On-chip detection of anisotropic thermopolarization in quartz

Abstract: Temperature gradients are widely used to drive and probe transport phenomena in solids, forming the basis of heat-to-charge conversion processes. In typical experiments, local heating is introduced to generate a temperature gradient, and the resulting electrical response is detected by separate electrodes. Such measurements usually regard heating purely as a source of thermal excitation. Here, we show that heating inherently generates mechanical stress through thermal expansion, which in turn produces measurable electrical signals via electromechanical coupling. Using quartz as a model piezoelectric system, we demonstrate that heat can be converted to electrical currents via thermally generated stress. The on-chip device used in our experiment enables us to probe the anisotropy of the piezoelectric tensor through the thermally generated current, exhibiting twofold and threefold responses for X-cut and Z-cut crystals, respectively. We further show that the response can be detected in both current and voltage modes. These results reveal a thermomechanical pathway for heat-to-charge conversion and establish a general platform for electrically probing thermomechanical responses in insulating materials.

• The paper demonstrates that AC Joule heating in quartz creates nonuniform thermal stress, which produces a measurable piezoelectric polarization and detector current at twice the heating frequency.
• The authors validate the thermal mechanism through quadratic heater-current scaling, frequency-dependent phase behavior, and a measured X-cut quartz diffusivity of (7 ± 1) × 10⁻⁶ m²/s.
• Crystal-orientation measurements reveal twofold and threefold angular symmetries in X-cut and Z-cut quartz, showing that heater–detector devices can both probe stress gradients and introduce thermomechanical signals into thermal measurements.

Overview

This paper demonstrates that a standard on-chip heater–detector geometry—an architecture ubiquitous in thermoelectric and spin-caloritronic measurements—can itself generate and detect an electromechanical signal arising from thermally induced stress (2605.17226). Using X-cut and Z-cut α-quartz as a model piezoelectric system, the authors show that AC Joule heating produces spatially nonuniform thermal expansion, whose associated in-plane stresses are converted into polarization via the piezoelectric tensor and read out as a second-harmonic current at a nearby metallic detector. The central claim is that heating in such devices is not merely a source of thermal excitation: it is an intrinsic, measurable thermomechanical actuator, providing a previously overlooked heat-to-charge conversion pathway.

Device and measurement principle

The devices consist of a 50 nm Au heater and a detector electrode, each $650~\mu$m long and $10~\mu$m wide, separated by $40~\mu$m, patterned by maskless photolithography and RF sputtering on quartz substrates. The heater is driven with an AC current $I = I_{\mathrm{heater}}\sin\omega t$ at frequencies of 0.01–50 kHz, and the detector is connected to a transimpedance amplifier with lock-in detection at $2\omega$.

The conversion chain is $$I \propto (\partial P/\partial\sigma)(\partial\sigma/\partial T)(dT/dt)$$. Since the heater temperature follows $$T(t) \propto I_{\mathrm{heater}}^2 \sin^2(\omega t)$$, the response must be quadratic in heater current and appear at twice the drive frequency. Both predictions are confirmed experimentally: a clear 6 Hz signal is observed when driving at 3 Hz, and the lock-in $X$ and $Y$ components of $I_{2\omega}$ at 1 kHz scale quadratically with $10~\mu$0.

Thermal origin of the signal

The phase of the detected current provides a stringent consistency check. Solving the one-dimensional diffusion equation for sinusoidal heating gives a phase lag proportional to $10~\mu$1, with $10~\mu$2. The measured phase indeed scales as $10~\mu$3 at high frequency, yielding a thermal diffusivity of $10~\mu$4 for X-cut quartz, in agreement with literature values. Deviations at low frequency are attributed to breakdown of the one-dimensional model when the diffusion length becomes comparable to the stage geometry. This quantitative agreement establishes that the generated current is thermal in origin rather than an electronic artifact.

Stress-field reconstruction from symmetry analysis

A key strength of the paper is the use of crystal symmetry to decompose the stress field. Device arrays with the heater–detector axis rotated by an angle $10~\mu$5 relative to the crystal axes reveal a twofold ($10~\mu$6) modulation for X-cut quartz and a threefold ($10~\mu$7) modulation for Z-cut quartz, matching the symmetry of the rotated piezoelectric tensor under a plane-stress approximation. The absence of phase-shifted components ($10~\mu$8 or $10~\mu$9 terms) implies negligible in-plane shear stress $40~\mu$0, so the surface stress tensor is approximately diagonal with components $40~\mu$1 and $40~\mu$2.

Because the finite-width electrode effectively detects the spatial variation of polarization across its edges ($40~\mu$3), the measured current probes stress gradients rather than magnitudes. Finite-element simulations (isotropic approximation, steady state, heater represented as a localized thermal input of roughly $40~\mu$4) show temperature rises below 1 K at the heater and confirm the hierarchy $40~\mu$5, consistent with the observed angular dependences and their signs. The FEM also reveals out-of-plane strain gradients, which do not contribute to piezoelectricity here but are relevant to flexoelectricity, addressed in an accompanying submission.

Voltage-mode detection

The thermomechanical polarization is also detected in voltage mode. Lateral (in-plane) voltage measurements between heater and detector reproduce the twofold and threefold angular symmetries for X-cut and Z-cut quartz, respectively. Out-of-plane (top–bottom) measurements show the same symmetries, although the authors note that fringing fields and geometry-dependent capacitive coupling reduce quantitative reliability in that configuration; current mode remains the more direct and quantitative probe of generated charge.

Limitations and open questions

Several assumptions bound the interpretation. The FEM model treats quartz as isotropic, excludes the electrodes explicitly, and is restricted to steady state, so it supports the qualitative stress field rather than a fully quantitative reproduction of the current amplitude. The plane-stress approximation and the edge-detection phenomenology for finite-width electrodes are approximations whose accuracy depends on the electrode aspect ratio and fringing fields. The one-dimensional diffusion model fails at low frequency, and capacitive heater–detector coupling is visible as amplitude modulation even at the low frequencies chosen to suppress it. Whether the technique can quantitatively extract absolute stress magnitudes, rather than symmetry and sign information, remains open, as does its extension to weaker electromechanical couplings such as flexoelectricity in centrosymmetric insulators, which the authors defer to their companion paper.

Conclusion

The paper establishes that heater–detector devices intrinsically convert heat into charge via thermally generated stress, verified through quadratic-in-current, $40~\mu$6 response, diffusive phase behavior, tensor-symmetry angular dependences, FEM support, and dual current/voltage readout. Beyond its immediate demonstration in quartz, the work identifies a thermomechanical artifact—or probe, depending on intent—that should be considered in any on-chip thermal transport measurement on piezoelectric or flexoelectric insulators.