Quantifying noise effects in optical measures of excited state transport

Time-resolved microscopy is a widely used approach for imaging and quantifying charge and energy transport in functional materials. While it is generally recognized that resolving small diffusion lengths is limited by measurement noise, the impacts of noise have not been systematically assessed or quantified. This article reports modeling efforts to elucidate the impact of noise on optical probes of transport. Excited state population distributions, modeled as Gaussians with additive white noise typical of experimental conditions, are subject to decay and diffusive evolution. Using a conventional composite least-squares fitting algorithm, the resulting diffusion constant estimates are compared with the model input parameter. The results show that heteroscedasticity (i.e., time-varying noise levels), insufficient spatial and/or temporal resolution, and small diffusion lengths relative to the magnitude of noise lead to a surprising degree of imprecision under moderate experimental parameters. Moreover, the compounding influence of low initial contrast and small diffusion length leads to systematic overestimation of diffusion coefficients. Each of these issues is quantitatively analyzed herein, and experimental approaches to mitigate them are proposed. General guidelines for experimentalists to rapidly assess measurement precision are provided, as is an open-source tool for customizable evaluation of noise effects on time-resolved microscopy transport measurements.

Rapid Exciton Transport and Structural Defects in Individual Porphyrinic Metal Organic Framework Microcrystals

To date, spectroscopic characterization of porphyrin-based metal organic frameworks (MOFs) has relied almost exclusively on ensemble techniques, which provide only structurally averaged insight into the functional properties of these promising photochemical platforms. This work employs time-resolved pump-probe microscopy to probe ultrafast dynamics in PCN-222 MOF single crystals. The simultaneous high spatial and temporal resolution of the technique enables the correlation of spectroscopic observables to both inter- and intracrystal structural heterogeneity. The pump-probe measurements show that significant differences in the excited state lifetime exist between individual PCN-222 crystals of an ensemble. On a single PCN-222 crystal, differences in excited state lifetime and photoluminescence quantum yield are found to correlate to microscale structural defects introduced at crystallization. Pump probe microscopy also enables the direct measurement of excited state transport. Imaging of exciton transport on individual MOF crystals reveals rapid, but subdiffusive exciton transport which slows on the 10s of ps time scale. Time-averaged exciton diffusion coefficients over the first 200 ps span a range of 0.27 to 1.0 cm2/s, indicating that excited states are rapidly transported through the porphyrin network of PCN-222 before being trapped. Together, these single-particle-resolved measurements provide important new insight into the role played by structural defects on the photochemical functionality of porphyrin-based MOFs.

Ultrafast Charge Injection in Silver-Modified Graphitic Carbon Nitride

Graphitic carbon nitride (gCN) is a promising organic platform for driving light-activated charge-transfer reactions in a number of valuable photocatalytic cycles. A primary limitation of gCN as a photocatalyst is its short excited-state lifetime, which is mediated by a high density of trap and defect sites that result in rapid excited-state decay and low photocatalytic efficiency. To enhance the catalytic activity, gCN is often functionalized with a metal co-catalyst; however, the mechanism by which metal co-catalysts enhance the reactivity has not been clearly established. In this work, the excited-state dynamics of gCN and silver-modified gCN are compared using ultrafast transient absorption and time-resolved photoluminescence spectroscopies. In silver-modified gCN, an ultrafast spectral shift in the silver plasmon resonance provides direct spectral evidence of electron transfer from gCN to the silver nanoparticles. The electron-transfer rate is competitive with other non-radiative relaxation pathways, with electron-transfer yields approaching 50%, thus providing an effective strategy for mitigating losses associated with defects and trap sites.

Photocatalytic Reduction of Aqueous Nitrate with Hybrid Ag/g-C3N4 under Ultraviolet and Visible Light

The concentration of nitrate in natural surface waters by agricultural runoff remains a challenging problem in environmental chemistry. One promising denitrification strategy is to utilize photocatalysts, whose light-driven excited states are capable of reducing nitrate to nitrogen gas. We have synthesized and characterized pristine and silver-loaded graphitic carbon nitrides and assessed their activity for photocatalytic nitrate reduction at neutral pH. While nitrate reduction does occur on the pristine material, the silver cocatalyst greatly enhances product yields. Kinetic studies performed in batch photoreactors under both UV and visible excitation suggest that nitrate reduction to produce aqueous nitrite, ammonium, and nitrogen gas proceeds via a cooperative water reduction on the silver metal domains to produce adsorbed H atoms. By varying the percentage of silver loading onto the g-C₃N₄, the density of metal domains can be adjusted, which in turn tunes the reduction selectivity toward various products.

