Photoinduced Tip–Sample Forces for Chemical Nanoimaging and

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Photo-induced tip-sample forces for chemical nano-imaging and spectroscopy Brian Thomas O'Callahan, Jun Yan, Fabian Menges, Eric Anton Muller, and Markus B. Raschke Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b01899 • Publication Date (Web): 06 Aug 2018 Downloaded from http://pubs.acs.org on August 7, 2018

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Nano Letters

Photo-induced tip-sample forces for chemical nano-imaging and spectroscopy

Brian T. O'Callahan,† Jun Yan, Fabian Menges, Eric A. Muller, and Markus B. Raschke* Department of Physics, Department of Chemistry, and JILA, University of Colorado at Boulder, Boulder, CO 80309

(Dated: July 27, 2018)

Abstract Control of photo-induced forces allows nanoparticle manipulation, atom trapping, and fundamental studies of light-matter interactions. Scanning probe microscopy enables the local detection of photo-induced eects, with nano-optical imaging and spectroscopy modalities being used for chemical analysis and the study of physical eects. Recently, the development of a novel scanning probe technique has been reported with local chemical sensitivity attributed to the localization and detection of the optical gradient force between a probe tip and sample surface via infrared vibrationally resonant coupling. However, the magnitude and spectral lineshape of the observed signals disagree with theoretical predictions of optical gradient forces. Here, we clarify this controversy by resolving and analyzing the interplay of several photo-induced eects between scanning probe tips and infrared resonant materials through spectral and spatial force measurements. Force spectra obtained on IR-active vibrational modes of polymer thin lms are symmetric and match the material absorption spectra in contrast to the dispersive spectral lineshape expected for the optical gradient force response. Sample thickness dependence shows continuous increase in force signal beyond the thickness where the optical dipole force would saturate. Our results illustrate that photo-induced force interactions between scanning probe tips and infrared-resonant materials are dominated by short-range thermal expansion and possibly long-range thermally-induced photo-acoustic eects. At the same time, they provide a clear guideline to detect and discriminate optical gradient forces from other photo-induced eects, which opens a new perspective for the development of scanning probe modalities exploiting ultra-strong opto-mechanical coupling eects in tip-sample cavities. Keywords: Chemical nanoimaging, Optical force, Photothermal, Infrared spectroscopy, PiFM, PTIR

†

*

Present address: [email protected] Corresponding author: [email protected]

ACS Paragon 1Plus Environment

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I.

INTRODUCTION

Optical forces are used as optical tweezers for nanoparticle manipulation [1], for atom trapping [2], and in cavity-optomechanics [3], and are the focus of much recent research into fundamental physical phenomena including the Casimir-Polder force [4]. A proposed method for measuring optical forces uses the tip of an atomic force microscope (AFM) at nanometer proximity to a sample. In this implementation, light illumination of the tip creates an electric polarization density p at the tip apex, which induces a coupled polarization density

⃗, p′ in the sample. The resulting mutual electromagnetic force is given by F⃗ = p⃗ · ∇E ⃗ . This so-called optical gradient force has been proposed as the with the optical eld E contrast mechanism for several recent AFM-based studies which have demonstrated chemical specicity with nanoscale spatial resolution, indicating a powerful new imaging and nanospectroscopy modality complementing scattering-scanning near-eld optical microscopy (sSNOM) [510] and photo-thermal infrared microscopy [1113]. However, these studies have painted a confusing picture regarding the actual contrast mechanism. While some studies assign the contrast to the optical gradient force [510], others assign it to material absorption and thermal expansion [1113]. The observed force magnitudes vary from 0.85 - 2.7 pN, with force gradients ranging from 2.1 - 3.7·10−5 N/m [9, 10]. However, recent theory predicts optical gradient force magnitudes over two orders of magnitude weaker under the typical experimental conditions at IR frequencies [1416]. Further, measured spectra of the photo-induced force exhibit an absorptive lineshape [8, 17], whereas theory predicts a dispersive spectral lineshape for the optical gradient force [14, 18]. In addition to an optical gradient force, several competing forces associated with photoexcitation exist and require careful consideration. For example, absorption and subsequent heating of the sample material results in thermal expansion, which underlies numerous imaging applications, including photoacoustic imaging and tomography [19]. Additionally, an AFM tip can detect thermal expansion and acousto-optical forces providing for chemical nano-imaging contrast with down to monolayer sensitivity [1113]. To resolve this controversy and distinguish dierent competing photo-induced forces between a tip and sample, we perform correlated and quantitative nanoscale spatial and IR spectral local-probe measurements. We observe symmetric force spectra that match the sample absorption spectrum, and measure force magnitudes up to 40 pN. Sample thickness ACS Paragon 2Plus Environment

