在奈米級(nano scale)半導體元件中，如何增加這些元件的效能(performance)是許多企業及研究者致力的目標之一。現今的半導體元件中，大部分是由薄膜系統所構成，在奈米尺寸下，其應變(strain)將直接影響元件間的載子遷移率(carrier mobility)，這個現象又可應用在所謂的應變工程(strain-engineering) [1-5]，即是利用晶體所受之應變來改善元件的效能。因此，應力對於元件的效能而言，將是扮演關鍵的角色之一。然而，目前存在的量測方法中，如穿透式電子顯微鏡(Transmission Electron Microscope, TEM)、同調性X光繞射成像(Coherent X-ray diffraction Image, CDI)和掠角繞射(Grazing incident X-ray diffraction, GIXD)分別受到破壞性量測、造價昂貴而無法廣泛被業界應用和穿透深度不足之缺點而有所限制。而在應變工程中，為了量測微小之應力，利用三光布拉格表面繞射的方法來發展”次皮米解析度之縱向剖析介面應力”，其布拉格表面繞射幾何，是由一個利用大角度入射(wide-angle incidence)以激發出對稱式布拉格繞射光(symmetric Bragg diffraction)，和一個沿著樣品表面傳遞之表面繞射光所組成。這項研究是利用布拉格表面繞射之幾何，並且選擇(004)/(202)、(004)/ (0-22)、(004)/ (4-22)三組面來進行。此外，為了實現以次皮米解析度剖析介面應力之實驗 ，我們選擇被半導體裝置廣泛應用的異質結構Si0.7Ge0.3/Si，以發展此項技術。最終，利用空間強度分佈之數據圖，並以多層邊界之X光動力繞射理論模擬空間強度數據，解析Si0.7Ge0.3/Si之異質接面的應力分佈。此外，此繞射方法未來或可將目前各量測應力技術之解析度，從奈米尺寸提升至次皮米尺寸。

For nano-semiconductor devices, how to enhance the device performance is one of the main goals of the semiconductor industries. As many devices are composed of thin-film systems in nano-scale, the carrier mobility would be directly governed by the strain of the thin film systems. The phenomenon could be applied to the strain-engineering [1-4] processes, which use the strain to improve the device performance and yet broaden their application [6]. Consequently, the strain is one of the important factors to the performeance of the device. However, the conventional methods of the strain measurement, transmission electron microscopy, TEM [7, 8], coherent X-ray diffraction image, CDI [9-13] and grazing incident X-ray diffraction, GIXD, are limited by destructive probing nature, the price of the instrument and the penetration depth, respectively. To dimension such a minor strain in strain-engineering processes, the depth profile with the sub-pico resolution of the interfacial strains are proposed by using three-beam Bragg-surface diffraction (BSD) [14, 15]. BSD is consisted of a symmetric Bragg diffraction at a wide-angle incidence and a surface diffraction, propagating along the interface of the sample. The three BSD, (004)/(202), (004)/ (0-22), (004)/ (4-22) were measured in this study. Moreover, we applied the hetero structure, Si0.7Ge0.3/Si, which are frequently used as semiconductor devices, to develop the technology of mapping the strain vs. depth with a sub-picometer resolution. Due to the structural proximity of the Si0.7Ge0.3 film and Si substrate, the surface diffraction of Si0.7Ge0.3 thin-film and Si substrate are simultaneously excited during the diffractive processes. Kiessig-like fringes are shown up in the vertical spatial intensity distributions (tth-scan). For mapping the stain in depth perpendicular to the hetero-junction, the spatial intensity were simulated by multi-layer dynamical theory [16-19] of X-ray diffraction for crystalline materials. Furthermore, the diffraction method reported in this dissertation may push the resolution of the current strain measurements from a dozen of nanometers to sub-pico meters regime in the future.

[1] Antoniadis, D.A. et al. Continuous MOSFET performance increase with device scaling: The role of strain and channel material innovations. IBM J. RES. & DEV. 50, 363-376 (2006).
[2] Hÿtch, M., Houdellier, F., Hüe, F., and Snoeck, E. Nanoscale holographic interferometry for strain measurements in electronic devices. Nature 453, 1086-1089 (2008).
