Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

K. T.
Butler
^{a},
B. J.
Dringoli
^{b},
L.
Zhou
^{cd},
P. M.
Rao
^{cd},
A.
Walsh
^{e} and
L. V.
Titova
*^{b}
^{a}Department of Chemistry, University of Bath, BA2 7AY, UK
^{b}Department of Physics, Worcester Polytechnic Institute, Worcester, MA 01609, USA. E-mail: ltitova@wpi.edu
^{c}Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA 10609, USA
^{d}Materials Science and Engineering Graduate Program, Worcester Polytechnic Institute, Worcester, MA 01609, USA
^{e}Department of Materials, Imperial College London, SW7 2AZ, UK

Received
21st August 2016
, Accepted 4th November 2016

First published on 7th November 2016

We explore ultrafast carrier dynamics and interactions of photoexcited carriers with lattice vibrational modes in BiVO_{4} photoanode material using time-resolved terahertz spectroscopy and first-principles phonon spectrum calculations. We find that photoexcited holes form bound polaron states by introducing lattice distortion that changes phonon spectrum and suppresses the A_{g} phonon mode associated with opposite motion of Bi and VO_{4} molecular units. At excitation fluence higher than 1 mJ cm^{−2} (or 2 × 10^{15} cm^{−2} per pulse), lattice distortion due to self-localized holes alters the lattice symmetry and vibrational spectrum, resulting in bleaching of THz absorption by A_{g} phonons. Concurrently, we observe a short lived population of free carriers which exhibit Drude conductivity with mobility on the order of 200 cm^{2} V^{−1} s^{−1}, orders of magnitude higher than typical carrier mobility in BiVO_{4}. The anomalously high carrier mobilities are explained in the framework of a Mott transition. This demonstration of enhanced transport suggests how engineering BiVO_{4} photoanodes to take advantage of free carrier transport under high excitation conditions may in the future significantly enhance performance of photoelectrochemical devices.

Low charge carrier mobility in BiVO_{4} is a consequence of strong carrier-phonon coupling, which favors formation of polarons, which are localized carriers (electrons or holes) accompanied by lattice distortion.^{6–10} Photoexcited electrons are thought to form small polarons, which are localized on the atomic scale around V^{4+} sites and move by thermally activated hopping, with an estimated activation energy on the order of 0.35 eV.^{6,8,11} The resulting electron diffusion length in undoped BiVO_{4} at room temperature is as low as 10 nm.^{12} Transport of photoexcited holes, which is critically important for the performance of the photoanode, is not yet well understood: while some theoretical studies predict small hole polarons with holes localized on O^{−} sites,^{11} others find that large hole polarons that spread over many lattice sites and exhibit band-like transport are more likely to form in the monoclinic form of BiVO_{4}.^{7} The hole diffusion length (∼100 nm) in BiVO_{4} is an order or magnitude larger than that of electrons.^{10}

Understanding the dynamics of photoexcited carriers and their coupling to lattice vibrational modes at early times (1–20 ps) after photon absorption is essential for elucidating carrier transport mechanisms in BiVO_{4} and addressing limitations of BiVO_{4} photoanodes. Ultrafast carrier dynamics in BiVO_{4} have been probed using transient optical absorption.^{13–16} These studies have indicated that photogenerated holes are trapped with a time constant on the order of 5–15 ps, giving rise to several long-lived absorption bands.^{13,14,16} The trapped holes are coupled to a low energy phonon mode, with irreducible representation A_{g}, associated with the opposite motion of Bi^{3+} and VO_{4}^{3−}.^{13,14} Coherent excitation of this phonon mode occurs simultaneously with the hole trapping suggesting that hole–lattice interaction favors formation of polarons within a few picoseconds following excitation.

