Abstract:
In this thesis, we present a force sensor for atomic force microscopy based on cavity optomechanical principles. We explain the function, design, fabrication and characterisation of the force sensor. The mechanical part of the force sensor consists of a cantilever with a very fine tip. Near the cantilever’s base is an LC circuit with resonance frequency in the range 4-5 GHz. The inductor consists of a superconducting meandering nanowire that changes its inductance when strained. Thus, the mechanical movement of the cantilever can be detected by measuring how the resonance frequency of the LC circuit changes. The mechanical movement gives rise to sidebands in the microwave spectrum. One detection method is based on the circuit being driven by two microwave tones while the cantilever is actuated near its mechanical resonance by a piezoelectric shaker mounted near the sensor. The amplitude of the measured signal depends on the phase difference between the motion of the cantilever and the microwave tones.
Key steps in the fabrication include release of the cantilever by etching away the substrate from both the front and back sides, and deposition of a tip on the free end of the cantilever. Fabrication is done over an entire semiconductor wafer and exhibits high yield. The optomechanical coupling strength g0 was measured in the order of a few Hertz at temperatures of a few millikelvin. However, an accurate calibration of the coupling constant relating mechanical movement of the cantilever to the shift of resonance frequency of the LC circuit was not possible due the presence of a non-thermal fluctuating force. We also present how the microwave losses in the LC circuit vary in the range 1.7-6 K. Our circuits exhibit higher losses than expected from thermal-equilibrium quasiparticles, which we attribute to the circuit dielectric. Quasiparticle losses set an upper limit on the quality factor that our circuits can achieve regardless of topology. In addition, the LC circuit exhibits a nonlinear relationship between current and kinetic inductance that enables parametric amplification of the mechanical sidebands. Thus, the presented force sensor integrates the force transducer (cantilever), the detector (LC circuit) and a parametric signal amplifier (via the nonlinearity of the LC circuit) in one and the same component.