Multiphoton Absorption Order of CsPbBr3 As Determined by

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Multiphoton Absorption Order of CsPbBr3 as Determined by Wavelength-Dependent Nonlinear Optical Spectroscopy Felix Ochieng Saouma, Constantinos C. Stoumpos, Mercouri G. Kanatzidis, Yong Soo Kim, and Joon I. Jang J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02286 • Publication Date (Web): 25 Sep 2017 Downloaded from http://pubs.acs.org on September 26, 2017

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The Journal of Physical Chemistry Letters

Multiphoton Absorption Order of CsPbBr3 as Determined by Wavelength-Dependent Nonlinear Optical Spectroscopy

Felix O. Saouma,† Constantinos C. Stoumpos,‡ Mercouri G. Kanatzidis,‡ Yong Soo Kim,§,* and Joon I. Jang||,*

†

Department of Physics, Applied Physics and Astronomy, State University of New York (SUNY)

at Binghamton, P.O. Box 6000, Binghamton, NY 13902, USA ‡

Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208,

USA §

Department of Physics and Energy Harvest-Storage Research Center (EHSRC), University of

Ulsan, 93 Daehak-ro, Nam-gu, Ulsan 44610, South Korea ||

Department of Physics, Sogang University, 35 Baekbeom-ro, Mapo-gu, Seoul 04107, South

Korea

Corresponding Authors: Yong Soo Kim and Joon I. Jang * Email: [email protected] (Y. S. Kim) & [email protected] (J. I. Jang).

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ABSTRACT: CsPbBr3 is a direct-gap semiconductor where optical absorption takes place across the fundamental bandgap. But this all-inorganic halide perovskite typically exhibits above-bandgap emission when excited over an energy level, lying above the conduction-band minimum.

We probe this bandgap anomaly using wavelength-dependent multiphoton

absorption spectroscopy and find that the fundamental gap is strictly two-photon forbidden, rendering it three-photon absorption (3PA) active.

Instead, two-photon absorption (2PA)

commences when the two-photon energy is resonant with the optical gap, associated with the level causing the anomaly. We determine absolute nonlinear optical dispersion over this 3PA2PA region, which can be explained by two-band models in terms of the optical gap. The polarization dependence of 3PA and 2PA is also measured and explained by the relevant selection rules.

CsPbBr3 is highly luminescent under multiphoton absorption at room

temperature with marked polarization and wavelength dependence at the 3PA-2PA crossover, and therefore, has potential for nonlinear optical applications.

“TOC Graphic”

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In addition to solar cells,1−3 halide perovskite materials have recently attracted attention because of their promising nonlinear optical (NLO) properties.4−15 Apart from being excellent light absorbers in the linear regime, they are also efficient nonlinear light absorbers.4−10 The observed multiphoton absorption (MPA) effects are directly related to the imaginary part of the nonlinear susceptibility which has an explicit frequency () dependence. Specifically, these are the thirdorder susceptibility, , for two-photon absorption (2PA) and the fifth-order susceptibility, , for three-photon absorption (3PA), respectively.16 The real part of the corresponding nonlinearity is responsible for nonlinear change in the refractive index and is related to the imaginary part by the Kramers-Kronig relations.17 In fact, some halide perovskite films exhibit very large responses, both real and imaginary, at exciton and/or subgap-state resonance.11−13 Band-to-band MPA and subsequent photoluminescence (PL) in bulk perovskite crystals have been reported,7−9 and have been explained within a two-band model.16−18 Similar effects can be observed from perovskite quantum dots where the mechanism for MPA is essentially the same, but the 2PA efficiency depends on the size of the dots with a power-law behavior.10 Hybrid halide perovskites are also good frequency converters, generating strong second harmonic generation and third harmonic generation.14,15 Clearly, the recent surge of NLO studies on the halide perovskites indicates their great potential as active components in optoelectronic devices with the added advantage of cost-effective fabrication.

