  We have developed a highly-sensitive integrated capacitance bridge for
quantum capacitance measurements. Our bridge, based on a GaAs HEMT amplifier,
delivers attofarad (aF) resolution using a small AC excitation at or below kT
over a broad temperature range (4K-300K). We have achieved a resolution at room
temperature of 10aF per root Hz for a 10mV AC excitation at 17.5 kHz, with
improved resolution at cryogenic temperatures, for the same excitation
amplitude. We demonstrate the performance of our capacitance bridge by
measuring the quantum capacitance of top-gated graphene devices and comparing
against results obtained with the highest resolution commercially-available
capacitance measurement bridge. Under identical test conditions, our bridge
exceeds the resolution of the commercial tool by up to several orders of
magnitude.