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b)

Fth. exp.

nnd

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s-SNOM

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nd-nr nd nd+nr

n1

FIG. 1. a) Photo-induced force experiment: mid-infrared light pulsed at repetition rate νr illuminates the tip-sample gap, with possible optical dipole force Fopt. and thermal expansion induced impulsive force Fth.

exp.

indicated, and simultaneous s-SNOM mode collecting tip-scattered near-

eld. b) Lock-in amplier receives tip dither frequency νd , tip motion h(t), and s-SNOM near-eld signal NFin demodulating at harmonics of the tip motion nνd . Fourier components of c) s-SNOM signal and d) cantilever dynamics with sidebands at frequencies νd ± νr due to mixing of cantilever motion and the photoinduced forces.

dependent measurements reveal a signal increase scaling over 100s of nm in lm thickness, whereas the optical gradient force is expected to saturate at distances of 10s of nm, scaling with the tip apex radius. Further, tip-sample distance dependent measurements indicate that the dominant force is related to direct physical tip-sample contact. We observe comparably weak spatially extended forces out to few 10s of nm distances from the sample surface that can be attributed to photo-thermally induced acoustic interactions. The combined results thus strongly support that thermal expansion is the dominant contrast mechanism and can explain the vast majority of photo-induced force-based chemical imaging results to date.

II.

EXPERIMENT

Figure 1a) shows the experimental approach based on an AFM (modied Vesta AFM-SP, Anasys Instruments) operating in dynamic mode feedback by driving and monitoring the cantilever motion at its fundamental resonant frequency νd = ν0 . A lock-in amplier (HF2LI, Zurich Instruments) receives the tip drive signal and the tip motion (h(t)), as measured by ACS Paragon 3Plus Environment

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a laser diode reected o the backside of the cantilever onto a four-quadrant photodiode (Fig. 1b). A TTL pulse output triggers a pulsed mid-IR quantum cascade laser (QCL, Daylight solutions) at a frequency νr set by an internal oscillator in the lock-in amplier. A high numerical aperture (NA = 0.48) o-axis parabolic mirror focuses the IR radiation onto the apex of the tip. In addition to the photo-induced forces Fphoto−ind. , the near-eld s

-SNOM response can also be monitored by collecting tip-scattered light, measured with a

mercury-cadmium-telluride (MCT) detector, and demodulating at higher harmonics of the tip motion nνd for integers n (Fig. 1c) [20].

The photo-induced force signal relies on the presence of a force gradient due to a nonuniform photo-induced force, which results in a varying force magnitude during a tip oscillation cycle as described previously [58]. The force gradient and the periodic excitation of the tip-sample forces at the laser repetition rate νr gives rise to a corresponding tip motion at sideband frequencies ν0 ± νr due to the nonlinear mixing between the tip motion and the time varying photo-induced force (Fig. 1d) [21]. We set νr to the dierence of the rst two vibrational frequencies of the cantilever ν0 and ν1 , i.e., νr = ν1 −ν0 . The photo-induced forces then resonantly drive the second bending mode, which dramatically improves sensitivity.

In an alternative technique, the second bending mode is used for AFM feedback (νd = ν1 ), and the rst bending mode used to monitor the photo-induced force. This variation permits operation using smaller tapping amplitudes due to the higher eective spring constant of the second bending mode, and improves sensitivity to strongly surface-conned forces.

