Supporting Information

Transcription

1 Supporting Information Light-Matter Interactions in Cesium Lead Halide Perovskite Nanowire Lasers Kidong Park, Jong Woon Lee, Jun Dong Kim, Noh Soo Han, Dong Myung Jang, Seonghyun Jeong, Jeunghee Park*, and Jae Kyu Song*, Department of Chemistry, Korea University, Jochiwon , Korea Department of Chemistry, Kyung Hee University, Seoul , Korea *Corresponding authors: address Contents I. Experimental details II. Exciton-polariton model III. Degree of polarization IV. Supporting Figures Figures S1-S12 V. References S1

2 I. Experimental details 1. Materials Commercially available PbCl 2 powder (Aldrich), PbBr 2 powder (Aldrich), PbI 2 powder (Aldrich), CsCl powder (Aldrich), CsBr powder (Aldrich), and CsI powder (Aldrich) were used without further purification. 2. Synthesis of CsPbX 3 perovskite NWs The PbX 2 and CsX (X = Cl, Br, or I) powders were placed inside a quartz tube reactor. The silicon (Si) substrate was positioned at a distance of 10 cm away from the powder source. Argon gas was made to flow continuously at a rate of 200 sccm through the reactor. The temperature of the powder sources was set at C and that of the Si substrate was set at approximately C. 3. Characterization The structures and compositions of the nanowires were analyzed by scanning electron microscopy (SEM, Hitachi S-4700), field-emission TEM (FEI TECNAI G kv), highvoltage TEM (HVEM, JEOL JEM ARM 1300S, 1.25 MV), and energy-dispersive X-ray fluorescence spectroscopy (EDX). High-resolution XRD analyses were performed using monochromatic radiation at 9B beam line of the Pohang Light Source (PLS) with monochromatic radiation. 4. Lasing detection For steady-state and time-resolved emission studies, an isolated single nanowire was selectively excited through an ultraviolet microscope objective by the second harmonic (355 nm) of a cavity-dumped oscillator (Mira/PulseSwitch, Coherent, 100 khz, 150 fs). The excitation diameter of the 355-nm pulses was about 50 m for homogeneous excitation of the single nanowire. The normal photoluminescence and lasing emissions were collected using the same objective and filtered using a rotatory linear polarizer, which were spectrally resolved using a monochromator, detected using a photomultiplier, and recorded using a time-correlated single photon counter (PicoHarp300, PicoQuant). S1 II. Exciton-polariton model The spectral spacing of the Fabry Pérot modes in the nanowires is explained based on the exciton-polariton model. S2-S5 The energy of the polariton, E(, k), is described by S2

3 ck E(, k) (S-1) ( ) where is the angular frequency, ( ) is the dielectric function of the medium, and k is k 2 x k 2 y k 2 z. The traveling wave in the exciton-polariton model is different from the classical wave in a vacuum by the factor of 1/ ( ). It is noted that ( ) in the exciton-polariton regime depends on the frequency, S2,S3 2 2 L T ( ) (1 ) 2 2 i T (S-2) where is the background dielectric constant, is the damping constant, is the prefactor, and T and L are the transverse and longitudinal resonance frequencies, respectively. For the vanishing damping condition with ħ L = 2.37 ev and ħ( L - T ) = ev, ( ) increases steeply with approaching the resonance energy. As a result, the dispersion curve of the polariton deviates from the photonic model (Figure S8). Hence, the group velocity of the confined photons in the nanowire decreases, which appears as the enhancement of the group refractive index of the nanowires. S4,S5 The non-classical, non-identical spectral spacing of the Fabry Pérot modes can be explained by the energy-wavevector diagram of the exciton-polariton (Figure 4e). The mode spacing in the high energy regime is smaller, because the mode in this regime energy is closer to the exciton resonance than are the other modes. III. Degree of polarization To observe the degree of polarization (DOP), the emission from single nanowires lying on a substrate is collected through a microscope objective with a high numerical aperture (Figure S10). The large collection angle of the objective assures that a part of the emission with the wavevector (k) parallel to the long-axis ( -emission) was observed, S6,S7 which is expected to exhibit a high gain in the geometry of the nanowires. In the rectangular waveguide approximation, the polarization of the fundamental transverse mode in the -emission is transverse-electric-like with a dominant E x component (Figure S10), S8 presumably due to the coupling with the substrate. The electric field parallel to the substrate plane (E x ) is distinguished from the perpendicular one (E y ) by the rotatory polarizer (Figure S10). S7 The lasing modes in S3

