Membrane-Based Scanning Force Microscopy

We report the development of a scanning force microscope based on an ultrasensitive silicon nitride membrane optomechanical transducer. Our development is made possible by inverting the standard microscope geometry—in our instrument, the substrate is vibrating and the scanning tip is at rest. We present topography images of samples placed on the membrane surface. Our measurements demonstrate that the membrane retains an excellent force sensitivity when loaded with samples and in the presence of a scanning tip. We discuss the prospects and limitations of our instrument as a quantum-limited force sensor and imaging tool.

Figure 1

(a) We use a 41-nm-thick silicon nitride membrane as the nanomechanical force sensor. A hole pattern acts as a phonon shield, while two coupled “defect” areas (labeled 1 and 2) undergo out-of-plane vibrations. We load gold nanoparticles and tobacco mosaic viruses onto one of the defect areas and measure the vibrations on the second one with a laser interferometer. The scanning force microscope is operated in high vacuum to avoid viscous damping. Figure adapted from Ref. [40]. (b) A 1550 nm laser is used to detect the membrane motion and a 980 nm laser drives the membrane via radiation-pressure forces. Membrane vibrations are detected with a lock-in amplifier (HF2LI). The ac output of the lock-in amplifier is used to modulate the potential of the scanning tip or the power of the driving laser. CT is the circulator, WDM is the wavelength-division multiplexer, SM is the semitransparent mirror, BPD is the balanced photodetector, and PLL is the phase-locked loop.

Figure 2

(a) Displacement power spectrum (PS) obtained by slowly sweeping $f_d$ applied through the modulated tip voltage. The red arrow marks the high-$Q$ mode used in this work. The force is applied through the modulated potential of the scanning tip far away from the surface. (b) Thermal displacement power spectral density (PSD) of the high-$Q$ mode. The solid line is a fit to the model of a harmonic resonator. The value $Q=2.6\times {10}^7$ is independently obtained from a ringdown measurement (inset) and agrees well with the peak width. The spring constant is $k=m(2\pi f_0{)}^2=1100$ N/m. (c)–(e) Shift of $f_0$, vibration amplitude, and $Q$ measured as a function of tip-surface distance $d$, respectively. The membrane is driven by a radiation pressure force with a constant amplitude. We define the touch position ($d=0$) from threshold values where $\mathrm{\Delta }f$ and $z_0$ exceed a set value. (For example, $\mathrm{\Delta }f=0.3$ Hz and $\mathrm{\Delta }{z}_0=30$% for the scans shown in this paper.) (f) The single-sided thermomechanical force noise $S_{\mathrm{th}}^{1/2}=4k_{B}T{\gamma }_0$ calculated from (c)–(e) and the fit results from (b). All measurements in the main manuscript are from a single membrane device. Data from additional devices are shown in the Supplemental Material [41].

Figure 3

The relative surface position $h_0$ is indicated by the same color bar for all images, with ticks separated by 20 nm. (a) Touch map of the membrane surface with gold nanoparticles (nominal average diameter of 50 nm) and TMV samples (diameter of 18 nm, used for $z$-scanner calibration [52]). Step size is 13 nm. Marks on the left-hand side indicate the positions of the linescans in (d). The membrane is driven by modulating the tip voltage. (b) High-resolution scan over the area indicated by a square in (a). Step size is 10 nm. (c) Same scan performed using radiation pressure driving. (d) Linescans extracted from the data in (a). Scans are vertically offset for clarity.