Room-Temperature Optical Tunability and Inhomogeneous

Letter pubs.acs.org/JPCL

Room-Temperature Optical Tunability and Inhomogeneous Broadening in 2D-Layered Organic−Inorganic Perovskite Pseudobinary Alloys Gaeẗ an Lanty,† Khaoula Jemli,† Yi Wei,†,∥ Joel̈ Leymarie,‡ Jacky Even,§ Jean-Sébastien Lauret,† and Emmanuelle Deleporte*,† †

Laboratoire Aimé Cotton, Ecole Normale Supérieure de Cachan, CNRS, Université Paris-Sud, Bât 505 Campus d’Orsay, 91405 Orsay, France ‡ Institut Pascal, Clermont Université, CNRS and Université Blaise Pascal, 24 Avenue des Landais, 63177 Aubière cedex, France § Université Européenne de Bretagne, INSA, FOTON, UMR 6082, 35708 Rennes, France ∥ School of Physics and Optoelectronic Engineering, Dalian University of Technology, N° 2 Linggong Road, Ganjingzi District, Dalian City, Liaoning Province, People’s Republic of China S Supporting Information *

ABSTRACT: We focus here our attention on a particular family of 2D-layered and 3D hybrid perovskite molecular crystals, the mixed perovskites (C6H5−C2H4−NH3)2PbZ4(1−x)Y4x and (CH3−NH3)PbZ3(1−x)Y3x, where Z and Y are halogen ions such as I, Br, and Cl. Studying experimentally the disorder-induced effects on the optical properties of the 2D mixed layered materials, we demonstrate that they can be considered as pseudobinary alloys, exactly like Ga1−xAlxAs, Cd1−xHgxTe inorganic semiconductors, or previously reported 3D mixed hybrid perovskite compounds. 2D-layered and 3D hybrid perovskites afford similar continuous optical tunability at room temperature. Our theoretical analysis allows one to describe the influence of alloying on the excitonic properties of 2D-layered perovskite molecular crystals. This model is further refined by considering different Bohr radii for pure compounds. This study confirms that despite a large binding energy of several 100 meV, the 2D excitons present a Wannier character rather than a Frenkel character. The small inhomogeneous broadening previously reported in 3D hybrid compounds at low temperature is similarly consistent with the Wannier character of free excitons. SECTION: Spectroscopy, Photochemistry, and Excited States

O

Figure 1.1,13,15−17 The octahedra consist of an inorganic layer in which each metal atom shares the halide ions with its neighboring metal atoms in 2D. The ammonium head of the organic groups R-NH3 binds to the halogen atoms of the inorganic sheet by hydrogen bonding. The organic groups selfassemble via π−π interactions (when the organic group contains aromatic groups) or through van der Waals force (when the organic group contains alkyl chains) to form biorganic layers. The crystallographic structure of the 2DOIPs

rganic−inorganic hybrid semiconductors based on metal halide units have attracted attention due to their potential applications in light-emitting optical devices1−7 and more recently in photovoltaic devices.8−12 Two-dimensional organic−inorganic perovskites (2DOIPs) constitute a particular class of materials in this family, with general chemical structures (R-NH3)2MX4 or (H3N-R-NH3)MX4, where R is an organic group, M a divalent metal such as Pb2+, and X a halogen such as Cl, Br, or I. These crystals are easily grown from solution and deposited by spin-coating on a substrate. They present a selforganized structure whose crystalline nature can be demonstrated by X-ray diffraction.1,13,14 In most 2DOIPs, metal and halide atoms form MX62− octahedra, as schematically shown in © XXXX American Chemical Society

Received: September 30, 2014 Accepted: October 29, 2014

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dx.doi.org/10.1021/jz502086e | J. Phys. Chem. Lett. 2014, 5, 3958−3963

