טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentBarkay Hadas
SubjectResonant Tunneling Phenomena in Multi-Dimensional
Systems
DepartmentDepartment of Chemistry
Supervisor Professor Emeritus Moiseyev Nimrod


Abstract

Resonances are long-lived states of a system that has sufficient energy to break into two or more subsystems. They are considered to be one of the most striking phenomena in scattering experiments. Under certain conditions, the transition probability of a particle scattered from a potential may reach 100%, even

if the particle does not have sufficient energy to pass "above " the potential barrier . This phenomenon is called "resonant tunneling". In this case , resonance states serve as intermediate states in the scattering process. Populating the resonance states leads to a highly efficient transition through the classically forbidden regime in phase space. The study of the properties of resonance states , their contribution to the transition probability and to the phase accumulated in the scattering process, are the main subjects of research in the present work .


In our work we derive a new formula for the resonant tunneling probability amplitude, using non-Hermitian quantum mechanics. We show that the complex density probability provides the measurable complex transition probability amplitude in scattering experiments. We study the partial widths of resonance states in an asymmetric potential, and show that the tendency of the resonance state to decay to the left or the right hand side depends on its energy position .


As a numerical model, which illustrates these subjects, we have chosen a one-dimensional asymmetric double-barrier model potential .


We use non-Hermitian adiabatic scattering theory to study a two-dimensional scattering event, where an electron is scattered from a quantum dot. We suggest a mechanism for the measured sharp phase change in the transition probability amplitude of electrons traversing the quantum dot. The proposed mechanism is a single electron phenomenon that involves interference between the two dimensional resonances of the quantum dot. We show that the dimensionality of the problem plays a key role in our mechanism .