We study backaction effects of phonon heating due to tunneling electrons on the current noise in atomic-sized junctions. Deriving a generalized kinetic approximation within the extended Keldysh Green''s functions technique, we demonstrate the existence of a characteristic backaction contribution to the noise in case of low external phonon damping.
We provide a physically intuitive interpretation of this contribution at large voltage in terms of slow fluctuations of the phonon occupation and show that it generally gives a significant correction to the noise above the phonon emission threshold.