Article pubs.acs.org/JPCC
Electronic Dynamics in Natural Iron Pyrite Studied by Broadband Transient Reflection Spectroscopy Shayne A. Sorenson, Joel G. Patrow, and Jahan M. Dawlaty* Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States S Supporting Information *
ABSTRACT: Iron pyrite (FeS2) is an abundant natural mineral with interesting physical and chemical properties, including its near IR bandgap and extremely high absorption coefficient throughout the visible range. The dynamics of photoinitiated carriers and their interactions with intrinsic and surface defects are still not fully understood, yet clearly are responsible for pyrite’s underwhelming photovoltaic and photocatalytic performance. Here we report, to our knowledge for the first time, broadband ultrafast transient reflection from single-crystal natural iron pyrite with several excitation wavelengths both higher and lower than the accepted nominal bandgap of pyrite. We also demonstrate a method to transform transient reflection to transient absorption, without requiring any assumptions regarding the magnitude of either the absorption coefficient or the refractive index, allowing for a more direct interpretation of our results. An important finding from this work is the observation of a long-lived weak signal when pumping with 0.58 eV, an energy well below the accepted bandgap, which may be evidence for direct optical excitation of either intrinsic trailing edges of the bands or midgap defect states. We identify that after approximately 10 ps the transient spectra due to pumping at 2.59, 1.58, and 0.91 eV all appear qualitatively similar, suggesting relaxation to a common carrier distribution. This common distribution appears to decay on two time scales of about 30 and ≫200 ps. Our results should play a role in understanding charge carrier dynamics within the intricate and complex band structure of pyrite and hopefully provide clarification and direction for future efforts in the development of iron pyrite based technologies.
■
INTRODUCTION
organic molecules have also been shown to adsorb readily on its surface.4,5 Such properties render pyrite a suspect in the origin of life on earth6−8 and an extremely intriguing material for application in sustainable energy technologies such as photovoltaics3,9−12 and photocatalysis.13,14 In addition to these, more suggested applications of iron pyrite continue to come forth, including broadband photodiodes sensitive in the near IR,12,15 inorganic sensitizers for solar cells,16,17 counter electrodes in dye-sensitized solar cells,18−21 electrocatalysts,22−24 and photocapacitors.25 The promise of such a strong and readily available absorber has so far been met with dismal performance. Pyrite photovoltaics routinely achieve less than 200 mV open-circuit voltage (VOC),11,12 far lower than predicted, presumably due to some combination of deep defect states as well as intrinsic and defect surface states.11,26−29 These same effects would most likely limit photocatalytic applications; however, this field is still in its infancy. In light of these challenges, much of the current pyrite research is focused on developing nanostructured and/or composite materials, and modest successes have been achieved.12,23,30 Despite this progress, the band structure of
Iron pyrite (FeS2) is one of the most abundant minerals in the earth’s crust, is extremely cheap to extract,1,2 and has a bandgap and absorption coefficient that allow for a penetration depth (1/α) around 20 nm throughout the visible spectrum.3 Small
Figure 1. Calculated density of states from Schena et al.35 The inset shows a zoomed-in region near the Fermi level. Though the band gap may be lower, the onset of optical absorption is consistently measured to be 0.9 eV. © 2016 American Chemical Society
Received: November 10, 2015 Revised: February 23, 2016 Published: March 28, 2016 7736
DOI: 10.1021/acs.jpcc.5b11036 J. Phys. Chem. C 2016, 120, 7736−7747
Article
The Journal of Physical Chemistry C
pump, single probe wavelength measurements and reveal only a small portion of the picture of the contributing states. In this paper we will present the transient reflection of pyrite using several pump energies and a visible broadband continuum probe along with a discussion relating these results to the current knowledge of the density of states and defects. An additional aspect of this work is a brief description of the method used to transform our data from transient reflection to transient absorption. Generally speaking, spectroscopy seeks to gain insight into a material by interrogating its complex index of refraction, n + iκ. The imaginary part κ, also known as the extinction coefficient, is often of particular interest as it contains information about a material’s optical absorption. For opaque materials such as pyrite, optical measurements are limited to reflection which has a well-known but nontrivial dependence on both index of refraction and the extinction coefficient, thereby complicating the extraction of κ. Several groups have transformed transient reflection data to transient absorption and/or transient changes in index of refraction based on approximations regarding the magnitudes of either κ, n, Δκ, or Δn (for example: n ≫ κ or Δκ ∝ Δn).47−49 In the case of pyrite and many other materials, where both n and κ are quite large, such approximations do not hold, and a more general approach is necessary. For steady state spectroscopic measurements, the Kramers−Kronig (KK) relations are a well-known way around this problem and have been used extensively. A generally applicable and mathematically concise application of the KK solution to convert transient reflection to transient absorption remains to be developed. Much work in this vein has been done by the research group of Kobayashi, wherein they have theoretically established, and experimentally verified, the validity of the KK relations in pump−probe experiments under certain conditions.48,50−52 Developing upon this foundation, we herein derive and apply a concise and conceptually transparent matrix transformation based on the KK relation and the series expansion of transient reflection with respect to change in both absorption and index of refraction.
