Ultrafast Spectrally Resolved Photoinduced Complex Refractive Index

Jan 25, 2019 - MacDiarmid Institute for Advanced Materials and Nanotechnology, Wellington 6140 , New Zealand. § The Dodd-Walls Centre for Photonic an...
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Ultrafast spectrally resolved photoinduced complex refractive index changes in CsPbBr perovskites 3

Ronnie Tamming, Justinas Butkus, Michael B Price, Parth Vashishtha, Shyamal Prasad, Jonathan E. Halpert, Kai Chen, and Justin M Hodgkiss ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.9b00091 • Publication Date (Web): 25 Jan 2019 Downloaded from http://pubs.acs.org on January 25, 2019

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Ultrafast spectrally resolved photoinduced complex refractive index changes in CsPbBr3 perovskites Ronnie R. Tamminga,b, §, Justinas Butkusa,b,§, Michael B. Price, a,b Parth Vashishthaa,b, Shyamal K. K. Prasada,b Jonathan E. Halperta,b Kai Chena,b,c*, and Justin M. Hodgkissa,b,c* a

School of Chemical and Physical Sciences, Victoria University of Wellington, New Zealand.

b

MacDiarmid Institute for Advanced Materials and Nanotechnology, New Zealand.

c

The Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand.

§ Both authors contributed equally to this work. Corresponding Authors * E-mail: [email protected]; [email protected]

ABSTRACT: The exceptional optoelectronic properties of metal halide perovskites have been illuminated by extensive spectroscopic studies. Recent measurements suggest strong photoinduced refractive index changes in these materials, which influence their functionality and obscure access to photoinduced extinction spectra from transient absorption spectroscopy, but such photorefractive effects are difficult to measure and model. Here, we use white light pulse interferometry – an experimentally straight forward adaptation of transient absorption spectroscopy – to directly probe photoinduced refractive index changes in CsPbBr3 films and nanocrystals on ultrafast timescales. Strong photoinduced refractive index changes are spectrally resolved and used to access extinction spectra, and these intrinsic optical parameters are then used to directly resolve more accurate photoexcited carrier temperatures and bandgap ACS Paragon Plus Environment

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renormalization, resolving ambiguities in the present literature. As well as understanding the intrinsic photoresponse of semiconductors, quantifying photoinduced refractive effects will be valuable for designing photonic devices including switches, lasers and concentrating photovoltaics.

KEYWORDS: Frequency domain interferometry, optical constants, transient absorption spectroscopy, photonic materials.

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Following reports of their high photovoltaic efficiencies,1,2 and their use in lasers3,4 and lightemitting diodes,5,6 metal halide perovskites have been studied extensively by ultrafast spectroscopy. Key perovskite semiconductor properties - such as photoexcited carrier temperature dynamics, photoinduced bandgap renormalization, values of effective mass, and carrier recombination– have been studied by ultrafast transient absorption (TA).7-13 All of these properties are characterized directly by their dynamic spectral shape. However, for high refractive index materials like perovskites, TA spectroscopy does not provide direct and immediate quantification of this shape. This is due to the presence of photoinduced changes in refractive index occurring simultaneously with changes in absorption, both of which ultimately affect the changes in transmission measured by TA.14,15 Just as elipsometric measurements of optical constants provide the true steady state extinction spectrum of a material, direct measurements of photoinduced refractive index are required to access photoinduced changes to intrinsic extinction spectra9,16,17 Along with the properties already listed above, understanding of the complex refractive index enables knowledge of carrier generation, band filling, plasma intraband transitions, and Coulombic carrier interactions.16,18,19 In the case of semiconductor nanocrystal dispersions, polarization of the solvent medium and scattering can also induce additional refractive index changes.20,21 While theoretical models describing photoinduced refractive index changes in inorganic semiconductors have been developed, direct experimental measurements are lacking.16 Direct knowledge of these refractive effects is also critical to inform the design of optoelectronic devices such as optical switches, photodetectors, modulators and recording devices, as well as single photon emitters and laser cavities.16,17,22

