Study Of Interaction Of Particles With Solids By Quantum And Classical Methods

Electron microscopy and electron spectroscopy techniques have been important tools for material characterization particularly on quantitative analysis. Study of elec-tron-solid interaction, as the physical basis of these techniques, is vital to quantitative interpretation of experimental electron microscopic image and electron spectra. It has been a significant research field of condensed matter physics. This thesis has theoret-ically studied the electron-solid interaction from different perspectives by employing classical Monte Carlo simulation method, wave mechanical method and Bohmian me-chanical method.Monte Carlo simulation method treats the random scattering process of electrons in a solid and the associated signal generation and emission process. It is easy for numerical calculation and becomes the most powerful tool in study of electron-solid interaction. However, the method is in principle of classical mechanics and omits elec-tron coherent scattering; application is then limited to amorphous and polycrystalline solids. When de Broglie wave length of electrons is comparable with lattice constant of crystalline the coherent scattering (diffraction effects) becomes obvious. Therefore, Monte Carlo simulation method of electron trajectory must be improved to take account of coherent scattering in single crystals.Bohmian mechanics is a theoretical formalism combining both the accuracy of the predictions of quantum mechanics and the capability of providing an intuitive inter-pretation of the physical phenomena involved. This alternative formalism of quantum mechanics presents significant conceptual differences from the conventional Copen-hagen interpretation. By Bohmian mechanics the particle trajectory is controlled by wave function, and the particle distribution follows that of wave function so that all statistical predictions agree exactly with those of standard quantum mechanics. In ad-dition to its interpretative importance, there has recently been growing interest from the computational point of view for its feature as a new calculation method.Chapter One reviews the development and present status of electron spectroscopy and electron microscopy, such as, Auger electron spectroscopy (AES), X-ray pho-toelectron spectroscopy (XPS), electron energy loss spectroscopy (EELS), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM). With development of aberration correction technique, aberration-corrected STEM instruments now routinely achieve a resolution of better than0.1nm. Atomic resolution was demonstrated in EELS and STEM based on aberration correction. For the crystal, the diffraction effects on the electron spec-troscopy are also significant. We also introduce Monte Carlo simulation method and wave mechanical method for simulation study in electron spectroscopy and electron microscopy.Chapter Two reviews the history of Bohmian mechanics. The fundamental equa-tions of motion of Bohm particles for single particle systems and for many-body sys-tems are outlined. We also summarize the basic postulates of Bohmian mechanics. It has been demonstrated by experiment and Bell theorem that only non-local hidden variable model can be compatible with standard quantum mechanics. We present the non-locality of Bohmian mechanics and its classical limit. We also discuss the quantum potential, which is a new physical quantity and connected to non-locality in Bohmian mechanics. The experiments to measure the quantum trajectory of single photon and to observe the nonlocality of Bohmian trajectories with entangled photons are outlined. Feynman path integrals are compared with Bohmian particle paths from various as-pects. Finally we present three numerical methods for calculation of Bohmian quantum trajectories.Chapter Three studies systematically with a Monte Carlo simulation method an important correction factor, the backscattering factor, in quantitative analysis by Auger electron spectroscopy. The primary energy ranges from the threshold energy of inner-shell ionization to30keV. The incident angle of primary beam and emission angle of Auger electrons are within0-89°. Principal Auger transitions in28pure elements are considered. The calculation employs a novel and general definition of backscattering factor, Casnati’s ionization cross section, up-to-date Monte Carlo model of electron scattering, and a large number of electron trajectories are simulated to reduce statistical error. Both the configuration geometries of concentric hemispherical analyzer (CHA) and the cylindrical mirror analyzer (CMA) for Auger electron detection are considered in the calculation. The calculated backscattering factors are found to describe very well an experimental dependence of Auger electron intensity on primary energy and on incident angle in literature. The calculated numerical values of backscattering factor are stored in an open and on-line database.Chapter Four employs the quantum mechanical Bloch-wave method and the reci-procity principle to describe electron transport in crystalline solids for determining the emission depth distribution function (EMDDF) of signal electrons in surface electron spectroscopy. The crystal structure and electron coherent scattering are explicitly taken into account while they are neglected in classical Monte Carlo methods. While electron inelastic scattering is treated with an optical potential, the EMDDF for Auger-electron emission from an Au (001) surface is calculated by the quantum method. The depen-dence of the EMDDF on emission angle and crystal structure has indicated that Auger electron emission intensity strongly depends on the emission direction and is sensitive to crystal structure. Comparisons made between the present results and classical Monte Carlo simulation results show pronounced differences due to electron-diffraction ef-fects. The mean escape depth (MED) which describes the surface sensitivity of Auger electron spectroscopy can also be evaluated. The present calculation shows that the MED for a crystalline solid is about half that for an amorphous solid from a Monte Carlo calculation.Chapter Five employs Bohmain mechanics to study electron diffraction in crys-tal. An investigation of electron scattering in a thin crystal has been performed. A time-independent interaction potential was employed to model a2D and3D crystal. Quantum trajectories were calculated through wave function by a numerical solution of the time-dependent Schrodinger equation. The probability density functions and quan-tum trajectories representing electron diffraction in real space were obtained from the calculation. The quantum trajectories provide an intuitive dynamics of the the elec-tron diffraction. For high energy electron diffraction in a crystal, we obtain the wave function by Bloch wave method. The quantum trajectories then present the formation process of electron channeling in crystal. Such example calculations show that the quantum trajectory method has great potential application to theoretical study of elec-tron interaction with solids, surface and nanostructures. Once electron inelastic scat-tering is included via an optical potential, the method can also be applied to electron spectroscopy techniques.Chapter Six studies helium atom scattering from a model surface in3D real space by using the Bohmian quantum trajectory theory. Helium atom scattering by solid surfaces is a well established technique for obtaining information about the structure, disorder and phonon spectra of the surface. The model surface was described by a3D interaction potential based on the model for the in-plane scattering of helium from a W(112) surface. The dynamic process of helium atom scattering has been presented by quantum trajectories of Bohmian particles. Bohmian mechanics becomes thus a new way to study atom-matter interaction.Chapter Seven presents a simulation of electron backscattering diffraction (EBSD) patterns with Bloch wave theory and reciprocity principle. EBSD pattern can provide important crystallographic information with high spatial resolution. For the simulation of an experimental image with a large field of view, a large number of reflecting planes are taken into account. Very good agreement is obtained for the simulated and experi-mental EBSD patterns of Mo (001) surface. Experimental features like zone-axis fine structure and higher-order Laue zone rings as well as relative intensity distribution are accurately reproduced.Chapter Eight is the summary of the thesis.