We obtain spectra of the photo-induced force by sweeping the laser wavelength. As model systems, we investigate the carbonyl (C=O) resonance of PMMA at ν¯ = 1735 cm−1 and the symmetric C-F stretches in polytetrauoroethylene (PTFE) at ν¯ ≈ 1152 cm−1 . Block copolymer samples were prepared by spin-coating a 1% w/v solution of PS-b-PMMA in toluene onto a native oxide silicon substrate. For the sample thickness dependent measurements, a 1% w/v solution of PMMA in toluene was spin-coated on a silicon substrate tilted at an

∼ 15◦ angle to create a tapered PMMA lm with variable lm thickness. The humidity during measurements is controlled by owing dry air into the AFM enclosure. ACS Paragon 4Plus Environment

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FIG. 2. a) Measured force spectrum of carbonyl resonance of PMMA (blue) with corresponding Lorentzian t (dashed) matches the imaginary part of the index of refraction Im(˜ n) = κ (green) [22]. b) Theoretical optical gradient force spectrum calculated using Eq. 1 and the real part of index of refraction Re(˜ n) both show dispersive behavior. c) AFM topography, d) s-SNOM amplitude, e) and force signal of a PS-PMMA block copolymer sample with laser tuned to the carbonyl resonance at ν¯C=O = 1735 cm−1 . The force signal shows high contrast, with strong signal on PMMA, with

∼ 25 nm spatial resolution and correlated with the s-SNOM amplitude (f).

III.

RESULTS

Figure 2a) shows the measured force spectrum of the PMMA sample normalized against a Si reference sample (circles) with a corresponding Lorentizan t (dashed). The force is peaked at the carbonyl resonance of PMMA, and the symmetric spectral lineshape matches that of the imaginary part of the dielectric function Im(˜ n) = κ(ω) obtained from ellipsometry [22] (green) within ±1.5 cm−1 accuracy. We calculate the expected optical gradient force using the dipole approximation to represent the polarizabilities of the tip and sample to rst order. In the dipole approximation, the sample is treated as a semi-innite half-space and the tip as a sphere of radius r with −1 , with ϵt the dielectric function of the tip (see supporting inpolarizability αt = 4πr3 ϵ0 ϵϵtt +2

formation for additional model details). When the tip is close to the sample surface, the ACS Paragon 5Plus Environment

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mutual interaction and coupling between tip and sample gives rise to a modied tip polar( ) ization of p = αt E0 + 16πϵ0βp , where the second term is the radiation reaction term, (r+h)3

β=

ϵs (ω)−1 , ϵs (ω)+1

and ϵs (ω) is the dielectric function of the sample. Solving the recursive relation

for p yields an eective polarizability αeff = p/E0 =

αt (1−βαt /16πϵ0 (r+h)3 )

that describes the

combined tip-sample system [20]. The eld acting on the tip dipole E = E0 + thus gives rise to an attractive force towards the sample given by ( ) 2 3E 0 2 ⃗ = Re α F⃗opt. = p⃗ · ∇E . eff 16πϵ0 (r + h)4

βαeff E0 16πϵ0 (r+h)3

(1)

We used a sphere radius of r = 10 nm to represent the tip apex radius of our commercially acquired tips (240AC-GG OPUS, Mikromasch, spring constant k ≈ 2 N/m). As shown in Fig. 2b), the calculated force using Eq. 1 is in the sub-10 fN range, and shows a dispersive lineshape, in agreement with recent electromagnetic simulations [14] and analytic theory [17, 23]. Its lineshape resembles the real part of the index of refraction (green). While this model for the coupled tip-sample polarizability does not consider the extended geometry of the tip shaft or nanoscale surface corrugations at the tip apex, it correctly describes the key physical principle, and has been successfully applied to previous near-eld spectroscopic studies [24, 25]. By raster-scanning the tip across the sample surface, using the rst cantilever mode for AFM feedback, we then obtain spatial images with resolution given by the tip apex radius of ∼ 25 nm. Figure 2c) shows the topography image of the PS-b-PMMA sample. The carbonyl resonant s-SNOM image at ν¯ = 1735 cm−1 shows strong signal on the PMMA domains (Fig. 2d) correlated with the force signal (Fig. 2e), both with ∼ 25 nm spatial resolution (inset), with correlation plot shown in Fig. 2f). Figure 3 shows the PMMA lm thickness dependence of the photo-induced force signal at the carbonyl resonance frequency measured on the tapered PMMA lm with thickness ranging from ≃ 7 − 250 nm (blue). The measured force monotonically increases over the entire thickness range. We calculate the lm thickness dependent thermal expansion based on the electric eld intensity within the PMMA lm given by:

