Ultrafast Tracking of Exciton and Charge Carrier Transport in Optoelectronic Materials on the Nanometer Scale

We present a novel optical transient absorption and reflection microscope based on a diffraction-limited pump pulse in combination with a wide-field probe pulse, for the spatiotemporal investigation of ultrafast population transport in thin films. The microscope achieves a temporal resolution down to 12 fs and simultaneously provides sub-10 nm spatial accuracy. We demonstrate the capabilities of the microscope by revealing an ultrafast excited-state exciton population transport of up to 32 nm in a thin film of pentacene and by tracking the carrier motion in p-doped silicon. The use of few-cycle optical excitation pulses enables impulsive stimulated Raman microspectroscopy, which is used for in situ verification of the chemical identity in the 100–2000 cm–1 spectral window. Our methodology bridges the gap between optical microscopy and spectroscopy, allowing for the study of ultrafast transport properties down to the nanometer length scale.


.1 Spatial characterization of pump pulse
The pump size was determined by recording the fluorescence intensity obtained from sample scanning fluorescent beads (TetraSpeck TM fluorescent microspheres, T7179, diameter ~100 nm) across the pump spot. The retrieved spatial intensity profile was fit to a Gaussian function yielding σ = 115 nm ( Figure 1e). This value is close to the expected diffraction limit of σ = 100 nm for a pulse centered at 560 nm and a numerical aperture (NA) of 1.1.

Temporal characterization
Optical pulses were characterized using a home-built second-harmonic generation frequencyresolved gating (SHG-FROG) setup. 1 Care was taken to match the path lengths in the pulsecharacterization arm with the sample stage arm for both pulses. Specifically, pump pulses were focused into the back-aperture of an identical microscope objective by a curved mirror (F = 200 mm) and reflectively collimated (F = 75 mm) before being sent to the SHG-FROG.
The retrieved pulse durations for pump and probe pulses were 9.8 and 6.8 fs, respectively ( Figure   S1). We remark that the same pump pulses were also compressed without the microscope objective, resulting in a pulse duration of 9.3 fs retrieved via SHG-FROG. Based on the required number of bounces on the chirped mirrors, we can estimate the induced group-velocity dispersion of our microscope objective to be ~1100 fs 2 , significantly lower than conventional high-NA multi-component objectives which typically exhibit >4000 fs 2 . 2 In addition to the temporal intensity and phase values, we also report the spectral intensity and phase values retrieved from SHG-FROG in Figure S2. We observe small residual oscillatory phase modulation over the full pulse bandwidth, which can be explained by residual phase oscillation imprinted on the pulses by the employed set of chirped mirrors as well as higher order dispersion effects arising in the setup. This effect prevents compression of our pulses to the transform limit but has only a weak impact on the temporal characteristics, as evident by the near-flat temporal phase (Figure 1c).  To fully compress the pulses for the employed objects, a more sophisticated pulse-compression scheme based on deformable mirrors or spatial light modulators is necessary. 3 To estimate the temporal chirp imprinted by the objective and wide-field lens onto a compressed probe pulse, we expanded our imaging path to spectrally-resolve the transient photoresponse from a diffraction-limited section of the image, as outlined in our previous works. 4 By integrating over all space, we can compute a spectrally-resolved transient reflection map ( Figure S3a) that highlights a probe chirp of ~700 fs from 670 -900 nm. This chirp temporally broadens the time resolution to ~50 fs at 740 nm for a 10 nm (full width half maximum) bandpass filter ( Figure S3b), but can be improved by employing narrower bandpass filters at the expense of detected photons. We note that the chromatic aberrations of our microscope objective result in spectral distortions induced by phase interference effects native to wide-field imaging in a spectrally-resolved measurement, as evident by the unphysical 'dip' in the transient reflection spectrum in Figure S2a. This effect can be reduced significantly by employing high-NA aberration corrected objectives, 4 which will, however, limit the shortest pump pulse durations that can be achieved.

