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Journal of Computational Electronics

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27-07-2024

A semi-classical Floquet-NEGF approach to model photon-assisted tunneling in quantum well devices

Authors: Nathan De Sutter, Emile Vanderstraeten, Dries Vande Ginste

Published in: Journal of Computational Electronics | Issue 6/2024

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Abstract

The non-equilibrium Green’s function formalism is often employed to model photon-assisted tunneling processes in opto-electronic quantum well devices. For this purpose, self-consistent schemes based on a quantum electrodynamical description of light–matter interactions have been proposed before. However, these schemes are typically computationally very demanding. Therefore, in this work, a novel semi-classical method based on Floquet–Green theory is proposed, which strongly mitigates the computational costs. By comparison to results obtained with a traditional, purely quantum mechanical technique, the new approach is validated, shown to be faster, and exhibits superior convergence properties. Finally, a two-band model for superlattice structures is constructed to further illustrate the advantages of the novel, advocated method.

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Esaki, L., Tsu, R.: Superlattice and negative differential conductivity in semiconductors. IBM J. Res. Dev. 14, 61–65 (1970). https://doi.org/10.1147/rd.141.0061CrossRef

Sun, J.P., Haddad, G., Mazumder, P., Schulman, J.: Resonant tunneling diodes: models and properties. Proc. IEEE 86(4), 641–660 (1998). https://doi.org/10.1109/5.663541CrossRef

Sweeny, M., Xu, J.: Resonant interband tunnel diodes. APL 54(6), 546–548 (1989). https://doi.org/10.1063/1.100926CrossRef

Zhou, S., Jiang, J., Cai, Q.: Small-signal ac response: a self-consistent non-equilibrium Green’s function approach. J. Phys. D: Appl. Phys. 38(2), 255 (2005). https://doi.org/10.1088/0022-3727/38/2/009CrossRef

Fox, A.M.: Optoelectronics in quantum well structures. Contemp. Phys. 37(2), 111–125 (1996). https://doi.org/10.1080/00107519608230339CrossRef

Onaran, E., Onbasli, M.C., Yesilyurt, A., Yu, H.Y., Nayfeh, A.M., Okyay, A.K.: Silicon-Germanium multi-quantum well photodetectors in the near infrared. Opt. Express 20(7), 7608–7615 (2012). https://doi.org/10.1364/OE.20.007608CrossRef

Wood, T.: Multiple quantum well (MQW) waveguide modulators. J. Light. Technol. 6(6), 743–757 (1988). https://doi.org/10.1109/50.4063CrossRef

Aoki, M., Suzuki, M., Sano, H., Kawano, T., Ido, T., Taniwatari, T., Uomi, K., Takai, A.: InGaAs/InGaAsP MQW electroabsorption modulator integrated with a DFB laser fabricated by band-gap energy control selective area MOCVD. IEEE J. Quantum Electron. 29(6), 2088–2096 (1993). https://doi.org/10.1109/3.234473CrossRef

Wakita, K., Kawamura, Y., Nakao, M., Asahi, H.: Long wavelength waveguide multiple quantum well optical modulators. IEEE J. Quantum Electron. 23(12), 2210–2215 (1987). https://doi.org/10.1109/JQE.1987.1073291CrossRef

10.

Koike, M., Shibata, N., Kato, H., Takahashi, Y.: Development of high efficiency GaN-based multiquantum-well light-emitting diodes and their applications. IEEE J. Sel. Top. Quantum Electron. 8(2), 271–277 (2002). https://doi.org/10.1109/2944.999180CrossRef

11.

Lee, W., Kim, M.H., Zhu, D., Noemaun, A.N., Kim, J.K., Schubert, E.F.: Growth and characteristics of GaInN/GaInN multiple quantum well light-emitting diodes. J. Appl. Phys. 107(6), 063102 (2010). https://doi.org/10.1063/1.3327425CrossRef

12.

Bulashevich, K., Mymrin, V., Karpov, S., Zhmakin, I., Zhmakin, A.: Simulation of visible and ultra-violet group-III nitride light emitting diodes. J. Comput. Phys. 213(1), 214–238 (2006). https://doi.org/10.1016/j.jcp.2005.08.011CrossRef

13.

Chang, S., Lai, W., Su, Y., Chen, J., Liu, C., Liaw, U.: InGaN-GaN multiquantum-well blue and green light-emitting diodes. IEEE J. Sel. Top. Quantum Electron. 8(2), 278–283 (2002). https://doi.org/10.1109/2944.999181CrossRef

14.

