Advances and challenges in dynamic photo-induced force microscopy

Abstract

Photo-induced force microscopy (PiFM) represents a scanning probe technique renowned for its ability to provide high-resolution spectroscopic imaging at the nanoscale. It capitalizes on the amplification of tip motion by photo-induced forces, which are influenced by the response of the local medium, spanning from induced dipole interactions to thermal expansion. The behaviors of these force responses exhibit complexity in connection with both far-field and near-field effects, depending on their spectroscopic origins. In this review, we aim to provide a comprehensive overview of prior research endeavors, shedding light on their technical intricacies. We provide the perspectives of photo-induced dipole force and photo-induced thermal force, while exploring the dynamic PiFM modes associated with each scenario. Our article targets individuals newly venturing into this field, offering a blend of theoretical foundations and practical demonstrations covering a range from fundamental principles to advanced topics.

Keywords: Amplitude modulation; Heterodyne; Homodyne; Nano-IR; Photo-induced dipole force; Photo-induced force microscopy and spectroscopy; Photo-induced thermal force.

Fig. 1

A timeline of the major developments of PiFM techniques

Fig. 2

a Schematic diagram of photo-induced force microscope under side-illumination geometry. Reprinted (adapted) with permission from Ref. [40], Copyright 2018 Jahng et al. b Theoretically expected mechanical eigenmodes of a microcantilever. Typically the second and third resonances are 6.27 and 17.55 times of the fundamental eigenmode, respectively [78]. c Graphical representation of the cantilever motion. z represents the instantaneous position of the tip end, $z_0$ denotes the average position of the cantilever, and $z_i$ signifies the oscillating amplitude of the i-th order motion. The light illuminates the tip-sample junction at the modulation frequency, ${\omega }_m$

Fig. 3

Experimental schemes of generalized heterodyne configurations. Reprinted (adapted) with permission from Ref. [42], Copyright 2018 American Chemical Society. a Experimental scheme of harmonic HT configuration. b Heterodyne mixing for the harmonic HT mode in frequency domain. c Experimental scheme of sequential HT configuration. d Heterodyne mixing for the sequential HT mode in frequency domain

Fig. 4

Schematics of a point dipole model and b finite dipole model for PiDF. z is the gap distance from the tip end to the sample surface, and $Z_0$ is the distance from the center of the spherical dipole to the sample surface. ${\overline{Z}}_0$ and ${\overline{Z}}_1$ are the distance from the induced charges of $Q_0$ and $Q_1$ to the sample surface, respectively. ${\tilde{\mu }}_t,{\tilde{Q}}_0$ and ${\tilde{Q}}_1$ are the image dipole and the image charges on the sample, respectively

Fig. 5

HM-PiFM and HT-PiFM responses are depicted relative to the average tip-sample distance, $z_0$. Theoretical calculations of a HM-PiFM amplitude and b reconstructed force are shown with respect to $\mathrm{\Lambda }=3\Re \{{\alpha }_t^{\ast }{\alpha }_s\}{|E_0|}^2/4\pi {\epsilon }_0$. Experimental measurements of c HM-PiFM amplitude and d reconstructed force on a 40 nm thickness Au nanowire are presented. e Measured reconstructed force on SiNc and glass at 809 nm resonance. Reprinted (adapted) with permission from Ref. [33], Copyright 2014 American Physical Society. Theoretical calculation of f HT-PiFM amplitude and g reconstructed force gradient with respect to $\mathrm{\Lambda }$. Experimental measurements of h HT-PiFM amplitude and i reconstructed force gradient on a 40 nm thickness Au nanowire and glass substrate. j Topography, k HT-PiFM, and l HM-PiFM images at $z_0=10$ nm. m Topography, n HT-PiFM, and o HM-PiFM images at $z_0=25$ nm. p Intensity dependence between HM-PiFM (green circle dots) and HT-PiFM (black square dots) measurements. Reprinted (adapted) with permission from Ref. [36], Copyright 2016 American Physical Society