[3] Paul, D.J. Si/SiGe heterostructures: from material and physics to devices and circuits. Semicond. Sci. Technol. 19, R75–R108 (2004).
[4] Ieong, M. et al. Silicon device scaling to the sub-10-nm regime. Science 306, 2057-2060 (2004).
[5] Yu, D., Zhang, Y., and Liu, F. First-principles study of electronic properties of biaxially strained silicon: Effects on charge carrier mobility. Phys. Rev. B 78, 245204 (2008).
[6] Grünebohm, A., Ederer, C., and Entel, P. First-principles study of the influence of (110)-oriented strain on the ferroelectric properties of rutile TiO2. Phys. Rev. B 84, 132105 (2011).
[7] Strachan, D.R. et al. Real-time TEM imaging of the formation of crystalline nanoscale gaps. Phys. Rev. Lett. 100, 056805 (2008).
[8] Lisiecki, I. et al. Structural investigations of copper nanorods by high-resolution TEM. Phys. Rev. B 61, 4968-4974 (1999).
[9] BUDAI, J.D. et al. X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates. Nature Mater. 2, (2003).
[10] Newton, M.C., Leake, S.J., Harder, R., and Robinson, I.K. Three-dimensional imaging of strain in a single ZnO nanorod. Nature Mater. 9, 120-124 (2010).
[11] Robinson, I. and Harder, R. Coherent X-ray diffraction imaging of strain at the nanoscale. Nature Mater. 8, 291-298 (2009).
[12] Gulden, J. et al. Coherent x-ray imaging of defects in colloidal crystals. Phys. Rev. B 81, 224105 (2010).
[13] Miao, J. et al. Atomic resolution three-dimensional electron diffraction microscopy. Phys. Rev. Lett. 89, 155502 (2002).
[14] Jen, C.-Y. and Chang, S.-L. Bragg-surface three-beam dynamical X-ray diffraction. Acta Cryst. A 48, 655-663 (1992).
[15] Hayashi, M.A. et al. Sensitivity of Bragg surface diffraction to analyze ion-implanted semiconductors. Appl. Phys. Lett. 71, 2614-2616 (1997).
[16] Authier, A. Dynamical Theory of X-Ray Diffraction (Oxford University Press,Oxford New York, 2004).
[17] Chang, S.-L. X-Ray Multiple-Wave Diffraction (Springer Verlag,Berlin, 2004).
[18] Stetsko, Y.P. and Chang , S.-L. An algorithm for solving multiple-wave dynamical X-ray diffraction equations. Acta Cryst. A 53, 28-34 (1997).
[19] Souvouov, A. et al. X-ray multiple diffraction from crystalline multilayers: Application to a 90° Bragg reflection. Phys. Rev. B 70, 224109 (2004).
[20] Sidikia, T.P. et al. Impact of the SiGe/Si interface structure upon the low temperature photoluminescence of a Si/Si1-xGex multiple quantum well. Materials Science in Semiconductor Processing 3, 389-393 (2000).
[21] Huang, C. et al. Lateral heterojunctions within monolayer MoSe2–WSe2 semiconductors. Nature Mater. 13, 1096-1101 (2014).
[22] Radtke, G. et al. Atomic-scale Ge diffusion in strained Si revealed by quantitative scanning transmission electron microscopy. Phys. Rev. B 87, 205309 (2013).
[23] Stoffel, M. et al. Local equilibrium and global relaxation of strained SiGe/Si„001… layers. Phys. Rev. B 74, (2006).
[24] Tinkham, B.P., Goodner, D.M., Walko, D.A., and Bedzyk, M.J. X-ray studies of Si/Ge/Si(001) epitaxial growth with Te as a surfactant. Phys. Rev. B 67, 035404 (2003).
[25] Maiti, C.K. et al. Hafnium oxide gate dielectric for strained-Si1-xGex. Solid-State Electronics 47, 1995-2000 (2003).
[26] Evans, K.L. et al. Characterization of epitaxial SiGe thin films on Si : analytical considerations. Surf. Interface Anal. 18, 129-136 (1992).