E(z) =

αeff E0 + E0 e−z/2δ , 2πϵ0 ϵ2 (ω)(z + h)3

(2)

with the intensity absorption depth of PMMA δ ≈ 0.8 µm determined by Beer's law, the complex dielectric function of PMMA ϵ2 (ω), and distance z from the PMMA/air interface. ACS Paragon 6Plus Environment

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PMMA

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0.1 0.0

0

50 100 150 PMMA thickness d (nm)

200

7.5

FIG. 3. Photo-induced force dependence on PMMA thickness (blue symbols). The relative thermal expansion calculated from Eq. 3 (blue line), and optical gradient force calculated for the PMMA/Si layered system (green, solid) and for a free standing PMMA layer (green, dashed) are shown for comparison.

The rst term describes the localized evanescent electric eld between the tip and sample based on the dipole approximation from above. The second term is the exponential decay of far-eld illumination within the PMMA layer. The thermal expansion ∆z is then obtained for a given lm thickness t using

∫

∆z(t) ∝ αT,PMMA

∫

t

|E(z)| dz + αT,Si 2

0

∞

|E(z)|2 dz,

(3)

t

where αT,x is the thermal expansion coecient, with x = Si, PMMA. The calculated thermal expansion (blue line) shows an increase with t up to the absorption depth of PMMA δ =

0.8 µm. In contrast, the optical gradient force (green) is largely thickness-independent, with only a slight increase below a lm thickness of 30 nm for the PMMA/Si sample structure, due to the higher IR dielectric function of Si. Figure 4a) shows approach curves on the PMMA lms of 60 nm (black), and 10 nm (blue) thicknesses, and the bare Si surface with laser tuned to the carbonyl resonance at ν¯ = 1735 cm−1 . In each case the force signal rises sharply at tip-sample contact (z = 0 nm). Only for the 60 nm case, an order of magnitude weaker long-range component emerges. This ACS Paragon 7Plus Environment

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Force Fphoto-ind. (pN)

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0 -5 -10

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FIG. 4. a) Photo-induced force approach curves on a 60-nm thick PMMA lm (black), 10-nm thick PMMA lm (blue), and Si (red) at the carbonyl resonance (ν¯ = 1735 cm−1 ). For each sample, a prominent increase in signal occurs only at the point of tip-sample contact (z = 0 nm). Only for the 60 nm lm, a long range force described by an exponential decay (magenta), with decay length l = 25 nm is observed. Predictions from the point-dipole model for the optical gradient force are shown in green. b) Approach curve measurement over a PTFE surface, with laser tuned to resonance with the C-F symmetric stretch at ν¯ = 1152 cm−1 . A weak attractive force is observed before the onset of the repulsive thermal expansion.

spatially extended force ts well to an exponential decay with 1/e decay length l = 25 nm (magenta). This force is correlated with a slight decrease in the tapping phase, indicating a repulsive character (see supporting information). Fits to a power law F (z) ∝ z α for

α > 0, generally give worse agreement to the measured distance dependence. The calculated distance dependence of the optical gradient force (green) shown for comparison is conned to tip-sample separations on the order of the tip apex radius r ≃ 20 nm. Note that a spectrum acquired 15 nm from tip-sample contact above the 60 nm thick PMMA lm shows a symmetric lineshape, closely matching the absorption prole of PMMA (see supporting information). These results indicate that the long-range force is associated with optical absorption. We additionally performed approach curves using small, e.g., as low as 2 nm tapping amplitudes to improve sensitivity to the possible optical gradient force acting on short length scales. However, only a similarly sharp rise in force at direct tip-sample contact is observed, even at the lowest tapping amplitudes of 2 nm, with no discernible long range behavior (see ACS Paragon 8Plus Environment

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Nano Letters

supporting information). Finally, we investigate weak tip-sample interactions occurring within the rst few nm of the surface that could be obscured by damping from adsorbed surface water. In order to reduce eects of the adsorbed water layer, we examine the hydrophobic surface of PTFE under a dry-air-purged environment as described above (relative humidity RH < 2%). We tune the laser to ν¯ = 1152 cm−1 , which is resonant with the C-F symmetric stretch vibration [26] and use small tapping amplitudes in the range 4-10 nm in order to increase sensitivity to few-nm short range forces. As shown in Figure 4b), we measure the tapping amplitude, tapping phase, and force signal as a function of tip-sample distance. When the tip is within