Controlling polaron formation at hematite surfaces by molecular functionalization probed by XUV reflection-absorption spectroscopy

A number of first row transition metal oxides are cheap, have suitable solar absorbance, and have reasonable bandgaps to drive water oxidation.¹ Hematite (α-Fe₂O₃), in particular, has been extensively studied for its ability to photocatalytically evolve oxygen from water. However, hematite suffers from poor charge carrier mobility (∼10⁻² cm² V⁻¹ s⁻¹).² Defect states are often implicated as the primary trap and recombination sites, and extensive work has been performed to remove these but with limited success.^3–8 However, it has recently been shown that photoexcited electrons in hematite form small polarons which limit carrier mobility through self trapping.^9,10 Notably, polaron formation is not directly associated with defect states.^10,11

Small polaron formation occurs via coupling between photoexcited electrons and phonons and is associated with ultrafast (few hundred femtoseconds) lattice expansion. While polaron formation is known to occur in bulk, there are a number of factors that make the energetics and dynamics of polaron formation unique to a surface. These include (1) the vibrational structure of molecular adsorbates, which also participate in carrier self-trapping^12–14 and (2) steric effects, which make lattice expansion at a surface energetically favorable by comparison to bulk.¹⁵ Theoretical predictions indicate that the thermodynamic driving force and kinetics of polaron formation are significantly different at the surface relative to the bulk.^15–18 The thermodynamics and kinetics of polaron formation can be described within a Marcus polaron hopping model. The hopping parameters are equivalent to the Marcus parameters, namely, polaron stabilization energy and activation energy, and can be used to describe both the kinetics of polaron formation and polaron hopping.¹⁹ The ability to manipulate the Marcus parameters by rational design principles allows control over polaron formation rates as well as polaron hopping rates. Because polaron formation is not directly mediated by defect states, tunable Marcus parameters offer a more efficient way to control surface electron dynamics compared to defect state passivation.

Given the fact that injection of photoexcited carriers from the surface of a material to the adsorbed reactant strongly influences the catalytic efficiency, it is imperative to study and control the dynamics of carrier self-trapping processes at the surface. However, to the best of our knowledge no direct experimental measurements have been made which differentiate polaron formation rates at the surface and in bulk. Additionally, several theoretical predictions indicate that polaron formation energetics are strongly influenced by surface adsorbates.²⁰ Surface adsorbates, like self assembled molecular monolayers, have many synthetic handles to tune the Marcus parameters. However, to the best of our knowledge, this approach has not been systematically explored. Extreme ultraviolet (XUV) light sources based on high harmonic generation (HHG) offer a unique ability to probe chemical state specific electron dynamics with femtosecond time resolution on a laboratory tabletop.^21–24 Recently, we have developed a surface-specific analog of XUV absorption spectroscopy in a reflection geometry which can provide element specific electron dynamics with surface specificity and femtosecond time resolution, making it a well-suited technique to study surface polaron formation.^10,11,25,26 In our recent contribution, we show that a transient hypsochromic shift at the iron M_2,3-edge can be assigned to a lattice expansion during polaron formation at the surface of photoexcited hematite.¹⁰ Time-resolved changes of this spectral feature give the polaron formation rate.

In this paper, we compare surface and bulk polaron formation in hematite based on a two-temperature model, which was recently proposed to describe polaron formation in bulk hematite.²⁷ The observed surface polaron trapping rate is approximately three times slower compared to the bulk rate in hematite. We show that the polaron formation rate can be tuned by a systematic surface fuctionalization of hematite using self-assembled monolayers (SAMS). SAMS of phenylphosphonic acid (PPA), 4-cyanophenylphosphonic acid (CN-PPA), and 4-methoxyphenylphophonic acid (OMe-PPA) were prepared on hematite thin films. Independent spectral signatures of lattice reorganization (hypsochromic shift at the iron M_2,3-edge) and activation barrier (polaron formation rate) are observed and applied within the framework of a Marcus type model of polaron formation. The thermodynamic driving force and kinetics of polaron formation are discussed and compared for bulk, surface, and molecularly functionalized hematite.

