Transfer Matrix Method For Crystal Lattice Line Structure

Nano-Science and Technology is a research frontier developed in the last decades. Electronic transport in nanoscaled structure exhibits a great deal of novel and marvelous properties and thus has received much current attention. In this thesis, the Transfer Matrix Method is applied to calculating two-terminal crystal system and crystal system with ring structure.The thesis consists of four chapters. In the first chapter, phenomena in nano systems are reviewed, such as Aharonov-Bohm effect and Resonant Tunneling effect, etc. In the second chapter, representative Low-dimensional Nanostructures, including two-dimensional quantum gas, Quasi-one-dimensional system, zero-dimensional Nanostructure and Nanoarray are considered separately. In the third chapter, several calculating methods in common use are discussed and compared, including Landauer-Buttiker Theory, Green's Function Method, Scatter Matrix Method and Transfer Matrix Method.The fourth chapter is the most important part of this thesis. The Transfer Matrix Method is applied to calculating the transmission properties of two-terminal crystal system and crystal system with ring structure. Without a loss of generality, the formulation in this work will only be carried out for systems with a single channel in each of the leads. Double potential barriers and multi potential barriers systems are calculated, and the electric transmission properties are discussed with different barrier height. The calculating results of two-dimensional crystal lattice line system reveal that when the energy level is less than the potential barrier height, electron can go through the potential barrier, and when the energy level is equal to the energy level between the two potential barriers height, the intensity of transmission is the biggest. Furthermore, the crystal systems with ring structure are calculated, and the Landauer-Biittiker effect is approved.