Skip to main content
Erschienen in: Optical and Quantum Electronics 11/2018

01.11.2018

A meshless method of line radial base function study of Gaussian wave packet broadening in few semiconducting mediums: electron–electron interaction effects

verfasst von: M. Solaimani, Mehrzad Ghorbani

Erschienen in: Optical and Quantum Electronics | Ausgabe 11/2018

Einloggen

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

search-config
loading …

Abstract

In this paper, we have studied the effect of electron–electron interaction on wave packet broadening in different semiconducting mediums in the presence of conduction band non-parabolicity. We have solved the resulting one dimensional fourth order Schrödinger equation by means of a meshless radial base function approach and 2nd order Runge Kutta method. We have compared different semiconducting mediums GaAs, GaN, AlN, InSb and GaSb and showed that in the absence of the electron–electron interaction, the Gaussian wave packet decays with time elapse while in the presence of the electron–electron interaction, the Gaussian wave packet localizes when time increases. Finally, Gaussian wave packet also localizes faster when we increase the electron–electron interaction strength.

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

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!

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!

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!

Literatur
Zurück zum Zitat Adachia, S.: GaAs, AlAs, and AlxGa1 _xAs: material parameters for use in research and device applications. J. Appl. Phys. 58, R1–R29 (1985)ADSCrossRef Adachia, S.: GaAs, AlAs, and AlxGa1 _xAs: material parameters for use in research and device applications. J. Appl. Phys. 58, R1–R29 (1985)ADSCrossRef
Zurück zum Zitat Aleomraninejada, S.M.A., Solaimani, M., Mohsenyzadeh, M., Lavaei, L.: Discretized Euler–Lagrange variational study of nonlinear optical rectification coefficients. Physica Scr. Phys. Scr. 93, 095803-1–095803-8 (2018)ADS Aleomraninejada, S.M.A., Solaimani, M., Mohsenyzadeh, M., Lavaei, L.: Discretized Euler–Lagrange variational study of nonlinear optical rectification coefficients. Physica Scr. Phys. Scr. 93, 095803-1–095803-8 (2018)ADS
Zurück zum Zitat Andrews, Mark: The evolution of free wave packets. Am. J. Phys. 76, 1102–1107 (2008)ADSCrossRef Andrews, Mark: The evolution of free wave packets. Am. J. Phys. 76, 1102–1107 (2008)ADSCrossRef
Zurück zum Zitat Bader, P., Blanes, S., Casas, F.: Solving the Schrödinger eigenvalue problem by the imaginary time propagation technique using splitting methods with complex coefficients. J. Chem. Phys. 139, 124117-1–124117-11 (2013)ADSCrossRef Bader, P., Blanes, S., Casas, F.: Solving the Schrödinger eigenvalue problem by the imaginary time propagation technique using splitting methods with complex coefficients. J. Chem. Phys. 139, 124117-1–124117-11 (2013)ADSCrossRef
Zurück zum Zitat Bednarek, S., Szafran, B., Lis, K.: Self-focusing of a quantum-well-confined electron wave packet interacting with a metal plate. Phys. Status Solidi B 243, 2811–2818 (2006)ADSCrossRef Bednarek, S., Szafran, B., Lis, K.: Self-focusing of a quantum-well-confined electron wave packet interacting with a metal plate. Phys. Status Solidi B 243, 2811–2818 (2006)ADSCrossRef
Zurück zum Zitat Diez, E., Dominguez-Adame, F., Sanchez, A.: Nonlinear resonant tunnelling through double-barrier structures. Phys. Lett. A 198, 403–406 (1995)ADSCrossRef Diez, E., Dominguez-Adame, F., Sanchez, A.: Nonlinear resonant tunnelling through double-barrier structures. Phys. Lett. A 198, 403–406 (1995)ADSCrossRef