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Price et al 9 attempted to decouple the intrinsic ultrafast photoinduced absorption and refractive index changes by simultaneously measuring the reflected and transmitted probe light in films of MAPI perovskite. However this method is experimentally difficult to implement, due to the often large amounts of light scatter deflected from the polycrystalline samples, is somewhat model dependent, and there is evidence from subsequent work23 that the magnitude of the refractive index change was thus overestimated. This uncertainty in the shape and magnitude of photoinduced refractive index change has subsequently added uncertainty into the quantification of the magnitude of both the bandgap renormalization, and the absolute carrier temperature distribution in perovskites following photoexcitation. These quantities are particularly important for high carrier density devices, like lasers 24,23 and concentrating photovoltaics. 25,26 Here, we employ a frequency domain interferometry technique that was first introduced in 1992 by Tokunaga et al.27, but has not yet been applied to semiconductors. The method is a simple adaptation of TA spectroscopy that allows direct spectral quantification of the photoinduced changes in the real part of the refractive index. We measure directly the spectrum of photoinduced refractive index changes for CsPbBr3 perovskite films and nanocrystal samples and are able to accurately calculate this from the standard TA spectra to confirm the reliability of our technique. We then show that band gap renormalization is the dominant source of the negative signal observed in CsPbBr3 perovskite TA spectra (agreeing with Ghosh et al.23), and give quantitative absolute measures of carrier temperature. We show that the measured photoinduced refractive index changes have direct implications for high carrier density devices, by quantifying their significant effects on concentrating photovolatics and laser structures for the first time. The interferometry experiment, depicted in Figure 1a, exploits the interference of a pair of white light continuum pulses. The pair of pulses – probe and reference – are generated in a Michelson ACS Paragon Plus Environment

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interferometer and then set to the same optical path through the sample and spectrometer to produce interference fringes on a multichannel detector. Since the pulses are dispersed by a diffraction grating in a spectrometer before the detector, the narrowed interaction bandwidth results in temporal broadening at the detector, ensuring that a pair of pulses that are temporally separated at the sample can still interfere on the detector. By adjusting the two interferometer arms, the probe and reference pulse arrival times at the sample are arranged to ensure that only the probe interacts with the excited sample, with the reference pulse arriving slightly before the excitation (pump) pulse. Thus, photoinduced changes to the sample refractive index results in a phase shift of the interference fringes.27 Photoinduced refractive index changes can be spectrally resolved by ensuring that the interference fringes have sufficient spectral density, which relates to the grating dispersion and the delay between the probe and reference pulses. In our setup, the probe arrives ~2 ps after the reference pulse, which limits the maximum time range for timeresolved measurements, although experimental modifications discussed later may alleviate this constraint. Further details about the experimental setup are included in the ESI, as well as information about sample preparation and characterisation.

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Figure 1. a) Schematic of frequency domain interferometer setup. b) Frequency domain interferometry spectrum showing interference fringes and single probe spectrum. The single probe spectrum is scaled by a factor of 2 for comparison. c) Pump-induced phase shift of interference fringes along with corresponding single probe (TA) spectrum without the interference pattern (scaled by a factor of 2). A small fraction of the total spectral range is shown here in expanded form for clarity. d) Phase difference spectrum of CsPbBr3 bulk film at 1.5 ps after excitation. Figure 1b shows an example of spectral interference fringes observed when the two white light pulses interfere on the detector, compared with the interference-free spectrum of a single probe when one of the interferometer arms is blocked. This experimental configuration allows for good fringe resolution, and the common beam path shared by the two white light beams ensures that measurement stability is not compromised by beam deflection. When the excitation pulse is introduced (Figure 1c), these interference fringes are superimposed on the regular TA spectrum, and a small pump-induced phase shift is seen. A full false colour plot over time is shown in ESI figure S3. It is possible to reliably resolve small phase shifts since the pump is chopped at half the probe frequency and sequential probe shots are compared. A pump-induced phase difference spectrum (Figure 1d) is then extracted using a Fast Fourier transform algorithm, windowed along small spectral increments, which can then be smoothed. The measured pump-induced phase difference spectrum is directly related to the refractive index change according to Equation 1, allowing for a simple recovery of pump-induced changes to the refractive index (Δn),28

∆𝜙 =

―∆𝑛𝜔𝑙 𝑐

(1)

where ω is the angular frequency, c is the speed of light and l is the thickness of the medium.

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Figure 2 shows the spectrally resolved refractive index changes for a CsPbBr3 film between 400 fs and 1.9 ps after photoexcitation. The spectra presented merge 3 spectral windows whose ~40 nm width is determined by the optimal grating dispersion for resolving interference fringes. We observe the expected derivative-like n spectra around the band edge16,29 with a maximum negative Δn of -0.034. The magnitude of the refractive index changes up to almost -0.06 was observed for a carrier density of 3 × 1017cm-3 (ESI Figure S4). These refractive index dynamics cannot be accurately predicted, but are vital in the design of nonlinear optical and photonic devices.

