1993physica status solidi (b)Requires access

A General Study of Tunnelling through Multibarrier Systems

Chandana Roy, Arif Khan

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Abstract

Abstract A study of the tunnelling through an arbitrary number N of rectangular barrier‐type potentials is reported. For this purpose, first the general form of the transmission coefficient (TC) for the system just mentioned is derived and therefrom the general form of conditions for resonant tunnelling is obtained. Our study indicates, among others, 1. the role of the Chebyshev polynomials of second kind in regard to TC, 2. the domains of energies for resonant tunnelling, and 3. the validity of one condition for resonant tunnelling through any even number of barriers.

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What this paper is about

Abstract A study of the tunnelling through an arbitrary number N of rectangular barrier‐type potentials is reported. For this purpose, first the general form of the transmission coefficient (TC) for the system just mentioned is derived and therefrom the general form of conditions for resonant tunnelling is obtained. Our study indicates, among others, 1. the role of the Chebyshev polynomials of second kind in regard to TC, 2. the domains of energies for resonant tunnelling, and 3. the validity of one condition for resonant tunnelling through any even number of barriers.

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Available abstract

Abstract A study of the tunnelling through an arbitrary number N of rectangular barrier‐type potentials is reported. For this purpose, first the general form of the transmission coefficient (TC) for the system just mentioned is derived and therefrom the general form of conditions for resonant tunnelling is obtained. Our study indicates, among others, 1. the role of the Chebyshev polynomials of second kind in regard to TC, 2. the domains of energies for resonant tunnelling, and 3. the validity of one condition for resonant tunnelling through any even number of barriers.

Key concepts: Quantum tunnelling, Physics, Quantum mechanics

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