Direct Correlation of Charge Carrier Transport to Local Crystal Quality in Lead Halide Perovskites

Although solution processing methods provide an attractive route toward development of low-cost functional materials, these accessible fabrication approaches can engender high concentrations of microscopic structural defects that are detrimental to performance. In lead halide perovskites, structural disorder derived from solution processing has been implicated as an important determiner of photophysical properties. However, a direct correlation between the functional properties of these materials and the local crystal structure in which non-equilibrium states evolve has remained elusive, in part because structural heterogeneities occur on length scales that defy conventional characterization techniques. To address this knowledge gap, we have combined ultrafast pump-probe microscopy and electron backscattering diffraction to directly correlate charge carrier transport with the local diffraction pattern contrast, an indicator of crystal quality. Spatial correlation of these measurements strongly suggests that even on individual single crystal CsPbBr₃ domains, microscopic variability in the crystal quality profoundly impacts the efficiency of charge carrier transport.

Spatiotemporal coupling of excited state dynamics in time-resolved microscopies

In the high-density excitation limit, as is often probed with ultrafast spectroscopies, spatial and temporal evolution of photogenerated excited states are strongly coupled, giving rise to artifacts that influence experimentally-determined material parameters. The interplay between spatial and temporal degrees of freedom is especially pronounced in pump-probe microscopy, where small laser spot sizes amplify the effects of spatiotemporal coupling on spectroscopic observables. To quantitatively model these effects, a continuum model is developed that accounts for laser spot size as well as nonlinear excited state decay and diffusion. It is shown that effective excitation densities cannot be used to determine quantitatively correct rate constants. Significant error is introduced unless experimental data is fit with a numerical model that accounts for spatial anisotropy in the excitation density. Furthermore, the quantitative determination of material diffusion coefficients is shown to be highly sensitive to experimental parameters.

Q-FADD: A Mechanistic Approach for Modeling the Accumulation of Proteins at Sites of DNA Damage

The repair of DNA damage requires the ordered recruitment of many different proteins that are responsible for signaling and subsequent repair. A powerful and widely used tool for studying the orchestrated accumulation of these proteins at damage sites is laser microirradiation in live cells, followed by monitoring the accumulation of the fluorescently labeled protein in question. Despite the widespread use of this approach, there exists no rigorous method for characterizing the recruitment process quantitatively. Here, we introduce a diffusion model that explicitly accounts for the unique sizes and shapes of individual nuclei and uses two variables: D_eff, the effective coefficient of diffusion, and F, the fraction of mobile protein that accumulates at sites of DNA damage. Our model quantitatively describes the accumulation of three test proteins, poly-ADP-ribose polymerases 1 and 2 (PARP1/2) and histone PARylation factor 1. D_eff for PARP1, as derived by our approach, is 6× greater than for PARP2 and in agreement with previous literature reports using fluorescence correlation spectroscopy and fluorescence recovery after photobleaching. Our data indicate that histone PARylation factor 1 arrives at sites of DNA damage independently of either PARP. Importantly, our model, which can be applied to existing data, allows for the direct comparison of the coefficient of diffusion for any DNA repair protein between different cell types, obtained in different laboratories and by different methods, and also allows for the interrogation of cell-to-cell variability.

Perovskite Carrier Transport: Disentangling the Impacts of Effective Mass and Scattering Time Through Microscopic Optical Detection

While carrier mobility is a practical and commonly cited measure of transport, it conflates the effects of two more fundamental material properties: the effective mass and mean scattering time of charge carriers. This Letter describes the correlation of two ultrafast imaging techniques to disentangle the effect of each on carrier transport in lead halide perovskites. Two materials are compared: methylammonium lead tri-iodide (MAPbI₃) and cesium lead bromide diiodide (CsPbBrI₂). By correlating photoinduced changes to the refractive index with a direct measure of carrier diffusion, both the carrier optical mass and mean scattering time are uniquely determined on microscopic length scales. These results show that the factor of 4 lower mobility of CsPbBrI₂ is due not to differing optical masses of charge carriers, which are measured to be similar in CsPbBrI₂ and MAPbI₃, but rather to a difference in mean carrier scattering time. The scope and limitations of the approach are discussed.

