Detection of MEMS Acoustics via Scanning Tunneling Microscopy

TL;DR

This work demonstrates a cryogenic, ultra-high-vacuum STM platform that actuates and reads high-Q MEMS membranes with picometer-scale precision, using three complementary modalities (Homodyne Detection, Feedback Resonance, and Z-Sweep Resonance) to probe membrane acoustics while minimizing perturbation. By modeling tip–membrane forces as a combination of Lennard-Jones and electrostatic interactions and leveraging LCPD measurements, the study characterizes both perturbative and non-perturbative regimes, maps lateral mode structures, and achieves exceptional force sensitivity down to the piconewton and potentially femtonewton scales under optimized conditions. The approach enables localized, quantum-compatible interrogation of mesoscopic mechanical motion, provides a path toward quantum-level readout, and offers a versatile platform for studying nanoscale forces, Casimir effects, and real-time membrane dynamics at cryogenic temperatures. Collectively, these findings establish STM-based nanomechanical sensing as a general, minimally invasive tool for exploring macroscopic quantum phenomena in membranes and related devices.

Abstract

Scanning tunneling microscopy (STM) and micro-electromechanical systems (MEMS) have traditionally addressed vastly different length scales - one resolving atoms, the other engineering macroscopic motion. Here we unite these two fields to perform minimally invasive-measurements of high aspect-ratio MEMS resonators using the STM tip as both actuator and detector. Operating at cryogenic temperatures, we resolve acoustic modes of millimeter-scale, high-Q membranes with picometer spatial precision, without making use of lasers or capacitive coupling. The tunneling junction introduces negligible back-action or heating, enabling direct access to the intrinsic dynamics of microgram-mass oscillators. In this work we explore three different measurement modalities, each offering unique advantages. Combined, they provide a pathway to quantum-level readout and exquisite high-precision measurements of forces, displacements, and pressures at cryogenic conditions. This technique provides a general platform for minimally-perturbative detection across a wide range of nanomechanical and quantum devices.

Figures (17)

• Figure 1: Experimental set-up.(a) A MEMS resonator containing a square superconducting membrane is supplied a DC and AC voltage, with a Scanning Tunneling Microscope (STM) tip probing the membrane. The oscillating voltage component drives the membrane motion, shown here in its (2,2) mode, while the tip measures a current as a result of this motion, which is ultimately converted to a DC current signal (see text). (b) Overview of interrogation windows of typical membrane motion detection techniques including: through an STM ($S_{\rm S}$), through optical means with a laser ($S_{\rm L}$), through capacitors ($S_{\rm C}$), and through piezoelectric signals ($S_{\rm P}$). (c-e) Three different measurement modalities: Homodyne Detection (c) shows the lock-in signal, after adjusting the phase to put the capacitive background on a different channel (light curve is a Lorentzian fit), Feedback Resonance (d) shows the tip height and Z-sweep Resonance (e) shows current response. Forward and backward sweeps are shown by arrow colors.
• Figure 2: Force Model(a) Diagram of relevant forces (Lennard-Jones force $F_{\rm LJ}$ and electrostatic force $F_{\rm ES}$) and the definition of amplitude $A$ and tip-membrane distance $d$, an arbitrary offset $d_0$, the distance to this offset $z$ and the membrane position variable $r$. The red circle indicates spherical approximation of the tip. (b) Simulated currents as described in the Methods. Five different driving frequencies are simulated, resulting in canted peaks in the current at five different tip heights $d$. Each set is repeated five times with different driving powers $P$. Legend shows relative driving power (see text). Six simulation results are highlighted in different colors. (c) Experimental data on a NbTiN membrane, with multiple measurements taken at a driving frequency of $278.61$ kHz for various powers, and one taken at $278.615$ kHz, $-85$ dBm. Shown are also $z_{\rm rise}$ and $z_{\rm drop}$.
• Figure 3: Local Contact Potential Differential(a) Z-sweep Resonance curves, showing the current as a function of tip height $z$, for various bias voltages $V_{\rm DC}$. All curve starting points (i.e. $z = 0$ nm) are offset according to the applied $V_{\rm DC}$. The tip height where the current starts to increase is shown as $z_{\rm rise}$. Inset: mapping of tip height to frequency shift (see text for more details) to turn $z_{\rm rise}$ into $f_{\rm rise}$. (b) Feedback resonance curves, showing the tip height as a function of drive frequency $f_{\rm drive}$, for various bias voltages $V_{\rm DC}$. All curve starting points (i.e. detuning = -70Hz) are offset according to the applied $V_{\rm DC}$. The frequency of increasing tip height is shown as $f_{\rm rise}$. (c) Detuning of resonance frequency as derived from panels a and b and a parabola fit for both data sets, yielding a local contact potential difference of $-92.6 \pm 4.3$ mV using the Z-sweep Resonance measuring modality and $+58.3 \pm 10.4$ mV using the Feedback Resonance measuring modality. Reference frequency $f_0^*$ to determine the detuning is derived from the fit shown in Fig. \ref{['fig:z-dependence']}a.
• Figure 4: Lateral dependence(a) Feedback Resonance measurements taken at various locations shown in panel b with corresponding Greek letters. Each curve is offset by for clarity. (b) Topographic image on which the data of panel a is taken, shown in three dimensions. Height axis indicates the off-resonance height of each measurement. Zoom-in indicates the accuracy with which the tip is able to maintain the same position to be $0.02$ nm. (c) Homodyne Detection measurements taken between $100$ kHz and $1000$ kHz on the gold-coated membrane. With the (1,1) mode at $150$ kHz, the vertical lines indicate the expected frequencies of higher modes. Red lines indicate modes not observed in panel c. Inset shows photograph of tip location. (d,e) Same as d, but for a different top positions. (f) Finite elements simulations of four selected modes on a square membrane. Colors indicate the absolute value of the amplitude. Three dots per membrane correspond to tip locations of panels c-e with corresponding colors.
• Figure 5: Long-range frequency sensitivity and force resolution.(a) Resonance frequency versus tip height $z_{\rm rise}$ over a 4 nm range, measured at $V_{\rm DC}=10$ mV (circles) and $V_{\rm DC}=1$ V (crosses). Separate fits to Eq. \ref{['eq:freq_shift']} are shown for each bias. Insets highlight the regimes where each fit works well. (b) Twenty repeats of 10 different frequencies, stepped in 10 mHz. The green dashed line indicates the threshold from which $\tilde{z}_{\rm rise}$ is determined. (c) Histograms of $\tilde{z}_{\rm rise}$ from data shown in panel b. The lowest and highest frequencies are shown. Mean of histograms areindicated by triangles. Using the values related to the two highest frequencies and Eq. \ref{['eq:forces_1']} we determine a detectable force difference of $\approx$6 pN.