  We study the chemical ordering in Bi$_2$Te$_{3-x}$Se$_x$ grown by molecular
beam epitaxy on Si substrates. We produce films in the full composition range
from x = 0 to 3, and determine their material properties using energy
dispersive X-ray spectroscopy, X-ray diffraction and Raman spectroscopy. By
fitting the parameters of a kinetic growth model to these results, we obtain a
consistent description of growth at a microscopic level. Our main finding is
that despite the incorporation of Se in the central layer being much more
probable than that of Te, the formation of a fully ordered Te-Bi-Se-Bi-Te layer
is prevented by kinetic of the growth process. Indeed, the Se concentration in
the central layer of Bi$_2$Te$_2$Se$_1$ reaches a maximum of only $\approx$ 75%
even under ideal growth conditions. A second finding of our work is that the
intensity ratio of the 0 0 12 and 0 0 6 X-ray reflections serves as an
experimentally accessible quantitative measure of the degree of ordering in
these films.

Materials Science