Zurück zum Zitat Diez, E., Dominguez-Adame, F., Macia, E., Sanchez, A.: Dynamical phenomena in Fibonacci semiconductor superlattices. Phys. Rev. B 54, 16792–16798 (1996)ADSCrossRef Diez, E., Dominguez-Adame, F., Macia, E., Sanchez, A.: Dynamical phenomena in Fibonacci semiconductor superlattices. Phys. Rev. B 54, 16792–16798 (1996)ADSCrossRef
Zurück zum Zitat Diez, E., Gomez-Alcala, R., Domínguez-Adame, F., Sanchez, A., Berman, G.P.: Rabi oscillations in semiconductor superlattices. Phys. Rev. B 58, 1146–1149 (1998)ADSCrossRef Diez, E., Gomez-Alcala, R., Domínguez-Adame, F., Sanchez, A., Berman, G.P.: Rabi oscillations in semiconductor superlattices. Phys. Rev. B 58, 1146–1149 (1998)ADSCrossRef
Zurück zum Zitat Fojon, O., Gadella, M., Lara, L.P.: The quantum square well with moving boundaries: a numerical analysis. Comput. Math Appl. 59, 964–976 (2010)MathSciNetCrossRef Fojon, O., Gadella, M., Lara, L.P.: The quantum square well with moving boundaries: a numerical analysis. Comput. Math Appl. 59, 964–976 (2010)MathSciNetCrossRef
Zurück zum Zitat Ford, G.W., O’Connell, R.F.: Wave packet spreading: temperature and squeezing effects with applications to quantum measurement and decoherence. Am. J. Phys. 70, 319–324 (2002)ADSCrossRef Ford, G.W., O’Connell, R.F.: Wave packet spreading: temperature and squeezing effects with applications to quantum measurement and decoherence. Am. J. Phys. 70, 319–324 (2002)ADSCrossRef
Zurück zum Zitat Haq, S., Hussain, A., Uddin, M.: On the numerical solution of nonlinear Burgers’-type equations using meshless method of lines. Appl. Math. Comput. 218, 6280–6290 (2012)MathSciNetMATH Haq, S., Hussain, A., Uddin, M.: On the numerical solution of nonlinear Burgers’-type equations using meshless method of lines. Appl. Math. Comput. 218, 6280–6290 (2012)MathSciNetMATH
Zurück zum Zitat Ismail, M.S.: Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method. Math. Comput. Simul. 78, 532–547 (2008)CrossRef Ismail, M.S.: Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method. Math. Comput. Simul. 78, 532–547 (2008)CrossRef
Zurück zum Zitat Kansa, E.J.: Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—II solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput. Math Appl. 19, 147–161 (1990)MathSciNetCrossRef Kansa, E.J.: Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—II solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput. Math Appl. 19, 147–161 (1990)MathSciNetCrossRef
Zurück zum Zitat Kuznetsov, A.V., Sanders, G.D., Stanton, C.J.: Wave-packet dynamics in quantum wells. Phys. Rev. B 52, 12045–12055 (1995)ADSCrossRef Kuznetsov, A.V., Sanders, G.D., Stanton, C.J.: Wave-packet dynamics in quantum wells. Phys. Rev. B 52, 12045–12055 (1995)ADSCrossRef
Zurück zum Zitat Lambert, J.D.: Numerical Methods for Ordinary Differential Systems: The Initial Value Problem. Wiley, New York (1991)MATH Lambert, J.D.: Numerical Methods for Ordinary Differential Systems: The Initial Value Problem. Wiley, New York (1991)MATH
Zurück zum Zitat Lundstrom, M.: Fundamentals of Carrier Transport, 2nd edn, p. 14. Cambridge University Press, Cambridge (2000)CrossRef Lundstrom, M.: Fundamentals of Carrier Transport, 2nd edn, p. 14. Cambridge University Press, Cambridge (2000)CrossRef
Zurück zum Zitat Monterola, C., Saloma, C.: Solving the nonlinear Schrödinger equation with an unsupervised neural network: estimation of error in solution. Opt. Commun. 222, 331–339 (2003)ADSCrossRef Monterola, C., Saloma, C.: Solving the nonlinear Schrödinger equation with an unsupervised neural network: estimation of error in solution. Opt. Commun. 222, 331–339 (2003)ADSCrossRef
