Quantum mechanical waves can create interferences and tunnel through barriers. The tunneling probability through a single barrier decreases exponentially as a function of barrier height and width. Two tunnel barriers separated by a flat, lower energy potential do not result in a series resistance-like behavior of double the exponential decay in transmission. Instead an interference pattern of multiple reflected waves can form in between the two barriers. Standing waves can form inside the double barrier structure for certain energies. At those resonance energies waves experience a surprising unity transmission through the double barrier structure as a whole. The double barrier structure can form a strong energy selective transmission filter.
This presentation shows that double barrier structures can show unity transmission for energies BELOW the barrier height, resulting in resonant tunneling. The resonance can be associated with a quasi bound state, and the bound state can be related to a simple particle in a box calculation. A strong relationship between the open and the closed system states only holds for extremely strongly confined low energy states. Relatistic open systems in terms of their barrier widths and heights do not relate well with the closed system results. The quasi-bound state has a finite lifetime / resonance width. Increasing barrier heights and widths increases resonance lifetime / electron residence time; it sharpens the resonance transmission width. Asymmetric barriers reduce the unity transmission.
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Università di Pisa, Pisa, Italy
- resonant tunneling diodes
- band structure
- course lecture