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# Nanophotonics

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# Long-living nonlinear behavior in CsPbBr3 carrier recombination dynamics

Fabio Gabelloni
• Dipartimento di Fisica e Astronomia, Università di Firenze, via G.Sansone 1, 50019 Sesto Fiorentino, Italy
• Other articles by this author:
/ Francesco Biccari
• Dipartimento di Fisica e Astronomia, Università di Firenze, via G.Sansone 1, 50019 Sesto Fiorentino, Italy
• LENS, via N.Carrara 1, 50019 Sesto Fiorentino, Italy
• Other articles by this author:
/ Naomi Falsini
• Dipartimento di Fisica e Astronomia, Università di Firenze, via G.Sansone 1, 50019 Sesto Fiorentino, Italy
• Other articles by this author:
/ Nicola Calisi
• Dipartimento di Ingegneria Industriale, Università di Firenze, via Santa Marta 3, 50139 Firenze, Italy
• Other articles by this author:
/ Stefano Caporali
• Dipartimento di Ingegneria Industriale, Università di Firenze, via Santa Marta 3, 50139 Firenze, Italy
• Other articles by this author:
/ Anna Vinattieri
• Corresponding author
• Dipartimento di Fisica e Astronomia, Università di Firenze, via G.Sansone 1, 50019 Sesto Fiorentino, Italy
• LENS, via N.Carrara 1, 50019 Sesto Fiorentino, Italy
• INFN, Sezione Firenze, via G.Sansone 1, 50019 Sesto Fiorentino, Italy
• orcid.org/0000-0002-0781-4002
• Email
• Other articles by this author:
Published Online: 2019-04-15 | DOI: https://doi.org/10.1515/nanoph-2019-0013

## Abstract

By means of time-resolved photoluminescence (TR-PL) spectroscopy, we present a detailed investigation of the carrier relaxation dynamics in a CsPbBr3 bulk sample and microcrystal ensemble at cryogenic temperature on a picosecond time scale. We provide evidence of a long temperature-dependent cooling rate for the excitons and free carriers population, with an initial cooling time constant of a few tens of picoseconds. A relaxation bottleneck in the thermalization process was found that cannot be explained by the Auger effect or hot phonon population, since we address a very low excitation regime, not commonly investigated in literature, where such processes are not effective. Adding a continuous wave optical bias to the picosecond excitation, we probed the photoinduced PL decrease of the localized states and the photoinduced PL increase of the population in the high energy states. A long recovery time from the photoinduced PL decrease was found for localized states and quite significant differences were detected, depending on the resonance/off resonance bias used in the experiment.

## 1 Introduction

Perovskites (PVK), hybrid organic-inorganic (H-PVK) and fully inorganic (I-PVK), are innovative materials with extreme relevance with regards to applications that span from photovoltaics [1], [2], [3] to LED, lasers [4], [5], [6], [7], sensors [8], [9] and generally speaking, optoelectronic devices, given their peculiar characteristics. In fact the low-cost chemical synthesis, the band-gap tunability, which is easily controlled by the composition, the possibility of several types of nanostructures, etc. [10] make PVK a possible substitute of III–V and IV semiconductors for innovative devices. The huge experimental and theoretical numbers of studies in the last decade confirm the interest of the scientific community in such materials. Most of the research has focused on H-PVK, especially as active materials for photovoltaic cells. However, several technological issues limit the performances of H-PVK, such as chemical instability, especially in the presence of moisture and after UV light exposure, and thermal instability, all effects that produce degradation and decomposition of the material [11], [12], [13]. Removing the organic part, which is mainly responsible for H-PVK degradation, has proved successful. Therefore, after the seminal work of Protesescu et al. [14], a great part of the research activity in this field was directed to I-PVK, in particular CsPbX3 (X=Cl, Br, I), as I-PVK are more suitable for applications where a long lifetime of the device is mandatory. As typical of research devoted to the development of new materials for innovative optoelectronic devices, a deep knowledge of the processes that rule the recombination dynamics of the carriers and excitons, and the relationship with the material crystallinity and stoichiometry, is necessary. In the case of PVK, since most of the investigated samples are assembled in the form of nanoparticles or microcrystals, it is clear that surface states can play a major role, affecting both the optical and electrical properties. For some applications recently under investigation such as high energy particle detectors [15], [16], bulk crystals (single or polycrystalline) are of interest; in this case, other kinds of defects, such as shallow or deep traps, can affect the recombination. Therefore, a comparative study of a bulk and a microcrystalline sample is relevant when considering that a different morphology/size is required depending on the specific application intended for the material.

