带电粒子与表面/界面电子气相互作用的量子流体动力学研究
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摘要
研究带电粒子与表面/界面电子气相互作用过程是固体物理、表面物理以及材料科学中的重要课题。这些研究在表面分析技术、固体材料表面改性技术、微电子器件加工技术等领域具有重要意义。载能带电粒子可以作为一种粒子束探针,通过其与材料表面发生相互作用,可以获得有关材料表面的成分、结构以及光电性的信息。如通过测量电子束在材料表面或内部的能量损失谱,可以确定材料的电激发特性及电子气的密度:利用离子束背散射或离子束沟道分析技术,可以确定材料的成分及结构。此外,在微/纳米结构制备工艺中,通过控制聚焦离子束与材料表面的相互作用过程,可以得到所需要的微/纳米结构图形(如光子晶体,MEMS等)。
本文主要采用线性量子流体动力学理论来研究带电粒子与不同的表面/界面(单层二维电子气、双层平行的二维电子气、镀有金属膜的纳米介质球、有限厚度/金属膜/绝缘基底等)相互作用过程,重点探索材料的量子效应、尺度效应对表面/界面的电激发过程产生感应电势、电子气的扰动密度以及入射粒子能量损失的影响。
在绪论部分,首先介绍了带电粒子与表面/界面电子气相互作用的研究及应用背景;其次,回顾了有关带电粒子在物质中能量损失的研究进展以及相关的理论模型;最后,针对目前研究中存在的问题,介绍了本文的研究计划和结构安排。
在第二章中,首先介绍了自洽的量子流体动力学模型,该模型通过我们熟知的宏观量(如:密度、能量、动量、速度等)反映了微观粒子之间的相互作用。把量子流体动力学模型与泊松方程相结合,在线性化基础上得到了带电粒子平行于二维电子气平面运动时的感应势、感应电子气密度、电子流体的速度场、阻止本领、侧向力和自能的表达式。计算结果表明,量子统计和量子衍射效应使感应势的振荡强度明显减弱,说明量子效应作用的结果是使电子气恢复平衡。在考虑量子效应的前提下,分析了入射粒子速度对感应势和感应电子气密度空间分布的影响。结果表明,当入射粒子的速度相对较高时,在其所在位置的后方感应势和感应电子气密度均出现了Ⅴ型振荡的尾流效应,并且粒子的速度越高,锥角越小,振荡的范围越大,波长越长。此外,还计算了电子气流体速度场的分布,结果表明,电子的振荡以纵波的形式向入射粒子运动的反方向传播。最后,计算了粒子的位置、阻尼系数、密度参数对阻止本领、侧向力和自能的影响。结果发现,当粒子距离电子气平面越近或者电子气的密度参数越小时,粒子损失的能量越多。而当阻尼系数趋于零时,电子气内出现了共振激发,此时在高速区能量损失达到最大。
在第三章中,研究了带电粒子平行于双层二维电子气平面运动时的电激发过程,得到了两个电子气平面相互耦合的感应势、感应电子气密度、阻止本领、侧向力和自能的表达式。计算结果表明,当带电粒子平行于两个电子气平面运动时,除了在粒子的后方出现了振荡的尾势外,还在两个平面所在位置出现了明显的尖峰。此外,当两个电子气平面间的距离较近时,相互耦合的结果是使阻止本领、侧向力和自能随速度变化曲线出现了明显的双峰结构,随着粒子与两个电子气平面距离的加大这种双峰结构消失。当两个电子气平面间的距离较小时,电子气密度参数也会对阻止本领、侧向力和自能随速度变化产生影响,使之出现明显双峰结构。
在第四章中,采用球坐标系下的线性量子流体动力学模型与恰当的边界条件相结合,研究了带电粒子与镀有金属膜的纳米介质球之间的相互作用。计算结果表明,当带电粒子在球表面附近运动时,球表面金属膜内的电子由于极化和激发而产生振荡的尾流效应。当粒子逐渐远离介质球时,感应势和感应电子气密度振荡的幅值变小,最大峰值所在位置也随粒子前移。此外,当入射粒子的速度小于某一临界速度时,感应势振荡的最大幅值随速度的增大而变大,反之,则随速度的增大而变小。最后,计算结果还显示,由于球形结构的特殊性,使粒子在接近而后远离小球过程中阻止本领的值先负后正,(即,小球始终对粒子吸引,其电场力对粒子先加速后减速):随着小球介电常数的增大,阻止本领的峰值变小并向低速区移动,说明由于介质球的存在,使得其极化电场和表面电子气扰动产生的感应电场对入射粒子的整体作用效应变弱了。
在第五章中,研究了带电粒子平行于半无限大绝缘基底表面上有限厚度金属膜运动时产生的电激发过程,得到了感应势、扰动电子气密度、阻止本领、侧向力以及自能的表达式。计算结果表明,当金属膜很薄时,在它的两个表面处均出现了振荡的电激发现象,而且,随着金属膜厚度的增大,在金属膜与绝缘基底交界面处的振荡逐渐减弱直到消失。另外,金属膜对入射粒子的库仑势有明显的屏蔽作用。本章还详细分析了膜的厚度、粒子位置、密度参数和基底介电常数对粒子的能量损失和受力情况的影响。最后,把通过量子流体动力学模型和局域介电函数模型计算的感应势和阻止本领进行了对比。比较结果表明,由量子流体动力学模型计算所得感应势的振荡幅值较小,且在金属膜的两个表面处变化比较平缓。对于阻止本领而言,在粒子距离金属膜较近的情况下,由两个模型所得的结果在高速时比较接近;当粒子距离金属膜较远时,由两个模型所得的结果无论在低速还是高速情况下都差别不大。
The interactions of charged particles with electron gases at surfaces or interfaces have been a very important research field in surface physics. In particular, it has been an interesting topic due to the applications in the structure analysis, surface modification and microelectronic device processing techniques. The energetic particles can be as a probe to detect the material component, structure and photoelectric information by interacting with the surfaces. For example, the excitation characteristics and the electron gas density of the material can be detected by measuring the electron energy loss spectrum, and the material component and structure can be obtained by ion backscattering or ion beam channelling technology. Besides, in the manufacture technology in micro- or nano-scale, the surface structure can be also obtained by modulating the interactions between the focused ion beam and the material surfaces (e.g. photonic crystals and MEMS).
In this thesis, a self-consistent linearized quantum hydrodynamic (QHD) model is developed to investigate the excitations of the electron gases at different surfaces or interfaces (including single layer and double layers electron gases plane, the infinitesimally thin metal film covering on the nano-dielectric sphere and finite thin metal film covering on a semi-infinite dielectric substrate). And focus on the investigations of influences of the quantum and scale effects of the materials on the induced potential, the perturbed electron gas density and the energy loss in the excitation process of surfaces and interfaces.
