Lattice dynamics of random and quasiperiodic heterostructures

We report on the quantum-mechanical displacement form factor in quasiperiodic and random heterostructures. A one-dimensional treatment is adopted to describe the longitudinal displacement along the growth axis. Elastic properties are assumed to be homogeneous, while the inhomogeneous mass density characterizes the heterostructure. In the low-frequency limit, the peak structure can be attributed to acoustic phonons, whereas for higher frequencies the quasiperiodic and random cases differ markedly. In the quasiperiodic case and constant momentum transfer, resonances separated by gaps occur and their number depends on the resolution in the frequency domain. The random case is dominated by an acoustic resonance becoming broader with increasing frequency. © 1988 Springer-Verlag.