  Alloys of Bi$_2$Te$_3$ and Sb$_2$Te$_3$ ((Bi$_{1-x}$Sb$_x$)$_2$Te$_3$) have
played an essential role in the exploration of topological surface states,
allowing us to study phenomena that would otherwise be obscured by bulk
contributions to conductivity. Thin films of these alloys have been
particularly important for tuning the energy of the Fermi level, a key step in
observing spin-polarized surface currents and the quantum anomalous Hall
effect. Previous studies reported the chemical tuning of the Fermi level to the
Dirac point by controlling the Sb:Bi composition ratio, but the optimum ratio
varies widely across various studies with no consensus. In this work, we use
scanning tunneling microscopy and Landau level spectroscopy, in combination
with X-ray photoemission spectroscopy to isolate the effects of growth factors
such as temperature and composition, and to provide a microscopic picture of
the role that disorder and composition play in determining the carrier density
of epitaxially grown (Bi,Sb)$_2$Te$_3$ thin films. Using Landau level
spectroscopy, we determine that the ideal Sb concentration to place the Fermi
energy to within a few meV of the Dirac point is $x\sim 0.7$. However, we find
that the post- growth annealing temperature can have a drastic impact on
microscopic structure as well as carrier density. In particular, we find that
when films are post-growth annealed at high temperature, better crystallinity
and surface roughness are achieved; but this also produces a larger Te defect
density, adding n-type carriers. This work provides key information necessary
for optimizing thin film quality in this fundamentally and technologically
important class of materials.