Fit performance
Here, we briefly illustrate the quality of a two-dimensional isotropic Gaussian fit to the pentacene transmission data. The differential point-spread function and the residual of the fitting routine are shown in Figure S4a and S4b, respectively, highlighting a very good representation of the central signal amplitude. The only residual that can be determined above the noise floor stems from diffraction rings associated with the Airy disk point-spread function intrinsic to wide-field detection.  Figure S4d). An estimate of the overall spatial accuracy can be retrieved by convoluting these two errors, resulting in a total accuracy of ~2.9 nm, sufficient to resolve the 10 nm increase obtained for pentacene in the first 200 fs.
The same approach for p-doped silicon results in a fit SD error of <2.0 nm and an SD fluctuation error of σ = 1.8 nm, resulting in an overall spatial accuracy of ~2.7 nm, again sufficient to resolve the observed growth of ~10 nm (Figure 4b).
Closer inspection of the transient point-spread function ( Figure S4a) reveals a slight asymmetry, particularly pronounced in the first positive diffraction ring. To establish if this has an impact on the fit performance, we repeated our spatial fitting procedure using a non-isotropic 2D Gaussian function ( Figure S5). We find that the standard deviations along the X and Y dimensions are identical within the noise-level, firmly ruling out a distorted point-spread function. We therefore attribute the observed

Transient absorption spectroscopy on thin pentacene films
Care has to be taken to avoid spectral overlaps of different transient features in a transient absorption microscope experiment, as different components can exhibit varying carrier density dependencies which can affect the overall recorded transient point-spread function. 6,7 To ensure that the selected probe wavelength of 790 nm is free of these effects and only reports on the photoinduced correlated triplet pair absorption band, we conducted ultrafast transient absorption spectroscopy on the same films that we measured in the microscope. Care was taken to use the same pump pulse as in the microscope (10 fs, 560 nm) to ensure the same excitation properties ( Figure S7). 8 The obtained early-time transient absorption spectra match previously published results 5 and allow us to identify the wavelength region > 710 nm to a clean photoinduced transient absorption band, allowing us to assess the spatial dynamics free of artefacts. We remark that the ground-state bleach and stimulated emission bands in pentacene are superimposed at 670 -690 nm, preventing straightforward microscopic investigations.

Wavelength-dependent ultrafast diffusion in pentacene films
To further verify that spectral overlap can be excluded as a factor causing the ultrafast expansion observed in pentacene, we repeated our transient absorption microscope studies at different probe wavelengths throughout the photoinduced absorption band. As we approach the band edge at 690 nm, spectral overlap of the photoinduced absorption and oppositely-valued stimulated emission and ground state bleach bands is expected to increase. Provided these features have different carrier dependencies, this could result in artificially narrowed point-spread functions, resulting in unphysical diffusion coefficients. Figure S8 shows the extracted means-square displacement curves for probe wavelengths at 710, 730 and 760 nm. Contrary to the above argument, we observe no significant differences in the spatial expansion between the three wavelengths within our signal-to-noise level and compared to probing the diffusion behavior at 790 nm (Figure 2c). The extracted diffusion coefficients are 158 ± 13, 157 ± 12 and 147 ± 16 cm 2 s -1 at 710, 730 and 760 nm, respectively, comparing well to the retrieved diffusion coefficient of 137 ± 18 cm 2 s -1 at 790 nm. The weak increase in diffusion coefficient might be attributed to an increase in spectral overlaps, but these changes are on the order of the retrieved errors, preventing a definite assignment.

Power dependence of early expansion regime in pentacene films
We investigated the expansion behavior of pentacene for different excitation densities within the linear absorption regime as judged by the power dependence on the differential transmission signal at 1 ps after photoexcitation. Here, we observed no fluence dependence on the diffusion coefficients for different signal levels ( Figure S9). We remark that these measurements were carried out on 12 different sample locations. Consequently, morphological changes to the transport behavior cannot be excluded, which manifest in the (non-correlated) spread of the obtained diffusion coefficients as compared to the intrinsic error bar for each measurement.