Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Kongresse
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Veranstaltungskalender Awards MyNewsletter Firmensuche
Kunden Login
Über Einzelzugang informieren
Über Unternehmenszugang informieren
Referenzkunden
Elektrische Antriebe und Energiesysteme 2025 | 26 + 27 März 2025

19. Internationaler MTZ-Fachkongress Zukunftsantriebe

Seien Sie bei der Konferenz dabei! Dort treffen Experten aus der Automobilindustrie, Energieerzeugung und Stromnetzbetrieb auf Vertreter aus Politik und Wissenschaft. Diskutiert werden wichtige Themen der Branche.
Erweiterte Suche
Anmelden
nach oben
Journal of Computational Electronics
Erschienen in:

19.06.2023

Recursive Green’s functions optimized for atomistic modelling of large superlattice-based devices

verfasst von: V. Hung Nguyen, J. -C. Charlier

Erschienen in: Journal of Computational Electronics | Ausgabe 5/2023

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The Green’s function method is recognized to be a very powerful tool for modelling quantum transport in nanoscale electronic devices. As atomistic calculations are generally expensive, numerical methods and related algorithms have been developed accordingly to optimize their computation cost. In particular, recursive techniques have been efficiently applied within the Green’s function calculation approach. Recently, with the discovery of Moiré materials, several attractive superlattices have been explored using these recursive Green’s function techniques. However, numerical difficulty issues were reported as most of these superlattices have relatively large supercells, and consequently a huge number of atoms to be considered. In this article, improvements to solve these issues are proposed in order to keep optimizing the recursive Green’s function calculations. These improvements make the electronic structure calculations feasible and efficient in modelling large superlattice-based devices. As an illustrative example, twisted bilayer graphene superlattices are computed and presented to demonstrate the efficiency of the method.
Vorheriger Artikel Full charge incorporation in ab initio simulations of two-dimensional semiconductor-based devices
Nächster Artikel DFTBephy: A DFTB-based approach for electron–phonon coupling calculations

