  Quantum fractal superlattices are microelectronic devices consisting of a
series of thin layers of two semiconductor materials deposited alternately on
each other over a substrate following the rules of construction of a fractal
set, here, a symmetrical polyadic Cantor fractal. The scattering properties of
electrons in these superlattices may be modeled by using that of quantum
particles in piecewise constant potential wells. The twist plots representing
the reflection coefficient as function of the lacunarity parameter show the
appearance of black curves with perfectly transparent tunnelling which may be
classified as vertical, arc, and striation nulls. Approximate analytical
formulae for these reflection-less curves are derived using the transfer matrix
method. Comparison with the numerical results show their good accuracy.
