Towards a point spread function for nanoscale chemical imaging

Abstract

Atomic force microscopy-infrared (AFM-IR) is an AFM based technique that measures mid-IR absorption spectra at nanometer spatial resolution. The technique of AFM-IR relies on the detection of the pulsed wavelength tunable IR laser induced thermal expansion of the sample area underneath the AFM tip. In this work, we present a theoretical investigation of the laser heating induced thermal expansion process and model it as a point spread function (PSF). This approach draws parallels to super resolution microscopy where the PSF is used to determine spatial resolution and to resolve features below the diffraction limit. By solving the inhomogeneous heat equation with a volumetric heat source, we obtain the PSF of AFM-IR in frequency domain displayed as surface displacement which in dependence of laser heating. To verify that simplified boundary conditions do not result in a significantly changed behavior a finite element model of heat conduction in solids and fluids (implemented in COMSOL Multiphysics 5.6) of more realistic sample geometries is used. In the experimental part, we prepared 1 µm thick samples by mixing polyethylene and PMMA beads with a diameter of about 140 nm. First results show that there is a frequency (pulse repetition rate) and pulse length dependence of the PSF in AFM-IR. The achievable spatial resolution is improved for short pulses and high frequencies. These results provide guidance for experimental parameters which can be considered as trade-off between spatial resolution and signal intensity.