Mechanistic Insights into AFM-IR Signal Formation and Probing Depth

Photothermal-based atomic force microscopy infrared (AFM-IR) spectroscopy enables nanoscale chemical imaging and subsurface characterization, yet the fundamental mechanisms governing its probing depth remain only partially understood. Classical thermal diffusion model predicts a length scaling of $f^{-1/2}$ with modulation frequency, whereas recent experiments observed a much stronger confinement of probing depth in AFM-IR close to $f^{-3/2}$. To resolve this discrepancy, we develop a unified analytical model that quantitatively links absorbed optical energy to the detected cantilever oscillation amplitude in AFM-IR. The model integrates frequency-dependent subsurface heat deposition, thermoelastic expansion with strain attenuation, and resonance-enhanced cantilever dynamics. Our analysis reveals that the effective probing depth ($d_{\mathrm{probe}}$) is not governed by thermal diffusion alone, but is strongly affected by optical and thermoelastic strain attenuation. These combined effects lead to an inverse frequency scaling ($d_{\mathrm{probe}} \propto f^{-1}$), indicating that mechanical transduction processes play a dominant role in determining depth sensitivity. This framework provides a mechanistic basis for the experimentally observed strong confinement of probing depth and offers quantitative guidelines for tuning depth sensitivity through excitation frequency, pulse conditions, sample architecture, and tip–sample coupling.