跳到主要內容

臺灣博碩士論文加值系統

(44.213.60.33) 您好!臺灣時間:2024/07/22 16:15
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:李振賓
研究生(外文):Chen-BinLee
論文名稱:二維奈米通道內之量子運動
論文名稱(外文):Quantum Motions in Two-Dimensional Nanochannels
指導教授:楊憲東楊憲東引用關係
指導教授(外文):ciann-Dong Yang
學位類別:博士
校院名稱:國立成功大學
系所名稱:航空太空工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:英文
論文頁數:134
中文關鍵詞:奈米通道複數力學量子漢彌爾頓力學量子力學多路徑現象電子的物質波非彈性散射
外文關鍵詞:nanochannelscomplex mechanicsquantum Hamilton mechanicsQuantum mechanicsmulti-path phenomenonelectronic matter wavesinelastic scattering
相關次數:
  • 被引用被引用:0
  • 點閱點閱:222
  • 評分評分:
  • 下載下載:28
  • 收藏至我的研究室書目清單書目收藏:0
量子力學需要大量的電子數(大的樣本數)才能呈現其機率預測的正確性。由於奈米通道內的電子數太少,樣本數不足,其表現出的少數電子行為與量子力學所預測的大量電子的平均行為有很大的差距。本論文提出複數力學(量子漢彌爾頓力學)的方法,可以針對個別電子在奈米結構內的量子行為做出完整的分析與預測。
首先吾人從單電子行為的觀點出發,以複數力學的方法建立電子在二維直線形奈米通道中的運動方程式,並說明通道內的電子運動及其機率分佈其實是源自量子位勢的作用,並且能夠滿足能量守恆定律。透過電子運動方程式的求解,吾人可以正確預測電子在通道內的穿透、穿隧以及反射等等之諸多波粒雙重性質。
其次本論文以單個電子的驗證為基礎,將之擴展到多電子的集體運動行為,從而正確預測,在半導體異質接面的二維奈米通道中,電導值呈現梯度量子化的現象。吾人利用一維穿隧效應去詮釋這個量子化現象,證實電子在通道內的運動等同於遭遇一個一維的等效位勢障。電子在此等效位勢障的作用下,何時會反射?何時會透射?均可由複數力學所建立的運動方程式得到正確的預測,而此預測是傳統的機率詮釋無法做到的。
實際的奈米通道由於加工上的限制,無法達到完美的 彎角,因此本論文的最後一章討論圓角形奈米通道對電子量子行為及電導值量子化的影響。藉由電子軌跡的求解,吾人可以計算通過通道的電子數目;並且證實此電子數目與由波函數所得到的電導值之間,存在著一個類比關係;亦即能夠讓大量電子通過通道的入射條件,同時也會造成電導值的大幅增加。

Electrons moving in some nanoelectronic devices may be so few that they do not averagely exhibit the mean motion predicted from quantum mechanics, which require a large enough ensemble of electrons to provide probabilistic description. Based on complex mechanics (quantum Hamilton mechanics), this dissertation provides complete analysis and correct predictions on the single-electron quantum motion within a 2D nanochannel, which otherwise cannot be analyzed by standard quantum mechanics.
Quantization and wave motion in nanochannels were conventionally treated from a probabilistic viewpoint. This dissertation shows how quantization and wave motion can be reproduced by a deterministic corpuscular description of electrons moving in the channel. The quantum Hamilton mechanics is exploited to derive electronic trajectories in the presence of the channelized quantum potential. The number of channels within the quantum potential is shown to be just the integer quantization levels of the conductance, and the conductance quantization is found to be a manifestation of the step-change nature of number of channels with respect to the electron incident energy. Three types of trajectory within the channel, tunneling, reflection and transmission, are solved analytically from the Hamilton equations of motion; meanwhile, explicit inequality criteria are derived to predict which type of motion will occur actually under a given incident condition. Upon solving the complex-valued Hamilton equations of motion, multiple paths between two fixed points come out naturally, and the collection of these multiple paths produces, what we call, electronic matter waves propagating within the channel.
