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研究生: 顏瑋廷
論文名稱: 對於垂直堆疊的量子點陣列之二階差分方程式的能階數值模擬
Numerical simulation of energy states for vertically aligned quantum dots array by second order finite di erence scheme
指導教授: 黃聰明
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2005
畢業學年度: 94
語文別: 英文
論文頁數: 23
中文關鍵詞: 有限差分法薛丁格方程式能階十字特徵曲線反十字特徵曲線量子點陣列
英文關鍵詞: Finite di erence method, The Schr¨odinger equation, Energy states, crossing eigencurve, anti-crossing eigencurve, quantum dot array
論文種類: 學術論文
相關次數: 點閱:143下載:3
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  • 我們提出簡單的數值方法去研究由不同大小量子點所垂直堆疊的三維量子點序列的電子性質。我們利用有限差分法去離散所需的薛丁格方程式,而且證明了此方程式是二階快速收斂的。在這一篇論文中,我們提供數值方法去計算各種量子點序列結構的能階以及研究對於兩個碟狀同軸堆疊的不同大小量子點間的反十字與十字交叉特徵曲線之存在。

    We present a simple numerical method to investigate the electronic
    properties of a three-dimensional quantum dot array model formed
    by di
    erent size vertically aligned quantum dots. The corresponding
    Schr¨odin-ger equation is discretized using the finite di
    erence method
    with a constant electron mass and confinement potential. The scheme
    is 2nd order accurate and converges extremely fast. In this paper, we
    propose numerical schemes to compute the energy levels of various QDA
    structures and research the existence of the anti-crossing and crossing
    eigencurve for QDA formed by two disk-shaped co-axial QDs with different
    size.

    1. Introduction.............................1 2. Vertically aligned quantum dot array.....2 3. Finite di erence scheme..................4 4. Numerical results........................9 5. Conclusion...............................14 References..................................19

