在本論文中，我們利用掃描穿隧顯微鏡 (STM) 和掃描穿隧能譜術 (STS) 研究具有平坦表面的鉛島的量子性質。研究內容包含：
1.鉛島中的週期性扭曲對量子井態強度調變影響之研究。
2.鏡像電位對銅(111)表面上鉛島量子井態影響之研究。
在第一個主題中，我們使用掃描穿隧能譜術探討成長在矽(111)表面三個原子層厚鉛島上的二種圖案的形成機制。結果顯示，鉛島表面圖案是由幾何的皺褶結構與局部電子結構疊加的結果。前者源自於二種介面鬆弛過程中所造成二種類型的週期性晶格扭曲。後者由於鉛島中量子井態的強度亦隨週期性晶格扭曲而調變，導致態密度局部變化，進而使圖案隨偏壓改變。量子井態強度調變可以歸因於晶格扭曲所導致的電子屏蔽效應。
在第二個主題中，我們使用掃描穿隧能譜術量測成長在銅(111)表面鉛島的量子井態。我們的觀察顯示，超過費米能階1.2電子伏特能量的量子井態受到鏡像電位的影響。隨著量子數增加，相鄰態的能量間隔是縮小而不是變寬，這與方型位能井的預測相反。我們考慮鏡像位能的影響並再相位累積模型中引進鏡像位能的相位貢獻以計算量子井態的能階，結果合理解釋相鄰態的能量間隔的縮小行為。這模型也顯示出鉛表面存在著一量子區間，在此量子區間中鏡像電位是消失的。此外，因量子井態存在，在穿隧能隙中的準鏡像電位態會被抑制。

In this thesis, low temperature scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) are utilized to study the quantum properties of Pb islands with flat top surface. There are two main topics: strength modulation of quantum-well states in Pb islands with periodic distortions on Si(111) and phase contribution of image potential on empty quantum-well states in Pb islands on the Cu(111) surface.
In the first topic, we used STS to explore three-atomic-layer Pb islands with two types of pattern grown on Si(111) surface. Our results demonstrate that the pattern appearing on the island surface is the superposition of geometric corrugation and local variation of the electronic structure. The former originates from two kinds of interface relaxation, resulting in two types of periodic distortion of the lattice. The latter is due to the periodic strength modulation of quantum-well states in Pb islands, causing inhomogeneity in the integration of the density of states and the bias-dependent pattern. This strength modulation of the quantum-well states can be attributed to the electronic screening effect induced by the lattice distortion in Pb islands.
In the second topic, we use STS to explore the quantum well states in the Pb islands grown on a Cu(111) surface. Our observation demonstrates that the empty quantum well states, whose energy levels lie beyond 1.2 eV above the Fermi level, are significantly affected by the image potential. As the quantum number increases, the energy separation between adjacent states is shrinking rather than widening, contrary to the prediction for a square potential well. By simply introducing a phase factor to reckon the effect of the image potential, the shrinking behavior of the energy separation can be reasonably explained with the phase accumulation model. The model also reveals that there exists a quantum regime above the Pb surface in which the image potential is vanished. Moreover, the quasi-image-potential state in the tunneling gap is quenched because of the existence of the quantum well states.

Acknowledgements……………………….……………………...…………..IV
Abstract…………………………………………….…………...…...…………...VI
List of Figures Captions…………………….………………...…………...IX

Chapter 1. Introduction…………………………………………………….1

Chapter 2. Experimental principles………………………………..….5
2.1 Principles of scanning tunneling microscopy (STM)……………………………...5
2.2 STM operating modes…………..………………………….....…..……….….…...6
(a) Constant current mode…………..………………………….…..…...….…...7
(b) Constant height mode………………………………………..……...….…...8
(c) Scanning tunneling spectroscopy (STS)……………...………...…...….…...9
2.3 Local density of state (LDOS)……………...…..……………....…………….......10
2.4 Quantum size effect (QSE) and Quantum well states (QWSs)...............................11
(a) Quantum size effect (QSE)………..………………………..……...….…...11
(b) Quantum well states (QWSs)……………………………………...….…...13
2.5 Three traditional growth modes..…………………………….…………...….…...15