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Granzner, R., Polyakov, V.M., Schwierz, F., Kittler, M., Luyken, R.J., Rösner, W., Städele, M.: Simulation of nanoscale MOSFETs using modified drift-diffusion and hydrodynamic models and comparison with monte carlo results. Microelectron. Eng. 83(2), 241–246 (2006)
2.
Fan, Z., Uppstu, A., Siro, T., Harju, A.: Efficient linear-scaling quantum transport calculations on graphics processing units and applications on electron transport in graphene. Comput. Phys. Commun. 185(1), 28–39 (2014)MathSciNetMATH
3.
Fan, Z., Garcia, J.H., Cummings, A.W., Barrios-Vargas, J.E., Panhans, M., Harju, A., Ortmann, F., Roche, S.: Linear scaling quantum transport methodologies. Phys. Rep. 903, 1–69 (2021)MathSciNetMATH
4.
Jacoboni, C., Reggiani, L.: The monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials. Rev. Mod. Phys. 55, 645–705 (1983)
5.
Hong, S.-M., Jungemann, C.: A fully coupled scheme for a Boltzmann-poisson equation solver based on a spherical harmonics expansion. J. Comput. Electron. 8, 225–241 (2009)
6.
Datta, S.: Electronic Transport in Mesoscopic Systems. Cambridge Studies in Semiconductor Physics and Microelectronic Engineering. Cambridge University Press, Cambridge (1995)
7.
Zhang, W., Fisher, T.S., Mingo, N.: The atomistic Green’s function method: an efficient simulation approach for nanoscale phonon transport. Numer. Heat Transfer Part B Fund. 51(4), 333–349 (2007)
8.
Mahdi, P.: The Non-Equilibrium Green’s Function Method for Nanoscale Device Simulation. Springer-Verlag, New York (2014)
9.
Lewenkopf, C.H., Mucciolo, E.R.: The recursive Green’s function method for graphene. J. Comput. Electron. 12(2), 203–231 (2013)
10.
Niquet, Y.-M., Nguyen, V.-H., Triozon, F., Duchemin, I., Nier, O., Rideau, D.: Quantum calculations of the carrier mobility: methodology, Matthiessen’s rule, and comparison with semi-classical approaches. J. Appl. Phys. 115(5), 054512 (2014)
11.
Lake, R., Klimeck, G., Bowen, R.C., Jovanovic, D.: Single and multiband modeling of quantum electron transport through layered semiconductor devices. J. Appl. Phys. 81(12), 7845–7869 (1997)
12.
Svizhenko, A., Anantram, M.P., Govindan, T.R., Biegel, B., Venugopal, R.: Two-dimensional quantum mechanical modeling of nanotransistors. J. Appl. Phys. 91(4), 2343–2354 (2002)
13.
Li, S., Ahmed, S., Darve, E.: Fast inverse using nested dissection for NEGF. J. Comput. Electron. 6, 187–190 (2007)
14.
Kazymyrenko, K., Waintal, X.: Knitting algorithm for calculating green functions in quantum systems. Phys. Rev. B 77, 115119 (2008)
15.
Anantram, M.P., Lundstrom, M.S., Nikonov, D.E.: Modeling of nanoscale devices. Proc. IEEE 96(9), 1511–1550 (2008)
16.
Cauley, S., Luisier, M., Balakrishnan, V., Klimeck, G., Koh, C.-K.: Distributed non-equilibrium green’s function algorithms for the simulation of nanoelectronic devices with scattering. J. Appl. Phys. 110(4), 043713 (2011)
17.
Do, V.-N.: Non-equilibrium green function method: theory and application in simulation of nanometer electronic devices. Adv. Nat. Sci: Nanosci. Nanotechnol. 5(3), 033001 (2014)
18.
Thorgilsson, G., Viktorsson, G., Erlingsson, S.I.: Recursive Green’s function method for multi-terminal nanostructures. J. Comput. Phys. 261, 256–266 (2014)MathSciNetMATH
19.
Zhang, X.W., Liu, Y.L.: Electronic transport and spatial current patterns of 2d electronic system: a recursive green’s function method study. AIP Adv. 9(11), 115209 (2019)
20.
Luisier, M., Schenk, A., Fichtner, W., Klimeck, G.: Atomistic simulation of nanowires in the \(s{p}^{3}{d}^{5}{s}^{*}\) tight-binding formalism: from boundary conditions to strain calculations. Phys. Rev. B 74, 205323 (2006)
21.
Bescond, M., Cavassilas, N., Lannoo, M.: Effective-mass approach for n-type semiconductor nanowire MOSFETs arbitrarily oriented. Nanotechnology 18(25), 255201 (2007)
22.
Luisier, M., Klimeck, G.: Atomistic full-band simulations of silicon nanowire transistors: effects of electron-phonon scattering. Phys. Rev. B 80, 155430 (2009)
