  Feedback-based control techniques are useful tools in precision measurements
as they allow to actively shape the mechanical response of high quality factor
oscillators used in force detection measurements. In this paper we implement a
feedback technique on a high-stress low-loss SiN membrane resonator, exploiting
the charges trapped on the dielectric membrane. A properly delayed feedback
force (dissipative feedback) enables the narrowing of the thermomechanical
displacement variance in a similar manner to the cooling of the normal
mechanical mode down to an effective temperature Te f f . In the experiment
here reported we started from room temperature and gradually increasing the
feedback gain we were able to cool down the first normal mode of the resonator
to a minimum temperature of about 124mK. This limit is imposed by our
experimental set-up and in particular by the the injection of the read-out
noise into the feedback. We discuss the implementation details and possible
improvements to the technique
