臺灣博碩士論文加值系統

這個工作主要是探討矽晶片上的微結構對非對稱表面繞射光的影響，並且利用動力繞射理論分析繞射圖譜的成因及其物理特性。接著，利用這一個結果來設計廣角入射X光光學元件並討論其元件的可行性。
本實驗是採用Si[001]矽晶片之掠角出射的繞射幾何，選定的原子面是Si(113)，而入射光能量則是 。實驗可以分為三個部份：第一、矽晶體的非對稱表面繞光：實驗上可以得到兩道掠角出射的繞射光，一道是Si(113)繞射光，另外一道則是Si(113)繞射光的鏡面反射光。使用動力繞射理論計算亦可得到相同的結果。第二、矽奈米線(Si-wire)對非對稱表面繞射光的影響：和矽晶體的實驗結果比較，有二道繞射光是矽奈米線造成，由矽奈米線和矽晶體的幾何，可以分析每一道繞射光的成因，並畫出其光路圖。第三、設計一個廣角入射X光波導管，其元件為金/矽奈米線/金的三層結構(Au/Si-wire/Au)，當表面繞射光和矽奈米線側壁的夾角小於內全反射角時，表面繞射光在水平的方向是會被金的薄膜侷限在矽奈米線內傳遞。
同時，本論文也將深入討論晶體內X光波場模態與晶體外繞射圖譜關連性之研究。吾人建立一個繞射圖譜的計算模型，只要比較實驗結果與理論計算結果，就可以得到晶體內激發模組和晶體外繞射圖譜的對應。
關鍵字：非對稱表面繞射光、動力繞射理論、廣角入射波導管

This work aims to study the diffraction pattern and dynamical analysis of asymmetric surface diffraction from a nano-structure on a chip. This studying is able to design a wide-angle incidence x-ray optical device using crystal surface diffraction. We have investigated the possibility of the opical device.
Nano-structures were prepared on a 6-in Si (001) wafer. The Si (113) is chosen as an asymmetric surface diffraction for the photon energy 8.8785 keV according to the Si crystal orientation and diffraction geometry. The experimental results may be summarized as follows. First, there are two diffraction peaks in vertical direction for bare silicon, which are diffracted beam Si (113) and specular reflection of Si (113). The experimental results are in good agreement with the theoretical calculations using the dynamical theory of x-ray diffraction. Second, four peaks were measured in vertical direction for silicon nano-wire. Two of peaks were from bare silicon due to width of silicon nano-wire is much smaller than incident beam spot in horizontal direction. The other two peaks due to a silicon nano-wire and its specular reflection. The ray tracing of a silicon nano-wire was drawn. Finally, the schematic design of wide-angle incidence x-ray waveguide is Au/Si/Au sandwich system with Si as the guiding layer and Au as cladding layer. The surface diffracted beam can be confined and propgated inside the silicon nano-wire if the total refection occurs.
In additional, I have introduced an algorithm, Diffraction Pattern Algorithm, to get the diffraction patter. The correlation between excitation of mode inside the crystal and diffraction pattern outside the crystal can be illustrated by experimental data and theoretical calculation using the algorithm.
Keyword: asymmetric surface diffracted beam, the dynamical theory of x-ray diffraction, wide-angle incidence x-ray waveguide

目錄
摘 要..........................................................................................................................I
Abstract.......................................................................................................................II
致 謝.......................................................................................................................IV
目 錄........................................................................................................................V
圖目錄.....................................................................................................................VIII
第1章導論...........................................................................................................1
第2章X光動力繞射理論.......................................................................................3
2.1 簡述X光動力繞射理論...................................................................................3
2.1.1 基本波場方程式(Fundamental equation of wavefield)............................3
2.1.2 特徵值方程式(Eigenvalue Equation)......................................................5
2.1.3 邊界條件:單片晶體.................................................................................8
2.1.4 色散表面和線性吸收係數.....................................................................11
2.1.5 波的傳遞模態(Mode of Wave Propagation)..........................................13
VI
2.2 計算範例......................................................................................................13
2.2.1 對稱兩光布拉格繞射(Symmetric Two-Wave Bragg Diffraction)............14
2.2.2 三光繞射..............................................................................................18
2.2.3 非對稱繞射...........................................................................................21
第3章繞射圖樣理論計算....................................................................................37
3.1 一維繞射圖樣理論計算................................................................................37
3.1.1 繞射圖樣演算法....................................................................................37
3.1.2 計算範例..............................................................................................42
3.2 二維繞射圖樣理論計算................................................................................52
3.2.1 繞射圖樣演算法....................................................................................52
3.2.2 範例......................................................................................................53
第4章X光廣角入射矽奈米線及波導管實驗........................................................55
4.1 表面繞射光..................................................................................................55
4.2 實驗架設......................................................................................................56
4.3 實驗結果及討論...........................................................................................58
4.3.1 矽晶體(Bare Si)....................................................................................58
4.3.2 矽奈米線(Silicon nano-wire).................................................................62
VII
4.3.3 Au/Si/Au三層結構之波導管..................................................................77
第5章結論與未來展望.......................................................................................84
參考文獻....................................................................................................................86

