusion schrödinger-Poisson model,” SIAM J. Appl. Math., vol. 66, no. 2, pp. 554–572, 2005; L. Barletti and C. Cintolesi, “Derivation of isothermal quantum fluid equations with Fermi-Dirac and bose-einstein statistics,” J. Stat. Phys., vol. 148, pp. 353–386, 2012) by comparing it with the Boltzmann-Wigner Transport Equation (BWTE) (O. Muscato, “Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode,” J. Comput. Electron., vol. 20, pp. 2062–2069, 2021) solved using a signed Monte Carlo method (M. Nedjalkov, H. Kosina, S. Selberherr, C. Ringhofer, and D. K. Ferry, “Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices,” Phys. Rev. B, vol. 70, pp. 115–319, 2004). A situation of high non equilibrium regime is investigated: electron transport in a Resonant Tunneling Diode (RTD) made of GaAs with two potential barriers in GaAlAs. The range of the suitable voltage bias applied to the RTD is analyzed. We find an acceptable agreement between QDD model and BWTE when the applied bias is low or moderate with a threshold of about 0.225 V over a length of 150 nm; it is found out that the use of a field dependent mobility is crucial for getting a good description of the negative differential conductivity in such a range. At higher bias voltages, we expect that QDD model loses accuracy.
-
Research ethics: Not applicable.
-
Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
-
Competing interests: The authors state no conflict of interest.
-
Research funding: The authors acknowledge the support from INdAM (GNFM) and from Università degli Studi di Catania, Piano della Ricerca 2020/2022 Linea di intervento 2 “QICT.” G. Nastasi acknowledges the financial support from the project PON R&I 2014-2020 “Asse IV - Istruzione e ricerca per il recupero- REACT-EU, Azione IV.4 - Dottorati e contratti di ricerca su tematiche dell’innovazione,” project: “Modellizzazione, simulazione e design di transistori innovativi.” G.N. acknowledges the support from GNFM (INDAM) Progetto GNFM 2023: “Uncertainty quantification for kinetic models describing physical and socio-economical phenomen” CUP E53C2200193000.
-
Data availability: Not applicable.
References
[1] J. P. Sun, G. I. Haddad, P. Mazumder, and J. N. Schulman, “Resonant tunneling diodes: models and properties in,” Proc. IEEE, vol. 86, no. 4, pp. 641–660, 1998. https://doi.org/10.1109/5.663541.Suche in Google Scholar
[2] O. Muscato, T. Castiglione, and C. Cavallaro, Ballistic Charge Transport in a Triple-Gate Silicon Nanowire Transistor in: COUPLED PROBLEMS 2015 – Proceedings of the 6th International Conference on Coupled Problems in Science and Engineering, 2015, pp. 666–676.Suche in Google Scholar
[3] L. Yang, Y. Hao, Q. Yao, and J. Zhang, “Improved negative differential mobility model of GaN and AlGaN for a terahertz Gunn diode,” IEEE Trans. Electron Devices, vol. 58, no. 4, pp. 1076–1083, 2011. https://doi.org/10.1109/ted.2011.2105269.Suche in Google Scholar
[4] V. Romano, M. Torrisi, and R. Tracinà, “Approximate solutions to the quantum drift-diffusion model of semiconductors,” J. Math. Phys., vol. 48, no. 2, p. 023501, 2007. https://doi.org/10.1063/1.2435985.Suche in Google Scholar
[5] A. El Ayyadi and A. Jüngel, “Semiconductor simulations using a coupled quantum drift-diffusion schrödinger-Poisson model,” SIAM J. Appl. Math., vol. 66, no. 2, pp. 554–572, 2005. https://doi.org/10.1137/040610805.Suche in Google Scholar
[6] P. Degond, S. Gallego, and F. Méhats, “An entropic Quantum Drift-Diffusion model for electron transport in resonant tunneling diodes,” J. Comput. Phys., vol. 221, no. 1, pp. 226–249, 2007. https://doi.org/10.1016/j.jcp.2006.06.027.Suche in Google Scholar
[7] S. Micheletti, R. Sacco, and P. Simioni, “Numerical simulation of resonant tunneling diodes with a quantum drift diffusion model,” in Scientific Computing in Electrical Engineering. Mathematics in Industry, vol. 4, Berlin, Heidelberg, Springer, 2004.10.1007/978-3-642-55872-6_34Suche in Google Scholar
[8] L. Barletti, G. Nastasi, C. Negulescu, and V. Romano, “Mathematical modelling of charge transport in graphene heterojunctions,” Kinet. Relat. Models, vol. 14, no. 3, pp. 407–427, 2021. https://doi.org/10.3934/krm.2021010.Suche in Google Scholar
[9] M. Nedjalkov, H. Kosina, S. Selberherr, C. Ringhofer, and D. K. Ferry, “Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices,” Phys. Rev. B, vol. 70, no. 11, p. 115319, 2004. https://doi.org/10.1103/physrevb.70.115319.Suche in Google Scholar