Especially, nonlinear perovskite

absorbers could be of significant use for multiphoton microscopy and spectroscopy,19,20 microfabrication,21,22 and optical limiting applications.23 Here we show anomalous multiphoton absorption behavior of CsPbBr3. Specifically, this all-inorganic perovskite exhibits bandgap anomaly stemming from significant mismatch between the “fundamental gap ( )” (determined by absorption measurement) and the “optical gap ( )” 3



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(by PL measurement), in which the latter is larger than the former due to the corresponding energy level lying above the conduction-band (CB) minimum. This atypical situation leads to so-called “above-bandgap emission”, which is rather ubiquitous in halide perovskites.9,24,25 We used a CsPbBr3 single crystal grown by a Bridgman method (see Methods) for studying this universal bandgap anomaly (Figure 1) at room temperature. The most striking effect is that we observe 3PA behavior even when the input photon energy, ℏ , is tuned for two-photon resonance with the fundamental gap, i.e., 2ℏ = , where ℏ is the Planck constant.

We

therefore monitored the wavelength-dependent MPA response and subsequent PL emission by scanning 2ℏ towards and beyond in order to investigate the 3PA-2PA crossover regime. The corresponding MPA dispersion with explicit polarization dependence was explained by twoband models15−17 and relevant selection rules.26–28 Our results imply that optical transition across the fundamental gap is strictly two-photon forbidden in this semiconductor, and therefore, the MPA order should be determined with respect to , not . The red trace in Figure 1 is the PL spectrum obtained under one-photon absorption (1PA) at =355 nm, overlaid with the absorption spectrum (black trace) obtained by UV-vis-NIR spectroscopy.25 Obviously, the absorption edge that defines the fundamental gap ( = 2.25 eV) lies ~0.1 eV below the PL peak ( = 2.35 eV). Recent theoretical studies on the origin of this above-bandgap PL in CsPbBr3 suggest defect states associated with the Br vacancy (VBr), existing above the CB edge.25,29 This has not yet been experimentally proven, and therefore, on a tentative bases we take the observed PL peak to be assigned to bound excitonic recombination. This implies that a photo-excited electron is quickly trapped by a VBr site upon optical excitation and eventually forms a bound exciton with a hole in the valence band (VB).

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population and relaxation dynamics of optical excitation are discussed in Section S1 of Supporting Information (SI).

Figure 1. Absorption (black) and PL (red) spectra of CsPbBr3 at room temperature. Mismatch (~0.1 eV) between the absorption edge (black dashed line) and the major PL peak (red dashed line) is evident and indicated by the arrow.

According to the measured bandgap energy of = 2.25 eV (or the corresponding wavelength = 550 nm), the 3PA and 2PA bands are predicted to span over the following ranges; 0.75 eV ℏ 1.125 eV (1650 nm 1100 nm) and 1.125 eV ℏ 2.25 eV (1100 nm 550 nm), respectively. Then, excitation by fundamental Nd:YAG (neodymiumdoped yttrium aluminum garnet) radiation at ℏ = 1.165 eV ( =1064 nm) should lead to 2PA of the crystal. Surprisingly, however, the intensity dependence indicates that 3PA actually occurs. Figure 2a shows the PL spectra from CsPbBr3 plotted as a function of incident pulse energy in the range of = 15.0 J–32.5 J – see Section S1 in SI for the spectral feature of the 5



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3PA-induced PL.

The corresponding spectrally integrated PL counts (dots) vs. the pulse

intensity are plotted in Figure 2b. The red trace is a cubic fit, thereby unambiguously confirming the case for 3PA.

Figure 2. (a) PL spectra under excitation at = 1064 nm for several pulse energies up to 32.5 J. (b) Corresponding PL counts (dots) as a function of intensity, fit by the cubic dependence (red), thereby confirming 3PA. The inset schematically illustrates the 3PA-induced PL process. (c) PL spectra under excitation at = 1000 nm for several pulse energies up to 15.0 J. (d) Corresponding PL counts (dots) as a function of intensity, fit by the quadratic dependence (red), thereby confirming 2PA. The inset schematically illustrates the 2PA-induced PL process.

