臺灣博碩士論文加值系統

第一部份

本論文以Current Spin Density Functional Theory為基礎，並考慮電子之非線性近似有效質量效應、Ben Daniel-Duke邊界條件、及有限hard-wall confinement potential，對兩種砷化銦/砷化鎵量子點內做三維多電子狀態數值模擬分析。

第一種量子點分子為三個垂直堆疊之InAs量子點（triple-dot 型式），我們研究其中六個電子之電子組態，數值結果顯示理論上可以將分子內此三對電子以外部磁場及電場提升其能量方式而將個別電子對分別放置於不同的InAs量子點內。

第二種量子點分子為charge-tunable型式，其電子光譜為米勒教授之研究團隊(Miller et al. [Phys. Rev. B56 (1997) 6764])以Capacitance-Voltage所實驗測量出。本分析研究模型為費力基教授之研究團隊(Filikhin et al. [Solid State Comm. 140 (2006) 483])所提出單電子模型之延伸。其數值結果對Capacitance-Voltage之實驗數據提供了很好地詮釋。本數值結果亦說明在不考慮與考慮有效質量效應的情形下做比較，電子之總能量差異性和exchange-correlation能量之變化情形。本研究更發現在磁場越高的狀態下有效質量效應會越顯著。對多電子計算模型而言，有效質量效應亦會越顯著。



第二部份

反應式射出成形加工法涉及用一種或兩種以上高分子流體以相當高的射速射入模具內，如此高的慣性效應通常會導致模內產生氣袋或流體流速分佈不均。所以對反應式射出成形加工法中如何設計模具入口幾何形狀以使射入流體之流速均勻已成為重要的研究問題之ㄧ。本文中發展一套既新又簡單的方法設計反應式射出成形模具入口最佳幾何形狀，其方式為加入幾個規則分佈的小凸島於魚尾模具之入口處以使射入模內流體之流速分佈更均勻。由於這些小凸島的放置位置與其尺寸大小會影響到流況，所以它們便成為最佳化設計之重要考慮因子。本文是以田口實驗設計配合計算模擬分析得到這些因子以達到最佳幾何配置目的，不同尺寸之小凸島對於流動均勻性的影響亦可以模擬分析之結果做統計分析評估。至於實際模內流體流動情形我們可以高速CCD加以記錄。本文實驗結果與Fluent軟體計算結果亦相當吻合。所以本文所提供之設計方法對於欲設計較佳之它種反應式射出成形模之工程師們有相當的幫助。

PART I

Based on the current spin density functional theory with non-parabolic effective mass approximation, Ben Daniel-Duke boundary conditions, and finite hard-wall confinement potential, a three-dimensional model is presented to study the multi-electron system in two different types of InAs/GaAs quantum dots (QDs).
For the first type, we study electronic configurations in a vertically stacked quantum triple-dot molecule (QDM) holding six electrons. We demonstrate theoretically a possibility to drive dynamically coupled electronic states, i.e., to relocate electrons from one dot to another with adjustable energy levels by means of both external magnetic and electric fields.
The second type is a charge-tunable QD for which the electron spectra have been obtained from the capacitance-voltage (CV) measurements by Miller et al. [Phys. Rev. B 56 (1997) 6764]. Our model is an extension of the single-electron model proposed by Filikhin et al. [Solid State Comm. 140 (2006) 483]. Our results can quantitatively well interpret the experimental CV data. It is shown that the energy differences between the parabolic and nonparabolic approximations are comparable with the exchange-correlation energies. Moreover, the nonparabolic effect is shown to be increasingly more significant than that of parabolic case in higher magnetic fields. It is also more pronounced for larger number of electrons.