Thin films of Fe₂O₃ with an approximate thickness of 12 nm were prepared by sputtering iron (5 nm) onto Au films followed by thermal oxidation to Fe₂O₃.²⁸ The substrate consisted of 15 nm of Ti and 50 nm of Au films, deposited by electron beam evaporation onto a thermal oxide (SiO₂, 500 μm, 100 facet). Kurt J. Lesker Co. Lab-18 was used for all depositions, and film deposition rates of titanium, gold, and iron were 0.8, 1.0, and 0.6 Å/s, respectively, as measured by a quartz crystal microbalance. The samples were annealed in air at 520 °C for 30 min with a ramp rate of 5 °C/min which gave a rustic red surface.²⁹ Hematite substrates were cleaned using basic piranha (H₂O₂: concentrated NH₃: water = 1:1:5) at 80 °C for 1 h to remove organic contaminants and to increase the hydrophilicity of surfaces.³⁰ Then, the samples were washed with MilliQ water and dipped in 4 mM aqueous solutions of the respective molecules. Finally, the samples were annealed in air at 140 °C for 12 h to facilitate bonding between the SAMS and the hematite surface.^31,32 Under humid conditions, unfunctionalized hematite surfaces are hydroxyl terminated.^33–35 We see evidence of this in the oxygen 1s XPS spectrum (Sec. 1, Fig. S3 in the supplementary material).

High resolution XPS analysis was performed to characterize all samples using a Kratos Axis Ultra x-ray photoelectron spectrometer (monochromatic Al Kα X-ray source, E_photon = 1486.6 eV). Multiplet XPS transitions at the iron 2p and phosphorus 2p were fit for all samples using Casa XPS software. All photoelectron spectra were referenced to adventitious carbon at 284.5 eV and are given in Sec. 1 (Figs. S1–S3) of the supplementary material.

Sum frequency generation (SFG) is inherently surface sensitive and readily gives infrared spectra (upconverted to the visible region) for fractions of a monolayer. The SFG system consists of an 80 MHz mode locked oscillator (12 nJ) which seeds a titanium sapphire regenerative amplifier (Spectra Physics Solstice Ace). The amplifier has a repetition rate of 2 kHz and outputs ∼90 fs pulses centered at 800 nm with an average power of ∼8 W. Seventy percent of the output is used to pump an optical parametric amplifier (TOPAS-Prime) followed by a noncollinear difference frequency generation (nDFG) accessory. The remaining 30% of the output is bandwidth narrowed to ∼10 cm⁻¹ using a fabry-perot etalon (Tecoptics, Finesse ∼78, FSR ∼30 nm). The beams are incident on the sample at 56° relative to surface normal and are overlapped spatially and temporally. The collected SFG signal is collimated and input into a spectrograph for imaging on a CCD (Andor Shamrock 303i and Newton). All spectra were taken in PPP (P-polarized, SFG, Visible and IR beam) polarization with the nonresonant signal suppressed.³⁶ See Sec. 2 of the supplementary material for a complete description of the experimental setup. Spectra reported in Figs. 3(a)–3(c) were integrated for 60 s, 60 s, and 180 s, respectively.

Extreme ultraviolet reflection absorption (XUV-RA) probes core to valence transitions which are inherently element and oxidation state sensitive. The XUV pulses are produced using high harmonic generation (HHG) and can be used to measure carrier dynamics with femtosecond (IRF ∼ 55 fs) time resolution. As indicated in the name, these measurements are performed in reflection geometry. Performing these measurements in reflection geometry at the near grazing angle (82° with respect to the surface normal) has a measured probe depth of ∼3 nm, making XUV-RA a surface sensitive measurement.^25,26 Measurements were performed under high vacuum due to attenuation of the XUV beam in air. Details of the instrument and experimental method have been described elsewhere.¹⁰ In short, 2.0 mJ of the 800 nm light is focused into a semiinfinite gas cell (SIGC) filled with helium gas (120 Torr) to generate XUV probe pulses (XUV; 36–72 eV) by HHG. No even order harmonics can be generated in a centrosymmetric medium. An additional symmetry breaking field of 40 μJ at 400 nm is overlapped spatially and temporally with the 800 nm driving field in the gas interaction region to produce both even and odd harmonics. The XUV beam is focused onto the sample using a gold toroidal mirror giving an incidence angle on the sample of 82° relative to surface normal. The specular reflection of the XUV beam from the sample is spectrally dispersed onto a CCD detector using an aberration corrected concave variable line spaced grating.

