  We report on the growth dynamic of CdTe thin films for deposition
temperatures ($T$) in the range of $150\,^{\circ}\mathrm{C}$ to
$300\,^{\circ}\mathrm{C}$. A relation between mound evolution and
large-wavelength fluctuations at CdTe surface has been established. One finds
that short-length scales are dictated by an interplay between the effects of
the formation of defects at boundaries of neighbouring grains and a relaxation
process which stems from the diffusion and deposition of particles (CdTe
molecules) torward these regions. A Kinetic Monte Carlo model corroborates
these reasonings. As $T$ is increased, the competition gives rise to different
scenarios in the roughening scaling such as: uncorrelated growth, a crossover
from random to correlated growth and transient anomalous scaling. In
particular, for $T = 250\,^{\circ}\mathrm{C}$, one shows that surface
fluctuations are described by the celebrated Kardar-Parisi-Zhang (KPZ)
equation, in the meantime that, the universality of height, local roughness and
maximal height distributions for the KPZ class is, finally, experimentally
demonstrated. The dynamic of fluctuations at the CdTe surface for other
temperatures still is described by the KPZ equation, but with different values
for the superficial tension ($\nu$) and excess of velocity ($\lambda$). Namely,
for $T = 150\,^{\circ}\mathrm{C}$ one finds a Poissonian growth that indicates
$\nu = \lambda = 0$. For $T = 200\,^{\circ}\mathrm{C}$, however, a
Random-to-KPZ crossover is found, with $\lambda > 0$ in the second regime.
Finally, for films grown at $T = 300\,^{\circ}\mathrm{C}$, one demonstrates
that a KPZ growth with $\lambda < 0$ takes place. We discuss the different
mechanisms leading to KPZ scaling which depend on $T$, and conjecture the
behavior of the phenomenological parameter $\lambda$ as function of the
deposition temperature.
