Comparison of traditional and impedance methods for quantum–sized structures simulation
Keywords:asymmetric potential barrier, quantum–mechanical impedance, tunneling, matched overbarrier transmission
AbstractIntroduction. Comparative analysis of traditional and impedance approaches in modeling asymmetric potential quantum–mechanical barrier are fulfilled.
Features of waves tunneling. The effect of waves tunneling are considered. The features of quantum–mechanical wave tunneling through asymmetric potential barrier are illustrated.
Traditional approach. Quantum–mechanical wave transmission through asymmetric poten-tial barrier on the basis of quantum–mechanical approach are explored. The expression for reflection coefficient is obtained.
Impedance approach. By using the impedance method, which is based on the concept of quantum–mechanical impedance and the theory of transmission lines, the expression of the reflection coefficient is obtained. The identity of expressions received by two approaches are demon-strated.
Tunneling regime. The expressions for transmission coefficient for tunneling regime in exact and approximate forms are obtained. Applicability of the approximate formula is presented.
Matched overbarrier transmission. The conditions of reflectionless resonant and nonresonant overbarrier transmission are obtained. Dependences of transmission coefficient for asymmetric barrier that illustrate unmatched and matched overbarrier transmission are presented.
Conclusions. Impedance method significantly simplifies modeling of quantum–mechanical structures in comparison with the traditional method of solving quantum–mechanical problems.
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