Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T06:15:34.726Z Has data issue: false hasContentIssue false

Phonons correction of the energy and photoionization cross section in polar semiconductors and hollow nanoparticles

Published online by Cambridge University Press:  11 June 2020

Safae M'zerd
Affiliation:
Group of Optoelectronic of Semiconductors and Nanomaterials, ENSAM, Mohammed V University in Rabat, Rabat10000, Morocco
Abdelali Talbi
Affiliation:
Faculty of Sciences, Laboratory of Physics Condensed Matter LPMC, Ibn Tofail University, Kenitra14000, Morocco
Mouad Bikerouin
Affiliation:
Renewable Energy and Advanced Materials Laboratory, International University of Rabat, Rabat11100, Morocco
Mohamed El Haouari
Affiliation:
Centre Régional des Matiéres de l'Education et de Formation (CRMEF), Tanger90060, Morocco
Noreddine Aghoutane
Affiliation:
Group of Optoelectronic of Semiconductors and Nanomaterials, ENSAM, Mohammed V University in Rabat, Rabat10000, Morocco
Mohamed El-Yadri
Affiliation:
Group of Optoelectronic of Semiconductors and Nanomaterials, ENSAM, Mohammed V University in Rabat, Rabat10000, Morocco
Zhi-Hai Zhang
Affiliation:
College of Physics and Electronic Engineering, Yancheng Teachers University, Yancheng224007, China
Jian-Hui Yuan
Affiliation:
Department of Physics, Guangxi Medical University, Nanning530021, China
Mostafa Sadoqi
Affiliation:
Department of Physics, St John's University, Jamaica, NY11439, USA
Gen Long*
Affiliation:
Department of Physics, St John's University, Jamaica, NY11439, USA
El Mustapha Feddi*
Affiliation:
Group of Optoelectronic of Semiconductors and Nanomaterials, ENSAM, Mohammed V University in Rabat, Rabat10000, Morocco
*
a)Address all correspondence to these authors. e-mail: [email protected]
Get access

Abstract

In this paper, we report a recent theoretical study of the calculation of the binding energy and photoionization cross section of a single dopant in a spherical hollow or core/shell quantum dot taking into account the interaction of the electron with longitudinal optical phonons. Using Frolich approach and Lee-low Pines transformation, we determine the impact of different parameters such as shell thickness and dopant position on the energy and optical response of a bound polaron for two types of ionic II–VI semiconductors CdTe and ZnSe with different phonon coupling constants. Regardless of the material used, the electron–phonon interaction visibly reduces binding energy. For photoionization cross section, a redshift of resonance peaks was found when the effect of phonons is taken into consideration or when the donor is moved away from the shell center. These calculations provide us insights when choosing between materials for optoelectronic applications.