The Journal of Physical Chemistry Letters

Letter

be tailored, especially for 2D compounds.17,34 As an example, by changing the halogen or the metal, the whole spectral region from the UV to the near-IR can be covered.35−43 Identically, optical band gap tuning can be achieved by halogen substitution in 3DOIPs.41−43 Other examples can be given concerning the characteristics of the organic group; due to the large variety of structures and energy gaps of the organic groups, incorporating different organic groups into the 2DOIP structures results in different optical and mechanical properties.44 In this Letter, we will focus our attention on a particular family of 2DOIPs based on 2-phenylethanamine; we will note (C6H5−C2H4−NH3)2 as PhE hereafter for convenience, and for example, (C6H5−C2H4−NH3)2 PbI4 will be referred as PhE−PbI4. The purpose of this Letter is to study 2D mixed perovskites (C6H5−C2H4−NH3)2PbZ4(1−x)Y4x with Z, Y = I, Br, or Cl and compare them with previously reported (CH3− NH3)PbZ3(1−x)Y3x 3D mixed perovskites. We show that these materials can be considered as pseudobinary alloys, in the same way as inorganic semiconductors such as Ga1−xAlxAs or Cd1−xHgxTe solid solutions. In the past, the pseudobinary alloys of inorganic semiconductors have raised important questions concerning the role of structural and chemical disorders, and systematic studies of this problem have been undertaken in order to investigate the nature of potential fluctuations and their influence on the electronic properties. Indeed, any contribution to a quantitative understanding of this point is of fundamental importance because, for a given application, this could guide the choice of a particular alloy among several pseudobinaries. Of course, this is a crucial point for applications involving a definite band gap that is not available in the perovskites containing one type of halogen ion, like in vertical microcavities studied in refs 3 and 4 or like in photovoltaic̈ devices to optimize the sunlight harvesting and realize perovskite solar cells with 20% efficiency for a single junction and 30% for a tandem configuration.45 Drawing on works done 30 years ago in inorganic semiconductors46−48 and developing a model to study the disorder-induced effects on their optical properties, we show that (C 6H 5−C 2H 4− NH3)2PbZ4(1−x)Y4x behaves as a perfect random alloy; this model should be transferred as well to (CH3−NH3)PbZ3(1−x)Y3x. Moreover, it is a further demonstration of the validity of the Wannier exciton picture in these perovskite molecular crystals. To synthesize the mixed perovskites (C 6H 5−C 2H 4− NH 3 ) 2 PbZ 4(1−x) Y 4x , the (C 6 H 5 −C 2 H 4 −NH 3 ) 2 PbY 4 and (C6H5−C2H4−NH3)2PbZ4 in DMF (dimethylformamide) are mixing with the molar ratio x. The 2D-layered self-assembled film is then prepared by spin-coating the mixed solution on quartz slides at 2000 rpm for 30 s, followed by an annealing at 95 °C for 1 min. The thickness of the films is about 25 nm, deduced from AFM (atomic force microscopy) measurements. The 2D ordering of the layers has been checked with Xdiffraction experiments.22,49 Absorption spectra of these films are measured at room temperature and are reported in Figure 2a for (C6H5−C2H4−NH3)2PbI4(1−x)Br4x and in Figure 2b for (C6H5−C2H4−NH3)2PbBr4(1−x)Cl4x. It can be seen that there is a continuous shift of the energy of the absorption peak as a function of x as in refs 37, 39, and 49. Noteworthy, a linear shift of the optical band gap is obtained for the 3DOIPs CH3− NH3PbBr3(1−x)Cl3x alloy over the [2.4−3.1 eV] energy range.41 By comparison, the 2DOIPs (C6H5−C2H4− NH3)2PbBr4(1−x)Cl4x alloy spans the [3.1−3.7 eV] energy range. This difference can be analyzed by a careful inspection of

Figure 1. Sketch of 2D organic−inorganic lead halide semiconductors. (a) a−c plane view and (b) a−b plane view.

