  We report a detailed study on low-frequency 1/f-noise in large-area
molecular-beam epitaxy grown thin (10 nm) films of topological insulators as a
function of temperature, gate voltage, and magnetic field. When the Fermi
energy is within the bulk valence band, the temperature dependence reveals a
clear signature of generation-recombination noise in the defect states in the
bulk band gap. However, when the Fermi energy is tuned to the bulk band gap,
the gate voltage dependence of noise shows that the resistance fluctuations in
surface transport are caused by correlated mobility-number density fluctuations
due to the activated defect states present in the bulk of the topological
insulator crystal with a density of D$_{it}=3.2\times10^{17}$ cm$^2$eV$^{-1}$.
In the presence of a magnetic field, noise in these materials follows a
parabolic dependence, which is qualitatively similar to mobility and
charge-density fluctuation noise in non-degenerately doped trivial
semiconductors. Our studies reveal that even in thin films of (Bi,Sb)$_2$Te$_3$
with thickness as low as 10 nm, the intrinsic bulk defects are the dominant
source of noise.