Type
Invited Paper
Copyright
Copyright © Materials Research Society 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Feng, X., Xiong, G., Zhang, X., and Gao, H.: Third-order nonlinear optical susceptibilities associated with intersubband transitions in CdSe/ZnS core–shell quantum dots. Physica B 383, 207212 (2006).CrossRefGoogle Scholar
Gong, S., Yao, D., Feng, X., and Jiang, H.: Quantum size dependent optical nutation in a core-shell CdSe/ZnS quantum dot. Microelectron. J. 37, 904 (2006).CrossRefGoogle Scholar
Talapin, D.V., Yu, H., Shevchenko, E.V., Lobo, A., and Murray, C.B.: Synthesis of colloidal PbSe/PbS core-shell nanowires and PbS/Au nanowire-nanocrystal heterostructures. J. Phys. Chem. C 111, 14049 (2007).CrossRefGoogle Scholar
Zeng, H., Sun, S., Li, J., Wang, Z., and Liu, J.: Tailoring magnetic properties of core/shell nanoparticles. Appl. Phys. Lett. 85, 792 (2004).CrossRefGoogle Scholar
Peng, X., Manna, L., Yang, W., Wickham, J., Scher, E., Kadavanich, A., and Alivisatos, A.P.: Shape control of CdSe nanocrystals. Nature 404, 59 (2000).CrossRefGoogle ScholarPubMed
Brokmann, X., Giacobino, E., Dahan, M., and Hermier, J.P.: Highly efficient triggered emission of single photons by colloidal CdSe/ZnS nanocrystals. Appl. Phys. Lett. 85, 712 (2004).CrossRefGoogle Scholar
Alivisatos, P.: The use of nanocrystals in biological detection. Nat. Biotechnol. 22, 47 (2004).CrossRefGoogle ScholarPubMed
Jaiswal, J.K. and Simon, S.M.: Potentials and pitfalls of fluorescent quantum dots for biological imaging. Trends Cell Biol. 14, 497 (2004).CrossRefGoogle ScholarPubMed
Zeng, H., Li, J., Wang, Z., Liu, J., and Sun, S.: Bimagnetic core/shell $\hbox {FePt}$/$\hbox {Fe}_{3}\hbox {O}_{4}$ nanoparticles. Nano Lett. 4, 187 (2004).CrossRefGoogle Scholar
Ivanov, S.A., Nanda, J., Piryatinski, A., Achermann, M., Balet, L.P., Bezel, I.V., Anikeeva, P.O., Tretiak, S., and Klimov, V.: Light amplification using inverted core/shell nanocrystals: Towards lasing in the single-exciton regime. J. Phys. Chem. B 108, 10625 (2004).CrossRefGoogle Scholar
Klimov, V., Mikhailovsky, A., Xu, S., Malko, A., Hollingsworth, J., Leatherdale, C.A., Eisler, H.J., and Bawendi, M.: Optical gain and stimulated emission in nanocrystal quantum dots. Science 290, 314 (2000).CrossRefGoogle ScholarPubMed
Kraabel, B., Malko, A., Hollingsworth, J., and Klimov, V.: Ultrafast dynamic holography in nanocrystal solids. Appl. Phys. Lett. 78, 1814 (2001).CrossRefGoogle Scholar
Petruska, M.A., Malko, A.V., Voyles, P.M., and Klimov, V.: High-performance, quantum dot nanocomposites for nonlinear optical and optical gain applications. Adv. Mater. 15, 610 (2003).CrossRefGoogle Scholar
Schaller, R.D., Sykora, M., Pietryga, J.M., and Klimov, V.: Seven excitons at a cost of one: Redefining the limits for conversion efficiency of photons into charge carriers. Nano Lett. 6, 424 (2006).CrossRefGoogle Scholar
Ellingson, R.J., Beard, M.C., Johnson, J.C., Yu, P., Micic, O.I., Nozik, A.J., Shabaev, A., and Efros, A.L.: Highly efficient multiple exciton generation in colloidal PbSe and PbS quantum dots. Nano Lett. 5, 865 (2005).CrossRefGoogle ScholarPubMed
Baskoutas, S., Jannussis, A., and Yianoulis, P.: Displaced squeezed number states of the phonon field in polar semiconductors. Phys. Rev. B 54, 8586 (1996).CrossRefGoogle ScholarPubMed
Pan, J. and Pan, H.: Size-quantum effect of the energy of a charge carrier in a semiconductor crystallite. Phys. Status Solidi B 148, 129 (1988).CrossRefGoogle Scholar
Klein, M., Hache, F., Ricard, D., and Flytzanis, C.: Size dependence of electron-phonon coupling in semiconductor nanospheres: The case of CdSe. Phys. Rev. B 42, 11123 (1990).CrossRefGoogle ScholarPubMed
Marini, J., Stébé, B., and Kartheuser, E.: Influence of the electron-phonon interaction on a donor like exciton in a semiconductor microsphere. Solid State Communications, 87, 435 (1993).CrossRefGoogle Scholar
Marini, J., Stébé, B., and Kartheuser, E.: Exciton-phonon interaction in CdSe and CuCl polar semiconductor nanospheres. Phys. Rev. B 50, 14302 (1994).CrossRefGoogle ScholarPubMed
Oshiro, K., Akai, K., and Matsuura, M.: Polaron in a spherical quantum dot embedded in a nonpolar matrix. Phys. Rev. B 58, 7986 (1998).CrossRefGoogle Scholar
Knipp, P. and Reinecke, T.: Effects of boundary conditions on confined optical phonons in semiconductor nanostructures. Phys. Rev. B 48, 18037 (1993).CrossRefGoogle ScholarPubMed
Roca, E., Trallero-Giner, C., and Cardona, M.: Polar optical vibrational modes in quantum dots. Phys. Rev. B 49, 13704 (1994).CrossRefGoogle ScholarPubMed
De la Cruz, R., Teitsworth, S., and Stroscio, M.: Interface phonons in spherical $\hbox {GaAs}$/$\hbox {Al}_{x}\hbox {Ga}_{1-x}\hbox {As}$ quantum dots. Phys. Rev. B 52, 1489 (1995).CrossRefGoogle Scholar
