Visualization of electron transport dynamics in quantum nanostructures

This thesis investigates electron transport dynamics in quantum nanostructures with electron-phonon and electron-photon interactions. A real-time visualization program is designed for calculating wavepacket propagation by solving the time-dependent Schrödinger equation with electron-phonon or electron photon interaction. It is used to analyze trapping in single quantum well and also Bloch oscillations in semiconductor superlattices. The trapping in quantum well is analyzed for electron-phonon and electronphoton interaction. The decay of the center of mass of the Bloch oscillations in semiconductor superlattices under electron-phonon interaction will be calculated by the program.; The above program is written using the Crank-Nicolson algorithm. However, this method is not able to solve for complicated Hamiltonians. There are other methods of solution of the time-dependent Schrödinger equation that extend the range of Hamiltonians that can be solved. However, they cannot be used for any complicated Hamiltonian. A new algorithm, called recursive error method (REM), is invented (patent pending) and tested on simple structures for quantifying efficiency and accuracy. It compares favorably to other methods in solving simple Hamiltonians and shows superb advantages for complicated multi-dimensional Hamiltonians.; The REM algorithm is used to analyze the coupling of two quantum boxes. A two-dimensional electron Hamiltonian must be used in the time-dependent Schrödinger equation resulting in massive computations. The real-benefit of the REM algorithm will only result if parallel computers are used, in which case the results for complicated Hamiltonians are obtained in real-time.