bulk iron pyrite (as opposed to nanostructured) and the concomitant dynamics of photoinitiated charge carriers are still not fully understood. It seems reasonable that any attempts at pyrite engineering would be well served by an understanding first of these fundamental characteristics. In recent years a fairly clear and consistent picture regarding the band structure of pyrite has been achieved, and there is general agreement between theoretical31−38 and experimental findings.39,40 A plot of the density of states (DOS), taken from Schena et al.,35 calculated using density-functional theory (DFT) with the PBE implemetation of the generalized gradient approximation is shown in Figure 1. Though various calculations may yield slight variations, this DOS illustrates well the position and character of the electronic bands of FeS2. Notable is the very large density of valence band states consisting of mainly Fe d character and the onset of optical absorption implied by the large density of states in the conduction band around 1 eV above the Fermi level (EF). Despite this general agreement, considerable debate continues regarding the presence and extent of a trailing conduction band (CB) minimum. Many DFT band structure calculations show a single swooping band at the CB minimum of S p character whose exact position is sensitive to the chosen method but can be as low as 0.3 eV.35 This is represented in Figure 1 by the nonzero density of states extending well below the accepted band gap. It is argued this band has, thus far, eluded clear experimental observation due to its relatively small density of states and potentially low transition dipole moment. Optical measurements usually place the band gap in the range of 0.8− 1.0 eV,11,41,42 with few exceptions, including one of the earliest reports on the optical properties of pyrite.43 Photoelectrochemical, conductivity, and surface tunneling spectroscopy, on the other hand, have yielded band gap energies in a much wider range from 0.4 to 1.0 eV,10,11,27,44,45 depending on the experiment and the model used. In the face of such varied results and predictions, clarification of a quantity as fundamental as the bandgap is certainly desirable. The edge of the conduction band is not the only point of confusionthe fact is the energies and densities of various defects at the surface and in the bulk add considerable complexity to the material properties of pyrite. At the onset of pyrite electrochemistry research it was proposed that surface states were responsible for its low VOC.10 Later Bronold et al. proposed that in addition to surface states a significant number of bulk defect states may also play a role in the charge carrier dynamics.29 It had already been shown experimentally that pyrite crystals typically had sulfur deficiencies on the order of a few percent.26 Very recently there were several studies, both scanning tunneling spectroscopy and Hall mobility measurements, that invoked a large density of surface states at the valence band (VB) maximum and/or CB minimum.27,28,33 Experimentalists have also claimed recently that surface states alone are inadequate to describe the low VOC and therefore included a large density of midgap deep defect states (localized states within the nominal band gap) to explain an impressive suite of experimental findings.11,28,45 In the face of such a complex band structure and lacking yet a complete experimental understanding, broadband ultrafast spectroscopy offers a critical perspective concerning the energy and lifetime of the states involved. Despite this apparent benefit such experiments, to our knowledge, have yet to be reported. There are three instances of transient reflection of pyrite in the literature of which we are aware;11,25,46 however, all were single
■
EXPERIMENTAL SECTION The natural iron pyrite crystal used in the transient reflection (TR) experiments was mined from Navajun, Spain and obtained from Geollector. The 1 cm3 crystal was cut into a slab about 1/3 cm thick, then cleaned by sonication in acetone followed by methanol. The crystal was characterized by Raman