Up to now, most studies concerning the recombination dynamics in I-PVK have addressed the room temperature regime, which is of course relevant for device operation. However, in order to gain a deep knowledge of the processes influencing the carrier recombination, it is also necessary to investigate the low temperature regime. In this paper, we present time-resolved photoluminescence (TR-PL) spectra of different CsPbBr3 samples (bulk sample [CR] and spin-coated [SC] microcrystal ensemble) to study the relaxation dynamics of free carriers and excitons in a low excitation regime (excitation density δ≈1016/cm3 carriers per pulse). In particular, we focus on the carrier thermalization regime that, on a picosecond time scale, is dominated by the interaction of the carriers with acoustic phonons. By adding a nonresonant/resonant continuous wave (CW) bias to the nonresonant excitation pulse, we show the significant non-linearity in the recombination dynamics for the low energy/high energy states of the PL band.

## 2 Experimental

Two different CsPbBr3 samples were investigated: a bulk sample (CR) and a SC microcrystal ensemble deposited on a glass substrate. In both cases, a CsPbBr3 solution was prepared by dissolving equal molar quantities of the precursors (CsBr and PbBr2) in dimethyl sulfoxide. The solution was stirred overnight to obtain a clear liquid. For the microcrystal ensemble, after the spinning, the sample was dried and annealed at 393 K for 10 min. The CsPbBr3 bulk sample was grown by antisolvent vapor-assisted crystallization (AVC) method [17], using methanol as antisolvent. Samples were finally encapsulated in a poly(methyl methacrylate) (PMMA) layer.

Scanning electron microscopy images of the bulk sample and of the SC sample are shown in Figure 1. It is worth noting the large size of CR, which was of the order of 1 mm, and its flat surfaces, indicating a very good optical quality. The X-ray diffraction (XRD) pattern reported in Figure 1C shows the presence of a few differently oriented crystalline domains, by the splitting of the diffraction spots, as shown in the inset. Evidence of a polycrystalline structure is commonly reported (e.g. ref. [18]) and the origin of the diffraction spots can be ascribed to twinning phenomena [15]. The SC sample consists of a collection of microcrystals, well separated among each other, with a large spread in size, from hundreds of nanometers to several micrometers. XRD analysis at room temperature indicates only small traces of spurious phases (CsBr and PbBr2), as shown by the presence of non-indexed peaks in Figure 1D, while the CsPbBr3 orthorhombic phase dominates.

Figure 1:

Morphological and structural characterization of the samples.

Scanning electron microscopy (SEM) images of the bulk sample (A) and the spin-coated microcrystalline film (B) and their X-ray diffraction (XRD) patterns (C) and (D), respectively. In the case of the bulk sample, the presence of a few differently oriented crystalline domains is evidenced by the splitting of the diffraction spots, as shown in the inset of panel (C). The numbers in (C) correspond to interplanar distances (Å).

Low temperature PL experiments were performed in a quasi-backscattering geometry, keeping the samples in a closed cycle cryostat at 10 K. A frequency-doubled mode-locked picosecond Ti-sapphire laser, operating at an 81.3 MHz repetition rate with 1.2 ps long pulses, was used for the TR-PL experiments. The maximum excitation intensity was about 10 W/cm2, corresponding to an estimated excitation density δ of about 2×1016 cm−3 carriers per pulse. TR-PL measurements were carried out using a synchroscan streak camera (time resolution 5 ps) after spectral dispersion of the detected signal through a 25 cm monochromator, equipped with a 300 grooves/mm grating (blaze 500 nm, spectral resolution of 2 meV). Eventually, CW-laser diodes at different wavelengths were used in combination with the picosecond pulses for probing the nonlinear response of the samples.

## 3 Thermalization of the free carrier population

TR-PL spectroscopy is a very efficient tool to investigate the processes ruling the relaxation and recombination of carriers and excitons. In this work, firstly we discuss the topic of carrier thermalization.