Faist, J., Capasso, F., Sivco, D.L., Sirtori, C., Hutchinson, A.L., Cho, A.Y.: Quantum cascade laser. Science 264(5158), 553–556 (1994). https://doi.org/10.1126/science.264.5158.553CrossRef

15.

Jirauschek, C., Kubis, T.: Modeling techniques for quantum cascade lasers. Appl. Phys. Rev. 1(1), 011307 (2014). https://doi.org/10.1063/1.4863665CrossRef

16.

Iotti, R.C., Rossi, F.: Nature of charge transport in quantum-cascade lasers. Phys. Rev. Lett. 87, 146603 (2001). https://doi.org/10.1103/PhysRevLett.87.146603CrossRef

17.

Wacker, A.: Gain in quantum cascade lasers and superlattices: a quantum transport theory. Phys. Rev. B 66, 085326 (2002). https://doi.org/10.1103/PhysRevB.66.085326CrossRef

18.

Barnham, K.W.J., Duggan, G.: A new approach to high-efficiency multi-band-gap solar cells. J. Appl. Phys. 67(7), 3490–3493 (1990). https://doi.org/10.1063/1.345339CrossRef

19.

Dahal, R., Pantha, B., Li, J., Lin, J.Y., Jiang, H.X.: InGaN/GaN multiple quantum well solar cells with long operating wavelengths. APL 94(6), 063505 (2009). https://doi.org/10.1063/1.3081123CrossRef

20.

Kadanoff, L., Baym, G.: Quantum Statistical Mechanics. W.A. Benjamin, New York (1962)

21.

Keldysh, L.V., et al.: Diagram technique for nonequilibrium processes. Sov. Phys. JETP 20(4), 1018–1026 (1965)MathSciNet

22.

Schwinger, J.: Quantum electrodynamics. I. A covariant formulation. Phys. Rev. 74, 1439–1461 (1948). https://doi.org/10.1103/PhysRev.74.1439MathSciNetCrossRef

23.

Perfetto, E., Uimonen, A., van Leeuwen, R., Stefanucci, G.: First-principles nonequilibrium Green’s-function approach to transient photoabsorption: application to atoms. Phys. Rev. A 92, 033419 (2015). https://doi.org/10.1103/PhysRevA.92.033419CrossRef

24.

Wang, J.S., Zeng, N., Wang, J., Gan, C.K.: Nonequilibrium Green’s function method for thermal transport in junctions. Phys. Rev. E 75, 061128 (2007). https://doi.org/10.1103/PhysRevE.75.061128CrossRef

25.

Tuovinen, R., van Leeuwen, R., Perfetto, E., Stefanucci, G.: Electronic transport in molecular junctions: the generalized Kadanoff–Baym ansatz with initial contact and correlations. Chem. Phys. 154(9), 094104 (2021). https://doi.org/10.1063/5.0040685CrossRef

26.

Jiang, H., Shao, S., Cai, W., Zhang, P.: Boundary treatments in non-equilibrium Green’s function (NEGF) methods for quantum transport in nano-MOSFETs. J. Comput. Phys. 227(13), 6553–6573 (2008). https://doi.org/10.1016/j.jcp.2008.03.018MathSciNetCrossRef

27.

Wei, W., Jianhui, L., Jianping, S., Ning, G.: Simulation of the electrical characteristics of a one-dimensional quantum dot array. Superlattices Microstruct. 44(6), 721–727 (2008). https://doi.org/10.1016/j.spmi.2008.09.004CrossRef

28.

Henrickson, L.E., Glick, A.J., Bryant, G.W., Barbe, D.F.: Nonequilibrium-Green’s-function theory of transport in interacting quantum dots. Phys. Rev. B 50, 4482–4496 (1994). https://doi.org/10.1103/PhysRevB.50.4482CrossRef

29.

Neophytou, N., Ahmed, S., Klimeck, G.: Non-equilibrium Green’s function (NEGF) simulation of metallic carbon nanotubes including vacancy defects. J. Comput. Electron. 6, 317–320 (2007). https://doi.org/10.1007/s10825-006-0116-4CrossRef

30.

Wang, W., Yang, X., Li, N., Xiao, G., Jiang, S., Xia, C., Wang, Y.: Transport study of gate and channel engineering on the surrounding-gate CNTFETs based on NEGF quantum theory. J. Comput. Electron. 13, 192–197 (2014). https://doi.org/10.1007/s10825-013-0499-yCrossRef

31.

Mandal, B., Sarkar, S., Pramanik, A., Sarkar, P.: Electronic structure and transport properties of sulfur-passivated graphene nanoribbons. J. Appl. Phys. 112(11), 113710 (2012). https://doi.org/10.1063/1.4768524CrossRef

32.

