  The spectroscopic resolution of tunneling measurements performed with a
scanning tunneling microscope is ultimately limited by the temperature at which
the experiment is performed. To take advantage of the potential high
spectroscopic resolution associated with operating an STM in a dilution
refrigerator we have designed a room temperature tunnel current amplifier
having very small back-action on the tunnel contact and allowing to nearly
reach the predicted energy resolution. This design is a modification of the
standard op-amp based tip-biasing current-voltage converter which implements
differential voltage sensing and whose back action on the tip voltage is only
~2 $\mu$V rms for a 14 MV/A transimpedance and 22 kHz bandwidth.