23.
Luisier, M., Klimeck, G.: Simulation of nanowire tunneling transistors: from the Wentzel–Kramers–Brillouin approximation to full-band phonon-assisted tunneling. J. Appl. Phys. 107(8), 084507 (2010)
24.
Fiori, G., Iannaccone, G.: Multiscale modeling for graphene-based nanoscale transistors. Proc. IEEE 101(7), 1653–1669 (2013)
25.
Alarcon, A., Nguyen, V.-H., Berrada, S., Querlioz, D., Saint-Martin, J., Bournel, A., Dollfus, P.: Pseudosaturation and negative differential conductance in graphene field-effect transistors. IEEE Trans. Electron Devices 60, 985–991 (2013)
26.
Nguyen, V.H., Triozon, F., Bonnet, F.D.R., Niquet, Y.M.: Performances of strained nanowire devices: ballistic versus scattering-limited currents. IEEE Trans. Electron Devices 60, 1506–1513 (2013)
27.
Cavassilas, N., Michelini, F., Bescond, M.: Theoretical comparison of multiple quantum wells and thick-layer designs in InGaN/GaN solar cells. Appl. Phys. Lett. 105(6), 063903 (2014)
28.
Nguyen, V.-H., Niquet, Y.-M., Triozon, F., Duchemin, I., Nier, O., Rideau, D.: Quantum modeling of the carrier mobility in FDSOI devices. IEEE Trans. Electron Devices 61(9), 3096–3102 (2014)
29.
Cavassilas, N., Claveau, Y., Bescond, M., Michelini, F.: Quantum electronic transport in polarization-engineered GaN/InGaN/GaN tunnel junctions. Appl. Phys. Lett. 110(16), 161106 (2017)
30.
Zhang, H., Guan, N., Piazza, V., Kapoor, A., Bougerol, C., Julien, F.H., Babichev, A.V., Cavassilas, N., Bescond, M., Michelini, F., Foldyna, M., Gautier, E., Durand, C., Eymery, J., Tchernycheva, M.: Comprehensive analyses of core-shell InGaN/GaN single nanowire photodiodes. J. Phys. D Appl. Phys. 50(48), 484001 (2017)
31.
Choukroun, J., Pala, M., Fang, S., Kaxiras, E., Dollfus, P.: High performance tunnel field effect transistors based on in-plane transition metal dichalcogenide heterojunctions. Nanotechnology 30, 025201 (2018)
32.
Bescond, M., Autran, J.L., Munteanu, D., Lannoo, M.: Atomic-scale modeling of double-gate MOSFETs using a tight-binding Green’s function formalism. Solid-State Electron 48(4), 567–574 (2004)
33.
Martinez, A., Bescond, M., Barker, J.R., Svizhenko, A., Anantram, M.P., Millar, C., Asenov, A.: A self-consistent full 3-d real-space NEGF simulator for studying nonperturbative effects in nano-MOSFETs. IEEE Trans. Electron Devices 54, 2213–2222 (2007)
34.
Groth, C.W., Wimmer, M., Akhmerov, A.R., Waintal, X.: Kwant: a software package for quantum transport. New J. Phys. 16(6), 063065 (2014)
35.
Hung, N.V., Charlier, J.-C.: Klein tunneling and electron optics in Dirac-Weyl fermion systems with tilted energy dispersion. Phys. Rev. B 97, 235113 (2018)
36.
Brun, B., Moreau, N., Somanchi, S., Nguyen, V.-H., Watanabe, K., Taniguchi, T., Charlier, J.-C., Stampfer, C., Hackens, B.: Imaging Dirac fermions flow through a circular Veselago lens. Phys. Rev. B 100, 041401 (2019)
37.
Hung, N.V., Charlier, J.-C.: Aharonov-Bohm interferences in polycrystalline graphene. Nanoscale Adv. 2, 256–263 (2020)
38.
Ozaki, T., Nishio, K., Kino, H.: Efficient implementation of the nonequilibrium Green’s function method for electronic transport calculations. Phys. Rev. B 81, 035116 (2010)
39.
Papior, N., Lorente, N., Frederiksen, T., García, A., Brandbyge, M.: Improvements on non-equilibrium and transport Green’s function techniques: the next-generation transiesta. Comp. Phys. Comm. 212, 8–24 (2017)MATH
40.
Zhang, W., Fisher, T.S., Mingo, N.: The atomistic green’s function method: an efficient simulation approach for nanoscale phonon transport. Numer. Heat Transfer Part B Fund. 51(4), 333–349 (2007)
41.
Lan, J., Wang, J.-S., Gan, C.K., Chin, S.K.: Edge effects on quantum thermal transport in graphene nanoribbons: tight-binding calculations. Phys. Rev. B 79, 115401 (2009)
42.
Mazzamuto, F., Hung, N.V., Apertet, Y., Caër, C., Chassat, C., Saint-Martin, J., Dollfus, P.: Enhanced thermoelectric properties in graphene nanoribbons by resonant tunneling of electrons. Phys. Rev. B 83, 235426 (2011)