Chapter 3. Experimental details……………............................……….17
3.1 Experiment instrument………………………………………...............................17
(a) UHV 109K STM…………………..………………………..……...….…...17
(b) UHV 4.3K STM………..………….………..……………………...….…...18
3.2 Ultra-high-vacuum (UHV) system…………….…………………………………20
(a) Dry rotary pump…………………..………………………..……...….…...21
(b) Turbo molecular pump………………….………..………………...….…...21
(c) Ion pump…………………………..………………………..……...….…...22
(d) Titanium sublimation pump (TSP)…………….………...………...….…...22
(e) Ionization gauge………………...…….....……..………...………...….…...23
3.3 Tip preparation……………………………………...……………………………23
3.4 Sample preparation.................................................................................................24
(a) Sputter system……………………..………………………..……...….…...24
(b) Anneal system……………………………....……………………...….…...25
(c) Evaporator system………………………......……………………...….…...26
References………………….....………………………...………………………...….27

Chapter 4. Strength modulation of quantum-well states in Pb islands with periodic distortions on Si(111)………...………...29
4.1 Introduction...............................................................................................……….29
4.2 Experimental method………………………………………………………….....31
4.3 Results and discussion……....................................................................................32
4.4 Conclusions……………….………………………...………………………...….43
References………………….....………………………...………………………...….43

Chapter 5. Phase contribution of image potential on empty quantum-well states in Pb islands on the Cu(111) surface.....45
5.1 Introduction...............................................................................................……….45
5.2 Experimental method………………………………………………………….....47
5.3 Results and discussion……....................................................................................48
5.4 Conclusions……………….………………………...……....................................61
References……………….........………………………...……………………...…… 62

Chapter 6. Conclusions…………………………....……………………….64

Appendix. Construction of homemade low temperature scanning tunneling microscopy system………...……………….….. 65
A-1 Introduction..............................................................................................……….65
A-2 Scanner………………………..…………………….………...............................66
A-3 Stepper…………………........………...……………………...............................68
A-4 The composition of the STM system…………....………………………………69
A-5 Cooling system………………………...……....……...…………………………71
A-6 Test measurements on the HOPG surface………...…..…………………………73
A-7 Conclusions………………………………………...……....................................74
References………………….....………………………...………………………...….74