is then bidimensional, consisting of an alternation of inorganic layers around 0.5 nm thick and of organic layers around 1 nm thick. In 3D organic−inorganic perovskites (3DOIPs), the wave functions of the electronic states associated with the optical band gap cover the entire inorganic lattice, which extends in the three directions.18 Organic cations trapped in small cages have an indirect effect on these electronic states, through lattice strain and distortion of inorganic octaedra, leading to phase transitions and a phenomenon related to the so-called “exciton switching”.19,20 In 2DOIPs, the electronic structure is bidimensional close to the band gap.21 Indeed, the wave functions of the electronic states close to the optical band gap only cover the 2D inorganic lattice, that is to say, the MX62− octahedra layers. Moreover, the HOMO−LUMO energy gap of the organic layers is higher than that of the inorganic layers, leading to a strong confinement of the monoelectronic states in the very thin inorganic layers. By virtue of the high contrast in dielectric constants between the organic layers and the MX62− layers, the Coulombic interaction in the well layer of 2DOIPs is strengthened by image charge effects, resulting in very large exciton binding energies of a few hundred meV and huge oscillator strengths.15,22 Because of their strong binding energies, very stable excitons are formed upon light excitation,23−25 and consequently, the 2DOIPs exhibit some photoluminescence (PL) and electroluminescence (EL) at room temperature, which makes them good candidates for realizing laser diodes (LDs), organic−inorganic light-emitting diodes (OILEDs),26,27 and nonlinear optical28 and polaritonic2,3,5,29,30 devices. A stable exciton is also measured at very low temperature in 3DOIPs,31 as predicted theoretically by solving the Bethe−Salpeter equation.20 However, it is now commonly accepted that inorganic lattice vibrations and tumbling of the organic cations lead to a strong exciton screening and almost free carriers at room temperature.32,33,19 The optical properties of 2DOIP and 3DOIP systems depend on several different factors, such as the characteristics of the organic and inorganic components; this flexibility makes them very attractive, allowing the properties of the materials to 3959



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Figure 3. Sketch of PhE−PbBr4(1−x)Cl4x mixed wells. The Br and Cl atoms are distributed in a randomized way inside of the inorganic layers.

Z atom. The probability px(n,Nexc) to find n Y atoms in the volume Vexc is given by the binomial distribution px (n , Nexc) = C Nnexc·x n·(1 − x)Nexc − n

(1)

where Nexc is the number of halogen sites in the volume Vexc. We assume that the energy of an exciton, whose volume Vexc contains n Y atoms among Nexc is n E = E PEPZ + (E PEPY − E PEPZ) · Nexc (2) where E = EPEPZ for pure PhE−PbZ4 (n = 0) and E = EPEPY for pure PhE−PbY4 (n = Nexc). The probability that the energy of the exciton is E, P(E), is then given by the following function, where n is extracted from the previous equation

Figure 2. Optical absorbance spectra of (a) PhE−PbI4(1−x)Br4x and (b) PhE−PbBr4(1−x)Cl4x.

⎛ ⎞ E − E PEPZ P(E) = px ⎜n = Nexc· , Nexc⎟ E PEPY − E PEPZ ⎝ ⎠

the vertical quantum confinement in 2DOIPs.50 The shift of the exciton absorption peak of (C6H5−C2H4−NH3)2PbY4 with Y = I, Br, of Cl has been explained by the valence band structure composed of a Pb(6s) orbital that is hybridized with the Y(np) orbitals (n = 5 for I, n = 4 for Br, and n = 3 for Cl);31,39 therefore, it can be understood that the energy of the absorption peak of the mixed perovskites comes from the hybridization of the Pb(6s), Z(mp), and Y(np) atomic orbitals. Additionally, it is observed that the fwhm (full width at halfmaximum) of the exciton absorption peak is strongly influenced by x; the fwhm shows a maximum at around x = 0.5, corresponding to a maximal inhomogeneity. In previous works,22 it has been shown that the absorption peak corresponds to free excitons. From the discussions about the disorder-induced effects on the broadening of electronic states in inorganic semiconductors such as (Ga,Al)As, (Cd,Zn)Se, or (Cd,Hg)Te,46−48 many observed features of disorder effects on free excitons have been accounted for from the assumption that excitons essentially feel the crystal potential inside of a critical volume Vexc, which is related to the spatial extension of the quasiparticles. Considering that disorder effects on this quasiparticle property arise from the statistical fluctuation of the composition in the exciton volume, we assume that the distribution of the Z and Y halogen atoms is uniform in the sample, that is to say, the Z and Y atoms are distributed in a randomized way inside of the inorganic layers, as schematized in Figure 3. The assumption is quite likely because if some aggregates of Z or Y atoms exist inside of the sample, we should have observed in the (C6H5−C2H4− NH3)2PbZ4(1−x)Y4x absorption spectra two separate lines corresponding to the absorption of (C 6 H 5 −C 2 H 4 − NH3)2PbZ4 and (C6H5−C2H4−NH3)2PbY4. Considering this assumption, the x parameter corresponds to the probability for a halogen site to be occupied by a Y atom, and 1−x is the probability for a halogen site to be occupied by a