For a ground state measurement, the reflectance of a sample (R_sample) is measured with respect to a silicon reference as given by

where I_sample and I_Si are the reflected XUV flux from the sample of interest and the silicon reference, respectively. To put this measured spectrum in log units and correct for the known reflectance of silicon, reflection-absorption is calculated as

Each ground state XUV-RA spectrum shown in Fig. S5 is a result of 180 s of total data averaging on the sample.

For the time-resolved experiment, each sample was excited to a charge-transfer excited state using a pump fluence of 5.2 mJ/pulse cm² centered at a wavelength of 400 nm (area = 3.47 mm²) with an angle of incidence of 70° relative to the surface normal. The XUV flux reflected from the hematite thin film is measured with both the optical pump beam on and off as a function of time delay between pump and probe pulses. The transient RA signal is reported in units of ΔmOD as given by

An Al filter (0.2 μm, Lebow) is installed just before the detector to completely remove any pump beam scatter from the measured XUV reflectance spectrum. The time delay between pump and probe beams is controlled using a retroreflector and a linear delay stage (Newport, ILS150CC) with ≥1 μm bidirectional repeatability. To avoid beam damage, the sample is rastered following the collection of each pump-off reference spectrum during data collection. The contour plots reported in Figs. 1(a) and 4(a)–4(c) represent the results of 681 s, 915 s, 1518 s, and 840 s of total data averaging at each of 47 time delays for Fe₂O₃, PPA-Fe₂O₃, CN-PPA-Fe₂O₃, and OMe-PPA-Fe₂O₃, respectively.

Figure 1(a) shows the time-resolved XUV-RA contour plot of a hematite thin film photoexcited at 400 nm. XUV probes the M_2,3-edge absorption of iron in the 50–60 eV energy range. Bandgap photoexcitation in hematite produces an excited charge-transfer state (O 2p → Fe 3d), where increased electron density around Fe³⁺ centers leads to the formation of Fe²⁺. Formation of Fe²⁺ in the excited charge-transfer state is identified by the presence of an increased positive absorption feature centered around 53 eV. Negative differential absorption centered around 54 eV is associated with the presence of electrons in the iron 3d conduction bands of hematite, resulting a decreased population of Fe³⁺. The zero crossing of the iron edge shifts by 1.4 eV within a picosecond, and no further spectral evolution was observed. This hypsochromic shift is a result of lattice expansion around the Fe²⁺ center in the excited state. In our previous contribution, using a simplified 2-state sequential kinetic process, we have identified this spectral evolution in hematite as surface trapping of electrons. This surface electron trapping is correlated with small polaron formation and is associated with ultrafast lattice expansion of Fe–O bonds around the Fe²⁺ metal center.¹⁰ 

Near-grazing angle XUV-RA has a probe depth of ∼3 nm and is therefore able to comment on polaron formation at the surface of hematite.^25,26 Recently, Carneiro et al. reported a two-temperature model to describe the small polaron formation in the bulk of photoexcited hematite.²⁷ This experiment was performed in a transmission geometry on Fe₂O₃ films, which were ∼25 nm thick or roughly 18 atomic layers assuming the interlayer thickness corresponds to the basel plane in Fe₂O₃ (c = 1.38 nm). By comparison, XUV-RA measurements with a 3 nm probe depth sample primarily the top 2–3 atomic planes in Fe₂O₃. In the following, we show that the same two-temperature model reported by Carneiro et al. can be used to describe surface polaron formation, but significantly different rates are observed at the surface compared to the bulk.