Figure 2. Extinction coefficient κ of pyrite, as measured by Choi et al., is shown along with a theoretical reflection spectrum obtained using the complex dielectric function of the same.31 Typical spectra for the white light probe and the 2.59 and 1.58 eV pumps are overlaid. The center positions of the 0.91 and 0.58 eV pumps, as measured by frequency doubling and upconversion (sum frequency generation with the 785 nm fundamental), respectively, are indicated by vertical lines. 7737
DOI: 10.1021/acs.jpcc.5b11036 J. Phys. Chem. C 2016, 120, 7736−7747
The Journal of Physical Chemistry C
Article
■
DATA ANALYSIS The transient reflection spectra, obtained as explained above, were made more amenable to interpretation by first transforming them to transient absorption spectra using the following procedure. When transient changes in reflection are relatively small (Δκ ≪ κ and Δn ≪ n), then to first order
spectroscopy and powder X-ray diffraction (XRD) prior to the ultrafast experiments. Raman spectra were obtained on a Raman microscope (XploRA ONE Horiba Scientific Instruments) with a 532 nm excitation wavelength, using the same face of the single crystal as was used for TR. XRD was performed using a Rigaku diffractometer (Cu K = 1.54118 Å) on a small portion of the crystal cut off and ground by mortar and pestle. Both the Raman (Figure S3) and the XRD data (Figures S1 and S2) (Supporting Information) matched those published in the literature of phase-pure iron pyrite samples.13,53 TR spectra were obtained using a 1 kHZ regenerative amplified Ti:sapphire laser (Coherent Legend Elite). A visible optical parametric amplifier (Coherent OPerA Solo) was used to generate each of the pump energies, while the probe pulses were prepared by focusing 0.3 mW of the remaining Ti:sapphire output onto a 3.0 mm thick sapphire window, resulting in white light continuum (WLC). Typical spectra for the probe and the 2.59 and 1.58 eV pumps are shown in Figure 2. The pump and probe were attenuated with variable neutral density filters to the desired power, and their polarizations were rotated prior to the sample to be parallel to each other and parallel with a ⟨010⟩ axis of the crystal. They were then focused together on the sample using a parabolic mirror with 6″ focal length. The pump and probe angles of incidence were approximately 10.8° and 3.6°, respectively. The diameter of the 2.59 eV pump spot was measured to be 0.72 mm, while that of the WLC probe was 0.15 mm. The spot diameters of the other pump energies (1.58, 0.91, and 0.58 eV) were estimated using the Rayleigh criterion to be 1.23, 2.15, and 3.27 mm, respectively. Using these spot sizes the pump fluence at each of the pump energies (in the order corresponding to 2.59, 1.58, 0.91, then 0.58 eV) was calculated to be 24.56, 8.48, 11.07, and 8.69 μJ/cm2. These fluences were used for all of the data presented here, except where fluence dependence is reported and fluences are explicitly stated otherwise. After reflecting off the sample and being recollimated, the probe was passed through a dye filter (IR780) to attenuate the overwhelming 800 nm component of the WLC. The probe spectrum in Figure 5 shows fringes from 1.5 to 2 eV that arise naturally from the supercontinuum generation process and lead to nonphysical fringes of the same period in the measured transient spectra with amplitude on the same order as the noise. This artifact is especially pronounced near the seed of the white light, from 1.5 to 1.65 eV, and prevents us from interpreting this portion of our spectra. For some of the results presented below (only where indicated) we have filtered out the fringes remaining in the region between 1.65 and 2.0 eV using a Gaussian filter of 0.062 eV width (fwhm). Transient reflection spectra were calculated using the reflection spectra of adjacent pumped and unpumped probe pairs measured on a high speed CCD camera (Princeton Instruments Pixis) mounted on a 0.3 m monochromator (iHR 320 Horiba Scientific Instruments). The transient spectrum at each time delay is the average of 1500 such pairs constituting a single time scan. Signal to noise was further improved by repeating each time scan 3 or 4 times and averaging again. The spatial mode and WLC spectrum were checked between each scan to ensure that no significant photodamage had accumulated.
