Supporting Information: Room temperature optically tunability and ...
Supporting Information:
Room temperature optically tunability and inhomogeneous broadening in 2D-layered organicinorganic perovskite pseudobinary alloys. Gaëtan Lanty,1 Khaoula Jemli,1 Yi Wei,1,4 Joël Leymarie,2 Jacky Even,3 Jean-Sébastien Lauret,1 Emmanuelle Deleporte,*1
1
Laboratoire Aimé Cotton, Ecole Normale Supérieure de Cachan, CNRS, Université Paris-Sud, Bât 505 Campus
d’Orsay, 91405 Orsay, France
2
Institut Pascal, Clermont Université, CNRS and Université Blaise Pascal, 24 Avenue des Landais, 63177 Aubière
cedex, France
3
Université Européenne de Bretagne, INSA, FOTON, UMR 6082, 35708 Rennes, France
4
School of Physics and Optoelectronic Engineering, Dalian University of Technology, N° 2 Linggong Road,
Ganjingzi District, Dalian City, Liaoning Province, P.R. China
1
CONTENTS: Inhomogeneous broadening as a function of x for PhE-PbI4(1-x)Br4x P2 References…………..……………...…………...……………….…...
P3
In order to see if it is possible to account for the dissymmetry of the curve representing the inhomogeneous broadening of the excitonic lines of the alloy PhEPbI4(1-x)Br4x as a function of x (figure 4), we perform a refinement of the model by introducing a variation of Nexc as a function of x. Figure S1b shows the best fit we have obtained: to account for the dissymmetry, Nexc varies linearly with x, from 55 for x = 0 to 20 for x = 1. Figure S1a exhibits the fit of the experimental values of the bandgap in the framework of this calculation : it can be seen that, with these values of Nexc, a linear fit reproduces very well the variation of the bandgap as a function of x. Two parameters may play a role in the variation of the inhomogeneous broadening as a function of x : the lattice parameter and the dielectric constant. The surfaces of the unit cell in the layer plane are Scell(I) = 0.6131 * 0.6185 = 0.3792 nm2 for PhE-PbI4 [S1] and Scell(Br) = 1.16070 * 1.16236 * sin(89.996) / 4 =0.3021 nm2 for PhE-PbBr4 [S2]. As Nexc = Vexc / Vcell = 1.5πa2/Scell, where a is the Bohr radius, and as Scell decreases from the case x = 0 to the case x = 1, if Nexc decreases as a function of x, it is because a decreases as a function of x. The variation of a is related to the variation of the exciton binding energy EX through the variation of the dielectric constant ε, assuming that the effective mass doesn’t depend on x (which is reasonable, even if the effective masses for 2D perovskites are not known, but in 3D perovskites [S3], the effective mass is thought to vary by a factor of 10% only between CH3NH3PbI3 and CH3NH3PbBr3): a is proportional to ε and EX is proportional to 1/ε2. From Scell(I) = 1.25 Scell(Br) and Nexc(I) = (55/20).Nexc(Br) = 2.75 Nexc(Br), we obtain a2(I) = 3.44 a2(Br) , ε(I) = 1.85 ε(Br) and then EX(I) = 0.29 EX(Br). The exciton binding energy is known in PhEPbI4 [S4] but not in PhE-PbBr4. But a comparison with 3D compounds is fruitfull to understand the trends. Indeed the exciton binding energies can be found at low temperature for CH3-NH3PbI3: EX3D(I) = 37-50 meV and CH3-NH3PbBr3: EX3D(Br) = 70-150 meV [S3]. The order of magnitude of the ratio EX3D(I) /EX3D(Br) is quite consistent with the ratio reported above for 2D compounds. In 3D perovskites, the trend is then that the dielectric constant decreases from I compound to Br compound to Cl compound, we think that the same kind of trend may reasonably be considered in 2D perovskites from I compound to Br compound and Cl compound. 2
Figure S1. (a) Room temperature experimental values (black squares) of the energy of the exciton absorption peaks as a function of x for PhE-PbI4(1-x)Br4x, linear fit of these experimental values for values of Nexc linearly varying from 55 to 20. Inset : Experimental absorption spectrum (black line) and simulation with a Gaussian line (red line). (b) Experimental values of the FWHM of the exciton absorption peaks (black squares) with their measurement uncertainties, fit of the experimental values (solid lines) with theoretical ones obtained in the framework of the model presented in the text, with Nexc linearly varying from 55 for x = 0 to 20 for x = 1.
References S1. Calabrese, J.; Jones, N.L.; Harlow, R.L.; Herron, N.; Thorn, D.L.; Wang, Y. Preparation and characterization of layered lead halide compounds, J. Am. Chem. Soc., 1991, 113, 2328-2330. S2. Mitzi, D.B. Synthesis, structure and properties of organic-inorganic perovskites and related materials. Progress in Inorganic Chemistry, John Wiley & Sons, Inc. : New York, NY, USA, 1999, 48, chapter 1, 1-122. S3. Tanaka, K.; Takahashi, T.; Ban, T.; Kondo, T.; Uchida, K.; Miura, N. Comparative study on the excitons in lead-halide-based perovskite-type crystals CH3NH3PbBr3 CH3NH3PbI3, Solid State Comm. 2003, 127, 619-623.
3
S4. Gauthron, K.; Lauret, J.-S.; Doyennette, G.; Lanty, G.; Al Choueiry, A.; Zhang, S.; Bréhier, A.; Largeau L.; Mauguin, O.; Bloch, J.; Deleporte, E. Optical spectroscopy of twodimensional layered (C6H5C2H4-NH3)2PbI4 perovskite. Optics Express, 2010, 18, 5912-5919.
