Use Of Excitonic Absorption And Its Effect On The Environment

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In our previous study [1], bandgaps of the title perovskites were roughly determined by extrapolating their absorption edges to the photon-energy axis, yielding 1.50 eV (n = ), 1.91 eV (n = 4), 2.03 eV (n = 3), 2.17 eV (n = 2), and 2.43 eV (n = 1), respectively. However, the presence of excitonic absorption slightly below the fundamental band edge caused some uncertainty in the bandgap estimation of each compound. This effect could be most serious for the bulk perovskite (n = ) because the exciton line is not clearly resolved from the band edge; while the stability of excitons at room temperature is still under debate, the basic optical response of MAPbI3 is excitonic. In order to evaluate the accurate dependence of χ^((3)) on the bandgap, E_g, in this work we estimated E_g of our perovskites by eliminating the excitonic contribution, which can be modeled with a Gaussian peak. The spectral location of the exciton peak was determined to match with the low-energy onset of the absorption edge while consistently keeping the width of the exciton peak ~52 meV for all the 2D perovskites and ~43 meV for MAPbI3. These peaks are shown in Figure S1 as solid curves for (a) n = , (b) n = 4, (c) n = 3, (d) n = 2, and (e) n = 1, respectively, overlaid with the experimental absorption spectra (colored traces).
Since the perovskites are direct-gap semiconductors [1], we plot 〖α(E)〗^2 E^2 as a function of photon energy, E, in Fig. S2(a) where α(E) is obtained by subtracting the

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