Hossain, T., Rahaman, M.: Band gap tuning and variable quantum barrier of armchair graphene nanoribbons by inducing antidote topologies. J. Comput. Electron. 23, 32–41 (2023). https://doi.org/10.1007/s10825-023-02108-7CrossRef

33.

Aeberhard, U., Morf, R.H.: Microscopic nonequilibrium theory of quantum well solar cells. Phys. Rev. B 77, 125343 (2008). https://doi.org/10.1103/PhysRevB.77.125343CrossRef

34.

Henrickson, L.E.: Nonequilibrium photocurrent modeling in resonant tunneling photodetectors. J. Appl. Phys. 91(10), 6273–6281 (2002). https://doi.org/10.1063/1.1473677CrossRef

35.

Dehdashti Akhavan, N., Umana-Membreno, G.A., Gu, R., Antoszewski, J., Faraone, L.: Optimization of Superlattice Barrier HgCdTe nBn Infrared Photodetectors Based on an NEGF Approach. IEEE Trans. Electron. Devices 65(2), 591–598 (2018). https://doi.org/10.1109/TED.2017.2785827CrossRef

36.

Moradinasab, M., Pourfath, M., Fathipour, M., Kosina, H.: Numerical study of graphene superlattice-based photodetectors. IEEE Trans. Electron. Devices 62(2), 593–600 (2015). https://doi.org/10.1109/TED.2014.2383354CrossRef

37.

Martinez, D.: Floquet–Green function formalism for harmonically driven Hamiltonians. J. Phys. A Math 36, 9827 (2003). https://doi.org/10.1088/0305-4470/36/38/302MathSciNetCrossRef

38.

Honeychurch, T.D., Kosov, D.S.: Quantum transport in driven systems with vibrations: Floquet nonequilibrium Green’s functions and the self-consistent Born approximation. Phys. Rev. B 107(3), 035410 (2023). https://doi.org/10.1103/physrevb.107.035410CrossRef

39.

Honeychurch, T.D., Kosov, D.S.: Timescale separation solution of the Kadanoff–Baym equations for quantum transport in time-dependent fields. Phys. Rev. B 100, 245423 (2019). https://doi.org/10.1103/PhysRevB.100.245423CrossRef

40.

Arrachea, L.: Green-function approach to transport phenomena in quantum pumps. Phys. Rev. B 72, 125349 (2005). https://doi.org/10.1103/PhysRevB.72.125349CrossRef

41.

Arrachea, L., Moskalets, M.: Relation between scattering-matrix and Keldysh formalisms for quantum transport driven by time-periodic fields. Phys. Rev. B 74, 245322 (2006). https://doi.org/10.1103/PhysRevB.74.245322CrossRef

42.

Cabra, G., Franco, I., Galperin, M.: Optical properties of periodically driven open nonequilibrium quantum systems. Chem. Phys. 152(9), 094101 (2020). https://doi.org/10.1063/1.5144779CrossRef

43.

Giovannini, U.D., Hübener, H.: Floquet analysis of excitations in materials. J. Phys. Mater. 3(1), 012001 (2019). https://doi.org/10.1088/2515-7639/ab387bCrossRef

44.

Datta, S.: Nanoscale device modeling: the Green’s function method. Superlattices Microstruct. 28(4), 253–278 (2000). https://doi.org/10.1006/spmi.2000.0920CrossRef

45.

Palsgaard, M., Markussen, T., Gunst, T.: Efficient first-principles calculation of phonon-assisted photocurrent in large-scale solar-cell devices. Phys. Rev. Appl. 10, 014026 (2018). https://doi.org/10.1103/PhysRevApplied.10.014026CrossRef

46.

Aeberhard, U.: Challenges in the NEGF simulation of quantum-well photovoltaics posed by non-locality and localization. Physica Status Solidi (b) 256(7), 1800500 (2019). https://doi.org/10.1002/pssb.201800500CrossRef

47.

Chang, Y., Schulman, J.N.: Modification of optical properties of GaAs-Ga1-xAlxAs superlattices due to band mixing. Appl. Phys. Lett. 43(6), 536–538 (1983). https://doi.org/10.1063/1.94410CrossRef

48.

Sancho, M.P.L., Sancho, J.M.L., Rubio, J.: Highly convergent schemes for the calculation of bulk and surface Green functions. J. Phys. F Met. Phys. 15(4), 851 (1985). https://doi.org/10.1088/0305-4608/15/4/009CrossRef

49.