Zurück zum Zitat Nassar, A.B., Miret-Artes, S.: Dividing Line between quantum and classical trajectories in a measurement problem: Bohmian time constant. Phys. Rev. Lett. 111, 150401-1–150401-5 (2013)ADSCrossRef Nassar, A.B., Miret-Artes, S.: Dividing Line between quantum and classical trajectories in a measurement problem: Bohmian time constant. Phys. Rev. Lett. 111, 150401-1–150401-5 (2013)ADSCrossRef
Zurück zum Zitat Nithiananthi, P., Jayakumar, K.: Diamagnetic susceptibility of hydrogenic donor impurity in low-dimensional semiconducting systems. Solid State Commun. 137, 427–430 (2006)ADSCrossRef Nithiananthi, P., Jayakumar, K.: Diamagnetic susceptibility of hydrogenic donor impurity in low-dimensional semiconducting systems. Solid State Commun. 137, 427–430 (2006)ADSCrossRef
Zurück zum Zitat Nobre, F.D., Rego-Monteiro, M.A., Tsallis, C.: Nonlinear relativistic and quantum equations with a common type of solution. Phys. Rev. Lett. 106, 140601-1–140601-4 (2011)ADSCrossRef Nobre, F.D., Rego-Monteiro, M.A., Tsallis, C.: Nonlinear relativistic and quantum equations with a common type of solution. Phys. Rev. Lett. 106, 140601-1–140601-4 (2011)ADSCrossRef
Zurück zum Zitat Solaimani, M., Aleomraninejad, S.M.A., Lavaei, L.: Optical rectification in quantum wells within different confinement and nonlinearity regimes. Superlattices Microstruct. 111, 556–567 (2017)ADSCrossRef Solaimani, M., Aleomraninejad, S.M.A., Lavaei, L.: Optical rectification in quantum wells within different confinement and nonlinearity regimes. Superlattices Microstruct. 111, 556–567 (2017)ADSCrossRef
Zurück zum Zitat Solaimani, M., Farnam, B., Ghalandari, M., SeyedShirazi, S.Z.: Wave localization in two dimensional parabolic periodic refractive index profiles: a 4th order Runge–Kutta study. Opt. Quant. Electron. 50, 114 (2018)CrossRef Solaimani, M., Farnam, B., Ghalandari, M., SeyedShirazi, S.Z.: Wave localization in two dimensional parabolic periodic refractive index profiles: a 4th order Runge–Kutta study. Opt. Quant. Electron. 50, 114 (2018)CrossRef
Zurück zum Zitat Su, Q., Smetanko, B.A., Grobe, R.: Relativistic suppression of wave packet spreading. Opt. Exp. 2, 277–281 (1998)ADSCrossRef Su, Q., Smetanko, B.A., Grobe, R.: Relativistic suppression of wave packet spreading. Opt. Exp. 2, 277–281 (1998)ADSCrossRef
Zurück zum Zitat Vatan, M., Farnam, B., Solaimani, M., Aleomraninejad, S.M.A.: Transport properties of a traveling wave packet through rectangular quantum wells and barriers. Optik 136, 281–288 (2017)ADSCrossRef Vatan, M., Farnam, B., Solaimani, M., Aleomraninejad, S.M.A.: Transport properties of a traveling wave packet through rectangular quantum wells and barriers. Optik 136, 281–288 (2017)ADSCrossRef
Zurück zum Zitat Vurgaftman, I., Meyer, J.R.: Band parameters for nitrogen-containing semiconductors. J. Appl. Phys. 94, 3675–3696 (2003)ADSCrossRef Vurgaftman, I., Meyer, J.R.: Band parameters for nitrogen-containing semiconductors. J. Appl. Phys. 94, 3675–3696 (2003)ADSCrossRef
Zurück zum Zitat Wood, C., Jena, D.: Polarization Effects in Semiconductors From Ab Initio Theory to Device Applications, p. 119. Springer, New York (2008)CrossRef Wood, C., Jena, D.: Polarization Effects in Semiconductors From Ab Initio Theory to Device Applications, p. 119. Springer, New York (2008)CrossRef
Metadaten
Titel
A meshless method of line radial base function study of Gaussian wave packet broadening in few semiconducting mediums: electron–electron interaction effects
verfasst von
M. Solaimani
Mehrzad Ghorbani
Publikationsdatum
01.11.2018
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 11/2018
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-018-1653-3

Weitere Artikel der Ausgabe 11/2018

Optical and Quantum Electronics 11/2018 Zur Ausgabe

Neuer Inhalt