Advances in the calculation of optical properties in superlattices; novel insights derived from the theory of finite periodic systems

Abstract

Using the genuine superlattice eigenvalues and eigenfunctions, and their parity symmetries, new transition selection rules are derived, and a novel approach for the explicit calculation of the optical spectra of periodic structures presented. The optical response and infrared spectra published in the last 40 years for (In, Ga)N and (Al, Ga)As superlattices, with different number of unit cellsn (varying from∼10 to∼400) and barrier and valley widths in the range of 2.5 nm to 40 nm, and different properties have been revisited. Among the various examples discussed here, we study the narrow peaks clustered in groups reported in high resolution spectra of blue-emitting devices, that could not be explained until now. These properties are faithfully reproduced and fully understood. We show that these effects are related to and depend on the surface energy levels and their tuneable detachment. We shown also that the optical transitions experimentally observed, but forbidden by the current optical physics, are really allowed transitions. Since the number of energy eigenvaluesEμ,νr,v and eigenfunctionsΨμ′,ν′r,v(z) is now much greater, the number of allowed matrix-elements can be extremely large (of the order ofn2ncnv∕2, withnc andnv the number of subbands in the conduction and valence bands). We show that this number can be reduced by using the eigenfunctions’ symmetries, which are behind the parity symmetry selection rules and the leading order selection rules. These rules reduce the number of matrix-elements evaluations from∼n2ncnv∕2 to∼nncnv∕2, i.e., depending on the superlattice, from about 1000 to 100. We discuss also a third rule, that collects the contributions of the surface and edge states, reducing the number of transitions even more toNs≤ncnv. With these rules, the main peaks are conserved and their number practically matches that of the real spectrum. Excellent agreements are found with experimental results.