Bednarek, S., Szafran, B., Adamowski, J., Essaoudi, I., and Stébé, B.: Phonon resonances in optical spectra of donors in quantum wells. Physica B 273, 947 (1999).CrossRefGoogle Scholar
Szafran, B., Stébé, B., Adamowski, J., and Bednarek, S.: Effect of the electron-phonon coupling on the ground state of a $\hbox {D}^{-}$ center in a spherical quantum dot. Phys. Rev. B 60, 15558 (1999).CrossRefGoogle Scholar
Verzelen, O., Ferreira, R., and Bastard, G.: Polaron lifetime and energy relaxation in semiconductor quantum dots. Phys. Rev. B 62, 4809 (2000).CrossRefGoogle Scholar
Fedorov, A., Baranov, A., and Inoue, K.: Exciton-phonon coupling in semiconductor quantum dots: Resonant raman scattering. Phys. Rev. B 56, 7491 (1997).CrossRefGoogle Scholar
Oshiro, K., Akai, K., and Matsuura, M.: Size dependence of polaronic effects on an exciton in a spherical quantum dot. Phys. Rev. B 59, 10850 (1999).CrossRefGoogle Scholar
Oshiro, K., Akai, K., and Matsuura, M.: Exciton–optical phonon interaction in a spherical quantum dot embedded in nonpolar matrix. Phys. Rev. B 66, 153308 (2002).CrossRefGoogle Scholar
Senger, R. and Bajaj, K.: Polaronic exciton in a parabolic quantum dot. Phys. Status Solidi B 236, 82 (2003).CrossRefGoogle Scholar
Bányai, L. and Koch, S.W.. Semiconductor Quantum Dots (World Scientific, Singapore, 1993).CrossRefGoogle Scholar
Melnikov, D.V. and Fowler, W.B.: Bound polaron in a spherical quantum dot: Strong electron-phonon coupling case. Phys. Rev. B 63, 165302 (2001).CrossRefGoogle Scholar
Melnikov, D.V. and Fowler, W.B.: Bound polaron in a spherical quantum dot: The all-coupling variational approach. Phys. Rev. B 64, 195335 (2001).CrossRefGoogle Scholar
Melnikov, D.V. and Fowler, W.B.: Electron-phonon interaction in a spherical quantum dot with finite potential barriers: The Fröhlich hamiltonian. Phys. Rev. B 64, 245320 (2001).CrossRefGoogle Scholar
El Haouari, M., Feddi, E., Dujardin, F., Restrepo, R., Mora-Ramos, M., and Duque, C.: Polaronic effects on the off-center donor impurity in $\hbox {AlAs}/\hbox {GaAs}/\hbox {SiO}_{2}$ spherical core/shell quantum dots. Superlattices Microstruct. 111, 457 (2017).CrossRefGoogle Scholar
M'zerd, S., El Haouari, M., Talbi, A., Feddi, E., and Mora-Ramos, M.: Impact of electron-lo-phonon correction and donor impurity localization on the linear and nonlinear optical properties in spherical core/shell semiconductor quantum dots. J. Alloys Compd. 753, 68 (2018).CrossRefGoogle Scholar
Fröhlich, H.: Interaction of electrons with lattice vibrations. Proc. R. Soc. A 215, 291 (1952).Google Scholar
El Haouari, M., Mora-Ramos, M., Talbi, A., Feddi, E., and Dujardin, F.: Effect of conduction band non-parabolicity on bound polaron fundamental state in GaN/InN core shell quantum dots. Physica E 103, 188 (2018).CrossRefGoogle Scholar
Lee, T.D., Low, F.E., and Pines, D.: The motion of slow electrons in a polar crystal. Phys. Rev. 90, 297 (1953).CrossRefGoogle Scholar
Aldrich, C. and Bajaj, K.: Binding energy of a mott-wannier exciton in a polarizable medium. Solid State Commun. 22, 157 (1977).CrossRefGoogle Scholar
Barseghyan, M., Hakimyfard, A., López, S., Duque, C., and Kirakosyan, A.: Simultaneous effects of hydrostatic pressure and temperature on donor binding energy and photoionization cross section in pöschl–teller quantum well. Physica E 42, 1618 (2010).CrossRefGoogle Scholar
Lax, M. and Herring, C.. Proc. Conf. Photocond., held at Atlantic City, November 4–6 (1954).Google Scholar
Keller, O.: Local fields in the electrodynamics of mesoscopic media. Phys. Rep. 268, 85 (1996).CrossRefGoogle Scholar
Lozovski, V. and Piatnytsia, V.: The analytical study of electronic and optical properties of pyramid-like and cone-like quantum dots. J. Comput. Theor. Nanosci. 8, 2335 (2011).CrossRefGoogle Scholar
Sali, A., Fliyou, M., and Loumrhari, H.: The effect of the electron-longitudinal optical phonons interaction on the photoionization in a quantum well. J. Phys. Chem. Solids 59, 625 (1998).CrossRefGoogle Scholar
El-Said, M. and Tomak, M.: Photoionization of impurities in infinite-barrier quantum wells. J. Phys. Chem. Solids 52, 603 (1991).CrossRefGoogle Scholar
Talbi, A., Feddi, E., Oukerroum, A., Assaid, E., Dujardi, F., and Addou, M.: Theoretical investigation of single dopant in core/shell nanocrystal in magnetic field. Superlattices Microstruct. 85, 581 (2015).CrossRefGoogle Scholar
Talbi, A., Feddi, E., Zouitine, A., El Haouari, M., Zazoui, M., Oukerroum, A., Dujardin, F., Assaid, E., and Addou, M.: Control of the binding energy by tuning the single dopant position, magnetic field strength and shell thickness in $\hbox {ZnS}$/$\hbox {CdSe}$ core/shell quantum dot. Physica E 84, 303 (2016).CrossRefGoogle Scholar