Exploring the Electronic Band Structure of Organometal Halide

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Exploring the electronic band structure of organometal halide perovskite via photoluminescence anisotropy of individual nanocrystals Daniela Täuber, Alexander Dobrovolsky, Rafael Camacho, and Ivan G. Scheblykin Nano Lett., Just Accepted Manuscript • Publication Date (Web): 27 Jul 2016 Downloaded from http://pubs.acs.org on July 27, 2016

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Exploring the electronic band structure of organometal

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halide perovskite via photoluminescence anisotropy of

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individual nanocrystals Daniela Täuber,* Alexander Dobrovolsky, Rafael Camacho§, and Ivan G. Scheblykin* Chemical Physics, Lund University, Box 124, SE-22100, Lund, Sweden §

Present address: Department of Chemistry, University of Leuven, Box 2404, B-3001 Leuven,

Belgium

Abstract. Understanding electronic processes in organometal halide perovskites – flourishing photovoltaic and emitting materials - requires unraveling the origin of their electronic transitions. Light polarization studies can provide important information regarding transition dipole moment orientations. Investigating individual methylammonium lead tri-iodide perovskite nanocrystals enabled us to detect the polarization of photoluminescence intensity and photoluminescence excitation, hidden in bulk samples by ensemble averaging. Polarization properties of the crystals were correlated with their photoluminescence spectra and electron microscopy images. We propose that distortion of PbI6 octahedra leads to peculiarities of the electronic band structure close to the band-edge. Namely, the lowest band transition possesses a transition dipole moment

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along the apical I-Pb-I bond resulting in polarized photoluminescence. Excitation of

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photoluminescence above the bandgap is unpolarized because it involves molecular orbitals delocalized both in the apical and equatorial directions of the perovskite octahedron. Trap-

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assisted emission at 77K, rather surprisingly, was polarized similar to the bandgap emission.

1. INTRODUCTION Organometal halide perovskites (OMHP) are crystal solids with a semiconductor electronic band structure.1 OMHPs have attracted increasing interest due to their electro-optical properties and their fabrication by solution processing, which are very suitable for photovoltaics and light emission applications.2–7 Crystallization from solution produces polycrystalline films consisting of particles of differing shape and a vast distribution of sizes, ranging from nanometers to micrometers. Solution based processes even yield highly crystalline nanowires with properties suitable for lasing2,7 or photodetection.8 As with semiconductors in general, defects play a critical role in determining their opto-electronic properties. The types of defects and their concentrations depend upon the preparation method employed and details of the conditions present during their preparation, which can vary from crystal to crystal and from one location in a film to another.6,9–11 Despite this inhomogeneity,6,9–16 most of the literature studies report on the properties of bulk OMHP films, in which the distributions of such observables are concealed by ensemble averaging. In order to see beyond this averaged-out picture, methods providing spatial resolutions better than the size of the crystals, or involving the investigation of individual crystals one by one, should be employed, as reflected by very recent publications.10,11,14,16–20 2


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Although these materials have been studied extensively during the past several years, the physical processes determining the functioning of OMHP are still not adequately understood.1,21

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One particular issue concerns the origin of the optical transitions behind the wide semiconductorlike band. Theoretical calculations predict the optical absorption spectrum to originate from a combination of several transitions between various valence and conduction bands formed from individual and hybridized orbitals of lead and iodide.22,23 To the best of our knowledge, experimental validation so far only comes from transient absorption experiments showing two independent transitions,24–26 and an ellipsometry study indicating three transitions.23 There are properties, however, that have virtually not been studied and discussed that can shed light on the perovskite band structure, namely the properties f photoluminescence (PL) and of PL excitation polarization. Light polarization measurements (e.g. fluorescence anisotropy and linear dicroism) are widely employed in molecular spectroscopy to assess the rotational diffusion of molecules, as well as energy transfer within multi-chromophoric systems, and for determining the origin of their transition dipole moments.27 The reason for the polarization properties not having attracted much attention in the scientific community is that the PL anisotropy of bulk OMHP samples is virtually zero.28 This is because of the general absence of photo-selection in semiconductors and of the ensemble averaging over randomly oriented disordered crystals in bulk samples. Electrons and holes lose the memory of the initial polarization of the absorbed photon through thermalization at the picosecond time scale, which is much shorter than the PL lifetime.24,25,28–30 Thus, observation of individual

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nanocrystals should enable one to detect hidden polarization. Luminescence two-photon microscopy has also shown a local anisotropic response of OMHP films.16

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In this paper we report on the polarization properties of PL emission and PL excitation of individual CH3NH3PbI3 crystals at different temperatures. The data on PL polarization are correlated to both PL spectra and to the topology of the nano-objects measured by scanning electron microscopy (SEM). These results are discussed in terms of the individual nano-object’s shape, size and crystal structure, and the origin of the electronic band structure of the material.

