Absorption F-sum Rule for the Exciton Binding. Energy in Methylammonium Lead Halide. Perovskites.

Transcription

1 Supporting information for: Absorption F-sum Rule for the Exciton Binding Energy in Methylammonium Lead Halide Perovskites. Nicola Sestu, Michele Cadelano, Valerio Sarritzu, Feipeng Chen, Daniela Marongiu, Roberto Piras, Marina Mainas, Francesco Quochi, Michele Saba*, Andrea Mura, Giovanni Bongiovanni*. Dipartimento di Fisica, Università degli Studi di Cagliari, I Monserrato, Italy. AUTHOR INFORMATION Corresponding Authors *M.S.: *G.B.: S1

2 AFM scans. Surface morphology was characterized by atomic force microscopy (AFM) with a NT-MDT Solver P47H-Pro in semi contact mode by a high-resolution non-contact silicon tip nm 10µm 0.00 nm FIGURE S1. Atomic Force Microscopy image of the surface of a MAPbBr 3 film employed for the optical analysis. The measured rms surface roughness is 15 nm. S2

3 60.00 nm 10µm 0.00 nm FIGURE S2. Atomic Force Microscopy image of the surface of a MAPbI 3 film employed for the optical analysis. The measured rms surface roughness is 4 nm. XRD patterns. Structural characterization was carried out by analyzing the X-ray diffraction patterns recorded by a Bruker D8-Discover diffractometer for thin films with parallel beam geometry and Cu Kα wavelength. Symmetric ω-2θ scans were obtained using a step size of 0.02 and time per step of 4 s. S3

4 100 CH 3 NH 3 PbBr 3 (Pm-3m) Intensity (a.u.) theta (deg) FIGURE S3. XRD pattern for a MAPbBr 3 film. PbI CH 3 NH 3 PbI 3 (I4/mcm) Intensity (a.u.) theta (deg) FIGURE S4. XRD pattern for a MAPbI 3 film. S4

5 F-sum rule for GaAs. In order to validate eh f-sum rule method to extract the exciton binding energy from absorption spectra, we applied our analysis to the most studied semiconductor in optoelectronics, i.e. GaAs, where the accepted value for the exciton binding energy is 4.2 mev, as measured without ambiguities from low-temperature data, where the exciton and continuum contributions are fully resolved (see figure S5). FIGURE S5. Pure GaAs absorption spectrum measured at T=1.2 K, reproduced from ref.1 Epitaxial GaAs grows along the c-axis and to account for degeneracy in the GaAs valence band, the so-called heavy- and light-hole bands, one needs to introduce a factor in the Elliott formula that weights the different contributions of the two bands: 2 1 S5

6 with,, Symbols are as follows: 1.26., reduced mass between conduction electron and valence heavy-hole;, reduced mass between conduction electron and valence light-hole; reduced excitonic mass. We employed the following values: m c =0.072 m 0 ; m hh =0.68 m 0 ; m lh =0.12 m 0, from ref m 0,, from ref.3 To perform the analysis, absorption data were extracted from published pdf files through the CurveSnap software, freely available online. We have chosen a classic paper on pure GaAs 1 (particularly a thinner film than the one in figure S5, so that the absorption peaks were not saturated) and a recent one on lightly doped GaAs 4, to show that the method does not depend on the linewidth of the exciton peak. Figure S6 show the spectra and the continuum contributions we considered in the analysis (pure GaAs: =5.5 mev; lightly-doped GaAs: =8.1 mev, 0.94 ev -1 ). The result from the application of the f-sum rule is in both cases 4.2±0.1 mev. S6

7 FIGURE S6. F-sum rule analysis applied to data from ref.1 (panel a) and ref.4 (panel b). REFERENCES (1) Fehrenbach, G. W.; Schäfer, W.; Ulbrich, R. G. Excitonic Versus Plasma Screening in Highly Excited Gallium Arsenide. Journal of Luminescence 1985, 30, (2) Ehrenreich, H. Band Structure and Electron Transport of GaAs. Phys. Rev 1960, 120, (3) Baldereschi, A.; Lipari, N. O. Direct Exciton Spectrum in Diamond and Zinc-Blende Semiconductors. Phys. Rev. Lett. 1970, 25, (4) Mui, S.; Ramaswamy, K.; Stanton, C. J.; Crooker, S. A.; Hayes, S. E. Manifestation of Landau Level Effects in Optically-Pumped NMR of Semi-Insulating GaAs. Physical Chemistry Chemical Physics 2009, 11, S7