PART II

Reaction injection molding involves the injection of two or more kinds of liquid polymers into a mold at relative high speed. Such high inertia effect may result in air pocket inside the mold or non-uniform velocity distribution. How to design the mold entry geometry to provide uniform velocity distribution becomes one of the major topics in reaction injection molding process. Thus a new and simple method was developed in this work to optimize the reaction mold entry design. Several regulation islands were located in a fish tail entrance to help distribute the flow more even. Dimensions and locations of the islands will affect the flow uniformity and become the factors to be optimized. Taguchi’s design of experiments coupled with computer flow simulation was used to achieve die geometry optimization. Effects of different dimensions of the islands on the flow uniformity can also be evaluated through statistical analyses in the flow simulation. Flow visualization technique was done by capturing flow images with high speed CCD. The experimental results showed very good agreements with the Fluent simulation results. The design methodology proposed here can help the molders in designing different reaction injection mold entries for better uniformity and performance.

Abstract ( Chinese ) I
Abstract ( English ) III
Acknowledgments VI
Contents VII
Tables IX
Figures X
Notations XIII

PARTＩ　Dynamic Control of Few-electron Molecular States in Quantum Dot Molecules by Magnetic and Electric Fields 1

Chapter 1 Introduction 2

Chapter 2 Theoretical model description 4

2.1 Introduction -----------------------------------------------------------4
2.2 Theoretical model ----------------------------------------------------6
2.3 Discretization of the Kohn-Sham equation -----------------------13 2.4 Discretization of the interface condition for the quantum dot--16
2.5 Discretization of the Poisson equation ----------------------------20

Chapter 3 A self-consistent method for the current spin density functional theory 22

3.1 Self-consistent method ----------------------------------------------22

Chapter 4 Cubic eigenvalue problem 24

4.1 Introduction -------------------------------------------------------- 24
4.2 Cubic Jacobi-Davison method (CJD method)------------------- 25
4.3 Storage scheme------------------------------------------------------ 27

Chapter 5 Numerical results 29

5.1 Results of three vertically aligned InAs/GaAs quantum dots--30
5.2 Results of charge-tunable InAs/GaAs quantum dot ------------34

Chapter 6 Conclusions 42

PART II A New Design Method to Improve Flow Uniformity in a Reaction Injection Mold Entry 46

Chapter 7 Introduction 47

Chapter 8 Flow simulation 50

Chapter 9 Taguchi’s design of experiments 55

9.1 Introduction ----------------------------------------------------------- 55
9.2 Design of experiments ---------------------------------------------- 55
9.3 Selecting the value of dimension character ---------------------- 56

Chapter 10 Results and Discussions 58

10.1 Response tables and figures ------------------------ 58
10.2 ANOVA analysis ------------------------------------- 59
10.3 Optimal Solution ------------------------------------ 59
10.4 Experiment Verification ---------------------------- 59