Ch1~Ch3
1.T.-C. Chiang, Surf. Sci. Rep. 39, 181 (2000).
2.T.-C. Chiang, Science 306, 1900 (2004).
3.M. Jalochowski, and E. Bauer, Phys. Rev. B 38, 5272 (1988).
4.W. B. Su, S. H. Chang, W. B. Jian, C. S. Chang, L. J. Chen, and T. T. Tsong, Phys. Rev. Lett. 86, 5116 (2001).
5.A. Crottini, D. Cvetko, L. Floreano, R. Gotter, A. Morgante, and F. Tommasini, Phys. Rev. Lett. 79, 1527 (1997).
6.B. J. Hinch, C. Koziol, J. P. Toennies, and G. Zhang, Europhys. Lett. 10, 341 (1989).
7.T. L. Chan, C. Z. Wang, M. Hupalo, M. C. Tringides, and K. M. Ho, Phys. Rev. Lett. 96, 226102 (2006).
8.L. Y. Ma, L. Tang, Z. L. Guan, K. He, K. An, X. C. Ma, J. F. Jia, and Q. K. Xue, Phys. Rev. Lett. 97, 266102 (2006).
9.D. A. Luh, T. Miller, J. J. Paggel, M. Y. Chou, and T. C. Chiang, Science 292, 1131 (2001).
10.Y. Guo, Y. F. Zhang, X. Y. Bao, T. Z. Han, Z. Tang, L. X. Zhang, W. G. Zhu, E. G. Wang, Q. Niu, Z. Q. Qiu, J. F. Jia, Z. X. Zhao, and Q. K. Xue, Science 306, 1915 (2004).
11.D. Eom, S. Qin, M. Y. Chou, and C. K. Shih, Phys. Rev. Lett. 96, 027005 (2006).
12.Y. S. Fu, S. H. Ji, X. Chen, X. C. Ma, R. Wu, C. C. Wang, W. H. Duan, X. H. Qiu, B. Sun, P. Zhang, J. F. Jia, and Q. K. Xue, Phys. Rev. Lett. 99, 256601 (2007).
13.Y. F. Zhang, Z. Tang, T. Z. Han, X. Ma, J. F. Jia, Q. K. Xue, K. Xun, and S. C. Wu, Appl. Phys. Lett. 90, 093120 (2007).
14.D. A. Evans, M. Alonso, R. Cimino, and K. Horn, Phys. Rev. Lett. 70, 3483 (1993).
15.J. J. Paggel, T. Miller, and T.-C. Chiang, Science 283, 1709 (1999).
16.R. K. Kawakami, E. Rotenberg, H. J. Choi, E. J. Escorcia-Aparico, M. O. Bowen, J. H. Wolfe, E. Arenholz, Z. D. Zhang, N. V. Smith, and Z. Q. Qiu, Nature 398, 132 (1999).
17.A. Mans, J. H. Dil, A. R. H. F. Ettema, and H. H. Weitering, Phys. Rev. B 66, 195410 (2002).
18.Y. F. Zhang, J. F. Jia, T. Z. Han, Z. Tang, Q. T. Shen, Y. Guo, Z. Q. Qiu, and Q. K. Xue, Phys. Rev. Lett. 95, 096802 (2005).
19.I. B. Altfeder, K. A. Matveev, and D. M. Chen, Phys. Rev. Lett. 78, 2815 (1997).
20.I. B. Altfeder, V. Narayanamurti, and D. M. Chen, Phys. Rev. Lett. 88, 206801 (2002).
21.R. Otero, A. L. Vázquez de Parga, and R. Miranda, Phys. Rev. B 66, 115401 (2002).
22.D. Wegner, A. Bauer, and G. Kaindl, Phys. Rev. Lett. 94, 126804 (2005).
23.S. M. Lu, M. C. Yang, W. B. Su, C. L. Jiang, T. Hsu, C. S. Chang, and T. T. Tsong, Phys. Rev. B 75, 113402 (2007).
24.W. B. Jian, W. B. Su, C. S. Chang, and T. T. Tsong, Phys. Rev. Lett. 90, 196603 (2003).
25.M. Hupalo, V. Yeh, T. L. Chan, C. Z. Wang, K. M. Ho, and M. C. Tringides, Phys. Rev. B 71, 193408 (2005).
26.E. Ogando, N. Zabala, E. V. Chulkov, and M. J. Puska, Phys. Rev. B 69, 153410 (2004).
27.P. M. Echenique, and J. B. Pendry, J. Phys. C: Solid State Phys. 11, 133 (1978).
28.A. M. Shikin, D. V. Vyalikh, G. V. Prudnikova, and V. K. Adamchuk, Surf. Sci. 487, 135 (2001).
29.R. M. Tromp, R. J. Hamers, and J. E. Demuth, Science 234, 304 (1986).
30.Z. Zhang, Q. Niu, and C.-K. Shih, Phys. Rev. Lett. 80, 5381 (1998).
31.W. B. Su, H. Y. Lin, Y. P. Chiu, H. T. Shih, T. Y. Fu, Y. W. Chen, C. S. Chang, and T. T. Tsong, Phys. Rev. B 71, 073304 (2005).
32.D. J. Griffiths, Introduction to Quantum Mechanics (2005).
33.Surface Science, an introduction by K.Oura, V.G. Lifshits, A. A. Saranin, A.V. Zotov, and M. Katayama.
34.G. L. Lay, J. Peretti, M. Hanbucken, and W. S. Yang, Surf. Sci. 204, 57 (1988).
35.W. B. Su, S. H. Chang, H. Y. Lin, Y. P. Chiu, T. Y. Fu, C. S. Chang, and T. T. Tsong, Phys. Rev. B 68, 033405 (2003).
36.J. Camarero, J. Ferren, V. Cros, L. Gomez, A. L. Vazquez de Parga, J. M. Gallego, J. E. Prieto, J. J. de Miguel, and R. Miranda, Phys. Rev. Lett. 81, 850 (1998).
37.Please refer to Specs Web site (http://www.specs.com).