Boykin, T.B., van der Wagt, J.P.A., Harris, J.S.: Tight-binding model for GaAs/AlAs resonant-tunneling diodes. Phys. Rev. B 43, 4777–4784 (1991). https://doi.org/10.1103/PhysRevB.43.4777CrossRef

50.

Driscoll, J.A., Varga, K.: Calculation of self-energy matrices using complex absorbing potentials in electron transport calculations. Phys. Rev. B 78, 245118 (2008). https://doi.org/10.1103/PhysRevB.78.245118CrossRef

51.

Anantram, M.P., Datta, S.: Effect of phase breaking on the ac response of mesoscopic systems. Phys. Rev. B 51, 7632–7639 (1995). https://doi.org/10.1103/PhysRevB.51.7632CrossRef

52.

Stefanucci, G., Kurth, S., Rubio, A., Gross, E.K.U.: Time-dependent approach to electron pumping in open quantum systems. Phys. Rev. B 77, 075339 (2008). https://doi.org/10.1103/PhysRevB.77.075339CrossRef

53.

Nguyen, V., Charlier, J.C.: Recursive Green’s functions optimized for atomistic modelling of large superlattice-based devices. J. Comput. Electron. 22, 1–16 (2023). https://doi.org/10.1007/s10825-023-02052-6CrossRef

54.

Pedersen, T.G., Pedersen, K., Brun Kriestensen, T.: Optical matrix elements in tight-binding calculations. Phys. Rev. B 63, 201101 (2001). https://doi.org/10.1103/PhysRevB.63.201101CrossRef

55.

Honeychurch, T.D., Kosov, D.S.: Full counting statistics for electron transport in periodically driven quantum dots. Phys. Rev. B 102, 195409 (2020). https://doi.org/10.1103/PhysRevB.102.195409CrossRef

56.

Aeberhard, U.: The nonequilibrium Green’s function picture of inelastic processes in nanostructure photovoltaics. J. Comput. Electron. 15, 1219–1232 (2016). https://doi.org/10.1007/s10825-016-0877-3CrossRef

57.

Lee, W., Jean, N., Sanvito, S.: Exploring the limits of the self-consistent Born approximation for inelastic electronic transport. Phys. Rev. B 79, 085120 (2009). https://doi.org/10.1103/PhysRevB.79.085120CrossRef

58.

Pereiro, J., Rivera, C., Navarro, A., Munoz, E., Czernecki, R., Grzanka, S., Leszczynski, M.: Optimization of InGan-GaN MQW photodetector structures for high-responsivity performance. IEEE J. Quantum Electron. 45(6), 617–622 (2009). https://doi.org/10.1109/JQE.2009.2013140CrossRef

59.

Ho, K.T., Chen, R., Liu, G., et al.: 3.2 Gigabit-per-second visible light communication link with InGaN/GaN MQW micro-photodetector. Opt. Express 26(3), 3037–3045 (2018). https://doi.org/10.1364/OE.26.003037CrossRef

60.

Bilitewski, T., Cooper, N.R.: Scattering theory for Floquet–Bloch states. Phys. Rev. A 91, 033601 (2015). https://doi.org/10.1103/PhysRevA.91.033601MathSciNetCrossRef

61.

Wang, J.: Time-dependent quantum transport theory from non-equilibrium Green’s function approach. J. Comput. Electron. 12, 343–355 (2013). https://doi.org/10.1007/s10825-013-0465-8CrossRef

62.

Wu, B.H., Cao, J.C.: A Floquet–Green’s function approach to mesoscopic transport under ac bias. J. Condens. Matter Phys. 20(8), 085224 (2008). https://doi.org/10.1088/0953-8984/20/8/085224CrossRef

63.

Brandes, T.: Truncation method for Green’s functions in time-dependent fields. Phys. Rev. B 56, 1213–1224 (1997). https://doi.org/10.1103/PhysRevB.56.1213CrossRef

64.

Špicka, V., Velický, B., Kalvová, A.: Non-equilibrium dynamics of open systems and fluctuation–dissipation theorems. Fortschr. Phys. 65(6–8), 1700032 (2017). https://doi.org/10.1002/prop.201700032MathSciNetCrossRef

Title: A semi-classical Floquet-NEGF approach to model photon-assisted tunneling in quantum well devices
Authors: Nathan De Sutter
Emile Vanderstraeten
Dries Vande Ginste
Publication date: 27-07-2024
Publisher: Springer US
Published in: Journal of Computational Electronics / Issue 6/2024
Print ISSN: 1569-8025
Electronic ISSN: 1572-8137
DOI: https://doi.org/10.1007/s10825-024-02203-3

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A semi-classical Floquet-NEGF approach to model photon-assisted tunneling in quantum well devices

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