Supporting Information. by Wavelength-Dependent Nonlinear Optical. Spectroscopy

Transcription

1 Supporting Information 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 * yskim2@ulsan.ac.kr (Y. S. Kim) & jjcoupling@sogang.ac.kr (J. I. Jang). S1

2 S1. Population and relaxation dynamics in CsPbBr3 CsPbBr3 is highly luminescent under optical excitation at room temperature, which was previously interpreted as free excitonic emission. 1-3 Our observation of the above-bandgap photoluminescence (PL) at 2.35 ev however demonstrates that transition can be far from ordinary. This is also supported by some first-principles calculations, 4,5 indicating the significant role of the Br vacancy (VBr) level that lies ~0.1 ev above the conduction-band (CB) minimum. In brief, when optical excitation is over the VBr level by one-photon absorption (1PA) (Figure S1a), the mechanism for the above-bandgap PL can be envisioned as follows. Figure S1. Schematic representations for the excitation and relaxation dynamics under 1PA, when the incident photon energy is tuned (a) above and (b) below the VBr level, lying 0.1 ev above the CB minimum. The optical gap (E op ) is defined the energy difference between VB and VBr. CsPbBr3 absorbs a photon by elevating an electron from the valence band (VB) to an excited state (ES) in the conduction band (CB). Upon thermal relaxation into the crystal lattice by phonon scattering (dashed arrows), the electron is captured by a localized Br vacancy center. S2

3 Finally, the captured electron binds with a hole in the VB to form a bound exciton. Radiative recombination of the bound exciton yields above-bandgap PL emission (green) at 2.35 ev. Similar emission was also observed in CsPbCl3 and MAPbX3 (X = Cl, Br, I). 5,6 CsPbBr3 also yields bandto-band PL (yellowish green) because phonon scattering to the CB minimum is also possible; see for example the minor peak (~2.25 ev) of the blue trace in Figure S4. The VBr level is also responsible for anomalous multiphoton absorption (MPA) as discussed in the main text. If the photon energy is tuned close to the fundamental bandgap (E g ) but below the VBr level, the resulting PL should be basically band-to-band (Figure S1b). For example, Figure S2a shows several PL spectra when the crystal was excited at λ = 532 nm (2.33 ev < E op ). The PL spectra were obtained using transmission geometry to suppress the excitation light. This collection geometry slightly modifies the PL spectra by the effect of PL reabsorption 7,8 throughout the macroscopic sample thickness d 1 mm. We found that this effect causes apparent redshift of ~5 nm in the PL spectra (the maximum PL position ~555 nm) in Figure S2a. Figure S2. (a) PL spectra under several excitation levels at λ = 532 nm. (b) Corresponding PL counts vs. input intensity, indicating 1PA. (c) Isotropic PL polarization dependence under 1PA. S3

4 Figure S3. PL counts vs. pulse energy at (a) λ = 1100 nm, (b) λ = 1090 nm, (c) λ = 1080 nm, and (d) λ = 1070 nm, respectively, superimposed by the cubic power fits (red curves). Figure S2b shows the corresponding intensity dependence of band-to-band PL emission. The linear fit (red line) to the data demonstrates that it corresponds to 1PA-induced PL emission. Furthermore, the PL does not have the polarization dependence as shown in Figure S2c, which is expected for 1PA in CsPbBr3. 9 Since 1PA occurs under excitation at λ = 532 nm, it is quite natural to expect 2PA when the crystal is excited at 1064 nm. Intriguingly, however, we found that 3PA occurs as confirmed by the cubic dependence in PL emission (Figure 2b). In fact, this MPA anomaly starts from the predicted 2PA onset wavelength (1100 nm) in terms of E g persisting up to λ = 1055 nm, which corresponds to the two-photon wavelength tuned to the optical gap (E op = 2.35 ev). For example, Figure S3 shows the PL counts as a function of input pulse energy when the sample was excited at (a) λ = 1100 nm, (b) λ = 1090 nm, (c) λ = 1080 nm, and (d) λ = 1070 nm, respectively. The corresponding intensity dependence agrees well with the 3PA case, where each red curve is the power-law fit, y = ax b, yielding the critical exponent of b = 3.0. S4

5 Figure S4. (a) Normalized PL spectra from CsPbBr3 at room temperature under 1PA (355 nm; blue), 2PA (1000 nm; red), and 3PA (1064 nm; black), respectively. The observed PL peak shift depends on the excitation order as a consequence of bandgap anomaly. (b) Comparison of PL spectra under 1PA and 3PA where the latter is scaled down to match with the shoulder peak, which corresponds to band-to-band transition. Figure S4a shows the normalized PL spectra from CsPbBr3 at room temperature obtained under 1PA (355 nm; blue), 2PA (1000 nm; red), and 3PA (1064 nm; black), respectively. The blueshift in the main PL peak was observed when excitation order is tuned from 3PA 2PA 1PA. While the 1PA-induced PL is dominated by the above-bandgap transition, the PL under 2PA or 3PA is essentially band-to-band, occurring across the fundamental bandgap; see for example Figure S4b that shows the PL spectrum under 3PA (black) properly scaled to match with the bandto-band component of the 1PA-induced PL (blue). The 2PA-induced PL is slightly skewed to the shorter wavelength compared with that under 3PA. This may arise from the Burstein-Moss effect 10 S5

