臺灣博碩士論文加值系統

隨著製造技術的進步，電子元件的尺寸越來越小，以目前的金屬氧化物場效應電晶體的通道長度就已短至0.12mm的尺寸。這造成量子效應越來越明顯，因此近幾年來很多量子井，量子線，量子點的研究越來越多。這篇論文主要是將量子點中的位能分佈設定成U形的結構，然後求出哈密頓運算符的特徵值（能量）和特徵函數（波函數）。並且分析半導體內能量對波數空間的分佈情況。

The size of electronic devices can be scaled down more small with more advanced process. For examples, the channel length of MOSFET has been scaled down to 0.12μm. However the quantum effect is observed obviously. Recently more and more researches are related to the quantum effect of devices, such as quantum wells, quantum wires, and quantum dots. In this thesis, the potential structure is set as U shape, and one may calculate the eigenvalue (energy) and eigenfunction (wave function) of Hamiltonian oparator. One can also analyze the relationship between energy E and wave vector k of electrons in semiconductor.

Contents
Chapter 1 Introduction 1
1-1 Fabrication 1
1-2 The Dimension of The System 2
1-3 The U shape structure Potential in
Schrodinger Equation 2
1-4 The Nonparabolic Model of Energy
Band Structures 3
Chapter 2 Wave Function in Quantum Dots 4
2-1 A General Model of Quantum Dots 4
2-2 The wave Function of The U Shape
Structure Potential 5
Chapter 3 Electron Energy Bands
3-1 Parabolic model 13
3-2 Nonparabolic model 15
Chapter 4 Conclusions 17
References 18

References
[1] Jian-Bai Xia, Wei-Dong sheng, J. Appl. Phys., Vol. 79, p7780(1996).
[2] B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. Van der Marel, and C. T. Foxon, Phys. Rev. Lett. 60, 848 (1988).
[3] D. A. Wharam, M. Pepper, H. Ahmed, J. E. F. Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie, and G. A. C. Jones, J. Phys. C 21, L209 (1988).
[4] Y. Takagaki and D. K. Ferry, Phys. Rev. B 45, 6715 (1992).
[5] H. U. Baranger, D. P. DiVincenzo, R. A. Jalabert, and A. D. Stone, Phys. Rev. B 44, 10637 (1991).
[6] F. Sols, M. Macucci, U. Ravaioli, and K. Hess, J. Appl. Phys. 66, 3982 (1989).
[7] K. Nakazato and R.J. Blaikie, J. Phys. C 3, 5729 (1991).
[8] H. Xu, Phys. Rev. B 47, 9537 (1993).
[9] J. B. Xia, Phys. Rev. B 38, 8365 (1988).
[10] H. Wu, D. W. L. Sprung, and J. Martorell, Appl. Phys. A 56, 127 (1993).
[11] C. S. Lent, Appl. Phys. Lett. 56, 2554 (1990).
[12] Jian-Bai Xia, Wei-Dong sheng, J. Appl. Phys., Vol. 81, 3201(1997).
[13] S. E. Ulloa, E. Castano, and G. Kirczenow, Phys. Rev. B 41, 12350 (1990)
[14] L. P. Kouwenhoven, F. W. J. Hekking, B. J. van Wees, C. J. P. M. Harmans, C. E. Timmering, and C. T. Foxon, Phys. Rev. B 44, 6531 (1991).
[15] H. Wu, P. W. L. Sprung, J. Martorell, and S. Klarsfeld, Phys. Rev. B 44, 6351 (1991).
[16] M. H. Leng and C. S. Lent, Phys. Rev. B 50, 10823 (1994).
[17] L. Esaki and L.L. Chang, 'Thin Solid Films 36, 285(1976).
[18] S.Yoshida, CRC Crif. Rev.Solid state Mater. Sci 11, 287(1984).
[19] G. Bauer, F. Kuchar, H. Heinrich low dimensional electronic systems, Springer-Verlag(1992).
[20] 呂助增, 固態電子學, 明文書局(1996).
[21] E. O. Kane, J. Phys. Chem. Solids 1, 249(1957).
[22] Chhi-Chong Wu and Harold N. Spector, Phys. Rev. B 3, 979 (1971).
[23] B. Kramer, Quantum Coherence in Mesoscopic Systems, ASI(1991)
[24] Gasiorowize, Stephen, Quantum Physics,(1996).
[25] John H. Davies, The Physics of Low dimensional semiconductors, (1998).