Figure 1(b) shows the two-temperature model used to describe photoexcited polaron formation by Carneiro et al..²⁷ According to this model, photoexcitation leads to the formation of a nonthermal electron population denoted by the charge-transfer state (N_e). Subsequently, electron-phonon scattering thermalizes the hot electron population with a time constant of τ_op to create a nonthermal population of lattice phonons, denoted as the optical phonon state (N_op). Polaron formation (N_pol) occurs as a bimolecular recombination between a charge-transfer state and phonon state with a time constant of τ_pol. A detailed description of the kinetic model and the associated differential rate equations are described in the supplementary material (Sec. 3). We obtain the vectors associated with the charge-transfer state and polaron state using a two-state sequential global analysis of the experimental data (Sec. 4 in the supplementary material). These vectors are then used to extract the amplitude coefficients of the charge-transfer state (pink circles) and polaron state (cyan squares), as shown in Fig. 1(c). Fits to the amplitude coefficients using the two-temperature kinetic model are shown as solid lines (pink and cyan) in Fig. 1(c). A good agreement between the experimental data and kinetic model suggests that the two-temperature model can be used to describe polaron formation at surfaces as well as in bulk. The fit gives an electron-phonon scattering time (τ_op) of 15–40 fs. The rate is similar to the reported values (30–60 fs) for bulk polaron formation, suggesting the association of the same optical phonon mode (659 cm⁻¹) in surface polaron formation.⁹ We note that the uncertainty in the electron-phonon scattering time is large due to the 55 fs instrument response time even though this response time has been accounted for in the fits by convolution. The association of the same optical phonon mode in surface polaron formation as in bulk is also consistent with previous measurements showing similar surface polaron formation dynamics in single crystalline and polycrystalline hematite.¹⁰ If free carriers coupled to distinct optical phonons at the surface compared to bulk, then different polaron formation dynamics would be expected based on the significantly higher surface roughness of polycrystaline hematite. However, similar polaron formation rates in single and polycrystalline hematite suggest that both polarons are coupled to the same phonon mode, entirely consistent with the observation here.

Fits to the amplitude coefficients using a two-temperature model [Fig. 1(c)] give a polaron formation time constant of (τ_pol) of 250 ± 40 fs. Fitted amplitude coefficients for the charge-transfer and polaron state reported by Carneiro et al.²⁷ are overlayed as solid black lines for a direct comparison. We note that the surface polaron formation rate (250 ± 40 fs) is about three times slower than the bulk polaron formation (90 ± 5 fs) in hematite.

To understand the difference in the rate (1/τ_pol) of polaron formation at the surface and in bulk, we use an Arrhenius kinetic equation [Eq. (4)] to obtain the activation barrier to polaron hopping. This equation relates the polaron formation rate (1/τ_pol) to the activation barrier of polaron hopping (ΔE_hop), the associated longitudinal optical phonon frequency (ω_LO), the lattice temperature (T), and the Boltzmann factor (k). By comparing the ratio of polaron formation rates in the surface and bulk, we obtain the activation barrier of polaron hopping. We use an activation barrier, ΔE_hop, for a bulk hematite of 190 meV and a lattice temperature of 600 K.³⁷ A lattice temperature of 600 K is assumed based on comparison to previous work, which employed a similar excitation density (8.5 × 10¹⁹ cm⁻³) in hematite as the present study.^27,38 In this calculation, we assume that $ωLOsur=ωLObulk$⁠, as described in the text above. A similar analysis was used previously by Porter et al. to compare the polaron hopping activation barrier in bulk hematite and in goethite nanorods³⁸ 

Using Eq. (4), we obtain a hopping energy of 239 ± 8 meV which is almost 50 meV higher than the 190 meV activation barrier reported for bulk hematite.²⁷ 

Within the framework of a Marcus electron transfer model, ΔE_hop can be equated to the activation energy (ΔE^act) between a free carrier and a small electron polaron¹⁹ and is given by the following equation:^39–42 