6 where the lower-order process of 2PA generates a higher carrier density, thereby causing the blueshift. 9 Considering that excitation at = 1064 nm initially generates hot carriers via 3PA with the exactly same kinetic energy as that under 1PA ( = 355 nm = 1064 nm/3), it is quite intriguing that the 3PA-induced PL spectrum does not show above-bandgap emission. This implies that the resulting PL spectra can be different because of distinct selection rules associated with 1PA and 3PA processes, respectively. 11 In other words, the excited state by 3PA has a different symmetry that does not relax to the VBr state but directly to the CB minimum, thereby exclusively causing band-to-band transition. S6

7 S2. Intensity-dependent PL from CsPbBr3 across the 3PA-2PA boundary Figure S5. PL spectra under several different excitation energies at (a) λ = 1055 nm, (b) λ = 1045 nm, (c) λ = 1030 nm, and (d) λ = 1015 nm. The brightness of the PL gradually increases with blueshift when λ decreases, reflecting the efficiency of wavelength-dependent 2PA. S7

8 Figure S6. PL counts vs. pulse energy at (a) λ = 1055 nm, (b) λ = 1045 nm, (c) λ = 1030 nm, and (d) λ = 1015 nm, respectively. The red curves are generated with a power-law fit to each data, yielding the power exponent, b = 2.78 for (a) and 2.0 for (b) (d), respectively. The intermediate value of b = 2.78 at 1055 nm implies the partial contribution by 2PA and 3PA (see Figure S7). Figure S7. PL counts vs. pulse energy at λ = 1055 nm fit by simultaneous 2PA and 3PA effects. S8

9 S3. MPA selection rules for CsPbBr3 The polarization dependence of 3PA and 2PA was measured by monitoring the relative PL counts upon excitation in transmission geometry as a function of θ without the LP and BS in Figure S8; rotating the HWP by φ rotates the polarization vector by 2φ θ. The BS was removed because the BS efficiency is polarization dependent. In our previous work, 9 we reported erroneous 3PA polarization dependence at λ = 1200 nm as a result of using the BS: For instance, negligible 3PA at θ = 60 o 120 o in Figure 6 of ref 8 arose because of lower input introduced by inefficient transmission by the BS over that particular angle range. The correct polarization dependence of 3PA is shown in Figure S9 with suitable dynamical parameters; these were set to zero in ref 9. Figure S8. Schematic for the experimental setup; NDF (neutral density filter), HWP (half-wave plate), LP (linear polarizer), and BS (beam splitter). Both LP and BS were removed for polarization-dependence measurements. S9

10 When the Poynting vector points along the (112) direction, the polarization vector, ε = (l, m, n), of the input beam in our excitation geometry can be written as l cos θ cos θ 3 sin θ 2 ε = ( m) = ( ) ( sin θ) = ( cos θ 3 + sin θ 2) (S1) n cos θ 3 where θ is the angle between the polarization vector and the (11 1) crystal direction and related to the HWP angle by θ = 2φ. i) 3PA selection rules The detailed theoretical description of 3PA selection rules for CsPbBr3 having the orthorhombic space group (D 2h ) is reported in our previous work. 9 In brief, they are closely related to those for a higher-symmetry point group (O h ), but extra dynamical parameters are required to take into account anisotropy. The allowed three-photon transitions for CsPbBr3 are represented by Γ 4 and Γ 5 : 12,13 Γ 4 : μl 2 (l 2 + ) 2 + νm 2 (m 2 + ) 2 + n 2 (n 2 + ) 2, Γ 5 : l 2 (m 2 n 2 ) 2 + m 2 (n 2 l 2 ) 2 + n 2 (l 2 m 2 ) 2, (S2) where three dynamical parameters of, μ, and ν are incorporated in Γ 4 to account for the orthorhombic crystal symmetry. These parameters should be determined experimentally. Similar dynamical parameters are also required for Γ 5, but we found that a best fit was obtained by using Γ 4 transition only. Figure S9 shows a representative example of Γ 4 with = 0, μ = 0.648, and ν = 0.730, which best explains our observation Figure 5a in the main text. S10

11 Figure S9. 3PA polarization dependence associated with Γ 4 when the dynamical parameters are set to = 0, μ = 0.648, and ν = for the sample oriented along the (112) direction. Here 0 o corresponds to ε = (11 1). ii) 2PA selection rules For CsPbBr3 having the orthorhombic space group ( D 2h ), the allowed two-photon transitions are represented by 14,15 A g : (l 1 l 2 + λ 1 m 1 m 2 + λ 2 n 1 n 2 ) 2, B 1g : [(l 1 m 2 + m 1 l 2 ) + λ 3 (l 1 m 2 m 1 l 2 )] 2, (S3) B 2g : [(n 1 l 2 + l 1 n 2 ) + λ 4 (n 1 l 2 l 1 n 2 )] 2, B 3g : [(m 1 n 2 + n 1 m 2 ) + λ 5 (m 1 n 2 n 1 m 2 )] 2. The corresponding selection rules for the degenerate 2PA case, i.e., l 1 = l 2 = l, m 1 = m 2 = m, and n 1 = n 2 = n, are given by S11

12 A g : (l 2 + λ 1 m 2 + λ 2 n 2 ) 2, B 1g : 4l 2 m 2, (S4) B 2g : 4l 2 n 2, B 3g : 4m 2 n 2, where λ 1 and λ 2 are dynamical parameters that need to be determined experimentally. We found that all the components in eq S4 are required to consistently explain our 2PA data with a single set of values, λ 1 = and λ 2 = see Figure 5b in the main text and Figure S10. Figure S10. Polarization dependence at (a) 1015 nm, (b) 1030 nm, (c) 1045 nm, and (d) 1055 nm along the (112) direction. The single red curve determined at 1000 nm (Figure 5b in the main text) reasonably fit all the polarization dependence data. S12

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