4 Figure 5 show the predominant E x component, where the polarizer angle to detect the E x component is denoted as 0 o. DOP is quantitatively described by the polarization ratio ( ), S7 I E x I E y (S-3) I I E x E y where I and I E are the collected intensities with the polarizer aligned to detect E y x and E y E x components, respectively. The DOP values of the three modes are fitted using of ~0.95 (Figure S11), which is indicative of the almost linearly polarized (E x ) waveguide mode. The DOP values of the modes are similar (Figure S11), which indicate that these modes belong to the same transverse mode, i.e., the fundamental transverse mode. Therefore, the non-classical, nonidentical spectral spacing between the lasing modes is from the dispersion curve in nanowires due to the strong light-matter interaction near the exciton resonance energy, rather than the simultaneous appearance of two different transverse modes. S4

5 IV. Supporting Figures Figure S1. XRD patterns of the inorganic perovskite nanowires. The peaks of CsPbCl 3, CsPbBr 3, and CsPbI 3 are indexed using the following reference values; a = Å and c = Å for tetragonal phase CsPbCl 3 (JCPDS ); a = Å, b = Å, and c = Å for orthorhombic phase CsPbBr 3 ; S9 and a = Å for cubic phase CsPbI 3. S10 S5

6 Figure S2. (a) Pseudo-cubic unit cell of CsPbBr 3 (a = 5.8 Å) is compared to orthorhombic unit cell of CsPbBr 3 (a = Å, b = Å, c = Å); S11 the parameters a and c of the orthorhombic unit cell are directed along diagonals of the faces of elementary cube and the parameter b is close to twice the edge of the cube. The table shows the values of the lattice parameters and the correlation index between the orthorhombic and cubic unit cells. The lattices of the orthorhombic and cubic unit cells are indexed using the subscript O and C, respectively. The [101] O direction of the orthorhombic unit cell is equivalent to [100] C of the cubic unit cell. The [121] O direction of the orthorhombic unit cell corresponds to [110] C of the cubic unit cell. S6

7 Figure S3. (a) The diameter of the excitation pulses is ~50 m at the substrate, which ensures the homogeneous excitation of the single nanowires. (b) The log-scale plot of the emission intensity indicates the S-shaped curve as a function of the excitation intensity. Figure S4. The lasing spectra of single CsPbBr 3 nanowires with lengths of (a) 14.7 m and (b) 2.4 m. S7

8 Figure S5. The photoluminescence intensities of a single (a) CsPbCl 3, (b) CsPbBr 3, and (c) CsPbI 3 nanowire are fitted with the absorption cross-sections ( ). Figure S6. (a) Time-resolved emission profiles of single inorganic perovskite nanowires at an excitation intensity of 0.1 J/cm 2. (b) Time-resolved emission profiles of single inorganic perovskite nanowires at an excitation intensity of 10 J/cm 2. S8

9 Energy (ev) Mode Spacing (mev) Reciprocal Nanowire Length ( m -1 ) Figure S7. The mode spacing of the Fabry Pérot modes in lasing CsPbBr 3 nanowires changes linearly with the inverse of the nanowire length, while the mode spacings are fitted with n = photon in cavity materials (n = 2.3) polariton k z [10 7 m -1 ] Figure S8. Comparison of the dispersion curve of the traveling wave in the exciton-polariton model (blue) to that in the classical model (red). S9

