平面及圓柱系統之電子激發效應

Abstract

本論文在探討運動之帶電粒子與固體間的非彈性交互作用，研究相關的理論模式，針對電子激發所產生的效應加以模擬與分析。 當帶電粒子在靠近固體表面移動時，其所產生的電子激發效應，對表面靈敏性散射能譜有很大的影響。根據電磁介電理論，這些激發效應可以用物質的介電函式來描述。在本論文中，所採用的是延伸式德魯特介電函式，在此函式中的所有參數是由實驗所量測到的光學數據及電子能量損失能譜來決定的。除此之外，建立介電函式時也考慮總和率的限制來確保精確性，並檢驗在能帶躍遷關鍵點之能量轉移及集體激發之電漿子能量以確認無誤。 在平面系統的電子激發效應方面，本研究推導之電子微分倒數非彈性平均自由行徑及非彈性平均自由行徑模式，可以適用在以任意入射角或出射角穿越固體表面並且離穿越點任意距離之電子。體及表面激發效應對於非彈性散射截面貢獻甚大，體激發效應只在固體裡面發生，而表面激發效應則會在靠近固體表面的兩側發生。由於在固體內部的表面激發效應和體激發效應會互相抵消，所以在真空中之表面激發效應就變得格外重要，而此真空部分之表面電漿子總激發機率通常以表面激發參數來描述。本研究主要探討當電子穿越III-V半導體固體表面的表面激發參數，其與穿越角、電子能量之關係。結果顯示，表面激發參數滿足一個簡單的算式。更進一步地，本研究也建立了非彈性交互作用的記憶效應模式，此一記憶效應詮釋了前次的非彈性交互作用會影響到下次的非彈性交互作用之現象。對於帶電粒子沿固體表面平行移動時，其感生電位、阻擋本領、微分倒數非彈性平均自由行徑和非彈性平均自由行徑之模式均被建構，研究顯示對某特定粒子能量，其考慮記憶效應的結果會座落在不考慮記憶效應之此粒子能量及上次非彈性作用前粒子能量的結果之間，而記憶效應會隨前次非彈性交互作用能量損失增加而變大。 在圓柱系統的電子激發效應方面，本研究推導出可以適用在平行於一般或鍍層圓柱結構之軸運動的電子和系統間的非彈性交互作用之模式。利用電磁介電理論，微分倒數非彈性平均自由行徑及倒數非彈性平均自由行徑的模式均被推導，且被應用在矽圓柱、矽空腔、矽圓柱管、長有二氧化矽膜之矽圓柱…等情況。結果顯示，表面激發效應會在表面兩側發生，而體激發效應只會在固體內部發生。且靠近表面時，表面激發效應會增加而體激發效應會減少，而能互補抵消。對於矽空腔來說，除了在極靠近表面的地方以外，其他地方的倒數非彈性平均自由行徑幾乎是固定值，大概等於無限大矽塊材之倒數非彈性平均自由行徑。對於長有二氧化矽膜之矽圓柱來說，非彈性交互作用則包含了體、表面和介面激發效應。而這些激發效應與電子跟表面或介面之距離、矽圓柱之半徑、二氧化矽膜之厚度…等有關。

In this dissertation, the models dealing with the inelastic interactions between a charged particle and a solid were developed. Based on inelastic-scattering models, simulations and analyses of electronic excitations were made. The electronic excitations produced by a charged particle moving near a solid surface play a crucial role in surface-sensitive spectroscopies. By the use of the dielectric response theory, these excitations can be described in terms of the dielectric functions of the materials. The dielectric functions employed in this dissertation were the extended Drude dielectric functions. All parameters in such function were determined by fits to the corresponding experimental optical data and electron energy-loss spectra. In addition, this function was constrained by sum-rules to assure the accuracy and examined to confirm critical-point energies in the interband transitions and plasmon energies in the collective excitations. In the work for the electronic excitations in planar systems, theoretical derivations of the differential inverse inelastic mean free path (DIIMFP) and inelastic mean free path (IMFP) for electrons crossing solid surfaces were made for different crossing angles and electron distances relative to the crossing point at the surface. Such inelastic cross-sections comprise mainly the contributions from volume and surface excitations. Volume and surface excitations occur when electrons travel, respectively, inside the bulk of the material and near the surface inside or outside the solid. Due to the rough compensation of surface and volume excitations inside the solid, one may pay attention to surface excitations in vacuum. The surface excitation parameters (SEPs) which describe the total probabilities of surface plasmon excitations by electrons traveling in vacuum before impinging on or after escaping from several semiconducting III-V compounds have also been calculated for electrons crossing the compound surfaces with various crossing angles and with various energies. The SEPs were then found to follow to a simple formula. Moreover, the model accounting for the memory effect, which describes the influence of the previous inelastic interaction on the succeeding inelastic interaction, of a charge particle between two successive inelastic interactions was established. Formulas of the induced potential, stopping power, DIIMFP and IMFP considering the memory effect were derived for a charged particle moving parallel to a solid surface. It was found that those with the memory effect for energy lay between the corresponding values without the memory effect for energy and previous energy . The memory effect increased with increasing energy loss, , in the previous inelastic interaction. In the work for the electronic excitations in cylindrical systems, the theories were developed to deal with inelastic interactions for an electron moving parallel to the axis of a cylindrical structure and a clad cylindrical structure. Formulas for the DIIMFP and inverse IMFP (IIMFP) were derived using dielectric response theory. The DIIMFPs and IIMFPs were calculated for a Si wire, a cavity in Si, a Si cylindrical tube, or a Si cylinder clad in a SiO2 film. The calculated results showed that surface excitations occurred as the electron moved near the boundary either inside or outside the solid, whereas volume excitations arose only for electron moving inside the solid. It was found that the probability for surface excitations increases and that for volume excitations decreases for an electron moving close to the surface. Near the surface, the decrease in volume excitations is compensated by the increase in surface excitations. For a cavity in Si, the IIMFP inside the solid can be approximated by a constant value equal to the IIMFP for the infinite Si, except in the immediate vicinity of the cavity boundary. For the Si cylinder clad in the SiO2 film, inelastic interactions were contributed from volume, surface and interface excitations. Calculated results showed that the relative importance of these excitations depended on the electron distance from the surface or interface of the cylindrical system, the radius of the Si cylinder, and the thickness of the SiO2 film.