  We describe a transducer for low-temperature atomic force microscopy based on
electromechanical coupling due to a strain-dependent kinetic inductance of a
superconducting nanowire. The force sensor is a bending triangular plate
(cantilever) whose deflection is measured via a shift in the resonant frequency
of a high-Q superconducting microwave resonator at 4.5 GHz. We present design
simulations including mechanical finite-element modeling of surface strain and
electromagnetic simulations of meandering nanowires with large kinetic
inductance. We discuss a lumped-element model of the force sensor and describe
the role of an additional shunt inductance for tuning the coupling to the
transmission line used to measure the microwave resonance. A detailed
description of our fabrication is presented, including information about the
process parameters used for each layer. We also discuss the fabrication of
sharp tips on the cantilever using focused electron beam-induced deposition of
platinum. Finally, we present measurements that characterize the spread of
mechanical resonant frequency, the temperature dependence of the microwave
resonance, and the sensor's operation as an electromechanical transducer of
force.