Chapter 11 Conclusions 61

Reference 78

Appendix 85

1. P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas, Phys. Rev. 136 (1964) B864.
2. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140 (1965) A1133.
3. D. P. DiVincenzo, Quantum computation, Science 270 (1995) 255.
4. B.~E. Kane, A silicon-based nuclear spin quantum computer, Nature 393 (1998) 133.
5. A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small , Quantum information processing using quantum dot spins and cavity QED, Phys. Rev. Lett. 83 (1999) 4204.
6. E. Biolatti, R. C. Iotti, P. Zanardi, and F. Rossi, Quantum information processing with semiconductor macroatoms, Phys. Rev. Lett. 85 (2000) 5647.
7. P. M. Petroff, A. Lorke, and A. Imamoglu, Epitaxially self-assembled quantum dots, Physics Today 54 (2001) 46.
8. M. Bayer, P. Hawrylak, K. Hinzer, S. Fafard, M. Korkusinski, Z. R. Wasilewski, O. Stern, and A. Forchel, Coupling and entangling of quantum states in quantum dot molecules, Science 291 (2001) 451.
9. B. W. Lovett, J. H. Reina, A. Nazir, and G. A. D. Briggs, Optical schemes for quantum computation in quantum dot molecules, Phys. Rev. B 68 (2003) 205319.
10. J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen and L. P. Kouwenhoven, Single-shot read-out of an individual electron spin in a quantum dot, Nature 430 (2004) 431.
11. G. Ortner, I. Yugova, G. Baldassarri Höger von Högersthal, A. Larionov, H. Kurtze, D. R. Yakovlev, M. Bayer, S. Fafard, Z. Wasilewski, and P. Hawrylak, Y. B. Lyanda-Geller,T. L. Reinecke, A. Babinski, M. Potemski, V. B. Timofeev and A. Forchel, Fine structure in the excitonic emission of InAs/GaAs quantum dot molecules, Phys. Rev. B 71 (2005) 125335.
12. H.-A. Engel and D. Loss, Fermionic Bell-state analyzer for spin qubits , Science 309 (2005) 586.
13. W. Wang, T.-M. Hwang, W.-W. Lin, and J.-L. Liu, Numerical methods for semiconductor heterostructures with band nonparabolicity, J. Comp. Phys. 189 (2003) 579-606.
14. T.-M. Hwang, W.-W. Lin, J.-L. Liu, W. Wang, Jacobi-Davidson methods for cubic eigenvalue problems, Num. Lin. Alg. Appl. 12 (2005) 605-624.
15 O. Voskobyonikov, J. L. Liu, and J. H. Chen, Magnetically driven coupling of electronic states in quantum dot molecules, phys. stat.sol. (c) 3 (2006) 3656.
16 M. Reimann and M. Manninen, Electronic structure of quantum dots, Rev. Mod. Phys. 74 (2002) 1283.
17 S. P. Kouwenhoven, D. R. Austing, S. Tarucha, Few-electron quantum. Dots, Rep. Prog. Phys. 64 (2001) 701.
18 R. C. Ashoori, H. L. Stormer, J. S. Weiner, L. N. Pfeiffer, S. J. Pearton, K. W. Baldwin, and K W. West , Single-electron capacitance spectroscopy of discrete quantum levels, Phys. Rev. Lett. 68, (1992) 3088.
19 H. Drexler, D. Leonard, W. Hansen, J. P. Kotthaus, and P. M. Petroff, Spectroscopy of Quantum Levels in Charge-Tunable InGaAs Quantum Dots, Phys. Rev. Lett. 73, (1994) 2252.
20 T. Schmidt, M. Tewordt, R. H. Blick, R. J. Haug, D. Pfannkuche, K. v. Klitzing, A. Foerster, and H. Lueth, Quantum-dot ground states in a magnetic field studied by single-electron tunneling spectroscopy on double-barrier heterostructures, Phys. Rev. B 51, (1995) 5570.
21 S. Tarucha, D. G. Austing, T. Honda, R. J. van der Hage, and L. P. Kouwenhoven, Shell Filling and Spin Effects in a Few Electron Quantum Dot, Phys. Rev. Lett. 77, (1996) 3613.
22 B. T. Miller, W. Hansen, S. Manus, R. J. Luyken, A. Lorke, J. P. Kotthaus, S. Huant, G. Medeiros-Ribeiro, and P. M. Petroff, Few-electron ground states of charge-tunable self-assembled quantum dots, Phys. Rev. B 56, (1997) 6764.
23 A. Lorke, R. J. Luyken, A. O. Govorov, J. P. Kotthaus, J. M. Garcia, and P. M. Petroff, Spectroscopy of Nanoscopic Semiconductor Rings, Phys. Rev. Lett. 84, (2000) 2223.
24 A. Emperador, M. Pi, M. Barranco, and A. Lorke, Far-infrared spectroscopy of nanoscopic InAs rings, Phys. Rev. B 62, (2000) 4573.
25 G. Pryor, Eight-band calculations of strained InAs/GaAs quantum dots compared with one-, four-, and six-band approximations, Phys. Rev. B 57, (1998) 7190.
26 J. A. Barker and E. P. O''Reilly, Theoretical analysis of electron-hole alignment in InAs-GaAs quantum dots, Phys. Rev. B 61, (2000) 13840.
27 Y. Li, J.-L. Liu, O. Voskoboynikov, C. P. Lee, and S. M. Sze, Electron energy level calculations for cylindrical narrow gap semiconductor quantum dot, Comput. Phys. Commun., 140 (2001) 399.
28 S. S. Li and J. B. Xia, Electronic states of InAs/GaAs quantum ring, J. Appl. Phys. 89, (2001) 3434.