In chapter 2, the electronic excitations induced by a charged particle moving parallel to two-dimensional electron gases plane are studied by means of the linearized QHD theory. The calculation results show that the influence of the quantum effects on the interaction process should be taken into account. The V shape oscillatory wake-field appears apparently behind the projectile particle when the particle speed becomes higher. As for the stopping power, lateral force and self-energy, the results indicate that the particle position, the damping coefficient and the electron gas density in equilibrium have effects on the peak value and position.
In chapter 3, the electronic excitation is investigated when the charged particle moving parallel to the layered electron gases system. Numerical results show that double peaks will occur in the stopping power, lateral force and self-energy curves caused by the two sheets structures, in which the electron polarization in both sheets contributes to the induced electric field. And the coupling of electric field of two sheets will gradually weaken when the distance of two surface increases. Further more, the parameter of electron gas density has effect on changes of the stopping power, lateral force and self-energy with the particle speed, and the double peaks appear obviously in the curves.
In chapter 4, we present a theoretical study on the interaction of the charged particle with a nano-dielectric sphere covered with infinitesimally thin metal film. The theoretical model is formulated in terms of linearized QHD equations, cooperated with trial solution of the electric potential with appropriate boundary condition. Numerical results indicate that an oscillatory wake effect exists in the electron gases during the interactions. Because of the limitation of the spherical structure, the value of stopping power is negative when the particle approaches the spherical surface and then becomes positive as the particle moves away from the sphere. In addition, as the relative permittivity is gradually larger, the peak values of the stopping power becomes smaller and shifts toward to low speed, which indicates that the total effects of polarized electric field and induced electric field on the charged particle become weaker.
In chapter 5, the interactions between charged particles and metal film covering on a semi-infinite dielectric substrate are investigated based on the linearized QHD theory under three-dimension. The calculation results show that an oscillatory wake field appears apparently behind the particle at two of the surfaces of the metal film, and the effects of the film thickness on the electron gas density cannot be neglected when film is thinner. Further more, the metal film has obvious screening effects on the coulomb potential of the projected particle. Besides, the dependence of the stopping power, lateral force and self-energy on the film thickness, particle position, density parameter and relative permittivity are analyzed. Finally, the results are compared with those based on the local frequency-dependent (LFD) dielectric approach. The comparison results indicate that the values of stopping power calculated from two models are almost in agreement with each other independent of proton speed when the charged particle moves away from the metal film. But, for the case of particle approaching the film, the results arising from two models are closer when the particle speed is higher.
