Optical image of a micromachined niobium resonator. (Top) A probe as fabricated in its silicon frame. The left part consists of the inductive coupling loops, while the right part shows the voltage maxima of the resonator that is terminated by the AFM tip. (Bottom) Close ups of these two areas. (Inset) Scanning electron micrograph taken after shaping the tip using focused ion beam. All metallized areas (a−g) are connected with “a” being the common node.
(a) Schematic of the scanner setup. (b) Photo of the microwave resonator mounted on the tuning-fork. Details are described in the text. (c) Measured transmission (S 21) at 0.3 K of the resonator in the panel above. Fit (solid line) shows a loaded quality factor of 14 600.
Pound-Drever-Hall microwave readout schematic. The details are discussed in the text. The bottom plots A−D sketch the microwave signal in the frequency domain at the corresponding points in the schematic. Black peak indicates the carrier frequency, red peaks the phase modulated side-band frequencies, and green the additional amplitude modulation introduced by the mechanical oscillations of the AFM tuning-fork. The diode mixes the high frequency signal down to DC and the various low frequency components in the spectrum. The bottom right plot shows a typical “error” signal measured at point F.
Illustration of the two different scanning modes used.
Scans over a superconducting surface with embedded topographic structures. Images obtained at 0.5 K with a scan speed of 0.8 μm/s and a microwave excitation of −80 dBm. The only post-scan processing applied is a planar fit. (a) Overlaid line traces from scans (b)−(d). (b) Topography in normal AFM mode. (c) Microwave resonator frequency shift obtained while scanning in AFM-mode. Acquired simultaneously with (b). (d) Topography obtained while using the microwave frequency as feedback signal, i.e., a surface of constant microwave resonance frequency, or constant capacitance. All other scan conditions the same as in (b).
Scan over a flat dielectric sample with microfabricated variations in dielectric thickness. (a) Sample cross-section. (b) and (c) are typical single line traces extracted from (e) and (f), respectively. (d) AFM image of the sample surface. (e) Simultaneously measured shift in resonance frequency of the microwave resonator. (f) Topography acquired in NSMM mode, i.e., a surface of constant capacitance. (e) is raw data, while in (d) and (f) a planar fit has been applied. Scans taken at 0.3 K with a microwave excitation power of −70 dBm.
(a) Capacitive sensitivity in NSMM mode for different excitation powers of the microwave resonator. −100 dBm corresponds to an energy equivalent to approximately 1000 photons for this particular resonator with Q i ≈ 16 000. Error bars are calculated assuming a fixed error in setpoint and ∂f/∂z of 5%, plus uncertainty in mechanical z-calibration of the microscope and various other constant errors in measurements of noise spectra. Measured on top of a metallic surface. (b) Microwave resonance frequency and (c) vertical displacement noise power spectral density (PSD) used to calculate the sensitivity for the high power point in (a). The PID in the PDH loop is tuned to a 150 Hz bandwidth. Peak values around 50 Hz yield a capacitive sensitivity of 64 × 10−21 F .
Article metrics loading...
Full text loading...