Figure 2. a) Measured and smoothed change of the real part of the refractive index from the pumpinduced phase shift from 400 fs to 1.9 ps with 300 fs time steps for CsPbBr3 pumped at 3.1 eV with a carrier density of 1.5 × 1017 cm-3. b) The change in the imaginary component of the refractive index obtained via KK transformation. c) Obtained transient extinction coefficient. In standard TA spectroscopy, changes in both the real and imaginary parts of the nonlinear susceptibility affect the measured differential transmission spectrum. These two effects cannot be decoupled using Kramers-Kronig (KK) relations as it violates the causality condition.30 In the case of the interferometry method however, only the real part of the refractive index is measured, and the ACS Paragon Plus Environment

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excitation pulse arrives between the two white light pulses, in which case the KK relations have been shown to remain valid.30 Therefore, not only can we directly access changes in refractive index, n, we can then apply a KK transform (further details in ESI) to recover the imaginary part of the non-linear susceptibility, i.e., the intrinsic photoinduced change to the extinction spectrum k (Figure 2b). The change in the absorption coefficient () is easily calculated from the transient complex refractive index spectrum, k, via equation 2.

Δ𝛼 =

4𝜋Δ𝑘 𝜆

(2)

The  spectra are shown in Figure 2c. We attribute the increased early absorption below the band gap to band gap renormalization, induced by the additional electrons/holes in the conduction/valence band and creating newly available states.11 After ~1.3 ps, the absorption becomes negative due to relaxing carriers filling these states. To confirm the reliability and validity of our technique, we reconstruct the standard differential transmission spectrum by applying Fresnel’s equations to the photoinduced changes in the real and imaginary parts of the refractive index. The full method is given in the ESI.

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Figure 3. a) Directly measured TA spectra (circles), and TA spectra reconstructed from photoinduced optical constant changes (solid lines) for CsPbBr3 pumped at 3.1 eV with a carrier density of 1.5 × 1017 cm-3 for 400 fs to 1.9 ps with 300 fs time steps. b) Change of transmission and reflection for the same carrier density at 400 fs. The TA spectra calculated from the measured refractive index changes are compared with standard TA spectra in Figure 3a. The standard TA spectra are readily measured under identical excitation conditions, simply by blocking the reference beam in the interferometer. The measured and reconstructed TA spectra match very well, confirming the reliability of the interferometry method and the approach taken to relate the real and imaginary parts of the refractive index and TA measurements. The spectra of a CsPbBr3 film each resolve the dominant ground-state bleaching peak centered around 2.36 eV at the band edge, accompanied by a sub-gap photo-induced absorption from bandgap renormalization at early times.9 In addition to spectral shapes, the absolute amplitude of the TA spectrum derived from interferometry is also in good agreement with the directly measured TA spectrum, noting that the only scaling factor used is the measured ACS Paragon Plus Environment

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sample thickness. The thickness used for the calculation (72.5 nm) is set by finding the best fit for the transient absorption signal and is close to the average measured thickness of ~100 nm (ESI figure 2).

For perovskites, with their high refractive indices, and highly scattering polycrystalline films, the influence of reflections on the TA signal is under debate,9,31 – particularly regarding whether the high energy negative feature is caused predominantly by reflection changes, or bandgap renormalization. To compare the change in transmission with the reflection, the change in signal is divided by the sum of the intrinsic transmission and reflection, Δ𝑇/(𝑅 + 𝑇) and Δ𝑅/(𝑅 + 𝑇), and is shown in Figure 3b. We again use the Fresnel equations to calculate the change in reflection from the transient refractive index.32 The calculated change in reflection is of significant amplitude and shows that it influences the shape of the photo bleach signal at the band edge, as observed by Price et al. However the diminishing change in reflection at higher energy (above 2.45 eV) agrees with the conclusion from Ghosh et al.31, that the primary factor responsible for the negative signal in TA spectra in that energy region is band gap renormalization. The effect of free carrier absorption on the TA signal is already determined to be in the order of 10-3 9. This only leaves the bandgap renormalization as possible primary source of the negative TA spectra in that region. This claim is supported by a simple model given in ESI Figure S6, where the effect of the bandgap renormalization on the imaginary refractive index is shown. A positive change of the imaginary refractive index is observed at higher energies in this model which is in the same order of magnitude as the measured index

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change (Figure 2b). This indicates that the enhanced absorption in this region originates from the bandgap renormalization. The refractive index changes also cause the absolute carrier distribution temperature to be overestimated by 132 K at 400 fs when measured by TA compared to calculating directly from the Δα spectra (ESI Figure S5). This occurs because the change in refractive index alters the slope of the high energy side of the TA spectrum, and the temperature is typically gained by fitting the Boltzmann distribution to this side of the bleach. 9,33 Unlike transient reflection measurements, the interferometry approach can be applied to a broad range of samples, including rough films, and suspensions of nanocrystals (NCs). Figure 4 shows the photoinduced change in refractive index measured for a suspension of CsPbBr3 NCs of 8.6 nm diameter, along with the standard TA spectrum of the sample. The n spectrum closely resembles that of the thin film as shown in Figure 4, confirming that CsPbBr3 NCs in the weak quantum confinement regime have similar photophysical properties to the bulk material. When photoexciting NCs in solution, polarization of the surrounding solvent medium provides an additional mechanism for photoinduced refractive index modulation. Although the present NC measurements do not span a sufficient spectral range for accurate KK transformation and quantitative modelling, the FDI method may in future allow solvent polarization effects to be experimentally quantified and related to effective medium theory.34