In this study, we explore photoconductive properties of BiVO_{4} with time-resolved THz spectroscopy (TRTS). A non-contact probe of microscopic conductivity, TRTS has already been successfully applied to uncover ultrafast carrier dynamics and conductivity mechanisms in a variety of bulk and nanostructured materials for solar energy conversion.^{17–27} As the bandwidth of THz pulses spans from ∼0.2 to 2.4 THz (8–80 cm^{−1}), corresponding to the energy range of 1–10 meV, transmission of THz pulses through samples is intrinsically sensitive to motion of free carriers over length scales of tens of nanometers as well as to low-frequency (<80 cm^{−1}) phonon modes. As a result, TRTS simultaneously provides insights into the dynamics of photoexcited carriers and carrier–lattice interactions that are not accessible by other techniques. Combining THz photoconductivity measurements with first-principles calculations of effects of photoexcitation on lattice dynamics allows us to elucidate the role of carrier-phonon coupling in photoconductivity of BiVO_{4} photoanodes. We find that at high carrier excitation density, vibrational excitation of the A_{g} mode by the THz probe pulse is hindered. This happens as a significant number of trapped holes are accompanied by local lattice distortions, and the IR-active A_{g} mode is transformed into other modes that do not couple to THz probe pulses efficiently. At the same time we observe a short-lived excess of free carriers with mobility which is several orders of magnitude higher than typical carrier mobility in BiVO_{4}.^{8–10} Moreover, effective mass theory predicts a Mott transition – whereby a critical density of localised states overlaps to form an extended band-like state – in the region of 10^{16} to 10^{17} cm^{−3}, which can explain the jump in conductivity associated with the bleaching of the A_{g} phonon mode. We briefly consider how this finding may be exploited to improve BiVO_{4} device performance through structural engineering.

Elucidating the nature of the processes that give rise to the observed fast photoconductivity dynamics requires analysis of the complex-valued, frequency-dependent THz conductivity spectra as a function of pump-probe delay times and excitation fluence. Frequency-dependent changes in sample properties induced by the pump pulse can be determined by detecting the changes in the amplitude and phase of the transmitted THz pulse. Fig. 2(a) shows the THz pulse transmitted through the unexcited BiVO_{4} film and the change in THz waveform 2 ps following excitation with a 3.0 mJ cm^{−3} fluence. Corresponding frequency-resolved transmitted THz intensities (proportional to the square of the amplitude) without photoexcitation and 2 ps after photoexcitation are given in Fig. 2(b). Photoexcitation slightly increases absorption of lower THz frequencies (<1.5 THz), and enhances transmission in ∼1.5–2.2 THz range. While those changes are subtle, they are clearly visible in the photoinduced absorbance change, Fig. 2(c) and conductivity, Fig. 2(d). The photoinduced THz absorption at low frequencies, which we will discuss shortly, can be attributed to free carrier absorption. The photoinduced reduction of THz absorption at higher frequencies can be fitted to a Lorentzian peak centered at ω_{Ag}/2π = 1.92 THz (or 64 cm^{−1}) with the damping constant Γ_{Ag}/2π = 0.48 THz (Fig. 2(c)). The center frequency of this absorption bleach feature is close to the frequency of the A_{g} phonon mode, which earlier transient optical absorption studies found to be coherently excited by 400 nm pulses.^{13,14} The total photoinduced change in conductivity (Fig. 2(d)) can be expressed as a combination of the Drude free carrier component and suppression of the Lorentz oscillator that represents the A_{g} phonon,

(1) |

Fig. 2 Effects of photoexcitation with 3.0 mJ cm^{−2}, 400 nm pulse at pump-probe delay of 2 ps. (a) THz waveform, transmitted through BiVO_{4} film without photoexcitation, and the change in the waveform due to excitation (scaled by a factor of 10 for clarity). (b) THz intensity (proportional to the square of the electric field amplitude) transmitted through non-excited and photoexcited sample, and (c) the corresponding photoinduced chance in THz absorbance (c) and complex conductivity (d). Solid line in (c) shows the fit of the experimental transient THz absorbance to a Lorentz function with the center frequency ω_{Ag}/2π = 1.92 THz and the damping constant Γ_{Ag}/2π = 0.48 THz. Solid and dashed lines in (d) a fit of the photoinduced real conductivity σ_{1} (solid red line) and imaginary conductivity σ_{2} (dashed blue line) to a Drude–Lorentz conductivity (eqn (1)) with τ = 35 fs and N = 2 × 10^{18} cm^{−3}. |

Fig. 3 summarizes the effects of excitation fluence on photoconductivity by following the THz absorption bleach as well as the frequency-resolved complex photoconductivity detected 2 ps after photoexcitation. Most notably, the absorption bleach in the vicinity of the A_{g} phonon mode becomes significantly more pronounced with increasing excitation fluence (Fig. 3(a)). At the same time, complex conductivity at low frequencies (<1.5 THz) acquires Drude-like character, indicating the presence of free carriers at early times after excitation (Fig. 3(b)). In the following discussion we analyze the photoinduced conductivity changes in this low frequency range that are not significantly affected by the absorption bleach at 1.92 THz within the framework of the Drude model. Lines in Fig. 3(b) are simultaneous fits of real (solid red squares) and imaginary (open blue circles) THz conductivity to the Drude model, .

