Research On Escape Dynamic Of Particles In Mesoscopic Devices

Since the mid-1980 s, investigations on the escape probability of particles have drawn much extensive attention in macro and micro fields, in which classical and quantum methods have been used respectively. With continuous improvement of mesoscopic devices whose scales are between the size of atoms and of materials measuring micrometres, it makes sense to study the escape of particles in mesoscopic systems. However, the dimensions of mesoscopic systems are usually too small to treat with classical mechanics or too large to deal by quantum mechanics.Fortunately, semiclassical theory, which can bridge the gap between quantum mechanics and its classical limit, has been extensively served as a relatively mature method in the research field of mesoscopic systems. This approach can be used to study the basic features of mesoscopic systems by presenting a simplified path integral formalism to combine the classical motion of electrons with quantum transport.Several research models on the mesoscopic systems within the framework of semiclassical theory have been proposed. Among these models, two-dimensional quantum billiards has become a popular prototype in the mesoscopic field. Previously, most studies concentrated on signatures of chaotic dynamics in closed mesostructure with a focus on the distributions of the probability density and the energy levels based on the periodic orbits theory and closed orbits theory. Recently, investigations on the transmission through open mesostructure have drawn much extensive attention, mainly due to remarkable advances in the fabrication of submicron semiconductor microstructures. The amplitude and phase carried by the classical trajectories of moving electrons in open quantum billiards can reflect the geometric stability and quantum coherence effect. The conductance g of the open quantum billiards is given by Landauer formula. Considering the width of the leads of the mesoscopic billiards is comparable to the electron de Broglie wavelength, the semiclassical approximations containing Kirchhoff diffraction, Fraunhofer diffraction, geometric theory of diffraction and uniform theory of diffraction have been put forward.In this thesis, we use a semiclassical approximation to study the escape of electrons through a circular mesostructure with the diffractive effect at the entrance lead taken into consideration.We find that the fluctuating shapes of the escape probability manifests a good agreement with the diffracted distributions of the incident angles for different transverse modes, and show that several classical trajectories with certain lengths have prominent contributions on the escape probability. In addition, we define the coherence factor to investigate the interference between electrons for different transverse modes and we find that it is the coherent backscattering that is responsible for the prominent interference. Moreover, we find there is a good correspondence between the distribution of classical trajectories and the time-reversed path. By defining the interacting factor, we find the interaction between electrons tending towards stability for several classical trajectories.The organization of the thesis is as follows. In the first chapter, we introduce the background and several basic conception associated with our research of the mesoscopic system. In the next chapter, we give the briefly representation of the core theories of our research methods. In the third chapter, we give the expression of the escape probability within the framework of a semiclassical approximation and introduce the classical trajectories of the moving electrons. The numerical results are given in the following, in which we analyze the effect of the incident angles and the lengths of classical trajectories on the escape probability by defining the diffracted distribution of classical trajectories(DDCT). Moreover, we calculate the coherence factor and the interacting factor to research the interference between electrons. The last chapter is the conclusions and outlook of our study.