In Figure 2A, a streak image of the PL time evolution for the bulk sample is shown for the fastest time scale, after nonresonant excitation at 3.35 eV, at a temperature of 10 K. The strong emission at 2.32 eV, which dominates at early times, comes from the free exciton (FE) recombination, as measured from reflectivity (Figure 2D) and in agreement with literature data [15], [18], while the low energy emission below 2.3 eV corresponds to bound exciton (BE) recombination, usually assigned to Br vacancy centers [19].

Figure 2:

Bulk sample.

(A) Photoluminescence (PL) time evolution after picosecond excitation at 3.35 eV. (B) PL decay at free carrier recombination (FCR), free exciton (FE) and bound exciton (BE) energies (log scale). (C) Rise of the PL for the FCR, FE and BE energies (linear scale). In green, the experimental time response is reported. (D) Time-integrated PL spectrum (blue) compared with the reflectivity spectrum (red). All the measurements reported in the figures were performed at 10 K.

The Stokes shift value between the PL and the reflectivity spectrum, which resulted in about 2 meV (Figure 2D), is in agreement with literature data [18] and provides evidence of a small inhomogeneous broadening due to disorder.

A significant emission above the FE transition was also detected: from the Arrhenius plot of the PL intensity versus temperature (not shown), we estimate an exciton binding energy of ≈30–35 meV, in agreement with literature data [20]. Therefore, the observation of PL emission at energies above the exciton line has to be ascribed to free carrier recombination (FCR). We want to remark that the polycrystalline nature does not affect the experimental results discussed here and only accounts for the inhomogeneous broadening of the PL spectrum.

PL decays, acquired with the streak camera in a time interval up to 800 ps, are shown in Figure 2B: non-exponential decays are shown at the BE and FE energies, while the FCR decay turns out to be exponential with a decay time of ≈50 ps. An estimate of the initial time decay constant gives values of about 80 and 120 ps for the FE and BE emissions, respectively. Figure 2C shows the risetime of the PL at the same energies as Figure 2B: for the FCR, the risetime is ≈10 ps, while it is ≈20 ps (30 ps) for FE (BE). The time-integrated spectrum is shown for the same experimental conditions in Figure 2D. The PL decay times measured for the different emissions (BE, FE, FCR) agree with literature data at low temperatures [21], [22]. The fast decay of FCR cannot be ascribed to surface recombination as indicated in ref. [23], because in consideration of the absorption length (≈100 nm) in our experimental conditions, it would require a very high mobility, not found in CsPbBr3 [24], [25]. Instead it is mainly due to the exciton formation, as also confirmed by its slightly superlinear dependence on the excitation power that is evidence of a prevalence of the exciton formation with respect to the other FCR decay channels.

From the streak images, such as the one shown in Figure 2, we can extract TR spectra at different delays; a set of spectra are shown in Figure 3.

Figure 3:

Bulk sample.

Time-resolved photoluminescence (TR-PL) spectra (in log scale) as extracted from streak images in different time scales. For each spectrum, the time delay with respect to the excitation is reported, while Δt corresponds to the time interval between two adjacent spectra. (A) Rise of the TR-PL, (B) early decay times, (C) longer decay times.

From Figures 2C and 3A, it can clearly be seen that the FE emission rises in about 15–20 ps, with a delay of 5–10 ps with respect to the FCR. This corresponds to the transfer of the FE from the high energy non radiative states into the K≤Kph radiative states, where K and Kph indicate the exciton and photon wavevectors, respectively [26]. Given the rise time and the carrier density value we can infer for the bimolecular exciton formation coefficient (C) at 10 K a lower limit C=5×10−6 cm3 s−1, to be compared, for example with that of GaN where C=1.2×10−6 cm3 s−1 [27]. The emission from FE initially dominates the PL spectra, and successively the excitons localize in shallow states and form bound excitons; Moreover a long living Urbach tail is detected, arising from localized states. A faster rise and decay is observed for the PL signal detected in the high energy side above the FE emission where the contribution comes from the free carriers recombination. From the TR spectra of Figure 3, it is seen that the high energy side of the PL, above the FE state, is characterized by an exponential tail with a slope which becomes steeper, increasing the delay. The presence of the exponential tail is evidence of a thermalization condition for the carriers, where the population can be described, in the non-degenerate case, by a Boltzmann distribution with an effective temperature Teff, which is a function of time [26]. Therefore, we can express the PL intensity I at a given time t by:

