跳到主要內容

臺灣博碩士論文加值系統

(3.236.110.106) 您好!臺灣時間:2021/07/24 06:41
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:劉懿嫻
研究生(外文):Liu Yi-Hsien
論文名稱:不規則形狀之三維軸對稱量子點的能階分布研究
論文名稱(外文):On the Spectrum of Axisymmetric 3D Quantum dot with irregular shape
指導教授:林文偉林文偉引用關係王偉成
指導教授(外文):Wen-Wei LinWei-Cheng Wang
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
畢業學年度:92
語文別:英文
論文頁數:30
中文關鍵詞:座標轉換系統解特徵值特徵向量量子能階
外文關鍵詞:curvilinear coordinate systeminterface problemquantum dotwave functionenergy statesJacobi-Davidson method
相關次數:
  • 被引用被引用:0
  • 點閱點閱:79
  • 評分評分:
  • 下載下載:8
  • 收藏至我的研究室書目清單書目收藏:0
此篇論文提供了一個有效率的方法去算量子的能階分布.我們用了一種和接觸面相似的網格作為其中之一的座標系統,再用此網格轉換成另一種座標系統,兩種座標系統在用weight function融合後去作離散. 而離散之後所形成的矩陣會為對稱正定矩陣.最後再使用Jacobi-Davidson 的方法算其特徵值以及特徵向量.且所算出的特徵值會有二階精度.
Abstract
We present a simple and efficient numerical method for calculating bound state energies and their corresponding wave function of a axisymmetric 3D QD model. The Schrodinger equation of the model is discretized by using a body fitting curvilinear coordinate system. The result matrix is symmetric and positive definite. The resulting matrix eigenvalue problem is then solved by using a Jacobi-Davidson based method. The scheme is 2nd order accurate and converges extremely fast.
目 錄
1. Introduction ...................................................1
2. The mathematical model ..............................2
3. The discretization method ............................3
4. The eigensolvers ..........................................13
5. Numerical results ........................................15
6. Conclusion ...................................................17
References ...........................................................18
Graphs .................................................................20
L. Jack, P. Hawrylak, A W\'{o}js, Quantum Dots,
Springer, Berlin, 1998.
R. Heitz, M. Veit, N. N. Ledentsov, A. Hoffmann,
D. Bimberg, V. M. Ustinov, P. S. Kop\'{e}v, Z. I. Alferov, Energy
relaxtion by multiphonon processes in InAs/GaAs quantum dots,
Phys. Rev. B56 (1997) 10435-10445.
G. Medeiros-Ribeiro, J. M. Garcia, P.
M. Petroff, Charging dynamics of InAs self-assembled quantum dots,
Phys. Rev. B 56 (1997) 3609-3612.
S. Mainmon, E. Finkman, G. Bahir, S. E. Schacham,
J. M. Petroff, Intersublevel transitions in InAs/GaAs quantum dots
in frared photodetectors, Appl. Phys. Lett. 73 (1998) 2003-2005.
L. Harris D. J. Mowbray, M. S. Skolnick, M.
Hopkinson, G. Hill, Emission spectra and mode structure of
InAs/GaAs self-origanized quantum dot lasers, Appl. Phys. Lett.
73 (1998) 969-971.
G. Iannaccone, A. Trellakis, U. Ravaioli,
Simulation of a quantum-dot flash memory, J. Appl. Physi. 84 (9)
(1998) 5032-5036.
G. Burkard, D. Loss, D. P. DiVincenzo, Couple
quantum gates, Rhvs. Rev. B 59 (1999) 2070-2078.
J. W. Gray, D. Childs, S. Malik, P. Siverns, C.
Roberts, P. N. Stavrinou, M. Whitehead, R. Murray, G. Parry,
Quantum dot resonant cavitylight emitting diode operating near
1300nm. Electron. Lett. 35 (1999) 242.
B.~H.~Nie, K.~A.~Anshelm, J.~C.~Campbell, and
B.~G.~Streetman. Multi-stacked quantum dot resonant-cavity
photodetector operating at 1.6 /spl mu/m. {\it Electron. Lett.},
34:694-695, 1998.
D. J.~BenDaniel and C. B.~Duke. Space-charge effects
on electron tunnelling. {\it Phys. Rev.}, 152(683), 1996.
Y.~Hirayama, J.~H.~Smet, L.-H.~Peng, C.~G. Fonstad,
and E.~P.~Ippen. Feasibility of 1.55 $\mu$m in tersubband photonic
devices using InGaAs/AlAs pseudomorphic quantum well structures.
Japanese J. Applied Phys. Part 1, 33:890-895, 1994.
O.~Voskoboynikov, S.~S.~Liu, and C.~P.~Lee.
Spin-dependent electronic tunnelling at zero magnetic field. Physical Review B, 58(23):15397-15400, December 1998.
J. Bramble, J. King, A finite element method for
interface problems in domains with smooth boundaries and
interfaces. Advances in Comput. Math.,6 (1996) 109-138.
Z. Chen, J. Zou Finite element methods and their
convergence for elliptic anda parabolic interface problems. Numer.
Math., 79, (1998), 175-202.
Wei-Cheng Wang. A Jump Condition Capturing Scheme for Ellipitic Interface Problems.
SIAM J. Sci. Comp. (2003)
Z.~Bai, G.~Sleijpen, and H.~van der Vorst.
Nonlinear eigenvalue problems. In Z.~Bai, J.~Demmel, J.~Dongarra,
A.~Ruhe and H.~van der Vorst, editors, Templates for the Solution
of Algebraic Eigenvalue Problems: A Practical Guide, chapter 9.
SIAM, Philadelphia, 2000.
Tsong-Ming Huang, Wen-Wei Lin, Wei-Cheng Wang and Wei-Chung
Wang. Numerical Simulation of Three Dimensional Pyramid Quantum
Dot. J. Comp. Phys., Vol 196, 208-232 (2004).
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top