Quantum analysis made for straight nanochannels are extended to curve-shaped nanochannels and the effect of rounded corners on the quantum properties of the nanochannels is studied. We also investigate the imperfect case of inelastic collisions within the nanochannels. Inelastic collisions have an effect on increasing the resistance of the nanochannel, which can be taken into account by imposing an imaginary potential on the confining potential within the nanostructure.

ABSTRACT IN CHINESE ii
ABSTRACT iv
致謝 vi
CHINESE ABSTRACT OF EACH CHAPTER vii
CONTENTS xiv
LIST OF TABLES xvi
LIST OF FIGURES xvii
NOMENCLATURE xxi
CHAPTER ⅠINTRODUCTION 1
1.1 Motivation 1
1.2 Literature Survey 2
1.2.1 Complex Potential and Quantum Trajectories 2
1.2.2 Quantization and Wave Motion 5
1.2.3 Properties of Electrons in Crossbar Structure 5
1.3 Main Contributions 7
1.4 Dissertation Organizations 9
CHAPTER Ⅱ FUNDAMENTALS OF COMPLEX MECHANICS 13
2.1 Nonlinear Quantum Dynamics 14
2.2 Chaos and Multiple Paths 17
2.3 Stability and Quantization 19
2.4 Bifurcation and Quantum Entanglement 21
CHAPTER Ⅲ COMPLEX POTENTIAL AND QUANTUM TRAJECTORIES 23
3.1 Wavefunctions in Straight Semiconductor Channel 23
3.2 Energy Conservation and Channelized Quantum Potential 30
3.3 Quantum Trajectories within the Conduction Channels 35
CHAPTER Ⅳ QUANTIZATION AND WAVE MOTIONS 53
4.1 Conductance Quantization in Nanochannels 55
4.2 Quantization of Transmission Coefficient 58
4.3 Tunneling Dynamics 67
4.4 Reflection and Transmission Dynamics 71
4.5 Multiple Paths and Electronic Matter Wave 74
CHAPTER Ⅴ ELECTRONIC QUANTUM MOTION IN CROSSBAR STRUCTURE WITH ROUNDED CORNERS 85
5.1 Wavefunctions in Crossbar Structure 86
5.1.1 Building Wavefunctions 86
5.1.2 Computing Boundary Conditions 88
5.2 The Spatial Distribution of Probability Density and Quantum Potential in Crossbar Structure 97
5.3 The Conductance and Electronic Trajectory in Crossbar Structure 99
5.3.1 The Conductance in Crossbar Structure 99
5.3.2 Quantum Trajectory in Rounded Crossbar Channel 102
5.4 Inelastic Scattering 104
5.5 Trajectory Interpretation of Conductance 107
CHAPTER Ⅵ CONCLUSIONS AND FUTURE WORK 124
REFERENCES 128
PUBLICATION LIST 133
VITA 134

[1]Lundberg T., “Quantum Ballistic Transport in Semiconductor Nanostructures: Effect of Smooth Features in Confining Potentials, Computational Materials Science 1994;3:78.
[2]Bohm D., “A Suggested Interpretation The Quantum Theory in Terms of “Hidden Variables, Physical Review 1952;85:166-79; 1952;85:180.
[3]Lundberg T., Sj?qvist E., and Berggren K.F., “Analysis of Electron Transport in a Two-dimensional Structure using Quantal Trajectories, J Phys: Condes Matter 1998;10:5583.
[4]Barker J. R., and Ferry D. K., “On the validity of quantum hydrodynamics for describing antidot array devices, Semiconductor Science Technology. 1998;13:A135.
[5]Yang C.D., “Quantum Dynamics of Hydrogen Atom in Complex Space, Annals of Physics 2005;319:399.