$I(t)∝DOS(E)exp(−EKBTeff(t))$(1)

where DOS(E) indicates the density of states and the effective temperature Teff depends on time. As seen from Figure 3C, after about 0.2 ns, the slope of the high energy tail does not show any remarkable further change, with a very slow decay. From an exponential fit of the high energy tail of the TR-PL spectrum at a time delay of 670 ps where Teff=Tfin, we find that Tfin=45 K. From Eq. (1), we can extract the DOS(E), shown in Figure 4A, where for comparison, a TR-PL spectrum at a time delay of 156 ps is shown. In the DOS(E), the excitonic peak at 2.32 eV clearly comes out.

Figure 4:

Bulk sample.

(A) Density of states (DOS) extracted from time-resolved photoluminescence (TR-PL) spectra, as discussed in the text, along with a TR-PL spectrum at 10 K. (B) A(t, T) for different time delays (log scale). (C) Effective temperature of the carriers Teff as a function of time delay. The red points refer to a thermal distribution, while the blue ones refer to an incomplete thermalization condition. The solid line in (C) is a fit with Eq. (2).

From Eq. (1), we find an exponential dependence on the energy for the quantity

$A\left(t, \text{\hspace{0.17em}}T\right)=\frac{I\left(t,\text{\hspace{0.17em}}{T}_{\text{eff}}\right)}{I\left({t}_{\infty },\text{\hspace{0.17em}}{T}_{\text{fin}}\right)}$

as illustrated in Figure 4B for a few TR-PL spectra. From such dependence, we can extract Teff which is plotted as a function of the time delay in Figure 4C, for a lattice temperature TL=10 K. An evident bottleneck in the relaxation is found and the effective temperature remains around 45 K for hundreds of picoseconds, after a fast initial decay. The blue points in Figure 4C correspond to TR-PL spectra (in the rise of the PL signal up to about 20 ps) where we can roughly estimate a temperature, but the thermalization is incomplete. Given the excitation density and the time resolution of our experiments, the thermalization regime that we investigated is dominated by the interaction of the carriers with acoustic phonons. In this case, the time evolution of Teff can be reproduced by [28]:

$Teff(t)=T∞*(Aexp(tτ1)+1Aexp(tτ1)−1 )2$(2)

corresponding to a temperature (energy) relaxation of the free carriers due to the carrier-acoustic phonon interaction via the deformation potential [29]. In Eq. (2), T indicates the final temperature (that should be the lattice temperature), τ1 is the time constant describing the fast relaxation and $A=\frac{\sqrt{{T}_{0}}+\sqrt{{T}_{\infty }}}{\sqrt{{T}_{0}}-\sqrt{{T}_{\infty }}}$ with T0 the carrier temperature at t=0. From the fit (solid line in Figure 4C) we get τ1=50 ps, T0=67 K and T=45 K. Such a value for T, higher than the lattice temperature, does not come from a lattice heating, as confirmed by the temperature dependence of the PL spectra. In fact, at 45 K the bound exciton emission becomes negligible with respect to the free exciton contribution, and by the high energy tail of quasi resonantly excited PL spectra, at 10 K, we extract a carrier temperature lower than 20 K (not shown). As expected from the model discussed in [28], [29], T should correspond to the lattice value (i.e. 10 K), but TR-PL spectra up to a delay of 1.5 ns show a temperature (T≈30 K) still above that of the lattice, indicating the presence of a very slow process.

Similar results were also found for the SC microcrystals: in this case, the PL is characterized by a band the peak energy of which, at 10 K, changes between 2.32 eV and 2.39 eV depending on the position on the sample, possibly due to differences in the local strain induced by the substrate [30]. Results for the band at 2.39 eV are shown in Figure 5, along with some normalized TR-PL spectra, extracted from the image of Figure 5, and the effective temperature of the carriers as a function of time delay.

Figure 5:

Spin-coated sample.

(A) Streak image. (B) Normalized time-resolved photoluminescence (TR-PL) spectra where the exponential tail is evidenced in black. (C) Effective temperature of the carriers Teff as a function of time delay: the continuous line is a fit with Eq. (2). Measurements refer to a lattice temperature of 10 K.

