Abstract
In the work, we propose an approach to “smart design” of heterostructures (quantum wells and superlattices) based on the combination of Inverse Scattering Problem Method and the direct solution of the eigenvalue problem for the Schr?dinger equation with reconstructed potentials. Potential shape reconstructed in this way can be substituted then by some approximation, so that the output spectrum obtained by solving the Schr?dinger equation with such approximated potential, differs only slightly from the input one. In our opinion, the approach can be used in many applications, for instance, for developing the new electronic devices such as tunable THz detectors.
Highlights
In recent years, we have been witnessing the rapid progress in nanoelectronics which is already on the way to continue the outstanding successes of microelectronics
In a particular case of quantum well (QW), the question is reduced to the following: suppose we have a number of quantum levels with the given distances between them; what potential shape QW should be in this case; or in other words, can we find the potential of QW, if the spectrum and the depth of QW are given? As we mentioned in the Introduction, the provisional positive answer to this question was obtained by means of the Inverse Scattering Problem Method (ISP)-method in [2]
The software works according to the following scheme: 1) At the input one should define the desirable energy spectrum, the charge carriers effective mass and to the first approximation, the width and depth of QW; 2) On the base of these data, an implemented algorithm calculates the shape of the potential; 3) In the step we solve the eigenvalue problem for the Schrödinger equation with the potential V(x), reconstructed in previous step; 4) One calculates the relative error, i.e. is the difference between the preset energy spectrum and the one obtained in the step 3)
Summary
We have been witnessing the rapid progress in nanoelectronics which is already on the way to continue the outstanding successes of microelectronics. This became possible among others, due to the development of technologies and techniques, such as, Molecular Beam Epitaxy (MBE), which enables depositing thin layers of different materials, one on the top of another, with almost atomic precision. In different areas of possible applications of the low-dimensional structures, one often needs to have a specific kind of spectrum known beforehand and a question arises: how to produce the QW with a predetermined spectrum? In different areas of possible applications of the low-dimensional structures, one often needs to have a specific kind of spectrum known beforehand and a question arises: how to produce the QW with a predetermined spectrum? At least from the theorist’s point of view, the question can be reformulated as follows: suppose that the spectrum of QW is known, and that is to say one knows the number of quantum levels and the energy distances between them (remember that the spectrum is not necessarily equidistant as in the case of parabolic QW or similar to the spectrum of rectangular well); can one reconstruct the QW-potential which supports this spectrum?
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