Here, ΔE^ps is the polaron stabilization energy or it can be described as the thermodynamic driving force of polaron formation, and E^rel is the lattice relaxation/reorganization energy, associated with polaron formation.^19,37

As noted before, the signature of polaron formation is associated with a hypsochromic shift at the iron M_2,3-edge and is accompanied by simultaneous lattice expansion along the Fe–O bond. This shift is 1.4 eV in hydroxyl-terminated hematite and is correlated with the Marcus lattice relaxation parameter, E^rel. The magnitude of this shift is related to the amount of expansion along the reaction coordinate (Fe–O bond). This qualitative relationship can be understood as the result of reduced core-hole screening, which increases the XUV transition energy as electron density on the oxygen ligands is removed from the photoexcited iron center. We note that the magnitude of this shift is larger for surface polaron formation relative to polaron formation in bulk (∼1 eV), indicating a greater Fe–O bond length expansion at the surface compared to bulk. Time constants of polaron formation, calculated activation energies, and observed hypsochromic shifts for bulk and surface polaron formation are given in Table I.

Figure 2 schematically depicts the Marcus potential energy surfaces which show the thermodynamics and kinetics of bulk and surface polaron formation from an excited free carrier. The activation energy (ΔE^act), polaron stabilization energy (ΔE^ps), and relaxation energy (E^rel) for polaron formation are noted. We also note that there are three regions in Marcus theory: (1) the normal region where E^rel > −ΔE^ps, (2) the barrierless region where E^rel = −ΔE^ps, and (3) the inverted region where E^rel < −ΔE^ps. Based on our calculation for the relaxation energy, we believe that our measurements fall in the normal Marcus region. The associated calculation and discussion are given in the supplementary material (Sec. 5 and Table S2) and are on the same order as predicted by theory.^18,43

Experimentally, we observed that the surface polaron formation rate (250 ± 40 fs) is about three times slower than bulk (90 ± 5 fs). This result indicates a higher activation barrier to polaron formation at the surface relative to the bulk, as tabulated in Table I and shown in Fig. 2. The tabulated values (both bulk and surface) of activation energy are on the same order with calculated values.¹⁸ The higher activation barrier (ΔE^act) of surface polaron formation may be a combined effect of both the polaron stabilization energy (ΔE^ps) and the lattice relaxation energy(E^rel), as shown in Eq. (5). According to Eq. (5), a higher ΔE^ps value decreases ΔE^act, while a higher E^rel value increases ΔE^act. It should be noted that a higher value of E^rel means the equilibrium position of the polaron potential energy surface moves to larger values of the reaction coordinate. Consequently, a proper quantitative comparison of ΔE^act requires an accurate knowledge of both ΔE^ps and E^rel along with the associated potential energy surface. Although theoretical calculation to obtain ΔE^ps and E^rel are computationally expensive in the solid state, several efforts have been made to address this.^15,18,43,44

Using values calculated by Rosso and Kerisit, we predict that the surface polaron stabilization energy (⁠$ΔEsurps$⁠) in Fe₂O₃ is greater by 90 meV relative to bulk (⁠$ΔEbulkps$⁠).¹⁸ A similar prediction for surface polaron stabilization has also been calculated for anatase TiO₂.¹⁵ Higher polaron stabilization energy would result in a lower activation barrier to polaron formation at the surface assuming that the reorganization energy does not change. However, experimentally, we observe a higher activation barrier for surface polaron formation (see Table I). The only way to account for this in a Marcus model is to increase the relaxation energy (E^rel) for surface polaron formation. Assuming a 90 meV greater polaron stabilization energy for the surface polaron, we estimate an increase in relaxation energy by 25% (0.3 eV). The associated calculation for estimating the relaxation energy is given in the supplementary material (Sec. 5 and Table S2). This observation is consistent with the predictions in the work of Rosso and Kerisit,¹⁸ which show that reorganization energy at the surface increases up to 25%, resulting in a higher activation barrier and lower electron hopping rate.¹⁸ This increase in the relaxation energy is the result of greater bond length expansion around the octahedral iron center at the surface.