Fig. 3 Excitation fluence dependence of photoinduced conductivity and phonon absorption bleach as observed 2 ps after photoexcitation. (a) Absorbance spectra at fluence ranging from 0.5 to 3.0 mJ cm^{−2}, (b) corresponding complex conductivity spectra, with red squares indicating real, and blue circles – imaginary conductivity components, and the lines representing fitting of data to the Drude conductivity model. (c) Fluence dependence of amplitude of photoinduced absorption bleach (red triangles), fast component of photoconductivity decay A_{1} (Fig. 1) (blue circles), and free photoexcited carrier density determined from Drude fit to frequency-resolved conductivity (black squares) (b). The green solid line is a guide to the eye. |

Taking a band effective mass for both electrons and holes as 0.3m_{e} from previous calculations^{33} and from the band structures calculated in this study, fitting complex conductivity to the Drude model yields instantaneous carrier density N as well as the carrier relaxation time τ. The relaxation time, 35 fs ± 10 fs, is found to be independent of excitation fluence or time after excitation, and the corresponding mobility μ = eτ/m* of short-lived free carrier population excited by 100 fs, 400 nm pulses is ∼200 cm^{2} V^{−1} s^{−1}, several orders of magnitude larger than steady-state carrier mobility associated with thermally-activated polaron transport. Free carrier density N at 2 ps after photoexcitation is plotted in Fig. 3(c) as solid black squares, along with the amplitude of 1.92 THz absorption bleach (solid red triangles) and the amplitude of the fast component of transient conductivity decay (−ΔT/T), shown as open blue circles. This shows that the increase in concentration of free carriers is concurrent with the THz absorption bleach.

Fig. 4 examines time evolution of the observed A_{g} phonon absorption bleach Fig. 4(a) as well as of free carrier conductivity (Fig. 4(b)) at the highest excitation fluence, 3 mJ cm^{−2}. As the absorption bleach is recovered, Drude-like conductivity decreases. In fact, the amplitude of the absorption bleach and free carrier density both decay on ∼1 ps time scale, the same time scale as photoconductivity decay at the same excitation fluence shown in Fig. 1, again suggesting that saturation of phonon absorption under high photoexcitation conditions and existence of free carriers exhibiting band-like transport are related phenomena.

In order to probe the microscopic origins of the photo-induced bleaching in the absorption spectrum we have performed first-principles lattice dynamics calculations. These calculations allow us to investigate how the vibrational spectrum of the crystal structure is affected by the presence of photo-generated carriers. Initially the neutral crystal in the monoclinic structure was fully relaxed and the vibrational spectrum calculated. The eigen frequencies of the Γ-point phonon modes, are plotted in Fig. 5, where the mode experimentally observed at 64 cm^{−1} is highlighted in yellow. It is the A_{g} mode involving the counter-motion of the Bi^{3+} ions and the VO_{4}^{3−} units. As this mode involves motion of oppositely charged molecular units, it is expected to be a particularly strong absorber in the infrared. This mode is also depicted by the phonon eigenvectors in the picture below the plot, where the phonon modes are represented by arrows. To simulate the generation of a hole, we then removed an electron from a 2 × 2 × 2 supercell of monoclinic BiVO_{4}. Within the Ewald summation employed, this is neutralised by a uniform negative background charge, thus ensuring charge neutrality and a convergent electrostatic potential. The resultant structure was then optimised, introducing an initial small distortion to allow for the formation of polaron. In this case the electronically perturbed crystal relaxes into a different space group from the neutral structure; P, as opposed to I4_{1}/a. The resultant vibrational phonon spectrum is plotted in Fig. 5 (center-right panel). The A_{g} mode involving the counter-motion of Bi^{3+} ions and the VO_{4}^{3−} units is no longer present in the phonon spectrum of the crystal with the trapped hole. The removal of the A_{g} mode from the phonon spectrum in the presence of the excess hole explains the observed photo-bleaching of this mode with increased photocarrier generation.

Under high excitation levels, the resulting transient temperature increase may lead to the increase in hopping mobility. However, the hopping mobility in an ideal oxide semiconductor has been demonstrated to have an upper limit of ∼70 cm^{2} V^{−1} s^{−1},^{34} significantly lower that the mobility observed in our measurements. Instead, we propose that the concurrent observation of suppression of absorption by the A_{g} mode and enhanced carrier transport may be related to a Mott transition. Above a certain critical concentration, localised charge carriers begin to interact and band-like transport is observed. The phenomenon of insulator to metallic conduction as a result of condensation of lattice impurities was described by Mott as the metal-nonmental (MNM) transition, originally in the context of dopants in group-IV semiconductors.^{35} Edwards and Sienko subsequently demonstrated the wider applicability of Mott criterion.^{36} In the case of BiVO_{4} a critical concentration of self-trapped holes, which cause the photo bleaching, can be related to the high carrier mobility.

