Quantum fractal superlattices

Fractal superlattices consist of a series of thin layers of two semiconductor materials alternately deposited on each other with widths corresponding to the rules of construction of a fractal set. The scattering of electrons in superlattices is obtained using the transfer matrix method for generalized Cantor fractal potentials that are characterized by a lacunarity parameter. The numerical results show the self-similarity of the reflection coefficient and the appearance of lacunarity-independent energies with perfectly transparent tunneling due to the bound states of the particle in each of the individual potential wells.