本文主要采用线性量子流体动力学理论来研究带电粒子与不同的表面/界面(单层二维电子气、双层平行的二维电子气、镀有金属膜的纳米介质球、有限厚度/金属膜/绝缘基底等)相互作用过程,重点探索材料的量子效应、尺度效应对表面/界面的电激发过程产生感应电势、电子气的扰动密度以及入射粒子能量损失的影响。
在绪论部分,首先介绍了带电粒子与表面/界面电子气相互作用的研究及应用背景;其次,回顾了有关带电粒子在物质中能量损失的研究进展以及相关的理论模型;最后,针对目前研究中存在的问题,介绍了本文的研究计划和结构安排。
在第二章中,首先介绍了自洽的量子流体动力学模型,该模型通过我们熟知的宏观量(如:密度、能量、动量、速度等)反映了微观粒子之间的相互作用。把量子流体动力学模型与泊松方程相结合,在线性化基础上得到了带电粒子平行于二维电子气平面运动时的感应势、感应电子气密度、电子流体的速度场、阻止本领、侧向力和自能的表达式。计算结果表明,量子统计和量子衍射效应使感应势的振荡强度明显减弱,说明量子效应作用的结果是使电子气恢复平衡。在考虑量子效应的前提下,分析了入射粒子速度对感应势和感应电子气密度空间分布的影响。结果表明,当入射粒子的速度相对较高时,在其所在位置的后方感应势和感应电子气密度均出现了Ⅴ型振荡的尾流效应,并且粒子的速度越高,锥角越小,振荡的范围越大,波长越长。此外,还计算了电子气流体速度场的分布,结果表明,电子的振荡以纵波的形式向入射粒子运动的反方向传播。最后,计算了粒子的位置、阻尼系数、密度参数对阻止本领、侧向力和自能的影响。结果发现,当粒子距离电子气平面越近或者电子气的密度参数越小时,粒子损失的能量越多。而当阻尼系数趋于零时,电子气内出现了共振激发,此时在高速区能量损失达到最大。
在第三章中,研究了带电粒子平行于双层二维电子气平面运动时的电激发过程,得到了两个电子气平面相互耦合的感应势、感应电子气密度、阻止本领、侧向力和自能的表达式。计算结果表明,当带电粒子平行于两个电子气平面运动时,除了在粒子的后方出现了振荡的尾势外,还在两个平面所在位置出现了明显的尖峰。此外,当两个电子气平面间的距离较近时,相互耦合的结果是使阻止本领、侧向力和自能随速度变化曲线出现了明显的双峰结构,随着粒子与两个电子气平面距离的加大这种双峰结构消失。当两个电子气平面间的距离较小时,电子气密度参数也会对阻止本领、侧向力和自能随速度变化产生影响,使之出现明显双峰结构。
在第四章中,采用球坐标系下的线性量子流体动力学模型与恰当的边界条件相结合,研究了带电粒子与镀有金属膜的纳米介质球之间的相互作用。计算结果表明,当带电粒子在球表面附近运动时,球表面金属膜内的电子由于极化和激发而产生振荡的尾流效应。当粒子逐渐远离介质球时,感应势和感应电子气密度振荡的幅值变小,最大峰值所在位置也随粒子前移。此外,当入射粒子的速度小于某一临界速度时,感应势振荡的最大幅值随速度的增大而变大,反之,则随速度的增大而变小。最后,计算结果还显示,由于球形结构的特殊性,使粒子在接近而后远离小球过程中阻止本领的值先负后正,(即,小球始终对粒子吸引,其电场力对粒子先加速后减速):随着小球介电常数的增大,阻止本领的峰值变小并向低速区移动,说明由于介质球的存在,使得其极化电场和表面电子气扰动产生的感应电场对入射粒子的整体作用效应变弱了。
在第五章中,研究了带电粒子平行于半无限大绝缘基底表面上有限厚度金属膜运动时产生的电激发过程,得到了感应势、扰动电子气密度、阻止本领、侧向力以及自能的表达式。计算结果表明,当金属膜很薄时,在它的两个表面处均出现了振荡的电激发现象,而且,随着金属膜厚度的增大,在金属膜与绝缘基底交界面处的振荡逐渐减弱直到消失。另外,金属膜对入射粒子的库仑势有明显的屏蔽作用。本章还详细分析了膜的厚度、粒子位置、密度参数和基底介电常数对粒子的能量损失和受力情况的影响。最后,把通过量子流体动力学模型和局域介电函数模型计算的感应势和阻止本领进行了对比。比较结果表明,由量子流体动力学模型计算所得感应势的振荡幅值较小,且在金属膜的两个表面处变化比较平缓。对于阻止本领而言,在粒子距离金属膜较近的情况下,由两个模型所得的结果在高速时比较接近;当粒子距离金属膜较远时,由两个模型所得的结果无论在低速还是高速情况下都差别不大。
The interactions of charged particles with electron gases at surfaces or interfaces have been a very important research field in surface physics. In particular, it has been an interesting topic due to the applications in the structure analysis, surface modification and microelectronic device processing techniques. The energetic particles can be as a probe to detect the material component, structure and photoelectric information by interacting with the surfaces. For example, the excitation characteristics and the electron gas density of the material can be detected by measuring the electron energy loss spectrum, and the material component and structure can be obtained by ion backscattering or ion beam channelling technology. Besides, in the manufacture technology in micro- or nano-scale, the surface structure can be also obtained by modulating the interactions between the focused ion beam and the material surfaces (e.g. photonic crystals and MEMS).
In this thesis, a self-consistent linearized quantum hydrodynamic (QHD) model is developed to investigate the excitations of the electron gases at different surfaces or interfaces (including single layer and double layers electron gases plane, the infinitesimally thin metal film covering on the nano-dielectric sphere and finite thin metal film covering on a semi-infinite dielectric substrate). And focus on the investigations of influences of the quantum and scale effects of the materials on the induced potential, the perturbed electron gas density and the energy loss in the excitation process of surfaces and interfaces.
