在這篇論文裡主要使用低能量電子繞射儀(LEED)和角解析光電子能譜(ARPES) 來測量Ag(111)上的Pb薄膜和PbAu合金薄膜的晶格和電子結構。首先，我們在85K的低溫下在Ag(111)上逐層生長Pb薄膜，觀察到隨著Pb覆蓋率的增加，Pb的量子阱態(QWS)的演變。通過校準好的QWS能量位置與覆蓋率，我們提取了在Ag(111)上Pb薄膜的頂面和底部界面處的QWS能量相關的總相位偏移。使用線性函數擬合的方式在量子相移累積模型中提取了QWS的相位偏移，成功地再現了QWS能量位置與覆蓋範圍的關係，這結果與實驗的量測非常匹配。通過LEED測量，我們發現在85K時Ag(111)上的1-ML Pb薄膜的晶格結構與RT時不同；兩者的晶格常數相同，均為3.48(±0.06)Å，但前者相對於Ag(111)的旋轉角為±13.8(±0.2)°，遠大於後者的±4.5(±0.2)°。通過使用重合晶格匹配模擬來找到在Ag(111)上Pb層的最佳晶格配置。事實證明，兩種晶格配置都對應於高階重合晶格匹配的大密度。在低温85K下生長的Ag(111)上的1-ML Pb薄膜的較大旋轉角度±13.8(±0.2)°削弱了Pb薄膜的QWS與Ag塊材態連續體之間的電子-電子相互作用，因此可以觀察到1-ML Pb薄膜的QWS能帶從表面區域中心分散。
在這之後濺鍍Au到1和2-ML的Pb薄膜上以形成PbAu合金，然後通過LEED和ARPES研究相應的晶格和電子結構。通過1-ML和2-ML Pb薄膜形成的PbAu合金的晶格常數均為5.774(±0.06)Å，但它們相對於Ag(111)的旋轉角度分別為0±0.1(0±0.3)°和±16.1(±0.2)°，因為前者直接在 Ag(111)上形成，而後者在1-ML Pb層/Ag(111)上形成。比較通過在Ag(111) 上的1-ML和2-ML Pb薄膜生長的PbAu合金的能帶結構與在Pb(111)塊材基底上形成的PbAu合金的能帶結構。我得出的結論是，如果需要在Pb薄膜上成長出來的PbAu合金和在Pb(111)基底上成長的PbAu合金相同，則Pb薄膜的層數至少需要2ML。最後，給出了在Ag(111)上通過1-ML Pb薄膜形成的PbAu合金的推測原子模型。

For the research presented in this thesis, I mainly used low energy electron diffraction (LEED) and angle-resolved photoemission spectroscopy (ARPES) to measure the lattice and electronic structures of Pb thin films and PbAu alloy thin films on Ag(111). At first, we grew layer-by-layer Pb thin films on Ag(111) at low temperature of 85K to observe the evolution of Pb quantum-well states (QWS) with increasing Pb coverage. Based on well-calibrated QWS energy positions versus coverage, we extracted the energy-dependent total phase shift of the QWS at the top surface and the bottom interface of Pb thin films on Ag(111). Using the linear function fitting to the extracted QWS phase shift in the quantum phase-shift accumulation model, I successfully reproduced the QWS energy positions versus coverage, which match the measured counterpart very well. From LEED measurement, we discovered that the lattice configuration of 1-ML Pb thin film on Ag(111) at 85 K is different from that at RT; both have the same lattice constant, 3.48(±0.06)Å, but the rotation angle of the former with respect to Ag(111) is ±13.8(±0.2)°, much larger than that of the latter, ±4.5(±0.2)°. I used coincident-lattice-match simulation to find optimal lattice configuration of Pb layer on Ag(111). It turns out that both lattice configurations correspond to large densities of high order coincident-lattice-match. The larger rotation angle, ±13.8(±0.2)°, of 1-ML Pb film on Ag(111) grown at 85 K weakens electron-electron interaction between the QWS of the Pb film and the Ag bulk-state continuum so that I can get to observe the QWS band of 1-Ml Pb film dispersing from the surface zone center.

I subsequently deposited Au onto Pb thin films of 1 and 2 ML in order to form PbAu alloy and then investigated the corresponding lattice and electronic structures by LEED and ARPES. The lattice constants of PbAu alloys formed via 1-ML and 2-ML Pb films were both 5.774(±0.06)Å, but their rotation angles with respect to Ag(111) were 0±0.1(0±0.3)° and ±16.1(±0.2)°, respectively, because the former formed directly on Ag(111) but the latter on top of 1-ML Pb layer/Ag(111). I compared the energy band structures of the PbAu alloy grown via the 1-ML and 2-ML Pb films on Ag(111) with the PbAu alloy formed on the Pb(111) bulk substrate. I get the conclusion that at least 2-ML Pb film is required to form the same PbAu alloy formed on bulk Pb(111). Finally, a speculative atomic model of the PbAu alloy formed via 1-ML Pb film on Ag(111) is given.

[1] Miller index。維基百科。查詢日期：2021/10/20。https://en.wikipedia.org/wiki/Miller_index。
[2] K. Oura, V.G.Lifshits, A.A.Saranin, A.V.Zotov, M.Katayama . (2003). Surface Science An introduction. New York: Springer-Verlag Berlin Heidelberg。
[3] Lattice Constants of all the elements in the Periodic Table。查詢日期：2021/10/26。https://www.schoolmykids.com/learn/interactive-periodic-table/lattice-constants-of-all-the-elements。
[4] Roger Nix(2022年02月22日)。Low Energy Electron Diffraction (LEED)。CHEMISTRY LIbreTexts。查詢日期：2022/08/11。
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Surface_Science_(Nix)/06%3A_Overlayer_Structures_and_Surface_Diffraction/6.02%3A_Low_Energy_Electron_Diffraction_(LEED)。
[5] Electron Inelastic Mean Free Path of Elements and Compounds。Globalsino。查詢日期：2021/11/02。https://www.globalsino.com/EM/page4809.html。
[6] Syed Naeem Ahmed(2015年)。Mean Free Path。ScienceDirect。
查詢日期：2021/10/11。https://www.sciencedirect.com/topics/physics-and-astronomy/mean-free-path
[7] (2012年02月09日)。Electron Mean Free Paths。Globalsino。
查詢日期：2021/10/11。
https://www.globalsino.com/micro/TEM/TEM9923.html。
[8] Wehnelt cylinder。維基百科。查詢日期：2021/10/11。https://en.wikipedia.org/wiki/Wehnelt_cylinder。
[9] Wei-chuan Chen, Tay-Rong Chang, Sun-Ting Tsai, S Yamamoto, Je-Ming Kuo, Cheng-Maw Cheng, Ku-Ding Tsuei, Koichiro Yaji, Hsin Lin, H-T Jeng, Chung-Yu Mou, Iwao Matsuda, S-J Tang, Signifcantly enhanced giant Rashba splitting in a thin film of binary alloy, New J.Phys.17, 083015 (2015)
[10] Particle in a one-dimensional lattice。維基百科。查詢日期：2022/08/11。https://en.wikipedia.org/wiki/Particle_in_a_one-dimensional_lattice。
[11] 蘇青森。真空技術精華。臺北市：五南。ISBN 978-957-11-3478-9 (2003)