Abstract
To describe a multilayer structure with arbitrary thicknesses of the interfaces between layers, we introduce a model in which the dependence of a material parameter along the axis of such a superlattice is described by a Jacobian elliptic sine function. Depending on the value of the modulus κ of the elliptic function, the model describes the limiting cases of multilayers with sharp interfaces where d is the thickness of the interface, l is the period of the superlattice) and of sinusoidal superlattices as well as all intermediate situations. We investigate the wave spectrum in such a superlattice. The dependences of the widths of the gaps in the spectrum at the boundaries of all odd Brillouin zones on the ratio are found. It is shown that the thicknesses of the interfaces can be determined if the experimental value of the relation between the widths of the first gap and any other gap is known.
- Received 6 December 1999
DOI:https://doi.org/10.1103/PhysRevB.62.2181
©2000 American Physical Society