Therefore, also in the case of the SC sample, a significant bottleneck in the temperature relaxation is found with a faster initial decrease of Teff with respect to what is found for the bulk sample. In this case, we get τ1=15 ps, T0=89 K and T=58 K. The results previously shown suggest that the same physical mechanism rules the thermalization both in the bulk and the SC sample. The most relevant difference is the relaxation time, which is three times faster for the SC sample, possibly due to a change of the deformation potential coefficient as a consequence of local strain [29]. To our knowledge, there are no results in the literature concerning this specific topic. With regards to the temperature relaxation at longer time delays, and the slow energy dissipation rate of the FCR, similar behavior is found for both samples, possibly related to a long-living free carrier population, especially in the case of the SC sample.

The relaxation bottleneck in H-PVK and I-PVK nanostructures [31], [32], [33], [34], [35], [36], [37], [38], [39] was recently reported and ascribed to several causes such as efficient Auger processes, hot phonons or polaron formations, that keep the carrier temperature higher than the lattice temperature. However, at the excitation density used in our experiment (δ≈1016 cm−3 carriers per pulse), both hot phonons and Auger heating are negligible, given the Auger coefficient in CsPbBr3 bulk, 3×10−27 −4×10−28 cm6 s−1 [40]; for the same reason, a screening of the exciton-phonon interaction can be excluded. The large polaron formation has been demonstrated in MAPbBr3 and CsPbBr3 [32], [36] and strongly affects the cooling in the first few picoseconds, but it is not relevant on the time scale we considered in our experiment. Therefore, the origin of the very slow cooling, in a time scale and an energy range where the interaction between free carriers and acoustic phonons prevails, must be searched for outside the previous causes. It is worth remarking that the persistent non negligible FCR population, living several hundreds of picoseconds (e.g. see Figure 2), may be related to the slowing down of the cooling. Persistent energetic electrons have been already observed in MAPbI3 [35] and FAPbI3 [41] and a reduced density of states has recently been proposed as the origin of the slow dynamics and cooling in CsPbI3 [42]. We recently demonstrated [43], for SC samples, that surface states can efficiently trap the carriers, with a long release time, providing a carrier reservoir for the radiative recombination: therefore, surface states can play a role in the thermalization process and similarly in bulk high energy long-living traps eventually related to small structural defects or inclusions (e.g. CsPbBr5, or PbBr2).

## 4 Nonlinear behavior of excitons and free carriers

TR-PL spectra previously shown reveal the complex nature of the radiative recombination where excitons, both free and bound, and free carriers contribute to the emission. In order to elucidate the interplay between the different populations, we performed TR-PL spectra adding different CW bias to the picosecond excitation pulse [44]. We used a CW laser diode at 405 nm, well above the PL energies for both the bulk and SC samples, a 532 nm laser diode for resonant excitation of the bulk sample and one at 515 nm for resonantly exciting the PL of the SC sample. We aimed to compare the response of the sample in the presence/absence of the bias: in fact, in the case of linear processes the PL, when the bias is added to the picosecond excitation, reproduces the sum of the PL obtained by separate excitation with the bias and the pulse. In some sense, in this way we can provide information similar to a pump-probe experiment and we can test the nonlinearities of the relaxation dynamics and recombination. However, since the maximum power used in our experiment is much lower than the one commonly used in pump-probe experiments, we are able to detect smaller nonlinearities.

In Figure 6A, for the bulk sample, we report the streak image acquired by subtracting the separate contribution to the PL of the CW nonresonant bias (Ib) and of the picosecond excitation (Ip) from the acquisition with both picosecond and bias (Ipb). In Figure 6B and C, we show the time evolution of the PL, as extracted from the corresponding streak image (Figure 6A) at different time delays. The low energy side (below 2.31 eV) shows a photoinduced PL decrease (PHD) with a long recovery time. The free exciton at 2.32 eV shows a faster recovery from the PHD with respect to the bound states, while the free carrier spectral region, after a small initial PHD, shows a photoinduced PL increase (PHI), which can be ascribed to a bimolecular radiative recombination process. It is relevant to note that our experiment allows only the detection of excitons in radiative states and therefore momentum relaxation can require tens of picoseconds, as long as the relaxation process proceeds through low energy phonon emission. In the spectra, the energy E0 marks the crossover between the sublinear and the superlinear regime.