(3)

In order to compare the theoretical results to the experimental ones, the experimental width of the absorption peaks obtained for pure PhE−PbZ4 and PhE−PbY4 have to be taken into account. We propose to take into account these widths considering EPEPY and EPEPZ as random variables, whose probability densities PY(EPEPY) and PZ(EPEPZ) are derived from the experimental optical density spectra (involving the fit of the experimental data with a Gaussian function). The optical density spectrum of the pseudobinary alloy is then obtained by adding all of the contributions of the different values of the random variable pairs (EPEPY, EPEPZ) weighted by their respective probabilities. Because we have assumed that Z and Y atoms are distributed in a randomized way inside of the inorganic layers, we will assume that the two probability densities PY(EPEPY) and PZ(EPEPZ) are independent; then it comes P(E) =

∑ ′ ′ EPEPY , EPEPZ

⎛ ⎞ ′ E − E PEPZ ′ )·PZ(E PEPZ ′ ) px ⎜n = Nexc· , Nexc⎟ ·PY(E PEPY ′ ′ E PEPY − E PEPZ ⎝ ⎠

(4)

Figures 4 and 5 show the energy positions and the widths of the absorption peaks, obtained within the framework of this model, for several values of Nexc, compared to the experimental data; a good agreement is observed for 25 < Nexc < 37 for PhE− PbI4(1−x)Br4x and 25 < Nexc < 29 for PhE−PbBr4(1−x)Cl4x. From this observation, we conclude that these mixed perovskites can be considered as pseudobinary alloys, in the same way as inorganic semiconductors such as Ga1−xAlxAs or Cd1−xHgxTe. Let us note that a dissymmetry is observed experimentally in the curve showing the fwhm as a function of x; the maximal value of the fwhm is obtained for x slightly larger than 0.5. The same kind of dissymmetry is also observed in inorganic solid solutions47 and is attributed to the fact that the lattice parameters as well as the dielectric constant indeed vary as a 3960



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Figure 4. (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 several values of Nexc. (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.

Figure 5. (a) Room-temperature experimental values (black squares) of the energy of the exciton absorption peaks as a function of x for PhE−PbBr4(1−x)Cl4x; linear fit of these experimental values for several values of Nexc. (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.

function of x. Assuming different exciton properties for pure compounds (Bohr radius, binding energy) gives a consistent explanation for the observed trend as well as the dissymmetry (see the detailed discussion in the Supporting Information and Figure S1). For a unit cell consisting of four atoms, we note that the obtained values of Nexc correspond to a spatial extension of the exciton over several unit cells. Therefore, it is possible from this study to describe more precisely the excitonic properties of the 2D perovskites through a relevant modeling of the excitonic wave function. In the PhE−PbZ4 2D perovskites, it is wellknown that the exciton is strongly confined in the inorganic layer. In fact, S. Zhang et al. have changed the organic part of the 2D perovskites44 and studied the optical properties of all of these materials; whatever the organic part is, the absorption and emission wavelengths barely depend on the nature of the organic part. This is a strong argument to confirm that the excitonic wave function can be considered as completely confined in the inorganic part of the 2D perovskite. This is a direct consequence of the confinement of the monoelectronic states in the 2D inorganic layers and the dielectric confinement afforded by the organic barrier.21 Moreover, experimental15 as well as theoretical results21 clearly demonstrate the anisotropic TE (transverse electric) character of the optical absorption at the optical band gap. We will thus consider that the wave function is zero outside of the inorganic layer. A detailed analysis on related hybrid perovskites has shown indeed that due to quantum and dielectric confinement effects, the