Probing Intrawire, Interwire, and Diameter-Dependent Variations in Silicon Nanowire Surface Trap Density with Pump-Probe Microscopy

Surface trap density in silicon nanowires (NWs) plays a key role in the performance of many semiconductor NW-based devices. We use pump-probe microscopy to characterize the surface recombination dynamics on a point-by-point basis in 301 silicon NWs grown using the vapor-liquid-solid (VLS) method. The surface recombination velocity (S), a metric of the surface quality that is directly proportional to trap density, is determined by the relationship S = d/4τ from measurements of the recombination lifetime (τ) and NW diameter (d) at distinct spatial locations in individual NWs. We find that S varies by as much as 2 orders of magnitude between NWs grown at the same time but varies only by a factor of 2 or three within an individual NW. Although we find that, as expected, smaller-diameter NWs exhibit shorter τ, we also find that smaller wires exhibit higher values of S; this indicates that τ is shorter both because of the geometrical effect of smaller d and because of a poorer quality surface. These results highlight the need to consider interwire heterogeneity as well as diameter-dependent surface effects when fabricating NW-based devices.

Screened Charge Carrier Transport in Methylammonium Lead Iodide Perovskite Thin Films

While organometal halide perovskites are promising for a variety of optoelectronic applications, the morphological and compositional defects introduced by solution processing techniques have hindered efforts at understanding their fundamental properties. To provide a detailed picture of the intrinsic carrier transport properties of methylammonium lead iodide without contributions from defects such as grain boundaries, we utilized pump-probe microscopy to measure diffusion in individual crystalline domains of a thin film. Direct imaging of carrier transport in 25 individual domains yields diffusivities between 0.74 and 1.77 cm² s^-1, demonstrating single-crystal-like, long-range transport characteristics in a thin film architecture. We also examine the effects of excitation density on carrier diffusivity, finding that transport is nearly independent of photoexcited carrier density between 6 × 10¹⁷ cm^-3 and 4 × 10¹⁹ cm^-3. Transport modeling of the observed density independence suggests that strong carrier-phonon scattering coupled with a large static relative permittivity is responsible for the unusual transport characteristics of methylammonium perovskite.

Imaging theory of structured pump-probe microscopy

With sub-micron spatial resolution and femtosecond temporal resolution, pump probe microscopy provides a powerful spectroscopic probe of complex electronic environments in bulk and nanoscale materials. However, the electronic structure of many materials systems are governed by compositional and morphological heterogeneities on length scales that lie below the diffraction limit. We have recently demonstrated Structured Pump Probe Microscopy (SPPM), which employs a patterned pump excitation field to provide spectroscopic interrogation of sub-diffraction limited sample volumes. Herein, we develop the imaging theory of SPPM in two dimensions to accompany the previously published experimental methodology. We show that regardless of pump and probe wavelengths, a nearly two-fold reduction in spectroscopic probe volume can be achieved. We also examine the limitations of the approach, with a detailed discussion of ringing in the point spread function that can reduce imaging performance.

Ultrafast, Light-Induced Electron Transfer in a Perylene Diimide Chromophore-Donor Assembly on TiO2

Surface-bound, perylenediimide (PDI)-based molecular assemblies have been synthesized on nanocrystalline TiO2 by reaction of a dianhydride with a surface-bound aniline and succinimide bonding. In a second step, the Fe(II) polypyridyl complex [Fe(II)(tpy-PhNH2)2](2+) was added to the outside of the film, also by succinimide bonding. Ultrafast transient absorption measurements in 0.1 M HClO4 reveal that electron injection into TiO2 by (1)PDI* does not occur, but rather leads to the ultrafast formation of the redox-separated pair PDI(•+),PDI(•-), which decays with complex kinetics (τ1 = 0.8 ps, τ2 = 15 ps, and τ3 = 1500 ps). With the added Fe(II) polypyridyl complex, rapid (<25 ps) oxidation of Fe(II) by the PDI(•+),PDI(•-) redox pair occurs to give Fe(III),PDI(•-) persisting for >400 μs in the film environment.