[27] Yasuda, T. et al. Measurement of Interface-Induced Optical Anisotropies of a Semiconductor Heterostructure: ZnSeyGaAs(100). Phys. Rev. Lett. 77, 326-329 (1996).
[28] Lee, M.L. et al. Strained Si, SiGe, and Ge channels for high-mobility metal-oxide-semiconductor field-effect transistors. J. Appl. Cryst. 97, 011101 (2005).
[29] Sander, D. et al. Stress, strain and magnetostriction in epitaxial films. J. Phys.: Condense Matter 14, 4165-4176 (2002).
[30] Jacobsen, R.S. et al. Strained silicon as a new electro-optic material. Nature 441, 199-202 (2006).
[31] Roberts, M.M. et al. Elastically relaxed free-standing strained-silicon nanomembranes. Nature Mater. 5, 388-393 (2006).
[32] Wolf, I.D. Micro-Raman spectroscopy to study local mechanical stress in silicon integrated circuits. Semicond. Sci. Technol. 11, 139-154 (1996).
[33] Bean, J.C. Strained-layer epitaxy of germanium-silicon alloys. Science 230, 127-129 (1985).
[34] Sun, L.D. et al. Strain Oscillations Probed with Light. Phys. Rev. Lett. 96, 016105 (2006).
[35] Tirry, W. and Schryvers, D. Linking a completely three-dimensional nanostrain to a structural transformation eigenstrain. Nature Mater. 8, 752-757 (2009).
[36] Warner, J.H., Young, N.P., Kirkland, A.I., and Briggs, G.A.D. Resolving strain in carbon nanotubes at the atomic level. Nature Mater. 10, 958-962 (2011).
[37] Brugger, H., Schaffler, F., and Abstreiter, G. In Situ Investigation of Band Bending during Formation of GaAs-Ge Heterostructures. Phys. Rev. Lett. 52, 141-144 (1984).
[38] Holt, M.V. et al. Strain imaging of nanoscale semiconductor heterostructures with X-ray Bragg projection ptychography. Phys. Rev. Lett. 112, 165502 (2014).
[39] SHAO-HORN, Y. et al. Atomic resolution of lithium ions in LiCoO2. Nature Mater. 2, 464-467 (2003).
[40] He, R. and Yang, P. Giant piezoresistance effect in silicon nanowires. Nature Nanotechnol. 1, 42-46 (2006).
[41] Benediktovich, A.I., Feranchuk, I.D., and Ulyanenkov, A. X-ray dynamical diffraction from partly relaxed epitaxial structures. Phys. Rev. B 80, (2009).
[42] Kohn, V.G. and Kazimirov, A. Simulations of Bragg diffraction of a focused X-ray beam by a single crystal with an epitaxial layer. Phys. Rev. B 75, (2007).
[43] Mau-Sen, C., Dynamical calculation for X-Ray 24-beam diffraction in a Fabry-Perot cavity of silicon, in Physics. 2008, National Tsing-Hua Univ.
[44] Ibers, J.A. and Hamilton, W.C. International tables for X-ray crystallography Vol. IV, Section 3 (IUCr,Birmingham, 1974).
[45] Reuter, M.G. and Hill, J.C. An efficient, block-by-block algorithm for inverting a block tridiagonal, nearly block Toeplitz matrix. Comput. Sci. Discov. 5, 014009 (2012).
[46] Leontiou, T., Tersoff, J., and Kelires, P.C. Suppression of Intermixing in Strain-Relaxed Epitaxial Layers. Phys. Rev. Lett. 236104 (2010).
[47] Kosemura, D., Tomita, M., Usuda, K., and Ogura, A. Stress Measurements in Si and SiGe by Liquid-Immersion Raman Spectroscopy. INTECH 247-278 (2012).
[48] Dismukes, J.P., Ekstrom, L., and Paff, R.J. Lattice parameter and density in germanium-silicon alloys. J. Phys. Chem. 68, 3021-3027 (1964).
[49] Bond, W.L. and Kaiser, W. Interstitial versus substitutional oxygen in silicon. J. Phys. Chem. Solids 16, 44-45 (1960).
[50] Chang, S.-L. Treatment for the intensity problem of n-beam kinematical reflections in a dynamical formalism. Acta Cryst. A 38, 41-48 (1982).