43.
Mazzamuto, F., Saint-Martin, J., Nguyen, V.H., Chassat, C., Dollfus, P.: Thermoelectric performance of disordered and nanostructured graphene ribbons using Green’s function method. J. Comput. Electron. 11, 67–77 (2012)
44.
Hung, N.V., Chung, N.M., Nguyen, H.-V., Saint-Martin, J., Dollfus, P.: Enhanced thermoelectric figure of merit in vertical graphene junctions. Appl. Phys. Lett. 105(13), 133105 (2014)
45.
Wang, J.-S., Agarwalla, B.K., Li, H., Thingna, J.: Nonequilibrium Green’s function method for quantum thermal transport. Front. Phys. 9, 673–679 (2014)
46.
Drouvelis, P.S., Schmelcher, P., Bastian, P.: Parallel implementation of the recursive Green’s function method. J. Comput. Phys. 215(2), 741–756 (2006)MathSciNetMATH
47.
Avouris, P., Heinz, T.F., Low, T.: 2D Materials: Properties and Devices. Cambridge University Press, Cambridge (2017)
48.
Ferrari, A.C., et al.: Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems. Nanoscale 7, 4598–4810 (2015)
49.
Geim, A.K., Grigorieva, I.V.: Van der Waals heterostructures. Nature 499, 419–425 (2013)
50.
Novoselov, K.S., Mishchenko, A., Carvalho, A., Castro Neto, A.H.: 2d materials and van der Waals heterostructures. Science 353(6298), aac9439 (2016)
51.
He, F., Zhou, Y., Ye, Z., Cho, S.-H., Jeong, J., Meng, X., Wang, Y.: Moiré patterns in 2d materials: a review. ACS Nano 15, 5944–5958 (2021)
52.
Wang, J., Mu, X., Wang, L., Sun, M.: Properties and applications of new superlattice: twisted bilayer graphene. Mater. Today Phys. 9, 100099 (2019)
53.
Andrei, E.Y., MacDonald, A.H.: Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020)
54.
Yoo, H., Engelke, R., Carr, S., Fang, S., Zhang, K., Cazeaux, P., Sung, S.H., Hovden, R., Tsen, A.W., Taniguchi, T., Watanabe, K., Yi, G.-C., Kim, M., Luskin, M., Tadmor, E.B., Kaxiras, E., Kim, P.: Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene. Nat. Mater. 18, 448–453 (2019)
55.
Sunku, S.S., Ni, G.X., Jiang, B.Y., Yoo, H., Sternbach, A., McLeod, A.S., Stauber, T., Xiong, L., Taniguchi, T., Watanabe, K., Kim, P., Fogler, M.M., Basov, D.N.: Photonic crystals for nano-light in moiré graphene superlattices. Science 362, 1153–1156 (2018)MathSciNet
56.
Zhao, P., Zhang, Q., Jena, D., Koswatta, S.O.: Influence of metal-graphene contact on the operation and scalability of graphene field-effect transistors. IEEE Trans. Electron Devices 58(9), 3170–3178 (2011)
57.
Barraza-Lopez, S., Kindermann, M., Chou, M.Y.: Charge transport through graphene junctions with wetting metal leads. Nano Lett. 12(7), 3424–3430 (2012)
58.
Do Nam, V., Le Anh, H.: Transport characteristics of graphene-metal interfaces. Appl. Phys. Lett. 101(16), 161605 (2012)
59.
Houssa, M., Iordanidou, K., Dabral, A., Augustin, L., Pourtois, G., Afanasiev, V., Stesmans, A.: Contact resistance at MoS\(_2\)-based 2d metal/semiconductor lateral heterojunctions. ACS Appl. Nano Mater. 2(2), 760–766 (2019)
60.
Sancho, M.P.L., Sancho, J.M.L., Rubio, J.: Quick iterative scheme for the calculation of transfer matrices: application to Mo (100). J. Phys. F: Met. Phys. 14(5), 1205 (1984)
61.
MacKinnon, A.: The calculation of transport properties and density of states of disordered solids. Z. Phys. B 59, 385–390 (1985)
62.
Umerski, A.: Closed-form solutions to surface Green’s functions. Phys. Rev. B 55, 5266–5275 (1997)
63.
Rivas, C., Lake, R.: Non-equilibrium green function implementation of boundary conditions for full band simulations of substrate-nanowire structures. Phys. Status Solidi (B) 239, 94–102 (2003)
64.
Rocha, A.R., García-Suárez, V.M., Bailey, S., Lambert, C., Ferrer, J., Sanvito, S.: Spin and molecular electronics in atomically generated orbital landscapes. Phys. Rev. B 73, 085414 (2006)
65.
Brück, S., Calderara, M., Bani-Hashemian, M.H., VandeVondele, J., Luisier, M.: Efficient algorithms for large-scale quantum transport calculations. J. Chem. Phys. 147, 074116 (2017)
