__Tunneling in quantum superlattices with variable lacunarity__

Fractal superlattices are composite, aperiodic structures comprised of alternating layers of two semiconductors following the rules of a fractal set. The scattering properties of polyadic Cantor fractal superlattices with variable lacunarity are determined. The reflection coefficient as a function of the particle energy and the lacunarity parameter present tunneling curves, which may be classified as vertical, arc, and striation nulls. Approximate analytical formulae for such curves are derived using the transfer matrix method. Comparison with numerical results shows good accuracy. The new results may be useful in the development of band-pass energy filters for electrons, semiconductor solar cells, and solid-state radiation sources up to THz frequencies.