Ch4
1.I. B. Altfeder, D. M. Chen, and K. A. Matveev, Phys. Rev. Lett. 80, 4895 (1998).
2.I. B. Altfeder, V. Narayanamurti, and D. M. Chen, Phys. Rev. Lett. 88, 206801 (2002).
3.V. Yeh, L. Berbil-Bautista, C. Z. Wang, K. M. Ho, and M. C. Tringides, Phys. Rev. Lett. 85, 5158 (2000).
4.W. B. Su, H. Y. Lin, Y. P. Chiu, H. T. Shih, T. Y. Fu, Y. W. Chen, C. S. Chang, and T. T. Tsong, Phys. Rev. B 71, 073304 (2005).
5.Z. Zhang, Q. Niu, and C.-K. Shih, Phys. Rev. Lett. 80, 5381 (1998).
6.S. H. Chang, W. B. Su, W. B. Jian, C. S. Chang, L. J. Chen, and T. T. Tsong, Phys. Rev. B 65, 245401 (2002).
7.W. B. Jian, W. B. Su, C. S. Chang, and T. T. Tsong, Phys. Rev. Lett. 90, 196603 (2003).
8.M. Hupalo, V. Yeh, T. L. Chan, C. Z. Wang, K. M. Ho, and M. C. Tringides, Phys. Rev. B 71, 193408 (2005).
9.T. L. Chan, C. Z. Wang, M. Hupalo, M. C. Tringides, W. C. Lu, K. M. Ho, Surf. Sci. 600, L179 (2006).
10.We did not detect any prominent localized states near the Fermi level in I-V spectra for the Pb film. Therefore, the small range of integration of the density of states for the topography image should approximate the true geometric surface structure.
11.Charles Kittel, Introduction to Solid State Physics (John Wiley & Sons, New York, 1986).

