  Ge/Si(001) multilayer heterostructures containing arrays of low-temperature
self-assembled Ge quantum dots and very thin Si$_x$Ge$_{1-x}$ layers of varying
composition and complex geometry have been studied using Raman spectroscopy and
scanning tunneling microscopy. The dependence of Raman spectra on the effective
thickness of deposited Ge layers has been investigated in detail in the range
from 4 to 18 \r{A}. The position and shape of both Ge and SiGe vibrational
modes are of great interest since they are closely related to the strain and
composition of the material that plays a role of active component in
perspective optoelectronic devices based on such structures. In this work, we
present an explanation for some peculiar features of Raman spectra, which makes
it possible to control the quality of the grown heterostructures more
effectively. A dramatic increase of intensity of both the Ge$-$Ge and Si$-$Ge
bands for the structure containing Ge layers of 10 \r{A} and anomalous shift
and broadening of the Si$-$Ge band for structures comprising Ge layers of 8 and
9 \r{A} thick were observed. In our model, the anomalous behavior of the Raman
spectra with the change of thickness of deposited Ge is connected with the
flatness of Ge layers as well as transitional SiGe domains formed via the
stress-induced diffusion from {105} facets of quantum dots. The conclusions are
supported by the STM studies and the numerical calculations.