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In fact, we confirmed that this unusual 3PA starts from = 1100 nm, which is the 2PAonset wavelength based upon = 2.25 eV, up to = 1055 nm that becomes two-photon resonant with = 2.35 eV (Section S2 in SI). A possible scenario for this apparent 3PA behavior is 2PA to the CB edge subsequently followed by excited-state absorption.30 This twostep process requires the initial population of carriers by 2PA at low excitation and a gradual shift to 3PA by additional transition to the excited state upon increasing the excitation intensity. However, no such trend in the MPA order was observed (Figure S3). The observed 3PA behavior persistent from the low-intensity regime then indicates that direct transition to the CB edge via 2PA must be strictly forbidden, although it is allowed under ordinary 1PA (Figure S2). As shown in the inset of Figure 2b, the CB edge is a “virtual state” in this case and it is represented by the dashed line to serve as a stepping stone for 3PA. Considering the range for the anomaly, the key to understanding of this 3PA is to recall the mismatch between and

arising from the VBr level that drastically alters the 2PA selection rules as detailed below. According to the 2PA selection rules26,27 for CsPbBr3 having the orthorhombic (Pnma) crystal symmetry, band-to-band transition can be represented by the linear combination of , , , and ; see Section S3 in SI for each component explicitly expressed in terms of the input polarization vectors, ( = 1 or 2). Clearly 2PA is nonzero when and coincide. However, the presence of Br vacancy centers leads to ≠ so that 2PA across contains the matrix element proportional to × only, rendering 2PA inactive under the degenerate scheme ( = ≡ ); here × corresponds to the second term of , , and in eq S3, respectively. The modification of the band structure by the extrinsic defect level lying close 7



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to the CB edge therefore yields the 2PA onset that must be defined in terms of , where the corresponding matrix elements contain the nonzero 2PA terms in eq S4. Therefore, 3PA occurs for 2ℏ and 2PA for 2ℏ ( = 527.5 nm). This is actually consistent with the intensity dependence at the 3PA-2PA boundary ( = 1055 nm), partially having 3PA and 2PA characteristics (Figure S7) together with the robust 2PA behavior for 1055 nm (Figure S6). For example, Figure 2c shows the PL spectra obtained under several excitation levels at = 1000 nm (2ℏ = 2.48 eV ). In Figure 2d the corresponding spectrally integrated PL counts (dots) are plotted as a function of input intensity. The red curve is the power-law fit, yielding the power exponent, # = 2.0, which clearly corresponds to the 2PA case. The inset schematically shows excitation by 2PA and subsequent relaxation when the input photon energy is two-photon resonant with . We determined the corresponding values of the 3PA coefficient, $ , and the 2PA coefficient, β, by monitoring the attenuation of the fundamental beam by CsPbBr3 as a function of input intensity under far-field transmission geometry. In our experiments, we varied the input intensity (pulse energy per unit time per unit area), &', by adjusting the transmission angle of a half-wave plate while fixing the sample position, ( = 0.254 cm, (Methods). The dots in Figure 3 correspond to the plots of input pulse energy, ) ', versus output pulse energy, * ', at (a) = 1064 nm (3PA) and (b) = 1000 nm (2PA), respectively. The black lines in Figures 3a and 3b represent the case when fundamental depletion is absent ($ = 0 and β = 0, respectively), i.e., input = output. Any deviation from the unit slope obtained from the ratio, * '/) ', is therefore the measure of MPA, which corresponds to the normalized transmittance throughout the sample thickness (, ≈ 1 mm) via 3PA and 2PA:31

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5A ln 891 : ; '< => : ;'< => ? ,B,

5A ln81 : D ' expHB ? ,B .

=

12⁄3 '

./ '

=

12⁄3 C'

.0 '

.0 '

@

./ '

3

3

@

(1)

(2)

Figure 3. ) ' vs * ' at (a) =1064 nm and at (b) = 1000 nm. The MPA effect is evident upon increasing the pulse energy as the data points deviate gradually from the black line, which corresponds to the case for no MPA. The red curves are fits by numerically solving eqs 1 and 2.