29 O. Voskoboynikov, Y. Li, H. M. Lu, C. F. Shih, and C. P. Lee, Energy states and magnetization in nanoscale quantum rings, Phys. Rev. B 66, (2002) 155306.
30 J. A. Barker, R. J. Warburton, and E. P. O''Reilly, Electron and hole wave functions in self-assembled quantum rings, Phys. Rev. B 69, (2004) 035327.
31 J. I. Climente, J. Planelles, and F. Rajadell, Energy structure and far-infrared spectroscopy of two electrons in a self-assembled quantum ring, J. Phys.: Condens. Matter 17, (2005) 1573.
32 T. Chakraborty and P. Pietiläinen, Optical Signatures of Spin-Orbit Interaction Effects in a Parabolic Quantum Dot, Phys. Rev. Lett. 95, (2005) 136603; Phys. Rev. B 71, (2005) 113305.
33 I. Filikhin, E. Deyneka, and B. Vlahovic, Modell. , Simul., Energy dependent effective mass model of InAs/GaAs quantum ring, Mater. Sci. Eng. 12, (2004) 1121.
34 I. Filikhin, E. Deyneka, B. Vlahovic, Single-electron levels of InAs/GaAs quantum dot: Comparison with capacitance spectroscopy, Physica E 31 (2006) 99.
35 I. Filikhin, E. Deyneka, B. Vlahovic, Non-parabolic model for InAs/GaAs quantum dot capacitance spectroscopy, Solid State Comm. 140 (2006) 483.
36 I. Filikhin, V. M. Suslov, B. Vlahovic, Modeling of InAs/GaAs quantum ring capacitance spectroscopy in the nonparabolic approximation, Phys. Rev. B 73, (2006) 205332.
37 O. Voskoboynikov, C. M. J. Wijers, J.-L. Liu, and C. P. Lee, The magneto-optical response of layers of semiconductor quantum dots and nano-rings, Phys. Rev. B, 71 (2005) 245332.
38 C. M. J. Wijers, J.-H. Chu, J.-L. Liu, and O. Voskoboynikov, Optical response of layers of embedded semiconductor quantum dots, Phys. Rev. B 74 (2006) 035323.
39 J.-L. Liu, J.-H. Chen, and O. Voskoboynikov, A model for semiconductor quantum dot molecule based on the current spin density functional theory, Comput. Phys. Commun., 175 (2006) 575.
40 G. Vignale and M. Rasolt, Density-functional theory in strong magnetic field, Phys. Rev. Lett. 59 (1987) 2360.
41 G. Vignale and M. Rasolt, Current- and spin-density-functional theory for inhomogeneous electronic systems in strong magnetic fields, Phys. Rev. B 37 (1988) 10685.