In a semiconductor matrix an isolated electronic defect (in our case the trapped hole) can be associated with a characteristic Bohr radius, which in turn is determined by the effective mass of the hole and the dielectric constant of the matrix; from effective mass theory,^{37}, where ε_{st} is the static dielectric constant, previously calculated as 52 (ref. 38) and is the hole effective mass, which is calculated from the band structure to be 0.3m_{e}, in agreement with previous calculations.^{33,38} At a critical concentration of these impurity wavefunctions overlap in the matrix to form a continual band. At this concentration the carriers in the impurity (hole) band can travel freely throughout the material, resulting in metallic conduction. The concentration (c) is obtained from .

Taking values for the physical properties discussed above, we obtain a critical concentration for the MNM transition of the order of 2 × 10^{16} cm^{−3}. This is below the value of the measured free carrier concentration ∼10^{17} cm^{−3} and suggests that the observed free carrier transport can arise as a result of the coalescence of localised states to form a transport band above a critical concentration. This critical concentration is only accessed when the intensity of incident radiation is sufficiently high to generate enough trapped holes. At these high fluences, saturation of the polaron hole states and the corresponding absorption bleach saturation occur very quickly, on sub-ps time scales after excitation, as has been suggested in earlier transient optical absorption studies.^{13,14} With fluence above the critical threshold of ∼1 mJ cm^{−2}, a significant portion of the polaron trap states are filled within a very short time, and an increase in fluence results in significant increase in free carrier concentration as manifested by the superlinear increase in the peak photoconductivity (Fig. 1). As self-trapped holes recombine with either free or trapped electrons and their concentration falls below the Mott concentration, band-like transport of the remaining photoexcited carriers is suppressed. At the same time, THz absorption by the A_{g} mode recovers. This occurs over 1–2 ps time scales. The experimentally-determined onset of the THz absorption bleach and concurrent band-like transport occurs when photoinjected carrier density is on the order of 10^{20} cm^{−3}. This is significantly higher than the estimated Mott concentration and the measured free carrier density values, indicating that most photoinjected carriers in high excitation regime are lost to recombination over ultra-short, sub-picosecond time scales that are not accessible in our experiments.

The observation of free carriers offers the possibility that the low conductivity bottleneck for the application of BiVO_{4} as a photoelectrode may be surmounted under constant concentrated illumination. The rapid recombination and decay of the carriers means that careful device structuring is required to exploit the improved conductivity. We can estimate the carrier diffusion length (L_{Diff}) of the band-like carriers from where T is the temperature, e is the elementary charge and the mobility and t is the carrier lifetime from generation until recombination, extraction or trapping.^{39} Taking t as ∼1 ps, which is the lifetime of free carriers in the high excitation fluence regime (Fig. 4(c)) and μ = 200 cm^{2} V^{−1} s^{−1}, we obtain a characteristic diffusion length of 22 nm. This means that engineering of nanostructured BiVO_{4}, with greater surface to volume ratios, in association with optical concentration to achieve enhanced fluence could result in photoanodes with all of the desirable properties of bulk BiVO_{4}, but greatly improved carrier mobilities. Possible avenues for realizing this regime may involve the use of nano-plasmonic devices to significantly concentrate light in nanostructured BiVO_{4}. However, care must be taken to avoid thermally damaging the material, if continuous excitation is to be used. Future studies will determine the photodamage thresholds in nano-plasmonic and BiVO_{4} composites.

In conclusion, we have studied photoexcited carrier dynamics in BiVO_{4} photoanode material using time-resolved terahertz spectroscopy. Extremely low carrier mobility due to pronounced polaron effects is known to limit efficiency of BiVO_{4} photoanodes. We find that above a threshold excitation density of 10^{15} photons per cm^{2} per 400 nm pulse, polaron states population surpasses critical Mott concentration, and a short-lived excess free carriers exhibit band-like transport with mobility on the order of 200 cm^{2} V^{−1} s^{−1}. Furthermore, combining terahertz spectroscopy with lattice dynamics calculations, we have shown that photoexcited holes form bound polaron states by introducing lattice distortion that alters changes the lattice symmetry and suppresses absorption at 1.92 THz (64 cm^{−1}) by A_{g} phonon mode. These findings will be important for engineering efficient nanostructured BiVO_{4} photoanodes.

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## Footnote |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ta07177e |

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