In eqs 1 and 2, the intensity-dependent parameters are defined by ;' ≡ 2$,IJJ ⁄ &' and L D' ≡ K&',IJJ , where the effective thicknesses ,IJJ = 81 H expH2M,?/2M ≅ 0.034 cm L and ,IJJ = 81 H expHM,?/M ≅ 0.054 cm were determined by using the linear attenuation

coefficient, M, of the fundamental beam.8,9,32 By incorporating &' in the numerical evaluation of eqs 1 and 2 with each MPA coefficient being the single fit parameter, the red curves were

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generated with $ = 0.16O0.04 cm3/GW2 and K = 5.0O0.5 cm/GW, respectively. The $ value determined at =1064 nm agrees well with our previous result.8 The K value determined at =1000 nm is also reasonable within the two-band model,17,18 when compared with K = 8.6 cm/GW at = 800 nm of CH3NH3PbBr3,7 which has = 2.21 eV.

Figure 4. (a) PL spectra under MPA for = 960 nm−1064 nm. (b) K determined by the PLbased WDZNS (dots). The red curve corresponds to the two-band model with P = 8200 and = 2.35 eV. A slight mismatch between the data points and the theory near the 2PA onset is attributed to the contribution from 3PA.

Figure 4a shows the observed PL spectra when was varied from 1064 nm to 960 nm with the pulse energy fixed at 10 J. Since the carrier generation rate, Q = K& ⁄2 : $& ⁄3, is proportional to the PL counts measured at each , the corresponding PL counts directly reflect K and/or $ within our experimental range that includes the 3PA-2PA boundary. Figure 4b shows the wavelength dependence of the spectrally integrated PL counts (dots) derived from Figure 4a, but scaled properly in accordance with the absolute data (K = 5 10


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cm/GW) determined at = 1000 nm. Therefore, Figure 4b corresponds to the absolute MPA dispersion. This PL method was previously employed to determine 3PA dispersion8 of CsPbBr3 in the range of 1100 nm–1700 nm as well as 2PA dispersion of CdTe based on wavelengthdependent Z-scan nonlinear spectroscopy (WDZNS).32 The red curve in Figure 4b is the theoretical 2PA dispersion calculated from a conventional two-band model using the Kane parameter, P = 8200, to fit the data:16–18

K = K SB =

TU

V.WX

9.

Y = P [3 .Z\

Z WX

>=\/3 >]

cm/GW,

(3)

where A ≈ 21 eV is nearly a material-independent constant, bA is the refractive index, and B is the dispersion parameter defined by = 2.35 eV in this case. Note that CsPbBr3 has a rather high P value, since the theoretical P value for a direct-gap semiconductor typically ranges from 1940 to 5200.17,32 This trend was also observed from our previous study on the 3PA efficiency which is 2–3 times higher when compared with the typical two-band model for 3PA.8 This implies that CsPbBr3 is a good multiphoton absorber. Lastly, the polarization dependence of MPA was investigated by monitoring the spectrally integrated PL counts as a function of polarization angle, c. Figure 5 shows the polarization dependence of (a) 3PA at = 1064 nm and (b) 2PA at = 1000 nm, respectively. The red curves are the fits based on 3PA,28 and 2PA selection rules,26,27 where the corresponding dynamical parameters were properly chosen to account for the orthorhombic crystal symmetry of CsPbBr3. As detailed in Section S3 of SI, under our excitation geometry, the polarization dependence of 3PA apparently looks similar to that of 2PA although the corresponding mathematical expressions are different – see eq S2 and S4, respectively. The polarization 11



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dependence across the 3PA-2PA boundary was also probed (Figure S10). No essential change in the polarization dependence was observed within our experimental range; for example, the series of 2PA polarization dependence observed in the range of = 1000 nm–1055 nm can be explained with the same dynamical parameters.

