H. Hysmith, N. Domingo, S. Jesse
Oak Ridge National Laboratory,
United States
Keywords: resistive switching, thermomechanical response, PFM
Summary:
When a conductive atomic force microscope (AFM) tip biases a resistive or leaky material, nanoscale current flow through the tip–sample junction produces intense local Joule heating. This highly confined power dissipation generates a measurable thermomechanical strain that bends the cantilever, providing a mechanical signature of current flow even in non-piezoelectric systems. Understanding and separating this response from genuine piezoelectric or electrostrictive deformation is essential for interpreting electromechanical measurements on resistive switching oxides, leaky ferroelectrics, and mixed ionic–electronic conductors. In this work, we explore the thermomechanical response that emerges from current heating at the AFM tip–sample junction by recording, in parallel, conductive-AFM (c-AFM) current maps and piezoresponse force microscopy (PFM) signals at the fundamental (f) and second-harmonic (2f) frequencies. This dual-frequency approach reveals how nanoscale current dissipation translates into local surface expansion and mechanical actuation. Experiments were performed on (i) a metallic electrode of known sheet resistance, used as a quantitative reference to calibrate the coupling between local Joule heating and cantilever deflection, and (ii) a resistive-switching oxide, where the formation and rupture of conductive filaments produce dynamic spatial variations in current density. A conductive tip was biased with a combined AC + DC voltage while maintaining mechanical contact. The DC bias established a steady conduction path, while the AC modulation enabled lock-in detection of both the first-harmonic PFM response (at f)—associated with linear piezoelectric or electrostrictive strain—and the second-harmonic response (at 2f)—arising from quadratic, power-dependent Joule heating. Because the dissipated power follows P=I2R, the local heating oscillates at 2f. By adjusting the drive frequency such that 2f coincided with the cantilever’s contact resonance (half-resonance excitation), the thermally induced oscillation was resonantly amplified. On the resistive electrode, the 2f signal scaled linearly with the current gradient under the ac voltage, confirming its origin in current-induced expansion. The amplitude and phase of this signal provided quantitative benchmarks for thermal-mechanical coupling and heat diffusion timescales within the tip–sample contact. On the resistive-switching oxide, the correlated c-AFM/PFM measurements revealed co-localized bursts of 2f response at sites where abrupt current increases indicated filament formation. These events were accompanied by transient phase shifts and hysteretic behavior in the first-harmonic channel, reflecting the interplay between ferroelectric polarization, electrochemical migration, and local Joule heating. Because electrostatic forces between the biased cantilever and sample can also produce spurious 2f oscillations, we further implement Kelvin-probe bias compensation and geometric modeling of cantilever capacitance to disentangle electrostatic and thermomechanical contributions. The combination of mechanical resonance amplification, harmonic detection, and electrostatic modeling establishes a quantitative framework for Joule-expansion microscopy. Overall, this work establishes a correlated c-AFM/PFM framework for disentangling electromechanical and thermomechanical contributions in leaky or switching materials. By directly linking local current, voltage, and mechanical strain, we open new avenues to quantify nanoscale energy dissipation and to track the spatiotemporal evolution of resistive switching phenomena with sub-100 nm resolution. This work was supported by the Center for Nanophase Materials Sciences (CNMS), a U.S. Department of Energy, Office of Science User Facility at Oak Ridge National Laboratory.