In chapter 2, the electronic excitations induced by a charged particle moving parallel to two-dimensional electron gases plane are studied by means of the linearized QHD theory. The calculation results show that the influence of the quantum effects on the interaction process should be taken into account. The V shape oscillatory wake-field appears apparently behind the projectile particle when the particle speed becomes higher. As for the stopping power, lateral force and self-energy, the results indicate that the particle position, the damping coefficient and the electron gas density in equilibrium have effects on the peak value and position.
In chapter 3, the electronic excitation is investigated when the charged particle moving parallel to the layered electron gases system. Numerical results show that double peaks will occur in the stopping power, lateral force and self-energy curves caused by the two sheets structures, in which the electron polarization in both sheets contributes to the induced electric field. And the coupling of electric field of two sheets will gradually weaken when the distance of two surface increases. Further more, the parameter of electron gas density has effect on changes of the stopping power, lateral force and self-energy with the particle speed, and the double peaks appear obviously in the curves.
In chapter 4, we present a theoretical study on the interaction of the charged particle with a nano-dielectric sphere covered with infinitesimally thin metal film. The theoretical model is formulated in terms of linearized QHD equations, cooperated with trial solution of the electric potential with appropriate boundary condition. Numerical results indicate that an oscillatory wake effect exists in the electron gases during the interactions. Because of the limitation of the spherical structure, the value of stopping power is negative when the particle approaches the spherical surface and then becomes positive as the particle moves away from the sphere. In addition, as the relative permittivity is gradually larger, the peak values of the stopping power becomes smaller and shifts toward to low speed, which indicates that the total effects of polarized electric field and induced electric field on the charged particle become weaker.
In chapter 5, the interactions between charged particles and metal film covering on a semi-infinite dielectric substrate are investigated based on the linearized QHD theory under three-dimension. The calculation results show that an oscillatory wake field appears apparently behind the particle at two of the surfaces of the metal film, and the effects of the film thickness on the electron gas density cannot be neglected when film is thinner. Further more, the metal film has obvious screening effects on the coulomb potential of the projected particle. Besides, the dependence of the stopping power, lateral force and self-energy on the film thickness, particle position, density parameter and relative permittivity are analyzed. Finally, the results are compared with those based on the local frequency-dependent (LFD) dielectric approach. The comparison results indicate that the values of stopping power calculated from two models are almost in agreement with each other independent of proton speed when the charged particle moves away from the metal film. But, for the case of particle approaching the film, the results arising from two models are closer when the particle speed is higher.
引文
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