4
Room temperature optically tunability and inhomogeneous broadening in 2D-layered organicinorganic perovskite pseudobinary alloys. Gaëtan Lanty,1 Khaoula Jemli,1 Yi Wei,1,4 Joël Leymarie,2 Jacky Even,3 Jean-Sébastien Lauret,1 Emmanuelle Deleporte,*1
1
Laboratoire Aimé Cotton, Ecole Normale Supérieure de Cachan, CNRS, Université Paris-Sud, Bât 505 Campus
d’Orsay, 91405 Orsay, France
2
Institut Pascal, Clermont Université, CNRS and Université Blaise Pascal, 24 Avenue des Landais, 63177 Aubière
cedex, France
3
Université Européenne de Bretagne, INSA, FOTON, UMR 6082, 35708 Rennes, France
4
School of Physics and Optoelectronic Engineering, Dalian University of Technology, N° 2 Linggong Road,
Ganjingzi District, Dalian City, Liaoning Province, P.R. China
1
CONTENTS: Inhomogeneous broadening as a function of x for PhE-PbI4(1-x)Br4x P2 References…………..……………...…………...……………….…...
P3
In order to see if it is possible to account for the dissymmetry of the curve representing the inhomogeneous broadening of the excitonic lines of the alloy PhEPbI4(1-x)Br4x as a function of x (figure 4), we perform a refinement of the model by introducing a variation of Nexc as a function of x. Figure S1b shows the best fit we have obtained: to account for the dissymmetry, Nexc varies linearly with x, from 55 for x = 0 to 20 for x = 1. Figure S1a exhibits the fit of the experimental values of the bandgap in the framework of this calculation : it can be seen that, with these values of Nexc, a linear fit reproduces very well the variation of the bandgap as a function of x. Two parameters may play a role in the variation of the inhomogeneous broadening as a function of x : the lattice parameter and the dielectric constant. The surfaces of the unit cell in the layer plane are Scell(I) = 0.6131 * 0.6185 = 0.3792 nm2 for PhE-PbI4 [S1] and Scell(Br) = 1.16070 * 1.16236 * sin(89.996) / 4 =0.3021 nm2 for PhE-PbBr4 [S2]. As Nexc = Vexc / Vcell = 1.5πa2/Scell, where a is the Bohr radius, and as Scell decreases from the case x = 0 to the case x = 1, if Nexc decreases as a function of x, it is because a decreases as a function of x. The variation of a is related to the variation of the exciton binding energy EX through the variation of the dielectric constant ε, assuming that the effective mass doesn’t depend on x (which is reasonable, even if the effective masses for 2D perovskites are not known, but in 3D perovskites [S3], the effective mass is thought to vary by a factor of 10% only between CH3NH3PbI3 and CH3NH3PbBr3): a is proportional to ε and EX is proportional to 1/ε2. From Scell(I) = 1.25 Scell(Br) and Nexc(I) = (55/20).Nexc(Br) = 2.75 Nexc(Br), we obtain a2(I) = 3.44 a2(Br) , ε(I) = 1.85 ε(Br) and then EX(I) = 0.29 EX(Br). The exciton binding energy is known in PhEPbI4 [S4] but not in PhE-PbBr4. But a comparison with 3D compounds is fruitfull to understand the trends. Indeed the exciton binding energies can be found at low temperature for CH3-NH3PbI3: EX3D(I) = 37-50 meV and CH3-NH3PbBr3: EX3D(Br) = 70-150 meV [S3]. The order of magnitude of the ratio EX3D(I) /EX3D(Br) is quite consistent with the ratio reported above for 2D compounds. In 3D perovskites, the trend is then that the dielectric constant decreases from I compound to Br compound to Cl compound, we think that the same kind of trend may reasonably be considered in 2D perovskites from I compound to Br compound and Cl compound. 2
Figure S1. (a) Room temperature experimental values (black squares) of the energy of the exciton absorption peaks as a function of x for PhE-PbI4(1-x)Br4x, linear fit of these experimental values for values of Nexc linearly varying from 55 to 20. Inset : Experimental absorption spectrum (black line) and simulation with a Gaussian line (red line). (b) Experimental values of the FWHM of the exciton absorption peaks (black squares) with their measurement uncertainties, fit of the experimental values (solid lines) with theoretical ones obtained in the framework of the model presented in the text, with Nexc linearly varying from 55 for x = 0 to 20 for x = 1.
References S1. Calabrese, J.; Jones, N.L.; Harlow, R.L.; Herron, N.; Thorn, D.L.; Wang, Y. Preparation and characterization of layered lead halide compounds, J. Am. Chem. Soc., 1991, 113, 2328-2330. S2. Mitzi, D.B. Synthesis, structure and properties of organic-inorganic perovskites and related materials. Progress in Inorganic Chemistry, John Wiley & Sons, Inc. : New York, NY, USA, 1999, 48, chapter 1, 1-122. S3. Tanaka, K.; Takahashi, T.; Ban, T.; Kondo, T.; Uchida, K.; Miura, N. Comparative study on the excitons in lead-halide-based perovskite-type crystals CH3NH3PbBr3 CH3NH3PbI3, Solid State Comm. 2003, 127, 619-623.
3
S4. Gauthron, K.; Lauret, J.-S.; Doyennette, G.; Lanty, G.; Al Choueiry, A.; Zhang, S.; Bréhier, A.; Largeau L.; Mauguin, O.; Bloch, J.; Deleporte, E. Optical spectroscopy of twodimensional layered (C6H5C2H4-NH3)2PbI4 perovskite. Optics Express, 2010, 18, 5912-5919.
4
