  We numerically investigate the effects of inhomogeneities in the energy
spectrum of aperiodic semiconductor superlattices, focusing our attention on
Thue-Morse and Fibonacci sequences. In the absence of disorder, the
corresponding electronic spectra are self-similar. The presence of certain
degree of randomness, due to imperfections occurring during the growth
processes, gives rise to a progressive loss of quantum coherence, smearing out
the finer details of the energy spectra predicted for perfect aperiodic
superlattices and spurring the onset of electron localization. However,
depending on the degree of disorder introduced, a critical size for the system
exists, below which peculiar transport properties, related to the pre-fractal
nature of the energy spectrum, may be measured.