參考文獻
[1]
A. Malik, A. R. Sandy, L. B. Lurio, G. B. Stephenson, S. G. J. Mochrie, I. McNultu, and M. Sutton, Phys. Rev. Lett. 81, 5832-5835 (1998).
[2]
S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, Phys. Rev. Lett. 78, 1275-1278 (1997).
[3]
M. J. Zwanenburg, J. F. Peters, J. H. H. Bongaerts, S. A. de Vries, D. L. Abernathy, J. F. van der Veen, Phys. Rev. Lett. 82, 1696-1699 (1999).
[4]
C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, Appl. Phys. Lett. 69, 1826-1828 (1996).
[5]
F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, Science, 297, 230-234 (2002).
[6]
E. Spiller and A. Segmüller, Appl. Phys. Lett. 24, 60-61 (1974).
[7]
C. Bergemann, H. Keymeulen, and J. F. van der Veen, Phys. Rev. Lett. 91, 204801-1 – 204801-4 (2003).
[8]
F. Pfeiffer, and T. Salditt, Phys. Rev. B 62, 16939-16943 (2000).
87
[9]
A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, T. Salditt, Phys. Rev. Lett. 94, 074801 (2005).
[10]
I. Bukreeva, A. Popov, D. Pelliccia, A. Cedola, S. B. Dabagov, and S. Lagomarsino, Phys. Rev. Lett. 97, 184801 (2006).
[11]
C. Fuhse, C. Ollinger, and T. Salditt, Phys. Rev. Lett. 97, 254801 (2006).
[12]
R. Colella, Acta cryst. A30, 413-423 (1974).
[13]
Ur. P. Stetsko, and S.-L. Chang, Acta Cryst. A53, 28-34 (1997).
[14]
S.-L. Chang, X-ray Multiple-Wave Diffraction Theory and Application, (Springer-Verlag, Berlin, 2004).
[15]
P. P. Ewald, and Y. Heno, Acta Cryst. A24, 5-15 (1986).
[16]
A. Authier, Dynamical theory of X-ray Diffraction, (Oxford university press, Oxford, 2004).
[17]
http://140.110.203.42/manage/fck_fileimage/file/bldoc/17BW20DCM.htm
[18]
B. W. Batterman and H. Cole, Rev. Mod. Phys. 36, 681-717 (1964).
[19]
邱茂森, X光共振腔之24光動力繞射計算,國立清華大學博士論文 (2008).
88
[20]
S.-L. Chang, Acta Cryst. A35, 543-547 (1979).
[21]
C.-Y Jen, and S.-L. Chang, Acta Cryst. A48, 655-663 (1992).
[22]
T. Bedyńska, Phys. Stat. Sol. (a) 25, 405-411 (1974).
[23]
J. Härtwig, Phys. Stat. Sol. (a) 37, 417-425 (1976).
[24]
T. Bedyńska, Phys. Stat. Sol. (a) 19, 365-372 (1973).
[25]
http://140.110.203.42/EFD.php?num=271
[26]
http://henke.lbl.gov/optical_constants/pert_form.html
[27]
朱培慈, X光廣角入射矽奈米線之表面繞射研究, 國立清華大學碩士論文 (2011).
[28]
S.-L. Chang, and M. -T. Tang, Acta Cryst. A44, 1065-1072 (1988).
[29]
J. Als-Nielsen and D. McMorrow, Elements of Modern X-ray Physics (Wiley,2001)
[30]
T. Salditt, S.P. Krüger, C. Fuhse, C. Bähtz, Phys. Rev. Lett. 100, 184801 (2008)
[31]
K. Giewekemeyer, S. P. Krüger, S. Kalbfleisch, M. Bartels, C. Beta, and T. Salditt, Phys. Rev. A 83, 023804-1 – 023804-7 (2011).
89
[32]
A. Kohlstedt, S. Kalbfleisch, T. Salditt, M. Reiche, U. Gösele, E. Lima, P. Willmott, Appl. Phys. A 91, 7-12 (2008).
[33]
A. Jarre, J. Seeger, C. Ollinger, and C. Fuhse, C. David, T. Salditt, J. Appl. Phys. 101, 054306-1 - 054306-6 (2008).
[34]
C. Ollinger, C. Fuhse, A. Jarre, T. Salditt, Physica B 357, 53-56 (2005).
[35]
S. P. Krueger, H. Neubauer, M. Bartels, S. Kalbfleisch, K. Giewekemeyer, P. J. Wilbrandt, M. Sprung and T. Salditt, J. Synchrotron Rad. 19, 227-236, (2012).
[36]
S. P. Krüger, K. Giewekemeyer, S. Kalbfleisch, M. Bartels, H. Neubauer, and T.