A method for the calculation of electronic states in a quantum well using the chain model
JOURNAL OF PHYSICS-CONDENSED MATTER(1990)
Abstract
A method for calculating the electronic states in a quantum well (QW) system is presented based on the tight-binding Hamiltonian within a one-band model and in terms of Dyson's equation. The Hamiltonian for the whole system is separated into two parts: one corresponds to an infinitely pure linear chain and the other describes a finite impurity chain confined to the QW region. The explicit solution to Dyson's equation for the QW can be obtained via a compact recursion relationship. The formulae have been demonstrated using particular examples. From the authors' numerical evaluation of the energy of the quasi-bound states for the QW and comparison with the usual effective-mass approximation, it shows that for both models the results are the same. They believe that their treatment may provide great flexibility for dealing with the problem in heterostructures.
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Key words
bound states,tight binding,effective mass,quantum well
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