  We achieve the enhancement of circular photogalvanic effect arising from the
photo-injection of spins in topological insulator thin films by tuning the
Fermi level ($E_{\rm F}$). A series of (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ thin films
were tailored so that the Fermi energy ranges above 0.34 eV to below 0.29 eV of
the Dirac point, i.e., from the bulk conduction band bottom to the valence band
top through the bulk in-gap surface-Dirac cone. The circular photogalvanic
current, indicating a flow of spin-polarized surface-Dirac electrons, shows a
pronounced peak when the $E_{\rm F}$ is set near the Dirac point and is also
correlated with the carrier mobility. Our observation reveals that there are
substantial scatterings between the surface-Dirac and bulkstate electrons in
the generation process of spin-polarized photocurrent, which can be avoided by
designing the electronic structure in topological insulators.
