A novel energy filter using semiconductor superlattices and its application to tunneling time calculations

An artificial quantum-mechanical filter using superlattice structures is proposed in this paper. By gradually changing the barrier widths of a superlattice according to a Gaussian function, a broad-band and almost zero sidelobe transmission profile can be obtained. The WKB approximation is applied to demonstrate the phenomena of abrupt change of transmission profile. The proposed structure allows the incident electrons to be nearly totally transmitted when the impinging electron energy is in the passband. On the other hand, a complete reflection occurs when the impinging energy is in the stopband. By adjusting the structure parameters, the desired passband and stopband of such a filter can be obtained. Time evolution of an electron wavepacket moving through the structure is calculated by numerically solving the time-dependent Schrodinger equation. Numerical results clearly demonstrate the characteristics of total transmission and reflection. By simulating the movement of a totally transmitted wavepacket, ambiguity results from the nature of the wavepacket in the determination of electron tunneling time can be avoided. The generalized concept of matched quantum-mechanical wave impedance (QMWI) analogous to transmission line theory is presented to explain the occurrence of total transmission of the proposed structure. The tunneling time (τ_QMWI) calculated based on the concept of QMWI is compared with the accurate tunneling time obtained by our simulation