Figure 5. Polarization dependence of (a) 3PA at = 1064 nm and (b) 2PA at = 1000 nm, respectively, along the (112) direction.

In conclusion, CsPbBr3 is a highly luminescent material under nonlinear absorption at room temperature, but exhibits the anomalous MPA order as characterized by our wavelengthdependent NLO spectroscopy. This anomaly is related to above-bandgap PL at 2.35 eV that lies above the fundamental gap, 2.25 eV. Although ordinary one-photon transition is allowed across the fundamental gap, the band-to-band transition is two-photon forbidden as confirmed by the 3PA behavior. The corresponding 3PA coefficient was measured to be $ = 0.16O0.04 cm3/GW2 at = 1064 nm. This unusual 3PA persists up to the optical gap, implying that the 2PA 12


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selection rules can be significantly altered by the extrinsic effect. We further probed the 2PA efficiency above the optical gap as a function of wavelength in order to determine the absolute 2PA dispersion. For instance, the measured 2PA coefficient is 5.0O0.5 cm/GW at = 1000 nm. We concluded that the perovskite semiconductor is a good multiphoton absorber directly based on the absolute magnitude of the 3PA and 2PA coefficients, which can be explained by the twoband model with a rather large Kane parameter.

We also experimentally investigated the

polarization dependence of MPA that agrees well with the theoretical prediction with consistently chosen dynamical parameters. Our study shows the intriguing MPA behavior of the all-inorganic perovskite, which is likely common to other perovskites including the emerging hybrid ones. The highly luminescent characteristic of CsPbBr3 under MPA at room temperature with marked polarization and wavelength dependence across the 3PA-2PA boundary indicates that it may be employed in MPA-related devices and applications.

METHODS Material Preparation. Our high-quality CsPbBr3 single crystal oriented along the (112) direction was prepared using a vertical Bridgman method. The detailed sample preparation and basic characterization including structural, optical, and thermoelectrical properties are reported elsewhere.8,25,33 NLO measurements. Our NLO experiments were conducted at room temperature utilizing WDZNS.32 The bulk single crystal was loaded into a sample holder that was mounted on a Zscan translation stage with extra X and Y control, where the corresponding confocal parameter

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(Rayleigh range) is ~0.07 cm and the beam waist at the focus is ~16 m. A train of 30-ps fundamental pulses ( = 960 nm–1100 nm) was produced from an optical parametric oscillator (OPO), which was synchronously pumped by the frequency-tripled output (355 nm) from an Nd:YAG laser with a repetition rate of 50 Hz. Primary wavelengths such as 355 nm, 532 nm, and 1064 nm were directly obtained from the Harmonic Unit (HU) pumped by the Nd:YAG laser.9 The polarization vector, = (e, g, b, of the incident beam was set parallel to the (11−1) direction of CsPbBr3. The pulse energy, ', was fine-tuned by the combination of a halfwave plate (HWP) and a linear polarizer (LP) with ' being the HWP angle before being focused onto the sample using a positive lens (h = 7.5 cm) with a spot size of ~57 m in Gaussian width. The corresponding sample position was ( = 0.254 cm away from the Z-scan focus. In order to minimize the reabsorption effect, the PL from the sample was collected in reflection geometry using a fiber-optic bundle which was coupled to a spectrometer equipped with a charge-coupled-device (CCD) camera (Figure S8). Thermal load to the sample, which can potentially cause a structural phase transition from orthorhombic to tetragonal or cubic phase, is negligible due to the slow repetition rate (50 Hz) of the laser. Rather than using conventional open-aperture Z-scan, we utilized the input-output technique to characterize $ and K; this method was employed to characterize the complete 3PA dispersion of CsPbBr3 for 1100 nm.8

For a given input wavelength, the sample

transmittance, ) ', was measured as a function of ' with a 5% neutral density filter (NDF) before the sample, thereby ensuring no MPA. This linear transmittance can be used as a reference for generating the normalized transmittance. With the same NDF placed after the sample, the sample transmittance in the nonlinear regime, * ', was measured, where we gradually varied ' starting from the lowest intensity. At low excitation levels, * ' = ) ' 14


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is expected. However, MPA would cause a gradual transmission loss in * ' when the input intensity increases.

