Abstract
本論文利用分波原理及介電理論計算彈性散射截面、非彈性散射截面及表面激發作用機率等基本物理量，並使用自行開發的蒙地卡羅程式集，深入探討電子在固體中遷移的情形，建立了X光光電子能譜學定量分析的模式，成功地複製各種出射角度的X光光電子能譜，驗證了表面激發效應在光電子能譜學定量分析的重要性。在基本作用截面計算方面，非彈性作用我們係引用實驗光學常數，利用介電函數模式及總合測試規則，成功地算出電子與固體外層電子的非彈性作用截面，適用的電子能量範圍涵蓋數十至數千電子伏特的寬廣能量區間，為目前表面分析較常引用且較為正確的非彈性作用截面資料。在表面激發機率計算方面，我們考慮斜角度入射及反衝效應，揚棄小角度散射近似，所得結果更符合電子實際運動情行。在能譜分析方面，我們將固體分為深層及表層兩部份，利用蒙地卡羅方法及帕松統計模式，分別計算X光光電子在深層及表層區域能量損耗的情形。在電子穿出固體表面時，表面激發作用引發的電子能量損耗也用帕松統計模式加以計算，深入探討表面激發作用對不同出射角度X光光電子能譜變動的影響。經過一系列計算之後，我們將所得的結果與金固體Au-4f光電子實驗能譜作一比較，發現加入表面激發作用後的理論模擬能譜與實驗能譜相當吻合，證實表面激發作用在X光光電子能譜定量分析方面，有非常重要的影響度，也印證了本論文所發展模式與方法的正確性。A quantitative description about the angular and energy spectraof probe electrons emitted by a solid sample is important insurface analyses. The X-ray photoelectron spectroscopy (XPS),for example, is a powerful technique applied in surfacecomposition analysis. An investigation of the surface effect onAu-4f XPS for different exit angles was made in this thesis. Itwas found that surface plasmon excitations made significantcontributions to spectra in single and plural energy-loss peaksand in the multiple loss background. Our approach involvedMonte-Carlo simulations of photoelectrons in the interiorregion of the solid and Poisson stochastic processes in thesurface region. The partial wave expansion method with theHartree-Fock-Wigner-Seitz solid potential was used to calculateelectron differential elastic cross sections. An extended Drudedielectric function model was employed to compute electrondifferential inverse mean free paths for volume excitations.These mean free paths in the surface region became spatially-varying. To overcome this phenomenon, Poisson stochasticprocess was employed to calculate the energy-loss in thesurface region. This process makes use of the total probabilityfor inelastic and surface interactions rather than thedifferential probability per unit pathlength required by MonteCarlo simulations. Differential probabilities for surfaceexcitations were determined using the same model dielectricfunction. Computed results on Au 4f XPS showd that surfaceplasmon excitations made significant contributions to thespectra in single and plural energy-loss peaks and in themultiple loss background. The simulated X-ray photoelectronspectra that included surface excitations agreed quite wellwith experimental data for different emission angles.