dimensionality of the Wannier exciton is very close to 2 (2.3).25,51 Let us name the axis perpendicular to the multilayers the z-axis. The thickness (along the z-axis) of the inorganic layer a0 is known from X-diffraction experiments, a0 = 0.6 nm.14 In the layer plane (x,y), we describe the fundamental state of the exciton by the 2D hydrogen-like normalized wave function

f1s2D (r ) =

2 −r / a ·e πa 2

(5)

with r=

x2 + y2

(6)

where a, the 2D Bohr radius in the layer plane, is taken here as an adjustable parameter. The volume Vexc can then be calculated as a function of the parameter a 3 Vexc = a0⟨πr 2⟩ = a0 πa 2 (7) 2 To obtain the relationship between Vexc and Nexc and then deduce a value for a, one has now to calculate the volume of the unit cell Vcell because Nexc = Vexc/Vcell. Considering the lattice parameters of the perovskite molecular crystals from refs 14 and 17, we deduce a 2D Bohr radius on the order of magnitude of 1.5 nm, which is substantially larger that the nearestneighbor distance of Pb ions (0.62 nm) and which is coherent with the values claimed in refs 15, 25, and 51. We conclude that because the excitonic wave function covers several unit cells in 3961



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ACKNOWLEDGMENTS The authors are very grateful to Pierre Audebert for fruitful discussions. This work is supported by Agence Nationale pour la Recherche (Grant PEROCAI), by Triangle de la Physique (Grant CAVPER), by DIM Nano-K (Grant PEROVOLT), and by Institut d’Alembert of Ecole Normale Supérieure de Cachan.

the layer plane, the exciton in PhE−PbZ4(1−x)Y4x exhibits a Wannier character rather than a Frenkel character, despite a large exciton binding energy on the order of magnitude of 250 meV.15,22 We may notice however that this very large binding energy is essentially related to out-of-plane dielectric confinement, while disorder averaged inhomogeneous broadening of the exciton line is related to the in-plane extension of the electron−hole pair wave function. Such a situation is also not unexpected if one considers that the excited state certainly has a strong charge-transfer character between the lead and the neighboring halides. It is quite likely that the transient pseudohalide radical (corresponding to a “hole”) can exchange electrons very fast with all of the neighboring halide ions, such as those extending formerly from the hole delocalization. Ab initio modeling of the electronic band structures of both 2D and 3D hybrid perovskites yield indeed small values for the valence band effective masses.18,20,21 On the other hand, the electron sitting on the halogen atom is likely to be exchanged somewhat slower. However, care should be taken for such a simplified picture because spin−orbit coupling has a strong impact on the conduction band states for both 2D and 3D hybrid perovskites, leading to reduced effective masses.18,21 From such considerations, the exciton extension on a few unit cells as well as a substantial hole-based photoconductivity could be expected in these materials, as already noticed in 3D perovskites. To summarize, we have seen that 2D-layered and 3D hybrid perovskites afford similar continuous optical tunability at room temperature. Moreover, we found that, despite the large exciton binding energy, the exciton wave function covers several cells in the layer plane and that the mixed perovskites (C6H5−C2H4− NH3)2PbI4(1−x)Br4x and (C6H5−C2H4−NH3)2PbBr4(1−x)Cl4x can be considered as pseudobinary alloys. The model of inhomogeneous broadening for free excitons is further refined by considering different Bohr radii for pure compounds. This model is expected to be transferable to 3D hybrid perovskite alloys, at low temperature where excitonic lines are observable. Indeed, the previously observed small inhomogeneous broadening of the excitonic lines at low temperature in ref 41 seem to be consistent with large values of Nexc and then is similarly consistent with the Wannier character of free excitons. Understanding the nature of the excitons in these hybrid materials is crucial for the use of perovskites in the field of polariton lasers, where the exciton−exciton interactions play an important role, or in the field of photovoltaic̈ devices where the excitons have to be ionized to yield free carriers.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Details of the inhomogeneous broadening as a function of x for PhE−PbI4(1−x)Br4x. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: Emmanuelle [email protected]. Tel: +33 (0)1 47 40 75 91. Notes

The authors declare no competing financial interest. 3962



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