[6]Kelly M.J., “Low-dimensional Semiconductors: Materials, Physics, Technology, Devices, Oxford University Press 1995.
[7]Ferry D.K., “Goodnick SM. Transport in Nanostructures, Cambridge University Press 1997.
[8]van Wees B.J., van Houten H., Beenakker CWJ, Williamson J.G., Kouwenhoven L.P., van der Marel D., and Foxon C.T., “Quantized Conductance of Point Contacts in a Two-dimensional Electron Gas, Physical Review Letter 1988;60:848.
[9]Wharam D.A., Thornton T.J., Newbury R., Pepper M., Ahmed H., Frost J.E.F., Hasko D.G., Peacockt D.C., Ritchie D.A., and Jones G.A.C., “One-dimensional Transport and The Quantization of The Ballistic Resistance, J Phys C: Solid State Phys 1988;21:L209.
[10]Kirczenow G., “Resonant Conduction in Ballistic Quantum Channels, Physical Review B 1989;39:10452.
[11]Xu H., Ji Z.L., and Berggren KF., “Electron Transport in Finite One-dimensional Quantum-dot Arrays, Superlattices and Microstructures 1992;12:237.
[12]Berggren K.F., and Ji Z.I., “Resonant Tunneling via Quantum Bound States in a Classically Unbound System of Crossed, Narrow Channels, Physical Review B 1991;43:4760.
[13]Berggren K.F., Besev C., and Ji Z.L., “Transition from Laminar to Vortex Flow in a Model Semiconductor Nanostructure, Physica Scripta 1992;T42:141.
[14]Bohm D., and Vigier J.P., “Model of The Causal Interpretation of Quantum Theory in Terms of a Fluid with Irregular Fluctuations, Physical Review 1954;96:208.
[15]Bohm D., and Hiley B.J., “Non-Locality and Locality of The Stochastic Interpretation of Quantum Mechanics, Phys Rep 1989;172:93.
[16]Yang C.D., “Trajectory Interpretation of the Uncertainty Principle in 1D Systems Using Complex Bohmian Mechanics, Physical Letter A 2008;372:6240.
[17]Yang C.D., “Quantum Motion in Complex Space, Chaos, Solitons and Fractals 2007;33:1073.
[18]Yang C.D., “Wave-Particle Duality in Complex Space, Annals of Physics, 2005;319:444.
[19]Yang C.D., “Quantum Hamilton Mechanics: Hamilton Equations of Quantum Motion, Origin of Quantum Operators, and Proof of Quantization Axiom, Annals of Physics 2006;321:2876.
[20]Yang C.D., “A New Hydrodynamic Formulation of Complex-valued Quantum Mechanics, Chaos, Solitons and Fractals 2009;42:453.
[21]Sze S.M., “Semiconductor devices, physics and technology, New York , Wiley, 1985.
[22]Singh J., “Physics of Semiconductors and Their Heterostructures, McGrawHill 1993.
[23]Madou M., “Fundamentals of Microfabrication, New York, 1997.
[24]Rolf E., and Norman J.M., “Fundamentals of semiconductor physics and devices, Singapore ;World Scientific, 1997.
[25]Mitin V.V., Kochelap V.A., and Stroscio M.A., “Quantum heterostructures: microelectronics and optoelectronics, Cambridge: Cambridge University 1999.
[26]Vladimir M., Viatcheslav K., and Michael A. Stroscio, “Introduction to nanoelectronics: science, nanotechnology, engineering, and applications, Cambridge: Cambridge University 2008.
[27]Gerald G., and Wolfram D., “Introduction to microsystem technology: a guide for students, Wiley 2008.
[28]Kelly M.J., and Weisbuch C., “The Physics and Fabrication of Microstructures and Microdevices, Springer-Verlag Berlin 1986.
[29]Bauer G., Kuchar F., and Heinrich H., “Two-dimensional Systems, Physics and New Devices, Springer-Verlag Berlin, 1986.