10 Figure S9. The lasing emission spectrum (left) matches the dispersion curve in the energy wavevector diagram of the exciton-polariton model (right). The comparison between the lasing emission spectrum and the dispersion curve of (a) long CsPbBr 3 nanowire (14.7 m), (b) short CsPbBr 3 nanowire (2.4 m), (c) CsPbCl 3 nanowire, and (d) CsPbI 3 nanowire. S10

11 Figure S10. (a) The electric fields parallel (E x ) and perpendicular (E y ) to the substrate (x-z) plane are shown with the wavevector (k) parallel to the long-axis. The inset shows a schematic of the polarization of the fundamental transverse mode (transverse-electric-like with the dominant E x component) adapted from ref. S8. (b) E x is separated from E y using a rotatory polarizer. S11

12 Intensity (a.u.) mode A mode B mode C Angle (degree) Figure S11. The DOPs in modes A, B, and C are all fitted using of S12

13 Figure S12. Integrated emission intensities of the inorganic perovskite nanowire lasers for a pulsed excitation with a high repetition rate, while being exposed to ambient atmospheric conditions at 1.2 P th. S13

14 V. References S1. Park, Y. J.; Oh, J. H.; Han, N. S.; Yoon, H. C.; Park, S. M.; Do, Y. R.; Song, J. K. Photoluminescence of Band Gap States in AgInS 2 Nanoparticles. J. Phys. Chem. C 2014, 118, S2. Rühle, S.; van Vugt, L. K.; Li, H. -Y.; Keizer, N. A.; Kuipers, L.; Vanmaekelbergh, D. Nature of Sub-Band Gap Luminescent Eigenmodes in a ZnO Nanowire. Nano Lett. 2008, 8, S3. Vanmaekelbergh, D.; van Vugt. L. K. ZnO Nanowire Lasers. Nanoscale, 2011, 3, S4. van Vugt, L. K.; Piccione, B.; Agarwal, R. Incorporating Polaritonic Effects in Semiconductor Nanowire Waveguide Dispersion. Appl. Phys. Lett. 2010, 97, S5. van Vugt, L. K.; Piccione, B.; Cho, C. H.; Nukala, P.; Agarwal, R. One-Dimensional Polaritons with Size-Tunable and Enhanced Coupling Strengths in Semiconductor Nanowires. PNAS. 2011, 108, S6. Johnson, J. C.; Yan, H.; Yang, P.; Saykally, R. J. Optical Cavity Effects in ZnO Nanowire Lasers and Waveguides. J. Phys. Chem. B 2003, 107, S7. Li, H.-Y.; Rühle, S.; Khedoe, R.; Koenderink, A. F.; Vanmaekelbergh, D. Polarization, Microscopic Origin, and Mode Structure of Luminescence and Lasing from Single ZnO Nanowires. Nano Lett. 2009, 9, S8. Zhu, H.; Fu, Y.; Meng, F.; Wu, X.; Gong, Z.; Ding, Q.; Martin V. Gustafsson, M. V.; Trinh, M. T.; Jin, S.; Zhu, X-Y. Lead Halide Perovskite Nanowire Lasers with Low Lasing Thresholds and High Quality Factors. Nat. Mater. 2015, 14, S9. Møller, C. N. Crystal Structure and Photoconductivity. Nature 1958, 182, S10. Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Krieg, F.; Caputo, R.; Hendon, C. H.; Yang, R. X.; Walsh, A.; Kovalenko, M. V. Nanocrystals of Cesium Lead Halide Perovskites (CsPbX 3, X = Cl, Br, and I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut. Nano Lett. 2015, 15, S11. Stoumpos, C. C.; Malliakas, C. D.; Peters, J. A.; Liu, Z.; Sebastian, M.; Im, J.; Chasapis, T. C.; Wibowo, A. C.; Chung, D. Y.; Freeman, A. J.; Wessels, B. W.; Kanatzidis, M. G. Crystal Growth of the Perovskite Semiconductor CsPbBr 3 : A New Material for High-Energy Radiation Detection. Cryst. Growth Des. 2013, 13, S14