42 G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures, Les Edition de Physique, Les Ulis (1990).
43 E. A. de Andrada e Silva, G. C. La Rocca, and F. Bassani, Spin-split subbands and magnato-ocillations in III-V asymmetric heterostructures, Phys. Rev. B 50 (1994) 8523.
44 J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45 (1992) 13244.
45 G. Vignale, M. Rasolt, and D. J. W. Geldart, Diamagnetic susceptibility of a dense electron gas, Phys. Rev. B 37, 2502 (1988).
46 T. L. Beck, Real-space mesh techniques in density functional theory, Rev. Mod. Phys. 72 (2000) 1041.
47 S. M. Reimann and M. Manninen, Electronic structure of quantum dots, Rev. Mod. Phys. 74 (2002) 1283.
48 Y. Nakamura, O. G. Schmidt, N. Y. Jin-Phillipp, S. Kiravittaya, C. Müler, K. Eberl, H. Gräberdinger, and H. Schweizer, J., Magnetically driven coupling of electronic states in quantum dot, Cryst. Growth 242 (2002) 339.
49. F. M. Sweeney, "Reaction Injection Molding Machinery and Processes,” Marcell Dekker, INC. New York 1987.
50. C. W. Macosko, "RIM, Fundamentals of Reaction Injection Molding," Munich, Vienna, New York, 1989.
51. J. M. Mckelvey, K. Ito, "Uniformity of Flow from Sheeting Dies," Polym. Eng. Sci., Vol.11, No.3, P 258-263, 1971.
52. Y. Matsubara, "Residence Time Distribution of Polymer Melt in the T-Die," Polym. Eng. Sci., Vol.20, No.3, P 212-214, 1980.
53. Y. Matsbara, "Residence Time Distribution of Polymer Melts in the Linearly Tapered Coat-Hanger Die," Polym. Eng. Sci., 23, 17-19, 1983.
54. B. Vergmes, P. Saillard, and J. F. Agassant, “Non-Isothermal Flow of a Molten Polymer in a Coat-Hanger Die," Polym. Eng. Sci., Vol.24, No.12, P 980-987, 1984.
55. W. K. Leonard, "Inertia and Gravitational Effects in Extrusion Dies for Non-Newtonian Fluids," Polym. Eng. Sci., Vol.25, No.9, 1985.
56. H. H. Winter and H. G. Fritz, "Design of Dies for the Distribution Problem," Polym. Eng. Sci., Vol.26, No.8, P 543-553, 1986.
57. H. G. Debry, T. G. Charbonneaux and C. W. Macosko, "Laminar Flow of a Thermosetting Polymer through a Coat-Hanger Die," Polym. Pro. Eng., Vol.4, 151-171, 1986.
58. T. J. Liu, C. N. Hong and K. C. Chen, "Computer-Aided Analysis of a Linearly Tapered Coat-Hanger Die," Vol.28, No.23, P 1517-1526, 1988.
59. K. Y. Lee and T. J. Liu, "Design and Analysis of a Dual-Cavity Coat-Hanger Die," Polym. Eng. Sci. Vol.29, No.15, P 1066-1075, 1989.
60. T. G. Charbonneaux, "Design of Sheet Dies for Minimum Residence Time Distribution: A Review," Polym. Plast. Tech. Eng., 30, 665-684, 1991.
61. S. H. Wen and T. J. Liu, "Three-Dimensional Finite Element Analysis of Polymeric Fluid Flow in an Extrusion Die, "Polym. Eng. Sci., Vol.34, 827-834, 1994.
62. C.L. Tucker III and N. P. Suh, “Mixing for Reaction Injection Molding I. Impingement Mixing of Liquids, “ Polym. Eng. Sci., 20, 875-885, 1980.
63. L. T. Manzione, "Simulation of Cavity Filling and Curing in Reaction Injection Molding, "Polym. Eng. Sci., Vol.21, 1234-1243, 1981.
64. C. N. Lekakou and S. M. Richardson, "Simulation of Reacting Flow during Filling in Reaction Injection Molding (RIM), "Polym. Eng. Sci., Vol.26, 1264-1275, 1986.
65. R. R. Hayes, H. H. Dammelongne and P.A.Tangny, "Numerical Simulation of Molding Filling in Reaction Injection Molding,” Polym. Eng. Sci., Vol.31, 842-848, 1991.
66. Y. Matsbara, "Design of Coat-Hanger Sheeting Dies Based on Ratio of Residence Times in Manifold and Slot," Polym. Eng. Sci., Vol.11, 716-719, 1988.