Thus, the ratio * '/) ' is the normalized transmittance that

corresponds to eqs 1 or 2 depending on the MPA order. The wavelength-dependent MPA efficiency was compared by monitoring the resulting PL counts as was tuned within our experimental range with the input intensity being kept constant. The method is similar to PL excitation spectroscopy but it takes place under 3PA or 2PA. Polarization dependence of 3PA and 2PA along the (112) direction was also probed by monitoring the resulting PL counts when the polarization vector was rotated: Without the LP, rotating the HWP by ' rotates the polarization vector by c = 2'. The measurement was carried out employing transmission geometry because the reflection mode using a beam splitter (BS) can lead to erroneous polarization dependence; the reflectance of the BS has strong polarization dependence. ASSOCIATED CONTENT AUTHOR INFORMATION Corresponding Authors: Yong Soo Kim and Joon I. Jang * Email: [email protected] (Y. S. Kim) & [email protected] (J. I. Jang). Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS The work was supported by the Basic Science Research Program (2017R1D1A1B03035539 and

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2015R1D1A3A03019609), Priority Research Centers Program (2009-0093818), and the Basic Research Lab Program (2014R1A4A1071686) through the National Research Foundation of Korea (NRF), funded by the Korean government. C. C. S and M. G. K. acknowledges support from the Office of Naval Research (Grant No. N00014-17-1-2231). Supporting Information Population and relaxation dynamics, intensity-dependent PL across the 2PA onset, and MPA selection rules

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third-order

optical

nonlinearity

in

the

layered

perovskite-type

material

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C.; Wibowo, A. C.; Chung, D. Y.; Freeman, A. J. et al. Crystal growth of the perovskite semiconductor CsPbBr3: A new material for high-energy radiation detection. Cryst. Growth Des. 2013, 13, 2722−2727.

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Figure 1. Absorption (black) and PL (red) spectra of CsPbBr3 at room temperature. Mismatch (~0.1 eV) between the absorption edge (black dashed line) and the major PL peak (red dashed line) is evident and indicated by the arrow. 80x61mm (300 x 300 DPI)


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Figure 2. (a) PL spectra under excitation at λ= 1064 nm for several pulse energies up to 32.5 µJ. (b) Corresponding PL counts (dots) as a function of intensity, fit by the cubic dependence (red), thereby confirming 3PA. The inset schematically illustrates the 3PA-induced PL process. (c) PL spectra under excitation at λ= 1000 nm for several pulse energies up to 15.0 µJ. (d) Corresponding PL counts (dots) as a function of intensity, fit by the quadratic dependence (red), thereby confirming 2PA. The inset schematically illustrates the 2PA-induced PL process. 159x128mm (150 x 150 DPI)



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Figure 3. E_b (ϕ) vs E_a (ϕ) at (a) λ=1064 nm and at (b) λ= 1000 nm. The MPA effect is evident upon increasing the pulse energy as the data points deviate gradually from the black line, which corresponds to the case for no MPA. The red curves are fits by numerically solving eqs 1 and 2. 159x80mm (150 x 150 DPI)


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Figure 4. (a) PL spectra under MPA for λ= 960 nm−1064 nm. (b) β(λ) determined by the PL-based WDZNS (dots). The red curve corresponds to the two-band model with K= 8200 and E_op= 2.35 eV. A slight mismatch between the data points and the theory near the 2PA onset is attributed to the contribution from 3PA. 159x63mm (150 x 150 DPI)



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Figure 5. Polarization dependence of (a) 3PA at λ= 1064 nm and (b) 2PA at λ= 1000 nm, respectively, along the (112) direction. 159x64mm (150 x 150 DPI)


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Multiphoton Absorption Order of CsPbBr3 As Determined by

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