We note that the increased lattice relaxation energy in surface polaron formation is correlated with the experimentally observed hypsochromic shift (Table I). Consequently, in Fig. 2, the x-axis can be represented as the lattice expansion parameter (e.g., Fe–O bond length) upon polaron formation. Increased lattice expansion (longer Fe–O bonds) will increase the equilibrium position of the parabolic potential energy surface, resulting in a higher relaxation energy. Based on these observations, we conclude that the surface relaxation energy overcomes the surface polaron stabilization energy, leading to a greater activation energy for surface polaron formation.

In order to investigate the effects of surface functionalization and to synthetically tune polaron formation dynamics, we functionalized the hematite surface with self assembled monolayers of phenylphosphonic acid (PPA), 4-cyanophenylphosphonic acid (CN-PPA), and 4-methoxyphenylphophonic acid (OMe-PPA). To confirm the presence of the molecule on the surface of hematite [Fig. 3(d)], we performed vibrational SFG and XPS measurements.

Figures 3(a)–3(c) show the vibrational sum-frequency generation spectra for PPA-Fe₂O₃, CN-PPA-Fe₂O₃, and OMe-PPA-Fe₂O₃, respectively. For PPA-Fe₂O₃, we observe a peak at 3055 cm⁻¹, characteristic of the aromatic C–H stretch in PPA.⁴⁵ For CN-PPA-Fe₂O₃, we observe a peak at 2225 cm⁻¹, characteristic of the CN stretch of the cyano group in CN-PPA.^46,47 For OMe-PPA-Fe₂O₃, we observe a series of C–H stretches at 3050, 2995, 2925, and 2887 cm⁻¹, which are associated with both the aromatic and methoxy groups in OMe-PPA.⁴⁸ These vibrational spectra qualitatively confirm the presence of the molecule of interest on Fe₂O₃. To quantify the absolute surface coverage of the monolayers, we turn to the XPS measurements at the iron 2p and phosphorus 2p edges, as shown in Figs. 3(e) and 3(f), respectively. XPS spectra at the iron 2p edge show multiplet structures for 2p_3/2 and 2p_1/2. Peaks at 710.5 eV, 712.2 eV, and 709.5 eV are associated with Fe³⁺ 2p_3/2, while peaks at 722.8 eV, 724.1 eV, and 726.2 eV are associated with Fe³⁺ 2p_1/2. Additionally, satellite peaks at 718.7 eV and 733.5 eV confirm the Fe³⁺ oxidation state in hematite.^49,50 XPS spectra at the phosphorus 2p edge show multiplet structures for 2p_3/2 and 2p_1/2. The peak at 133.7 eV is associated with 2p_3/2, while the peak at 132.8 eV is associated with 2p_1/2.⁵¹ The integrated XPS spectra were used to calculate the coverage of each monolayer on the hematite surface as explained in the XPS section of the supplementary material (Sec. 1). We find surface coverages between 45% and 53% in all samples studied here. Influence of beam exposure on the sample during time-resolved XUV-RA measurements was carefully investigated and found to be minor. Associated discussion and change in surface coverage due to beam exposure are shown in Sec. 1 (Figs. S1, S2, and S4 and Table S1) of the supplementary material, which confirm that the molecular surface layer is stable during experiments.

We performed time-resolved XUV-RA measurements on functionalized hematite surfaces and obtained the corresponding polaron formation rate for each of the functionalized surfaces using a two-temperature model. Transient XUV-RA spectra of functionalized hematite samples are shown as contour plots in Figs. 4(a)–4(c) for PPA, CN-PPA, and OMe-PPA functionalized hematite surfaces, respectively. Spectral vectors associated with the charge-transfer state and polaron state are shown as insets in Figs. 4(d)–4(f), and normalized spectra are shown for comparison in the supplementary material (Fig. S9). Corresponding amplitude coefficients of the charge-transfer state (pink circles) and polaron state (cyan squares) are in good agreement with the two-temperature model as shown by the solid lines. Fitted time constants of polaron formation along with the calculated activation energy and observed hypsochromic shift (Fig. S10 and Table S3) are tabulated in Table II. Similar to Porter et al., we have fixed τ_op to 30 fs across all the sample to obtain the fits to τ_pol using the two-temperature model.³⁸ Previously, we mentioned that the relative uncertainty in the measurement of τ_op (15–40 fs) is large as it closely matches the instrument response time (55 fs). However, associated fits without constraining τ_op have also been performed and show a negligible difference in the fits to τ_pol (Fig. S11 and Table S4). We also note the presence of coherent oscillations in the contour plots of Fig. 4. A Fourier transform analysis confirms the presence of quantum beats, and the origin of this coherence is part of an ongoing investigation.

