Abstract
Hot electrons cooling by phonons in GaAs/AlAs cylindrical quantum wire (CQW), under the influence of an intense electromagnetic wave (EMW), is studied theoretically. Analytic expression for the electron cooling power (CP) is derived from the quantum transport equation for phonons, using the Hamiltonian of interacting electron–optical phonon system. Both photon absorption and emission processes are considered. Numerical results show that the CP reaches maximum when the energy difference between electronic subbands equals the energy of an optical phonon plus the photon energy. Under the influence of the EMW, the negative CP is observed showing that electrons gain energy from phonon and photon instead of losing their energy. Also, the CP increases with increasing the EMW amplitude. Our results theoretically clarify the mechanism of the electron cooling process by phonons in the GaAs/AlAs CQW under the EMW, which is of significance for designing and fabricating high-speed nanoelectronic devices based on this material.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Balkan, N. (ed.): Hot Electrons in Semiconductors: Physics and Devices. Oxford University Press, Oxford (1998)
Bau, N.Q., Phong, T.C.: Calculations of the absorption coefficient of a weak electromagnetic wave by free carriers in quantum wells by the Kubo–Mori method. J. Phys. Soc. Jpn. 67, 3875–3880 (1998)
Betz, A.C.: Hot electron cooling by acoustic phonons in graphene. Phys. Rev. Lett. 109, 056805–056809 (2012)
Bhargavi, K.S., Kubakaddi, S.S.: High field transport properties of a bilayer graphene. Physica E 56, 123–129 (2014)
Bhargavi, K.S., Kubakaddi, S.S.: Electron cooling in three-dimensional Dirac fermion systems at low temperature: effect of screening. Phys. Status Solidi Rapid Res. Lett. 10, 248–252 (2016)
Butler, S.Z.: Progress challenges, and opportunities in two-dimensional materials beyond graphene. ACS Nano 7(4), 2898–2926 (2013)
Castro Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., Geim, A.: The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009)
Das Sarma, S., Adam, S., Hwang, E.H., Rossi, E.: Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407–470 (2011)
Fletcher, R., Pudalov, V.M., Feng, Y., Tsaousidou, M., Butcher, P.N.: Thermoelectric and hot-electron properties of a silicon inversion layer. Phys. Rev. B 56, 12422–12428 (1997)
Gaška, R., Mickevičius, R., Mitin, V., Grubin, H.L.: Hot-electron overcooling and intersubband population inversion in quantum wires. Semicond. Sci. Technol. 9, 886–888 (1994)
Gaška, R., Mickevičius, R., Mitin, V., Stroscio, M.A., Iafrate, G.J., Grubin, H.L.: Hotelectron relaxation dynamics in quantum wires. J. Appl. Phys. 76, 1021–1028 (1994)
Gupta, A., Sakthivel, T., Seal, S.: Recent development in 2D materials beyond graphene. Prog. Mater. Sci 73, 44–126 (2015)
Hoi, B.D., Phuong, L.T.T., Phong, T.C.: Magneto-optical absorption and cyclotron–phonon resonance in graphene monolayer. J. Appl. Phys. 123, 094303 (2018)
Iacopi, F., Boeckl, J.J., Jagadish, C. (ed.): Book Series: Semiconductors and Semimetals, 2D Materials, 95, 2–340 (2016)
Kaasbjerg, K., Bhargavi, K.S., Kubakaddi, S.S.: Hot-electron cooling by acoustic and optical phonons in monolayers of MoS\(_2\) and other transition-metal dichalcogenides. Phys. Rev. B 90, 165436 (2014)
Kang, N.L., Lee, Y.J., Choi, S.D.: Derivation of the DC conductivity in a quantum well by using an operator algebra technique. J. Korean Phys. Soc. 44, 1535–1541 (2004)
Kubakaddi, S.S.: Interaction of massless Dirac electrons with acoustic phonons in graphene at low temperatures. Phys. Rev. B 79, 075417-1–075417-6 (2009)
Kubakaddi, S.S.: Cerenkov emission of acoustic phonons electrically generated from three-dimensional Dirac semimetals. J. Appl. Phys. 119, 195701 (2016)
Kubakaddi, S.S.: The role of vector potential coupling in hot electron cooling power in bilayer graphene at low temperature. Physica E 95, 144–148 (2018)
