ABSTRACT
FIGURE 4.1 Schematic arrangement of GaAs and AlAs bilayers deposited following the Fibonacci sequence ABAAB.... The AlAs layers (electronic barriers) have all the same (nominal) thicknesses (17 Å), whereas the GaAs layers (electronic wells) take on two di¤erent values (42 and 20 Å). (Values taken from ref.[2].)
of the ideal Fibonacci sequence consists of a dense peaks given by the wave vectors,[3]
qn1;n2 = 2
(n1 + n2); (4.2)
Keeping expression (2.3) in mind one realizes that to Eq.(4.1) when n1 and n2 are successive Fibonacci num-experiments the entire di¤ractogram pro…le is dominated by be properly labeled in terms on integers belonging to the set are Fibonacci numbers themselves. This fact indicates that are essentially equivalent in practice. these expressions one expects that every increase in exper-
will reveal new peaks in what was previously unresolved characteristic feature was nicely demonstrated by high-di¤raction (synchrotron) studies, clearly demonstrating the of order (namely, periodic and quasiperiodic) coexisting in the same sample at di¤erent length scales (Fig.4.2).[4] This novel feature distinguishes quasiperiodic superlattices from usual periodic ones, opening promising avenues for new materials design. In fact, since di¤erent physical phenomena have their own relevant physical
scales, by properly matching the characteristic length scales of elementary excitations propagating through the system, one can exploit the physical properties related to the quasiperiodic order we have introduced in the system. To this end, one should consider the possible role of structural imperfections which are inevitably introduced during the growth process. Quite interestingly, detailed structural characterization studies have shown that disorder does not seriously disrupt the overall coherence of the quasiperiodic sequence, so that most physical properties related to quasiperiodic order are robust enough. This property prompted the interest in the potential applications of quasiperiodic layered structures composed of di¤erent materials arranged according to di¤erent kinds of aperiodic sequences.[2]
The rapid progress achieved in growth technologies, like molecular beam epitaxy, magnetron sputtering, or vacuum deposition, has made it possible to grow arti…cial structures with di¤erent aperiodic modulations of chemical composition along the growth direction. For the sake of illustration in Table 4.1 we list some representatives among the plethora of aperiodic heterostructures grown during the last two decades.