Reversible strain-induced electron-hole recombination in silicon nanowires observed with femtosecond pump-probe microscopy

Strain-induced changes to the electronic structure of nanoscale materials provide a promising avenue for expanding the optoelectronic functionality of semiconductor nanostructures in device applications. Here we use pump-probe microscopy with femtosecond temporal resolution and submicron spatial resolution to characterize charge-carrier recombination and transport dynamics in silicon nanowires (NWs) locally strained by bending deformation. The electron-hole recombination rate increases with strain for values above a threshold of ∼1% and, in highly strained (∼5%) regions of the NW, increases 6-fold. The changes in recombination rate are independent of NW diameter and reversible upon reduction of the applied strain, indicating the effect originates from alterations to the NW bulk electronic structure rather than introduction of defects. The results highlight the strong relationship between strain, electronic structure, and charge-carrier dynamics in low-dimensional semiconductor systems, and we anticipate the results will assist the development of strain-enabled optoelectronic devices with indirect-bandgap materials such as silicon.

Imaging charge separation and carrier recombination in nanowire p-i-n junctions using ultrafast microscopy

Silicon nanowires incorporating p-type/n-type (p-n) junctions have been introduced as basic building blocks for future nanoscale electronic components. Controlling charge flow through these doped nanostructures is central to their function, yet our understanding of this process is inferred from measurements that average over entire structures or integrate over long times. Here, we have used femtosecond pump-probe microscopy to directly image the dynamics of photogenerated charge carriers in silicon nanowires encoded with p-n junctions along the growth axis. Initially, motion is dictated by carrier-carrier interactions, resulting in diffusive spreading of the neutral electron-hole cloud. Charge separation occurs at longer times as the carrier distribution reaches the edges of the depletion region, leading to a persistent electron population in the n-type region. Time-resolved visualization of the carrier dynamics yields clear, direct information on fundamental drift, diffusion, and recombination processes in these systems, providing a powerful tool for understanding and improving materials for nanotechnology.

Direct imaging of free carrier and trap carrier motion in silicon nanowires by spatially-separated femtosecond pump-probe microscopy

We have developed a pump-probe microscope capable of exciting a single semiconductor nanostructure in one location and probing it in another with both high spatial and temporal resolution. Experiments performed on Si nanowires enable a direct visualization of the charge cloud produced by photoexcitation at a localized spot as it spreads along the nanowire axis. The time-resolved images show clear evidence of rapid diffusional spreading and recombination of the free carriers, which is consistent with ambipolar diffusion and a surface recombination velocity of ∼10(4) cm/s. The free carrier dynamics are followed by trap carrier migration on slower time scales.

Synthetically encoding 10 nm morphology in silicon nanowires

Si nanowires (NWs) have been widely explored as a platform for photonic and electronic technologies. Here, we report a bottom-up method to break the conventional "wire" symmetry and synthetically encode a high-resolution array of arbitrary shapes, including nanorods, sinusoids, bowties, tapers, nanogaps, and gratings, along the NW growth axis. Rapid modulation of phosphorus doping combined with selective wet-chemical etching enabled morphological features as small as 10 nm to be patterned over wires more than 50 μm in length. This capability fundamentally expands the set of technologies that can be realized with Si NWs, and as proof-of-concept, we demonstrate two distinct applications. First, nanogap-encoded NWs were used as templates for Noble metals, yielding plasmonic structures with tunable resonances for surface-enhanced Raman imaging. Second, core/shell Si/SiO2 nanorods were integrated into electronic devices that exhibit resistive switching, enabling nonvolatile memory storage. Moving beyond these initial examples, we envision this method will become a generic route to encode new functionality in semiconductor NWs.

Modeling and correction of distorted two-dimensional Fourier transform spectra from pixelated pulse shaping devices

Two-dimensional Fourier transform spectra of a three level model system are simulated using a non-perturbative density matrix formalism. The electric field distortions resultant from using pixelated pulse shaping devices to produce phase-locked pulse pairs are modeled and the effects on the recovered spectra are examined. To minimize spectral distortions, a temporal filtering scheme is employed which eliminates contributions from spurious sample polarizations.

