Accelerated Carrier Relaxation through Reduced Coulomb Screening in Two-Dimensional Halide Perovskite Nanoplatelets

Transcription

1 Supporting Information Accelerated Carrier Relaxation through Reduced Coulomb Screening in Two-Dimensional Halide Perovskite Nanoplatelets Verena A. Hintermayr 1,2, Lakshminarayana Polavarapu 1,2, Alexander S. Urban 1,2,3*, Jochen Feldmann 1,2* 1 Chair for Photonics and Optoelectronics, Department of Physics, Ludwig-Maximilians-Universität München, Amalienstr. 54, Munich, Germany. 2 Nanosystems Initiative Munich (NIM) and Center for NanoScience (CeNS), Schellingstr. 4, Munich, Germany. 3 current address: Nanospectroscopy Group, Department of Physics, Ludwig-Maximilians-Universität München, Amalienstr. 54, Munich, Germany urban@lmu.de; feldmann@lmu.de

2 Supporting Note 1. The Elliott model To be more quantitative we analyse our linear absorption spectra by applying the Elliott formula 21,22 for 3D αα(ωω) = [AA Θ(ħωω EE GG )DD 3DD CCCC (ħωω)] ππππeeππππ sinh(ππππ) + AA EE BB 3DD 4ππ nn=1 nn 3 δδ ħωω EE GG + EE 3DD BB nn 2 and for 2D EE BB xx = ħωω EE GG ee ππππ αα(ωω) = [AA Θ(ħωω EE GG )DD 2DD CCCC (ħωω)] cosh(ππππ) + AA EE BB 2DD 4ππ δδ ħωω EE nn+ 1 GG + EE 2DD BB nn= nn In both formulas, the first term describes the absorption into the electron-hole pair continuum states, which is enhanced by the Coulomb interaction (Sommerfeld factor), while the second term describes the absorption into the series of bound electron-hole pair states (excitons). This model is applicable to systems with hydrogen-like excitons, also known as Wannier-Mott excitons, with excitonic Bohr radii aa BB much larger than the lattice constant of the crystal aa llllllttiiiiii. The Elliott-model reproduces the absorption spectra of halide perovskite nanoplatelets quite well and allows for locating the positions of the 1s exciton resonance and the onset of the continuum absorption. However, for the 2D case there are still some deviations, especially in the spectral region between the lowest exciton peak and the continuum onset, where the model predicts it to nearly drop to zero (compare Figure S1 in the Supporting Information). Considering that the nanoplatelet is only nm wide, and estimating the excitonic Bohr radius from the binding energy, via: aa BB 2 = ħ2 2μμEE BB, with μμ being the reduced mass of the electron-hole pair, we see that for aa BB = 1nnnn aa llllllllllllll = 0.66 nnnn, the condition of aa BB aa llllllllllll is not well fulfilled, likely signifying that the excitonic behavior will deviate from the hydrogen like approach

3 Figure S1 TEM images of 2D (3 ML) NPls. Observed at different magnifications, the images clearly show individual NPls and stacks of multiple NPls. Figure S2 TEM images of quasi-3d NPls. Observed at different magnifications, the lateral size of the quasi-3d NPls is similar to the 2D NPls, however the strong contrast indicates that they are significantly thicker.

4 Figure S3 Fitting of the Elliot model to absorption spectra. a,b, Measurement (black squares) and calculation according to Elliott model (green solid line) is shown for the quasi-3d (a) and 2D (b) case. In each case the contribution of the continuum and the first four excitonic peaks is considered for the calculation. Table S1. Laser fluences and cooling lifetimes of charge carriers in quasi-3d and 2D NPLs. Quasi- 3D 2D Laser fluence (kw/cm²) Cooling lifetime (ps) Laser fluence (kw/cm²) Cooling lifetime (ps) ± ± ± ± ± ± 0.01

5 Figure S4 Resonant excitation of the 1s exciton state. a,b, Transient of differential absorption at the energetic position of the 1s exciton of 3D (a) and 2D (b) NPls with time delays up to 2.5ps and 80ps, respectively. While in the 3D case the excitons rapidly dissociate into free electron-hole pairs within 200 fs (a) this does not occur for the 2D case (b). Instead, the resonantly excited excitons thermalize within 10 ps to larger KK xx,yy = 0 states. The excited carriers subsequently recombine in both cases.