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Figure 4. Transient absorption spectrum and corresponding relative smoothed photoinduced changes in refractive index of CsPbBr3 NC suspension measured at 1.5 ps after 400 nm pump excitation with a fluence of 15 µJcm-2

As a final demonstration of the utility of the transient interferometry technique, we show the impact of refractive index changes on potential perovskite devices. In lasers, excitation density dependent refractive index modulation across the gain spectrum governs the cavity mode frequencies.24 For a simple semiconductor laser cavity, the fundamental emission wavelength 𝜆0 is given by equation 3,

𝜆0 =

2𝑛𝐿 𝑚

(3)

where L is the length of the cavity, n is the real refractive index and m is an integer.24 For CsPbBr3, the amplified spontaneous emission wavelength at room temperature is around 530 nm,35,36 which is in the region of the largest decrease of n. For this wavelength, the refractive index of this perovskite is 2.20, 37 resulting in a optimized cavity length of (a multiple of) 240.9 nm. At our highest carrier density of 3 × 1017 cm-3 , Δn is the maximum negative change of -0.06, meaning that the optimized cavity length is increased to 247.7nm. Since a typical lasing threshold carrier ACS Paragon Plus Environment

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density is found to be 9.9 × 1017 cm-3 23, which is higher than the maximum carrier density measured in this report, this effect will be more pronounced for laser applications. Also, for high carrier density concentrating photovolatics, which are now being very seriously considered for perovskites, 25,26 the refractive index is vital in considering the cavity modes and design of the device. In figure 5, we show the effect of the change in refractive index on absorbed light intensity in a CsPbBr photovoltaic device stack. The Jsc is reduced by 2.3% and 6.5% at an approximate equivalent of 100 and 250 suns respectively. Thus, for serious deployment of concentrating perovskite photovoltaics, the cavity design must be optimised for the refractive index that will be present with the appropriate high carrier density.

Figure 5, The absorption and reflection contributions of the CsPbBr and PCBM layer for a high irradiance solar cell. The light to dark colour indicate excitation of 0, ~100 and ~250 sun equivalents respectively, based on estimations from Wang et al 26. The simulation is done using the model from Burkhard et al. 38 Additional information on the model is given in ESI Figure S7. A limitation of the FDI method in the present implementation is that the pump-probe time range is constrained to ~2 ps. This constraint arises because the probe and reference beams follow the same path, meaning that they must be temporally close enough to interfere on the detector, and since the pump must arrive between the probe and reference, their temporal spacing defines the ACS Paragon Plus Environment

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maximum time range. This constraint could be alleviated by spatially separating the probe and reference beams at the sample, with only the probe interacting with the excited region, but both beams arriving at the same time. This might be achieved using referencing schemes that allow probe and reference arms to be separated and recombined immediately before and after the sample using polarization-based beam splitters.39 Conclusion We have built a frequency domain interferometer as an easily implemented adaptation of a TA spectrometer, and used the method to extract the photoinduced refractive index changes in CsPbBr3 perovskite bulk films and NCs. The time-resolved spectral changes in the real part of the refractive index were used to calculate the photoinduced extinction coefficient changes via KK relations, and these intrinsic optical constants were found to quantitatively account for conventional TA signals, validating our new approach. We used the intrinsic refractive index and extinction spectra to accurately resolve time dependent absolute carrier temperatures in CsPbBr perovskite films – showing that previous TA methods overestimated carrier temperatures – as well as quantifying the extent to which bandgap renormalisation governs the dynamic spectral response of these films. Refractive index changes similar to the bulk perovskite material were also successfully measured in perovskite NCs, proving that large perovskite NCs are in the weak quantum confinement regime, and revealing the broad applicability of the method beyond thin films. Finally, we showed how our measured dynamic refractive index changes should guide the design of high carrier density devices – using lasers and concentrating photovoltaics as examples. ASSOCIATED CONTENT

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Supporting Information. Synthesis details, spectroscopy setup and analysis details, supplementary spectroscopic data. The Supporting Information is available free of charge on the ACS Publications website at DOI: ….. AUTHOR INFORMATION Corresponding Authors * E-mail: [email protected]; [email protected] Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT We are thankful to Aleksa Djorovic for valuable discussions. J.M.H. and J.E.H. each acknowledge funding support from Rutherford Discovery Fellowships, M.B.P. acknowledges support from a Rutherford Foundation New Zealand postdoctoral fellowship, and J. M. H., K. C., and J.E.H. also acknowledge support from the Marsden Fund of New Zealand. REFERENCES (1)

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