Kubakaddi, S.S., Suresha, K., Mulimani, B.G.: Energy loss rate of two-dimensional electron gas in GaInAs/AlInAs, InSb/AlInSb and GaSb/AlGaAsSb heterostructures. Physica E 18, 475–484 (2003)
Lee, S.-C., Galbraith, I., Pidgeon, C.R.: Influence of electron temperature and carrier concentration on electron-LO-phonon intersubband scattering in wide GaAs/Al\(_x\)Ga\(_{1-x}\)As quantum wells. Phys. Rev. B 52, 1874–1881 (1995)
Ma, Y., Fletcher, R., Zaremba, E., D’lorio, M., Foxon, C.T., Harris, J.J.: Energy-loss rates of two-dimensional electrons at a GaAs/Al\(_x\)Ga\(_{1-x}\)As interface. Phys. Rev. B 43, 9033–9044 (1991)
Masale, M., Constantinou, N.C.: ElectronLO-phonon scattering rates in a cylindrical quantum wire with an axial magnetic field: analytic results. Phys. Rev. B 48, 11128–11134 (1993)
Mitin, V.V., Gaška, R., Mickevičius, R.: Ultrafast relaxation of hot electrons in quantum wires. In: Proceedings of SPIE 2142, Ultrafast Phenomena in Semiconductors, 69 (May 6, 1994), https://doi.org/10.1117/12.175911
Mori, N., Ando, T.: Magnetophonon resonance in monolayer graphene. J. Phys. Soc. Jpn. 80, 044706 (2011)
Nguyen, C.V.: Magneto-optical transport properties of monolayer MoS2 on polar substrates. Phys. Rev. B 96, 125411 (2017)
Qu, S.-X., Cleland, A.N., Geller, M.R.: Hot electrons in low-dimensional phonon systems. Phys. Rev. B 72, 224301-1–224301-7 (2005)
Sangwan, V.K., Hersam, M.C.: Electronic transport in two-dimensional materials. Annu. Rev. Phys. Chem. 69, 299–325 (2018)
Shadrin, V.D., Kistenev, F.E., Serzhenko, F.L.: Influence of quantum wire electron confinement on intrasubband polaroptical scattering rates. J. Appl. Phys. 75, 985–988 (1994)
Sippel, P.: Femtosecond cooling of hot electrons in CdSe quantum-well platelets. Nano Lett. 15, 2409–2416 (2015)
Smith, H., Jensen, H.H.: Transport Phenomena. Oxford University Press, Oxford (1989)
Stange, A., Sohrt, C., Yang, L.X., Rohde, G., Janssen, K., Hein, P., Oloff, L.-P., Hanff, K., Rossnagel, K., Bauer, M.: Hot electron cooling in graphite: supercollision versus hot phonon decay. Phys. Rev. B 92, 184303 (2015)
Stroscio, M.A., Dutta, M.: Phonons in Nanostructures. Cambridge University Press, Cambridge (2001)
Wang, X.F., Lei, X.L.: Polar-optic phonons and high-field electron transport in cylindrical GaAs/AlAs quantum wires. Phys. Rev. B 49(7), 4780–4789 (1994)
Xu, W.: Emission of acoustic and optical phonons by hot electrons in a two-dimensional electron system in parallel magnetic fields. Phys. Rev. B 54, 2775–2784 (1996)
Xu, W., Dong, H.M., Li, L.L., Yao, J.Q., Vasilopoulos, P., Peeters, F.M.: Optoelectronic properties of graphene in the presence of optical phonon scattering. Phys. Rev. B 82, 125304–125309 (2010)
Yarmohammadi, M.: Strain effects on the optical conductivity of gapped graphene in the presence of Holstein phonons beyond the Dirac cone approximation. AIP Adv. 6(8), 085008 (2016)
Yarmohammadi, M.: Thermodynamic properties of gapped graphene in the presence of a transverse magnetic field by considering holstein phonons. J. Electron. Matter. 46(2), 747–757 (2017a)
Yarmohammadi, M.: The electronic properties, electronic heat capacity and magnetic susceptibility of monolayer boron nitride graphene-like structure in the presence of electron–phonon coupling. Solid State Commun. 253, 57–62 (2017b)
Yarmohammadi, M., Mirabbaszadeh, K., Shirzadi, B.: The effects of Rashba spinorbit coupling and Holstein phonons on thermodynamic properties of BN-doped graphene. Int. J. Mod. Phys. B 31(8), 1750045 (2017)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pham, K.D., Nguyen, C.V., Hieu, N.N. et al. Theoretical investigation of hot electron cooling process in GaAs/AlAs cylindrical quantum wire under the influence of an intense electromagnetic wave. Opt Quant Electron 50, 342 (2018). https://doi.org/10.1007/s11082-018-1606-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-018-1606-x