Polaron formation at the molecularly functionalized hematite surfaces is different than that at the surface of hydroxyl-terminated hematite. Considering the functionalized Fe₂O₃ rates in terms of the Marcus model provides insight into the effect of surface functionalization on the polaron stabilization energy. Polaron formation is fastest (146 ± 28 fs) in the OMe-PPA functionalized sample, while it is slowest (263 ± 63 fs) for CN-PPA functionalized hematite. This confirms that polaron formation and hopping dynamics can be tuned by molecular surface functionalization.

We also note that the activation energy barrier of CN-PPA functionalized hematite is 241 meV, which is similar to the hydroxyl hematite (239 meV). However, the hypsochromic shift for CN-PPA is 1.1 eV, which is 0.3 eV less than hydroxyl-terminated hematite. This observation suggests that the self-assembled monolayer sterically hinders the hematite surface, resulting in a smaller lattice expansion of the Fe–O bonds and a smaller magnitude of lattice relaxation energy upon polaron formation. Therefore, to reconcile the similar activation energy between hydroxyl hematite and CN-PPA functionalized hematite, the parabolic minimum must move upward. Consequently, this analysis suggests that the CN-PPA termination destabilizes polaron formation at the hematite surface. The higher activation energy observed for PPA and OMe-PPA surfaces indicate that these SAMs do not destabilize the polaron to the same extent as CN-PPA. However, at present, we do not provide an exact mechanism for polaron stabilization/destablization by SAMs on hematite. This is because a detailed quantitative comparison of polaron formation rate with Marcus parameters requires theoretical support, and this is the subject of an ongoing investigation.

Using time resolved XUV-RA spectroscopy, we described the surface polaron formation in Fe₂O₃ for the first time. We show that surface polaron formation can be described by an established two-temperature kinetic model for polaron formation. Using this model, we find that the surface polaron formation rate is about three times slower compared to a similar process in bulk. We additionally show that these dynamics are sensitive to the surface functionalization of Fe₂O₃. Utilizing a Marcus model to describe polar formation, we have shown how the observed kinetic rates are influenced by activation energy, lattice reorganization energy, and stabilization energy. This analysis shows that polaron formation is slower at a surface compared to bulk due to a greater lattice reorganization energy at the surface and that in both cases, electron-phonon scattering occurs on the time scale of the experimental instrument response. Theoretical calculations are necessary to better understand the relationship between polaron formation and molecular functionalization. However, the ability to control the electron dynamics at the surface of hematite by molecular functionalization provides exciting directions for future research with relevance for improving interfacial charge transport dynamics at hematite surfaces.

The supplementary material contains the details of the (1) Characterization—XPS (quantitative), SFG (qualitative), and static XUV-RA; (2) Vibrational sum frequency generation instrument layout; (3) Two-temperature kinetic model; (4) Charge-transfer and polaron state for unfunctionalized hematite; (5) Calculation of relaxation energy; (6) Comparison of fits for the charge-transfer and polaron states; (7) Hypsochromic shift of the zero-crossing; and (8) Fits for the unconstrained two-temperature model.

XUV-RA measurements were supported by the Air Force Office of Scientific Research under AFOSR Award No. FA95550-19-1-0184. The setup of the SFG vibrational spectrometer used for sample characterization was supported by the National Science Foundation under NSF Award No. 1665280.