Figure 6:

Bulk sample.

(A) Image reporting the time evolution of the nonlinear signal Ipb – (Ip + Ib). (B), (C) Time-resolved photoluminescence (TR-PL) spectra extracted from (A).

The results are summarized for the bulk sample in Figure 7, comparing the case of nonresonant and resonant bias, with a power of 500 μW in both cases.

Figure 7:

Bulk sample.

(A) Time evolution of the zero-crossing energy E0. (B), (C) Nonlinear contribution evaluated as indicated in the text for the bulk sample when nonresonant (B) or resonant (C) bias is used for three different spectral regions: the bound exciton (BE), the free exciton (FE), and the free carrier recombination (FCR).

Firstly, as shown in Figure 7A, the significant shift of E0 with time comes out, corresponding to a relaxation dynamics within the band from the free to the bound states; few hundreds of picoseconds are required before reaching the complete exciton localization. Quite remarkable, also, is the recovery time from the PHD of the localized emission, again in the time scale of a few hundreds of picoseconds. A PHI is always observed for the FCR emission, as previously stated, because of a bimolecular radiative recombination process. The PHD at the BE energy is a consequence of the partial saturation of the involved sites and persists in time; for the FE the initial PHD can be the result of a partial saturation of the localization sites and/or of a scattering with the free carriers that removes the exciton from the radiative states [44]. In fact, as shown in Figure 7B and C, with the same power of the bias the FE recovery of the superlinear behavior is faster and more pronounced in the resonant case, where a lower density of excitons and FCR is created as a consequence of the lower absorption coefficient. The recovery from the sublinear regime and the transition to a superlinear behavior, coming from the bimolecular exciton formation process, are faster at the higher energies of the FE band and are evidence of a non negligible contribution related to the localization degree. Results for the SC sample are reported in Figure 8.

Figure 8:

Spin-coated sample.

(A) Nonlinear response for the nonresonant bias. (B) Nonlinear response for the resonant bias. The dashed line (blue) corresponds to the PL signal.

The PL spectra of the SC sample do not show a clear signature of the bound exciton band, as observed for the bulk sample, but instead a larger inhomogeneous broadening. The results of Figure 8A indicate a significant photoinduced PL decrease of the low energy side of the emission, with a faster recovery with respect to the bulk sample, which we ascribe mainly to the saturation of the localized sites. The high energy side shows, instead, a photoinduced PL increase due to the free carrier population. Only a superlinear behavior is observed for resonant bias (Figure 8B), because of an efficient exciton formation in our experimental conditions.

We want to emphasize that, even though in our experiment we address only the behavior of excitons and free carriers investigating macroscopic areas of the samples (tens of μm2), the technique used can be applied to samples of different size and morphology and, in combination with microphotoluminescence setups, will allow the study of single nanocrystals.

## 5 Conclusions

We present experimental results concerning the relaxation and thermalization process in a CsPbBr3 bulk sample and microcrystal ensemble on a picosecond time scale. High resolution low temperature TR-PL measurements provide evidence of a thermalized carrier distribution, which, however, remains hotter than the lattice. Given our experimental conditions, such a relaxation bottleneck cannot be explained by the Auger effect or hot phonon population; it can tentatively be ascribed to a long-living population released by high energy traps, the origin of which is eventually related to surfaces; an additional investigation regarding this point is in progress. Moreover, significant long-lasting non-linearities in the emission are found. The measured photoinduced PL decrease comes from the saturation of the localized/bound states, whereas the photoinduced PL increase observed in the high energy side of the PL spectrum can be related to the bimolecular radiative recombination from the free carrier population.

## Acknowledgments

This work has been performed under the framework of the project no. 2017.0756 Advanced optical spectroscopy for interface control in perovskite-based solar cells, and within the project no. 2016.1084 Stabilized perovskites for high-efficiency eco-friendly light emitters and solar cells (PERBACCO), both funded by Fondazione CARIFI Bando 2016 and 2017. The authors warmly thank Professor Franco Bogani, University of Florence, for helpful discussions.

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Revised: 2019-03-12

Accepted: 2019-03-28

Published Online: 2019-04-15

Citation Information: Nanophotonics, Volume 8, Issue 9, Pages 1447–1455, ISSN (Online) 2192-8614,

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