Self-Similar Behavior in Semiconductor Superlattices

The scattering of particles in fractal superlattices has been analyzed by means of the transfer matrix method. The fractal superlattice consists of alternating layers of semiconductor materials following the rule of a Cantor set. This problem can be represented by a model of quantum particles scattering in piecewise constant potential wells. Fractal properties of the reflection coefficient versus the particle energy curves are examined comparatively to the curves when using the corresponding periodic potentials. The degree of self-similarity of the output variables has been quantified by means of the correlation function.