[30]Mark A.R., and Wiley P.K., “Nanostructure Physics and Fabrication, Boston :Academic Press, 1989.
[31]Peeters F.M., “The Quantum Hall Resistance in Quantum Wires“, Superlatt. Microstruct. 1989;6:217.
[32]Devreese J.T., and Peeters F.M., “The Physics of The Two-dimensional Electron Gas, New York :Plenum, 1987.
[33]Schult R. L., Ravenhall D. G., and Wyld H.W., “Quantum Bound States in a Classically Unbound System of Crossed Wires, Physical Review B 1989;39:5476.
[34]Eugster C.C., del Alamo J. A., Melloch M.R., and Rooks M. J., “Quantum Hall Effect and General Narrow-wire Circuits, Physical Review B 1990;41:12760.
[35]Takagaki Y., and Ferry D. K., “Quantum-interference Effects of Edge Channels in The Presence of an Antidot Potential, Physical Review B 1993; 48:8152.
[36]Vacek K., kasai H., and Okiji A., “Ballistic Transport in the Bent Quantum Wire, J.of The phys. Soc. Jpn 1992;61:27.
[37]Wu H., Sprung D.W.L., Martorell J., and Klarsfeld S., “Quantum Wire with Periodic Serial Structure, Physical Review B 1991;44:6351.
[38]Ji Z.L., and Berggren K.F., “Quantum Bound States in Narrow Ballistic Channels with Intersections, Physical Review B 1992;45;6652.
[39]Kawamura T., and Leburton J.P., “Quantum ballistic transport through a double-bend waveguide structure: Effects of disorder, Phys. Rev. 1993;48:8857.
[40]Xu H., “Ballistic Transport in Quantum Channels Modulated with Double-bend Structures, 1993;47:9537.
[41]Stone A.D., and Lee P.A.,“Effect of Inelastic Processes on Resonant Tunneling in One Dimension, Physical Review letter 1985;54:1196.
[42]Wang Y., Wang J., and Guo H., “Effects of Inelastic Processes on The Transmission in a Coupled-quantum-wire System, Physical Review B 1993;47:4348.
[43]Akis R., Bird J.P., and Ferry D.K., “ The Efects of Inelastic Scattering in Open Quantum Dots: Reduction of Conductance Fluctuations and Disruption of Wave-function ‘scarring’ , J.Phys.:Condens. Matter 1996;8:L667.
[44]Feynman R.P., Hibbs A.R., “Quantum Mechanics and Path Integrals, New York: McGraw-Hill 1965.
[45]Yang, C.D., “Complex Mechanics, Asian Academic Publisher Limited, ISSN 2077-8139, Hong Kong, 2010.
[46]Bohm D., “A suggested interpretation of the quantum theory in terms of hidden variable, Physical Review 1952;85:166.
[47]Yang, C.D., “The origin and proof of quantization axiom in complex spacetime, Chaos, Solitons and Fractals 2007;32:274.
[48]Yang, C.D., and Wei, C.H., “Parameterization of All Path Integral Trajectories, Chaos, Solitons and Fractals 2007;33:118.
[49]Yang, C.D., and Wei, C. H., “Strong Chaos in One-Dimensional Quantum System, Chaos, Solitons & Fractals 2008;37:988.
[50]Yang, C.D., “Stability and Quantization of Complex-Valued Nonlinear Quantum Systems, Chaos, Solitons & Fractals 2009;42:711.
[51]Kittel C., “Introduction to Solid State Physics“, Hoboken, NJ :Wiley 2005.
[52]Yang C.D., “Complex Tunneling Dynamics, Chaos, Solitons and Fractals 2007;32:312.
連結至畢業學校之論文網頁點我開啟連結
註: 此連結為研究生畢業學校所提供,不一定有電子全文可供下載,若連結有誤,請點選上方之〝勘誤回報〞功能,我們會盡快修正,謝謝!
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top