[10] O. Muscato, “Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode,” J. Comput. Electron., vol. 20, no. 6, pp. 2062–2069, 2021. https://doi.org/10.1007/s10825-021-01734-3.Suche in Google Scholar
[11] O. Muscato, “A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation,” Commun. Appl. Ind. Math., vol. 8, no. 1, pp. 237–250, 2017. https://doi.org/10.1515/caim-2017-0012.Suche in Google Scholar
[12] L. Shifren, C. Ringhofer, and D. K. Ferry, “A Wigner function-based quantum ensemble Monte Carlo study of a resonant tunneling diode,” IEEE Trans. Electron Devices, vol. 50, no. 3, pp. 769–773, 2003. https://doi.org/10.1109/ted.2003.809434.Suche in Google Scholar
[13] D. Querlioz, P. Dollfus, V. N. Do, A. Bournel, and V. L. Nguyen, “An improved Wigner Monte-Carlo technique for the self-consistent simulation of RTDs,” J. Comput. Electron., vol. 5, no. 4, pp. 443–446, 2006. https://doi.org/10.1007/s10825-006-0044-3.Suche in Google Scholar
[14] L. Barletti and C. Cintolesi, “Derivation of isothermal quantum fluid equations with Fermi-Dirac and bose-einstein statistics,” J. Stat. Phys., vol. 148, no. 2, pp. 353–386, 2012. https://doi.org/10.1007/s10955-012-0535-5.Suche in Google Scholar
[15] L. Luca and V. Romano, “Quantum corrected hydrodynamic models for charge transport in graphene,” Ann. Phys., vol. 406, pp. 30–53, 2019. https://doi.org/10.1016/j.aop.2019.03.018.Suche in Google Scholar
[16] D. Querlioz and P. Dollfus, The Wigner Monte Carlo Method for Nanoelectronic Devices, New York, Wiley, 2010.Suche in Google Scholar
[17] M. Lundstrom, Fundamentals of Carrier Transport, Cambridge, Cambridge Univ. press, 2000.10.1017/CBO9780511618611Suche in Google Scholar
[18] A. Jüngel, Quasi-hydrodynamic Semiconductor Equations, Basel, Bikhäuser, 2001.10.1007/978-3-0348-8334-4Suche in Google Scholar
[19] R. Pinnau, “A Scharfetter-Gummel type discretization of the quantum drift diffusion model,” in PAMM: Proceedings in Applied Mathematics and Mechanics, vol. 2, Berlin, WILEY-VCH Verlag, 2003, pp. 37–40.10.1002/pamm.200310010Suche in Google Scholar
[20] G. Nastasi and V. Romano, “A full coupled drift-diffusion-Poisson simulation of a GFET,” Commun. Nonlinear Sci. Numer., vol. 87, pp. 105–300, 2020. https://doi.org/10.1016/j.cnsns.2020.105300.Suche in Google Scholar
[21] MATLAB, Version 9.10.0 (R2021a), Natick, Massachusetts, The MathWorks Inc, 2021.Suche in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Editorial
- Thermodynamic costs of temperature stabilization in logically irreversible computation
- Hydrodynamic, electronic and optic analogies with heat transport in extended thermodynamics
- Variations on the models of Carnot irreversible thermomechanical engine
- Revisit nonequilibrium thermodynamics based on thermomass theory and its applications in nanosystems
- On the dynamic thermal conductivity and diffusivity observed in heat pulse experiments
- On the influence of the fourth order orientation tensor on the dynamics of the second order one
- Lack-of-fit reduction in non-equilibrium thermodynamics applied to the Kac–Zwanzig model
- Optimized quantum drift diffusion model for a resonant tunneling diode
- The wall effect in a plane counterflow channel
- Buoyancy driven convection with a Cattaneo flux model
- Thermodynamics of micro- and nano-scale flow and heat transfer: a mini-review
- Poroacoustic front propagation under the linearized Eringen–Cattaneo–Christov–Straughan model
Artikel in diesem Heft
- Frontmatter
- Editorial
- Thermodynamic costs of temperature stabilization in logically irreversible computation
- Hydrodynamic, electronic and optic analogies with heat transport in extended thermodynamics
- Variations on the models of Carnot irreversible thermomechanical engine
- Revisit nonequilibrium thermodynamics based on thermomass theory and its applications in nanosystems
- On the dynamic thermal conductivity and diffusivity observed in heat pulse experiments
- On the influence of the fourth order orientation tensor on the dynamics of the second order one
- Lack-of-fit reduction in non-equilibrium thermodynamics applied to the Kac–Zwanzig model
- Optimized quantum drift diffusion model for a resonant tunneling diode
- The wall effect in a plane counterflow channel
- Buoyancy driven convection with a Cattaneo flux model
- Thermodynamics of micro- and nano-scale flow and heat transfer: a mini-review
- Poroacoustic front propagation under the linearized Eringen–Cattaneo–Christov–Straughan model