Fig. 6

a Schematic representation of the total thermal expansion when the tip oscillates at ${\omega }_2=6.27{\omega }_1$ and the light modulates at ${\omega }_m=7.27{\omega }_1$. The constant oscillation component (blue solid line, $\mathrm{\Delta }{L}_g$) occurs at ${\omega }_m$, while the tip-induced component (red solid line, $\mathrm{\Delta }{L}_t$) appears at ${\omega }_s=|{\omega }_m\pm {\omega }_2|={\omega }_1$. b Calculated thermalization time with respect to the pulse width. Schematic illustrations of c global thermal expansion ($\mathrm{\Delta }{L}_g$) and d tip-enhanced thermal expansion ($\mathrm{\Delta }{L}_t$), corresponding to the case described in (a). Reprinted (adapted) with permission from Ref. [84], Copyright 2022 American Physical Society

Fig. 7

Analytical models of photo-induced thermal expansion force at the tip-sample junction. a Sketch of thermal expansion force mediated by tip-sample interatomic force. b Calculation of the force-distance curve between the Au tip and the PS film with respect to the tip-sample distance z by implementing the interatomic force model (blue solid line). The red dashed line represents the changed tip-sample force due to the 100 pm thermal expansion. The red solid line represents the difference, $\mathrm{\Delta }{F}_{\mathit{ts}}(z)$. Reprinted (adapted) with permission from Ref. [84], Copyright 2022 American Physical Society. Schematics of PiTF from the Hamaker potential model describing c global thermal expansion force $(L\gg R)$ and d tip-enhanced thermal expansion force $(L\sim R)$. Reprinted (adapted) with permission from Ref. [95], Copyright 2023 Jahng et al.

Fig. 8

Optomechanical damping force at the tip-sample junction. a Schematics of optomechanical damping response. b Comparison of the experiment (diamond) and Eq. (37) (solid line) for approach curve of normalized HT-PiFM amplitude. c Schematics and point spectrum of monolayer 4-MBT on template-stripped gold showing resonance at 1495 cm$_{}^{-1}$. Reprinted (adapted) with permission from Ref. [56], Copyright 2016 Almajhadi et al.

Fig. 9

HM-PiFM and HT-PiFM responses for PiTF. a Theoretical calculation of tip-enhanced (red solid line), global (blue solid line), total thermal expansions (black solid line), and field-enhancement (black dashed line) as the increase of thickness. b Comparison between PiFM and PTIR response as a function of PS thickness as measured at the white dashed line cuts in j to l. Reprinted (adapted) with permission from Ref. [57], Copyright 2019 Jahng et al. c HT-PiFM and d PTIR spectra for the different PS film thicknesses on Si substrate in the range between 1560 and 1380 cm$_{}^{-1}$, respectively. The black dashed line in c is the FTIR result of bulk PS. Detection frequency shifts of HT-PiFM amplitude in e the attractive region (set-point 90% of free oscillation amplitude) and f the repulsive region (set-point 45% of free oscillation amplitude) for different PS thickness, respectively. Reprinted (adapted) with permission from Ref. [55], Copyright 2018 American Chemical Society. g HT-PiFM amplitude (red solid line), the driving phase (black solid line), h the driving amplitude (blue solid line), and the DC deflection (green solid line) with respect to the tip-sample distance. i Topography, j HT-PiFM, k HM-PiFM, and (l) PTIR images of the PS wedge. Reprinted (adapted) with permission from Ref. [57], Copyright 2019 Jahng et al.

