  Electrostatic force microscopy at cryogenic temperatures is used to probe the
electrostatic interaction of a conductive atomic force microscopy tip and
electronic charges trapped in localized states in an insulating layer on a
semiconductor. Measurement of the frequency shift of the cantilever as a
function of tip-sample shows discrete peaks at certain voltages when the tip is
located near trap centers. These discrete changes in frequency is attributed to
one by one filling of individual electronic states when the quantized energies
traverses the substrate conduction band fermi energy as tip-sample voltage is
increased. Theoretical analysis of the experiment suggests that such
measurement of the cantilever frequency shift as a function of bias voltage can
be interpreted as an AC force measurement, from which spectroscopic information
about the location, energy and tunneling times of localized states can be
deduced. Experimental results from study of a sample with InAs quantum dots as
trap centers is presented.