Competition between Ultrafast Energy Flow and Electron Transfer in a Ru(II)-Loaded Polyfluorene Light-Harvesting Polymer

This Letter describes the synthesis and photophysical characterization of a Ru(II) assembly consisting of metal polypyridyl complexes linked together by a polyfluorene scaffold. Unlike many scaffolds incorporating saturated linkages, the conjugated polymer in this system acts as a functional light-harvesting component. Conformational disorder breaks the conjugation in the polymer backbone, resulting in a chain composed of many chromophore units, whose relative energies depend on the segment lengths. Photoexcitation of the polyfluorene by a femtosecond laser pulse results in the excitation of polyfluorene, which then undergoes direct energy transfer to the pendant Ru(II) complexes, producing Ru(II)* excited states within 500 fs after photoexcitation. Femtosecond transient absorption data show the presence of electron transfer from PF* to Ru(II) to form charge-separated (CS) products within 1-2 ps. The decay of the oxidized and reduced products, PF(+•) and Ru(I), through back electron transfer are followed using picosecond transient absorption methods.

Enhanced triplet formation in polycrystalline tetracene films by femtosecond optical-pulse shaping

Polycrystalline tetracene films have been explored using weak ∼ 30 fs visible laser pulses that excite the lowest singlet exciton as well as coherent vibrational motion. Transient difference spectra show a triplet absorption which arises following singlet fission (SF) and persists for 1.6 ns without decay. Adaptive pulse shaping identifies multipulse optimal fields which maximize this absorption feature by ∼ 20%. These are comprised of subpulses separated by time delays well correlated with the period of lattice vibrations suggesting such modes control the yield of SF photochemistry.

Facile collection of two-dimensional electronic spectra using femtosecond pulse-shaping Technology

This letter reports a straightforward means of collecting two-dimensional electronic (2D-E) spectra using optical tools common to many research groups involved in ultrafast spectroscopy and quantum control. In our method a femtosecond pulse shaper is used to generate a pair of phase stable collinear laser pulses which are then incident on a gas or liquid sample. The pulse pair is followed by an ultrashort probe pulse that is spectrally resolved. The delay between the collinear pulses is incremented using phase and amplitude shaping and a 2D-E spectrum is generated following Fourier transformation. The partially collinear beam geometry results in perfectly phased absorptive spectra without phase twist. Our approach is much simpler to implement than standard non-collinear beam geometries, which are challenging to phase stabilize and require complicated calibrations. Using pulse shaping, many new experiments are now also possible in both 2D-E spectroscopy and coherent control.

Amine−Hydrogen Halide Complexes: Experimental Electric Dipole Moments and a Theoretical Decomposition of Dipole Moments and Binding Energies

The Stark effect has been observed in the rotational spectra of several gas-phase amine-hydrogen halide complexes and the following electric dipole moments have been determined: H(3)(15)N-H(35)Cl (4.05865 +/- 0.00095 D), (CH(3))(3)(15)N-H(35)Cl (7.128 +/- 0.012 D), H(3)(15)N-H(79)Br (4.2577 +/- 0.0022 D), and (CH(3))(3)(15)N-H(79)Br (8.397 +/- 0.014 D). Calculations of the binding energies and electric dipole moments for the full set of complexes R(n)()(CH(3))(3)(-)(n)()N-HX (n = 0-3; X = F, Cl, Br) at the MP2/aug-cc-pVDZ level are also reported. The block localized wave function (BLW) energy decomposition method has been used to partition the binding energies into contributions from electrostatic, exchange, distortion, polarization, and charge-transfer terms. Similarly, the calculated dipole moments have been decomposed into distortion, polarization, and charge-transfer components. The complexes studied range from hydrogen-bonded systems to proton-transferred ion pairs, and the total interaction energies vary from 7 to 17 kcal/mol across the series. The individual energy components show a much wider variation than this, but cancellation of terms accounts for the relatively narrow range of net binding energies. For both the hydrogen-bonded complexes and the proton-transferred ion pairs, the electrostatic and exchange terms have magnitudes that increase with the degree of proton transfer but are of opposite sign, leaving most of the net stabilization to arise from polarization and charge transfer. In all of the systems studied, the polarization terms contribute the most to the induced dipole moment, followed by smaller but still significant contributions from charge transfer. A significant contribution to the induced moment of the ion pairs also arises from distortion of the HX monomer.