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2008 | 6 | 1 | 97-104
Tytuł artykułu

Exact analytical solutions for shallow impurity states in symmetrical paraboloidal and hemiparaboloidal quantum dots

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The problem of a shallow donor impurity located at the centre of a symmetrical paraboloidal quantum dot (SPQD) is solved exactly. The Schrödinger equation is separated in the paraboloidal coordinate system. Three different cases are discussed for the radial-like equations. For a bound donor, the energy is negative and the solutions are described by Whittaker functions. For a non-bound donor, the energy is positive and the solutions become coulomb wave functions. In the last case, the energy is equal to zero and the solutions reduce to Bessel functions. Using the boundary conditions at the dot surfaces, the variations of the donor kinetic and potential energies versus the size of the dot are obtained. The problem of a shallow donor impurity in a Hemiparaboloidal Quantum dot (HPQD) is also studied. It is shown that the wave functions of a HPQD are specific linear combinations of those of a SPQD.
Wydawca

Czasopismo
Rocznik
Tom
6
Numer
1
Strony
97-104
Opis fizyczny
Daty
wydano
2008-03-01
online
2008-03-26
Twórcy
autor
  • Laboratoire d’Electronique et Optique des Nanostructures de Semiconducteurs, Faculté des Sciences, Département de Physique, B. P. 20, El Jadida, Morocco, eassaid@yahoo.fr
  • Département de Mathématiques, Centre Pédagogique Régional, El Jadida, Morocco
autor
  • Ecole Normale Supérieure d’Enseignement Technique, Mohammedia, Morocco
  • Institut de Physique et d’Electronique de Metz, 1 Boulevard Arago, 57078, Metz, France
Bibliografia
  • [1] M. Grundman, D. Bimberg, N.N. Ledentsov, Quantum Dot Heterostructures (Wiley, Chichester, 1998)
  • [2] M. Sugawara, Self-Assembled InGaAs/GaAs Quantum Dots, Semiconductors and Semimetals 60 (Academic, Toronto, 1999)
  • [3] Zh. I. Alferov, Quantum wires and dots show the way forward, III-Vs Rev. 11, 47 (1998)
  • [4] P. Bhattacharya, et al., IEEE Trans. Elec. Dev. 46, 871 (1999) http://dx.doi.org/10.1109/16.760392[Crossref]
  • [5] H. Ishikawa, et al., J. Vac. Sci. Technol. A 16, 794 (1998) http://dx.doi.org/10.1116/1.581060[Crossref]
  • [6] L. Harris, D.J. Mawbray, M.S. Skolnic, M. Hoplcinson, G. Hill, Appl. Phys. Lett. 73, 969 (1998) http://dx.doi.org/10.1063/1.122055[Crossref]
  • [7] H. Temkin, G.J. Dolan, M.B. Panish, S.N.G. Chu, Appl. Phys. Lett. 50, 413 (1987) http://dx.doi.org/10.1063/1.98159[Crossref]
  • [8] K. Kash, A. Scherer, J.M. Worlock, H.G. Graighead, M.C. Tamargo, Appl. Phys. Lett. 49, 1043 (1986) http://dx.doi.org/10.1063/1.97466[Crossref]
  • [9] T. Fukui, S. Ando, Y. Tokuhara, T. Toriyama, Appl. Phys. Lett. 58, 2018 (1991) http://dx.doi.org/10.1063/1.105026[Crossref]
  • [10] K. Murakoshi, et al., J. Chem. Soc., Faraday Trans. 4, 579 (1998) http://dx.doi.org/10.1039/a707192b[Crossref]
  • [11] J. Hambrock, A. Birkner, R.A. Fisher, J. Mater. Chem. 11, 3197 (2001) http://dx.doi.org/10.1039/b104231a[Crossref]
  • [12] Al.L. Efros, A.L. Efros, Sov. Phys. Semicond. 16, 772 (1982)
  • [13] J.Y. Marzin, G. Bastard, Solid State Commun. 92, 437 (1994) http://dx.doi.org/10.1016/0038-1098(94)90524-X[Crossref]
  • [14] L.C. Lew Yan Voon, M. Willatzen, Semicond. Sci. Technol. 10, 416 (1995) http://dx.doi.org/10.1088/0268-1242/10/4/006[Crossref]
  • [15] S. Le Goff, B. Stébé, Phys. Rev. B 47, 1383 (1993) http://dx.doi.org/10.1103/PhysRevB.47.1383[Crossref]
  • [16] A. Wojs, P. Hawrylak, S. Fafard, L. Jacak, Phys. Rev. B 54, 5604 (1996) http://dx.doi.org/10.1103/PhysRevB.54.5604[Crossref]
  • [17] L.C. Lew Yan Voon, M. Willatzen, Mathematics and computers in simulation 65, 337 (2004) http://dx.doi.org/10.1016/j.matcom.2004.01.006[Crossref]
  • [18] M. van den Broek, F.M. Peeters, Physica E 11, 345 (2001) http://dx.doi.org/10.1016/S1386-9477(01)00169-2[Crossref]
  • [19] G. Cantele, D. Ninno, G. Iadonisi, J. Phys.-Condens. Mat. 12, 9019 (2000) http://dx.doi.org/10.1088/0953-8984/12/42/308[Crossref]
  • [20] G. Cantele, D. Ninno, G. Iadonisi, Nano Lett. 1, 121 (2001) http://dx.doi.org/10.1021/nl0055310[Crossref]
  • [21] J. Even, S. Loualiche, J. Phys. A-Math. 36, 11677 (2003)
  • [22] C.C. Yang, Y.S. Huang, Phys. Lett. A 278, 88 (2000) http://dx.doi.org/10.1016/S0375-9601(00)00750-7[Crossref]
  • [23] L. Landau, E. Lifchitz, Mécanique quantique (Moscou, Mir, 1966)
  • [24] M. Abramovitz, I.A. Stegun, Handbook of mathematical functions (Dover, New York, 1970)
  • [25] M. Willatzen, L.C. Lew Yan Voon, Physica E 16 (2003)
  • [26] Y. Kayanuma, Phys. Rev. B 62, 15334 (2000)
  • [27] J. Even, S. Loualiche, J. Phys. A-Math. Gen. 37, L289 (2004) http://dx.doi.org/10.1088/0305-4470/37/27/L01[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-008-0070-9
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