Ch5
1.D. A. Evans, M. Alonso, R. Cimino, and K. Horn, Phys. Rev. Lett. 70, 3483 (1993).
2.J. J. Paggel, T. Miller, and T.-C. Chiang, Science 283, 1709 (1999).
3.R. K. Kawakami, E. Rotenberg, H. J. Choi, E. J. Escorcia-Aparico, M. O. Bowen, J. H. Wolfe, E. Arenholz, Z. D. Zhang, N. V. Smith, and Z. Q. Qiu, Nature 398, 132 (1999).
4.A. Mans, J. H. Dil, A. R. H. F. Ettema, and H. H. Weitering, Phys. Rev. B 66, 195410 (2002).
5.Y. F. Zhang, J. F. Jia, T. Z. Han, Z. Tang, Q. T. Shen, Y. Guo, Z. Q. Qiu, and Q. K. Xue, Phys. Rev. Lett. 95, 096802 (2005).
6.I. B. Altfeder, K. A. Matveev, and D. M. Chen, Phys. Rev. Lett. 78, 2815 (1997).
7.I. B. Altfeder, V. Narayanamurti, and D. M. Chen, Phys. Rev. Lett. 88, 206801 (2002).
8.W. B. Su, S. H. Chang, W. B. Jian, C. S. Chang, L. J. Chen, and T. T. Tsong, Phys. Rev. Lett. 86, 5116 (2001).
9.R. Otero, A. L. Vázquez de Parga, and R. Miranda, Phys. Rev. B 66, 115401 (2002).
10.D. Wegner, A. Bauer, and G. Kaindl, Phys. Rev. Lett. 94, 126804 (2005).
11.S. M. Lu, M. C. Yang, W. B. Su, C. L. Jiang, T. Hsu, C. S. Chang, and T. T. Tsong, Phys. Rev. B 75, 113402 (2007).
12.M. Jalochowski, and E. Bauer, Phys. Rev. B 38, 5272 (1988).
13.A. Crottini, D. Cvetko, L. Floreano, R. Gotter, A. Morgante, and F. Tommasini, Phys. Rev. Lett. 79, 1527 (1997).
14.C. A. Jeffrey, E. H. Conrad, R. Feng, M. Hupalo, C. Kim, P. J. Ryan, P. F. Miceli, and M. C. Tringides, Phys. Rev. Lett. 96, 106105 (2006).
15.D. A. Luh, T. Miller, J. J. Paggel, M. Y. Chou, and T. C. Chiang, Science 292, 1131 (2001).
16.Y. Guo, Y. F. Zhang, X. Y. Bao, T. Z. Han, Z. Tang, L. X. Zhang, W. G. Zhu, E. G. Wang, Q. Niu, Z. Q. Qiu, J. F. Jia, Z. X. Zhao, and Q. K. Xue, Science 306, 1915 (2004).
17.D. Eom, S. Qin, M. Y. Chou, C. K. Shih, Phys. Rev. Lett. 96, 027005 (2006).
18.Y. S. Fu, S. H. Ji, X. Chen, X. C. Ma, R. Wu, C. C. Wang, W. H. Duan, X. H. Qiu, B. Sun, P. Zhang, J. F. Jia, and Q. K. Xue, Phys. Rev. Lett. 99, 256601 (2007).
19.Takashi Uchihashi, Jianwei Zhang, Jörg Kröger, and Richard Berndt, Phys. Rev. B 78, 033402 (2008).
20.Y. F. Zhang, Z. Tang, T. Z. Han, X. Ma, J. F. Jia, Q. K. Xue, K. Xun, and S. C. Wu, Appl. Phys. Lett. 90, 093120 (2007).
21.E. Ogando, N. Zabala, E. V. Chulkov, and M. J. Puska, Phys. Rev. B 69, 153410 (2004).
22.P. M. Echenique, and J. B. Pendry, J. Phys. C: Solid State Phys. 11, 133 (1978).
23.T.-C. Chiang, Surf. Sci. Rep. 39, 181 (2000).
24.A. M. Shikin, D. V. Vyalikh, G. V. Prudnikova, and V. K. Adamchuk, Surf. Sci. 487, 135 (2001).
25.R. Otero, A. L. Vázquez de Parga, and R. Miranda, Surf. Sci. 447, 143 (2000).
26.S. Ogawa, S. Heike, H. Takahashi, and T. Hashizume, Phys. Rev. B 75, 115319 (2007).
27.R. C. Jaklevic, and John Lambe, Phys. Rev. B 12, 4146 (1975).
28.U. Höfer, I. L. Shumay, Ch. Reuß, U. Thomann, W. Wallauer, and Th. Fauster, Science 277, 1480 (1997).
29.E. G. McRae, Rev. Mod. Phys. 51, 541 (1979).
30.M. Milun, P. Pervan, and D. P. Woodruff, Rep. Prog. Phys. 65, 99 (2002).
31.G. Binnig, K. H. Frank, H. Fuchs, N. Garcia, B. Reihl, H. Rohrer, F. Salvan, and A. R. Williams, Phys. Rev. Lett. 55, 991 (1985).
32.R. S. Becker, J.A. Golovchenko, and B.S. Swartzentruber, Phys. Rev. Lett. 55, 987 (1985).
33.W. B. Su, S. M. Lu, C. L. Lin, H. T. Shih, C. L. Jiang, C. S. Chang, and T. T. Tsong, Phys. Rev. B 75, 195406 (2007).
34.W. B. Su, S. M. Lu, H. T. Shih, C. L. Jiang, C. S. Chang, and T. T. Tsong, J. Phys.: Condens. Matter 18, 6299 (2006).

Appendix
1.Please refer to Attocube systems Web site (http://www.attocube.com).
2.Please refer to Swagelok Web site (http://www.swagelok.com).
3.Please refer to LakeShore Web site (http://www.lakeshore.com).