⎤ ⎛ ∂R ⎞ 1 ⎡⎛ ∂R ⎞ ΔR = ⎢⎜ ⎟ Δκ + ⎜ ⎟ Δn⎥ ⎝ ∂n ⎠κ ⎦ R R ⎣⎝ ∂κ ⎠n
(1)
In our case the impetus behind Δκ and Δn is the optical excitation (pump) pulse; however, this analysis is general, and the cause of the induced change in reflection need not be restricted. Assuming the dielectric function of the material remains constant throughout the duration of the probe pulse then we also know that Δn and Δκ form a Hilbert transform pair (this is equivalent to the familiar Kramers−Kronig relation).50,51 If we write the Hilbert transformation as an operator Ĥ , then ⎛ ∂R ⎞ ⎤ 1 ⎡⎛ ∂R ⎞ ΔR = ⎢⎜ ⎟ + ⎜ ⎟ Ĥ ⎥Δκ = Â (Δκ ) R R ⎣⎝ ∂κ ⎠n ⎝ ∂n ⎠κ ⎦
(2)
The second equality in eq 2 rewrites the entire expression as a single operator acting on Δκ to arrive at ΔR . If Δκ and ΔR , R R which are continuous functions of wavelength, are discretized as vectors, then the operator Ĥ and subsequently  can be written as a matrix. The factors
( ∂∂Rκ )n and ( ∂∂Rn )κ can be determined
analytically from the expression for reflectance, which for the case of normally incident light in air has the relatively simple form R=
(1 − n)2 + κ 2 (1 + n)2 + κ 2
(3)
Finally, multiplying eq 2 on the left by the inverse operator  −1 provides a simple formula for calculating the transient absorption from the transient reflection. −1 ⎛ ΔR ⎞ ⎟ Δκ =  ⎜ ⎝ R ⎠
(4)
The only assumptions made are that the transient changes in the complex index of refraction were small and temporally constant throughout the duration of the probe pulse (in other words, the measured response is causally related to the probe) and that the probe was normally incident. For our experiment the duration of the probe pulse is less than 50 fs throughout its spectrum, leading us to conclude that the first assumption is good for all pump−probe delays greater than 200 fs. Where the incidence angle of the probe beam in our experiments was 3.6° the second assumption is not strictly true; however, including the incidence angle dependence of the reflectance in eq 3 and of ΔR in eq 1 is possible. Doing so shows that in this particular instance the correction for deviations from normal incidence to the terms involved in the transformation are 3 orders of magnitude smaller than the uncorrected terms themselves. The angle-dependent factors can therefore be safely neglected for the treatment of the data presented here. A full discussion on this point along with a graphic illustration of the conclusion can be found in the Supporting Information. The real (n) and imaginary (κ) parts of the index of refraction used in our transformation matrix were calculated 7738
DOI: 10.1021/acs.jpcc.5b11036 J. Phys. Chem. C 2016, 120, 7736−7747
Article
The Journal of Physical Chemistry C from the published experimental complex dielectric function of Choi.31 One possible limitation of this transformation arises upon recognizing that the Hilbert transform is an integral transform, and its effect on a function at one point depends on that function at all other points. This transformation is, therefore, only rigorously true when the transient reflection data and the steady state complex index of refraction data extend to all wavelengths. This is easily seen by inspecting the expression for the transform ∞
∫−∞ ωΔn−(ωω′)′ dω′
1 Δκ(ω) = Ĥ (Δn)(ω) = p.v. π
(5)
where “p.v.” indicates the principal value of the integral. Here the kernel 1/(ω − ω′) ensures that the weighting of values for Δn at ω′ far from ω in the integral will be small, and such terms will not make a significant contribution. This means that data termination will only pose a problem at the edges of our transformed spectra where heavily weighted terms in the integral are missing. For this reason our measured transient reflection spectra were padded with a variety of extrapolation schemes prior to transformation in order to determine how much of the spectrum is effected by the edge termination (Figures S9−S11). These tests showed that interpretation should not be made within about 0.1 eV of the probe extrema (see Supporting Information for details). This restriction applies both to the low energy edge of the data where the range of the CCD was the physical limitation as well as the high energy edge of the data where the bandwidth of the probe was the physical limitation.
Figure 3. Dimensionless transient reflection (ΔR/R) of a natural iron pyrite single crystal. An excitation energy of 2.59 eV was used here with a fluence of 24.6 μJ/cm2, and the reflection of the broadband probe was measured as a function of delay relative to the pump. The top panel shows transient spectra at various probe delays relative to the pump. The bottom panel shows transient absorption as a function of probe delay for several discrete probe energies.
■
RESULTS As representative transient reflection data, the averaged difference spectra ( ΔR ) of the WLC probe at various delays R with respect to the 2.59 eV pump pulse are shown in Figure 3. As explained, each spectrum presented is the average of 3 or 4 such spectra independently measured. The standard deviation for any point was between 10 and 20% of the average value for the 2.59 and 1.58 eV pump energies and about 100% in the case of the 0.91 and 0.58 eV pump energies. The signal-to-noise ratio (SNR) after averaging was generally around 20 for the two higher energy pumps and 3 for the lower energy pumps. As mentioned above, the transient signal near the seed of the WLC probe, in the range of 1.50−1.65 eV, shows modulations likely arising from the poor spectral quality of the WLC (see Figure 5); consequently the signal in that region will not be interpreted. Looking at Figure 3, the major observations are a broad feature of increased reflection in the low energy range (