Fig. 10

a Calculated PiDF (blue dashed line) and PiTF (red solid line) alongside PiFM data (black square dots) for a 60 nm PS film on a Si substrate. Reprinted (adapted) with permission from Ref. [57]. Copyright 2019 Jahng et al. b Far-field optical responses showing the imaginary (black dots) and real (blue dots) parts of SiNc, alongside PiFM response (red dots). Reprinted (adapted) with permission from Ref. [34]. Copyright 2015 American Chemical Society. c Representation of the real (dashed black line) and imaginary (solid black line) parts of quartz permittivity, along with the calculated effective absorption coefficient (red solid line). d PTIR spectrum measured using resonance-enhanced contact mode AFM-IR on pure quartz. e PiFM spectrum obtained with a driving amplitude of 1 nm and a 90% setpoint amplitude on pure quartz, compared with previously measured s-SNOM amplitude spectrum on pure quartz (blue dashed line). Reprinted (adapted) with permission from Ref. [51]. Copyright 2024 Oxford University Press. f Complex dielectric function $\epsilon (\lambda )$ of InAsSb derived from IR reflectivity spectrum fitting, and absorption of a thin ENZ layer (thickness = 100 nm) determined from $\epsilon (\lambda )$ at p-polarized oblique incidence (${60}^{\mathit{o}}$). g Near-field spectra on HDS relative to the substrate signal obtained with s-SNOM (tungsten probe) and PiFM (gold-coated silicon probe). Experimental PiFM signal (blue curve) and simulation (gray curve) are presented. h Amplitude (green curve) and phase (red curve) difference between the HDS and substrate of s-SNOM measurement and simulation, respectively. Reprinted (adapted) with permission from Ref. [108]. Copyright 2019 American Chemical Society

Fig. 11

Frequency domain time-resolved PiFM measurement. a Schematic representation of the evolution of the photo-induced force, with the characteristic heating time ${\tau }_h$ during the “on” period and cooling time ${\tau }_{\mathit{rel}}$ during the “off” period. b Cantilever is driven through the photo-induced force, which is modulated at either $f_m=f_0$ or $f_m=f_0/2$. c Topography of the sample, consisting of a PS layer on a Si wafer. d PiFM signal of the PS layer at 1492 cm$_{}^{-1}$ and $f_m=f_0$. e PiFM signal of the PS layer at 1492 cm$_{}^{-1}$ and $f_m=f_0/2$. f Cooling time map at 1492 cm$_{}^{-1}$. g Topography of the a silver nanoparticle on a Si wafer. PiFM images recorded with h $f_m=f_0$, i $f_m=f_0/2$, and j $f_m=f_0/3$. The 809 nm laser light is polarized along the direction of the arrow in h. Reprinted (adapted) with permission from Ref. [43]. Copyright 2023 American Chemical Society

Fig. 12

Distinguishing photo-induced forces by using Dofn [101]. a Simulated photo-induced forces from a nanorod on polymethyl methacrylate (PMMA) substrate measured by an PiFM probe in the time domain. b Illustrated corresponding photo-induced forces in the frequency domain, showing distinct phase distributions of the gradient force ($F_g$, cyan), photothermal force ($F_{\mathit{th}}$, black), and photoacoustic force ($F_{\mathit{PA}}$, orange). c PiFM topography of a nanorod. d Overall force map of the nanorod. e The phase of the photo-induced force with the background phase correction ${\varphi }_{\mathit{pif}}(\overrightarrow{r})-{\varphi }_{\mathit{PA}}+{90}^o$. The optical gradient force, $F_g$, is dominant at two ends of the nanorod, where the phase is close to 180 degrees. The photothermal force, $F_{\mathit{th}}$, is dominant at the body of the nanorod, where the phase is between 0 and 90 degrees. The photoacoustic force is dominant outside of the nanorod, where the phase is around 90 degrees. The decoupled amplitude of the measured f photothermal force and g optical gradient force. Simulated h photothermal force map and i optical gradient force map at 100 ns after the raising edge. j Measured optical force spectra on the substrate (black), at the end (red), and the center (blue) of the nanorod, as indicated in c. Reprinted (adapted) with permission from Ref. [101]. Copyright 2023 Wang et al.

Fig. 13

Schematic for tip-sample distance dependent force under different working modes of nano-IR methods. a Contact mode, b peak force tapping mode, c tapping mode (repulsive regime), and d non-contact mode (attractive regime). Each region is noted by the blue area in intermolecular force curve on the right side, respectively. The red region schematically illustrates the tip-enhanced near-field under the tip apex. Reprinted (adapted) with permission from Ref. [113]. Copyright 2023 American Chemical Society