    [1] E.A. de Andrada e Silva, G.C. La Rocca and F. Bassani, Optical transition
    energies for lead-salt semiconductor quantum wells, Phys. Rev. B 60(12),
    8859, (1999).
    [2] D.G. Austinga, Y. Tokura and S. Tarucha, Addition energy spectrum of
    a quantum dot disk up to the third shell, Physica E 11, 63-67, (2001).
    [3] M. Bayer, P. Hawrylak, K. Hinzer, S. Fafard, M. Korkusinski,
    Z.R. Wasilewski, O. Stern, and A. Forchel, Coupling and entangling
    of quantum dot molecules, Science , 451-453, (2001).
    [4] M. Bayer, O. Schilling, A. Forchel, T.L. Reinecke, P.A. Knipp,
    Ph. Pagnod-Rossiaux and L. Goldstein, Splitting of electronic levels with
    positive and negative angular momenta in In0.53Ga0.47As/InP quantum
    dots by a magnetic field, Phys. Rev. B, 15810-15814,(1996).
    [5] R.H. Blick, D. Pfannkuche, R.J. Haug, K.V. Klitzing and K. Eberl, Formation
    of a coherent mode in a double quantum dot, Phys. Rev. Lett. 80,
    4032-4035, (1998).
    [6] G. Burkard, G. Seelig and D. Loss, Spin interactions and switching in vertically
    tunnel-coupled quantum dots, Phys. Rev. B 62, 2581-2592, (2000).
    [7] S. Fafard, Z.R. Wasilewski, C.Ni. Allen, K. Hinzer, J.P.McCa
    rey and
    Y. Feng, Lasing in quantum-dot ensembles with sharp adjustable electronic
    shells, Applied Physics Letters 75, 986-988, (1999).
    [8] L.R.C. Fonseca, J.L. Jimenez and J.P. Leburton, Electronic coupling in
    InAs/GaAs self-assembled stacked double-quantum-dot systems, Phys.
    Rev. B 58, 9955-9960, (1998).
    20
    [9] F. Gelbard and K.J. Malloy, Modeling quantum structures with the
    boundary element method, Journal of Computational Physics 172, 19-39,
    (2001).
    [10] H. Heidemeyer, S. Kiravittaya, C. Muller, N.Y. Jin-Phillipp and
    O.G Schmidt, Closely stacked InAs/GaAs quantum dots grown at low
    growth rate, Applied Physics Letters 80, 1544-1546, (2002).
    [11] T.-M. Hwang,W.-W. Lin, J.-L. Liu andW.Wang, Fixed point methods for
    a semiconductor quantum dot model, Mathl. Comput. Modelling 40(5/6),
    519-533, (2004).
    [12] T.-M. Hwang and W.Wang, Analyxing and visualizing a discretized semilinear
    elliptic problem with Neumann boundary conditions, Numer. Meth-
    ods Partial Di
    er.Equ. 18(3), 261-279, (2002).
    [13] T.-M. Hwang, W.-W. Lin, W.-C. Wang and W.Wang, Numerical simulation
    of three dimensional pyramid quantum dot, Journal of Computational
    Physics 196, 208-232, (2004)
    [14] T.-M. Hwang and W.Wang, Energy states of vertically aligned quantum
    dot array with nonparabolic e
    ective mass, Computers and Mathematics
    with Applications 49, 39-51, (2005)
    [15] T.-M. Hwang, W.Wang andW.-H.Wang, Numerical methods and findings
    for di
    erent size vertically aligned quantum dot array, accepted Computer
    Physics Communications
    [16] H.T. Johnson, V. Nguyen and A.F. Bower, Simulated self-assembly and
    optoelectronic properties of InAs/GaAs quantum dot arrays,Journal of
    Applied Physics 92, 4653-4663, (2002).
    [17] M. Korkusiski and P. Hawrylak, Electronic structure of vertically stacked
    self-assembled quantum disks, Phys. Rev. B 63, 195311, (2001).
    21
    [18] M.-C. Lai, A note on finite di
    erence discretizations for Poisson equation
    on a disk, Numer. Methods Partial Di
    er.Equ. 17(3), 199-203, (2001).
    [19] S. Le Go
    and B. St´eb´e, Influence of longitudinal and lateral confinements
    on excitons in cylindrical quantum dots of semiconductors, Phys. Rev. B
    47, 1383-1391, (1993).
    [20] R. Leon, S. Fafard, P.G. Piva, S. Ruvimov and Z. Liliental-Weber, Tunable
    intersublevel transitions in self-forming semiconductor quantum dots,
    Phys. Rev. B 58, R4262-R4265, (1998).
    [21] Y.Li,O. Voskoboynikov, C.P. Lee and S.M. Sze, Calculation of induced
    electron states in three-dimensional semiconductor artificial molecules,
    Computer Physics Communications 147, 209-213, (2002).
    [22] R.V.N. Melnik and K.N. Zotsenko, Computations of coupled electronic
    states in quantum dot/wetting layer cylindrical structures, In Com-
    putational Science-ICCS 2003, (Edited by P. Sloot, D. Abramson, A.
    Bogdanov, J. Dongarra, A. Zomayz, and Y. Gorbachev), pp. 343-349,
    Springer-Verlag, (2003).
    [23] M.V. Maximov, Yu.M. Shernyakov, A.F. Tsatsul’nikov, A.V. Sakharov,
    V.M. Ustinov, A.Yu. Egorov, A.E. Zhukov, A.R. Kovsh, P.S. Kop’ev,
    L.V. Asryan, Zh.I. Alferov, N.N. Ledentsov, D. Bimberg, A.O. Kosogov
    and P. Werner, High-power continuous-wave operation of a In-
    GaAs/AlGaAs quantum dot laser, Journal of Applied Physics 83, 5561-
    5563, (1998).
    [24] M.A. Migliorato, L.R. Wilson, D.J. Mowbray, M.S. Skolnick, M. Al-
    Khafaji , A.G. Cullis and M. Hopkinson, Structural and optical studies
    of vertically aligned InAs/GaAs self-assembled quantum dots, Journal of
    Applied Physics 90, 6374-6378, (2001).
    22
    [25] K. Ono, D.G. Austinga, Y. Tokura and S. Tarucha, Angular momentum
    selectivity in tunneling between two quantum dots, Physica B 314, 450-
    454, (2002).
    [26] J.J. Palacios and P. Hawrylak, Correlated few-electron states in vertical
    double-quantum-dot systems, Phys. Rev. B 51, 1769-1777, (1995).
    [27] C. Pryor, Quantum wires formed from coupled InAs/GaAs strained quantum
    dots, Phys. Rev. Lett. 80, 3579-3581, (1998)
    [28] Th. Schapers, G. Engels, J. Lange, Th. Klocke, M. Hollfelder and H. Luth,
    E
    ect of the heterointerface on the spin splitting in modulation doped
    In(x)Ga(1−x) As/InP quantum wells for b → 0 , J. Appl. Physi. 83(8),
    4324, (1998).
    [29] G. Schedelbeck, W. Wegscheider, M. Bichler and G. Abstreiter, Coupled
    quantum dots fabricated by cleaved edge overgrowth: From artificial
    atoms to molecules, Science 278, 1792-1795, (1997).
    [30] G. Sek, K. Ryczko, J. Misiewicz, M. Bayer, F. Klopf, J.P. Reithmaier
    and A. Forchel, Photoreflectance spectroscopy of vertically coupled In-
    GaAs/GaAs double quantum dots, Solid State Communications 117(7),
    401-406, (2001).
    [31] W. Sheng and J.-P. Leburton, Anomalous quantum-confined stark e
    ects
    in stacked InAs/GaAs self-assembled quantum dots, Phys. Rev. Lett. 88,
    167401, (2002)
    [32] S. Taddei, M. Colocci, A. Vinattieri, F. Bogani, S. Franchi, P. Frigeri,
    L. Lazzarini and G. Salviati, Vertical coupling and transition energies in
    multilayer InAs/GaAs quantum-dot structures, Phys. Rev. B 62, 10220-
    10225,(2000).
    23
    [33] O. Voskoboynikov, C.P. Lee and O. Tretyak, Spin-orbit splitting in semiconductor
    quantum dots with a parabolic cofinement potential, Phys. Rev.
    B 63, 165306, (2001).
    [34] O. Voskoboynikov, S.S. Liu and C.P. Lee, Spin-dependent electronic tunnelling
    at zero magnetic field, Phys. Rev. B 58(23), 15397-15400, (December
    1998).
    [35] W.Wang, T.-M. Hwang, J.-C. Jang, A second-order finite volume scheme
    for three dimensional truncated pyramidal quantum dot, accepted Com-
    puter Physics Communications
    [36] Z.R. Wasilewski, S. Fafard and J.P. McCa
    rey, Size and shape engineering
    of vertically stacked self-assembled quantum dots, Journal of Crystal
    Growth 201-202, 1131-1135, (1999).

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