66.
Hung, N.V., Paszko, D., Lamparski, M., Van Troeye, B., Meunier, V., Charlier, J.C.: Electronic localization in small-angle twisted bilayer graphene. 2D Mater. 8(3), 035046 (2021)
67.
Gadelha, A.C., et al.: Localization of lattice dynamics in low-angle twisted bilayer graphene. Nature 590, 405–409 (2021)
68.
Hung, N.V., Hoang, T.X., Charlier, J.C.: Electronic properties of twisted multilayer graphene. J. Phys. Mater. 5(3), 034003 (2022)
69.
de Trambly Laissardiére, G., Mayou, D., Magaud, L.: Localization of Dirac electrons in rotated graphene bilayers. Nano Lett. 10(3), 804–808 (2010)
70.
Hung, N.V., Dollfus, P.: Strain-induced modulation of Dirac cones and van hove singularities in a twisted graphene bilayer. 2D Mater. 2, 035005 (2015)
71.
Bistritzer, R., MacDonald, A.H.: Moiré bands in twisted double-layer graphene. Proc. Natl. Acad. Sci. 108(30), 12233–12237 (2011)
72.
Cao, Y., Fatemi, V., Fang, S., Watanabe, K., Taniguchi, T., Axiras, E., Jarillo-Herrero, P.: Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018)
73.
Brun, B., Moreau, N., Somanchi, S., Nguyen, V.-H., MreńcandKolasińska, A., Watanabe, K., Taniguchi, T., Charlier, J.-C., Stampfer, C., Hackens, B.: Optimizing Dirac fermions quasi-confinement by potential smoothness engineering. 2D Mater. 7(2), 025037 (2020)
74.
Young, A.F., Kim, P.: Quantum interference and Klein Tunnelling in graphene heterojunctions. Nat. Phys. 5, 222–226 (2009)
75.
Rickhaus, P., Maurand, R., Liu, M.-H., Weiss, M., Richter, K., Schönenberger, C.: Ballistic interferences in suspended graphene. Nat. Commun. 4, 2342 (2013)
76.
Datta, S.: Nanoscale device modeling: the Green’s function method. Superlattices Microstruct. 28(4), 253–278 (2000)
77.
TB-SIM code: \(www.mem-lab.fr/en/Pages/L_{-}SIM/Softwares/TB_{-}Sim.aspx\)
78.
NanoTCAD ViDES: \(http://vides.nanotcad.com\)
79.
Nemec, N., Cuniberti, G.: Hofstadter butterflies of bilayer graphene. Phys. Rev. B 75, 201404 (2007)
80.
Hasegawa, Y., Kohmoto, M.: Periodic landau gauge and quantum hall effect in twisted bilayer graphene. Phys. Rev. B 88, 125426 (2013)
81.
Moon, P., Koshino, M.: Energy spectrum and quantum hall effect in twisted bilayer graphene. Phys. Rev. B 85, 195458 (2012)
82.
Crosse, J.A., Nakatsuji, N., Koshino, M., Moon, P.: Hofstadter butterfly and the quantum hall effect in twisted double bilayer graphene. Phys. Rev. B 102, 035421 (2020)
83.
QuanSheng, W., Liu, J., Guan, Y., Yazyev, O.V.: Landau levels as a probe for band topology in graphene moiré superlattices. Phys. Rev. Lett. 126, 056401 (2021)
84.
Yin, L.-J., Bai, K.-K., Wang, W.-X., Li, S.-Y., Yu, Z., Lin, H.: Landau quantization of Dirac fermions in graphene and its multilayers. Front. Phys. 12, 127208 (2017)
85.
Hejazi, K., Liu, C., Balents, L.: Landau levels in twisted bilayer graphene and semiclassical orbits. Phys. Rev. B 100, 035115 (2019)
Metadaten
Titel
Recursive Green’s functions optimized for atomistic modelling of large superlattice-based devices
verfasst von
V. Hung Nguyen
J. -C. Charlier
Publikationsdatum
19.06.2023
Verlag
Springer US
Erschienen in
Journal of Computational Electronics / Ausgabe 5/2023
Print ISSN: 1569-8025
Elektronische ISSN: 1572-8137
DOI
https://doi.org/10.1007/s10825-023-02052-6

Weitere Artikel der Ausgabe 5/2023

Simulation and dynamical analysis of a chaotic chameleon system designed for an electronic circuit

  • Open Access

Full charge incorporation in ab initio simulations of two-dimensional semiconductor-based devices

  • Open Access

Special issue on ab initio simulations of electron and phonon transport in nanostructures

Comparative study of multi-physics generated small dipoles in conducting media

Single-event effect hardening of the Schottky contact super barrier rectifier (SSBR) with high-k gate dielectric

Electronic structure and optical and thermoelectric response of lead-free double perovskite BaMgLaBiO6: a first-principles study