2. RESULTS To characterize the organization of the transition dipole moments responsible for the PL emission and PL excitation in individual CH3NH3PbI3 crystals, we used two-dimensional polarization imaging (2D-POLIM) based on wide-field fluorescence microscopy. In this technique, the PL intensity (I) of each pixel in the image plane is recorded as a function of both the electric field orientation of the linearly polarized excitation light (φex) and the orientation of the PL emission analyzer (φem). From this function I(φex, φem) termed the polarization portrait, we obtain the modulation depths of the PL excitation (Mex) and of the PL emission (Mem) polarizations, as well as the corresponding phase angles θex and θem, as shown in Figure 1b (see SI for details). The modulation depth values reflect the degree of alignment of the dipoles responsible for PL excitation (Mex) or for PL emission (Mem). The phases show the averaged effective orientation of the corresponding transition dipole moments.

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Figure 1: (a) Scheme of the 2D-polarization imaging (2D POLIM) setup also showing the orientation of the perovskite nanowires and of the platelets in the sample plane. (b) PL intensity I(φex, φem) as measured for the perovskite nanowire NW2 (Figure 2) at 77K, shown as a polarization portrait. Its integration over one of the angles reduces I(φex, φem) to a function in the form of Malus’ law, ( ) = ( + ( − ) ), where Mi modulation depth and θi - phase, with the index i = “ex” and i = “em” when integrated over φem, and φex, respectively.

The dependence of the PL intensity on each of the polarization angles, I(φex) and I(φem), is shown

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in Figure 2 for six nano-objects, together with their SEM micrographs (see SI regarding 5


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preparation of the samples). In such a polar representation, an ideal dipole emitter/absorber (Mex= Mem=1) appears as an “8-shaped” function (cosine squared in polar coordinates) having a

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minimum intensity of zero, whereas an isotropically absorbing or emitting object (Mex or Mem=0) has a circularly shaped polar plot, the signal thus not depending on φex or φem. For wire-shaped perovskite nano-objects (nanowires, NW), Mem values as high as 0.7 were observed (Figure 2e, NW1), whereas Mex was much smaller. The largest PL excitation polarization Mex was observed for NW5 shown in Figure 2c,g,k, yielding Mex = 0.16±0.02, independent of the temperature. Apart from a few weakly polarized objects, polarization was generally larger in PL emission than in PL excitation (Mem> Mex), as can be seen from the modulation depth correlation plot (Figure 2a). Most of the weakly polarized objects were OMHP platelets (Figure 2d,h,l)) possessing no PL excitation or emission polarization.

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Figure 2: Correlation between the polarization properties of the nano-objects and their physical shape. SEM images of six nano-objects overlaid with polar plots showing the polarizations of PL excitation (blue) and PL emission (red) at 77K (a-d), 152K (e-h) and 295K (i-l). The modulation depths for each nano-object are given in red (Mem) and in blue (Mex). The largest PL emission polarization, Mem = 0.71, was found for NW1 at 152 K (in e). The largest PL excitation polarization was observed for NW5, shown in (c, g and k), yielding Mex = 0.16±0.02. The polarization phases are illustrated in (a) by blue (excitation) and red (emission) arrows. The phase of PL emission was usually along the NW’s long axis, whereas the phase for PL excitation did not correlate with the orientation of the long axis. Nano-objects appearing as platelets did not show any polarization at all (d, h and i). The PL emission polarization was higher at low temperatures than at room temperature (compare Figure 2a-h and Figure 2i-l), and the polarization orientation, θem, usually coincided with the

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depth (degree of polarization) of 0.18 for an individual 7.5 µm long OMHP NW at room temperature when excited by linearly polarized light.2 This result agrees qualitatively with our

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room temperature observations of Mem ranging from 0.12 to 0.29 for the 12 studied NWs having diameters in the range from 0.16 µm to 0.39 µm. In contrast to PL emission polarization, for the much weaker PL excitation polarization no preferential orientation with respect to the main axis of the NWs was observed; see Figure S1 in SI.

Figure 3: Relations for degrees of PL polarizations for all studied nano-objects. (a) Correlation between Mex and Mem at T=77K (♦ ♦, light blue), T=152K ( , dark blue) and T=295K ( , red). Apart from a few weakly polarized nano-objects, Mem > Mex. (b) Dependence of Mem (♦ ♦) and (c) Mex ( ) on the diameter (d) of the nano-objects at 77K, the color code indicating the aspect ratio (L/d) for each of the nano-objects (L is the object length). Considerable PL polarization (Mem > 0.1) was only found for d ≤ 0.6 µm. No dependence of Mex and Mem on the aspect ratio (L/d) is evident. Figure 3b and 3c exemplify the relation between the modulation depths (Mex and Mem) and the diameter d of the nano-objects as well as their aspect ratios. For the 28 single nano-objects that 8


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correlation between the aspect ratio of the NWs and their degree of PL excitation or PL emission polarization. a PL intensity image

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Figure 4: Low-coverage sample containing irregular OMHP nanocrystals. (a) PL intensity image, (b) Mem image. The blue background in (b) shows the regions in which the PL intensity was below the threshold for determination of the polarization properties. (c) Correlation between PL intensity and Mem for each pixel of the image. High Mem values were only found for low intensity pixels. The observation of high degrees of PL polarization in excitation and in emission being only found for nano-objects of small size was further supported by investigating irregularly shaped nanocrystals prepared by unimolar single step deposition (Figure 4a).31,32 High Mem values were only found for low intensity pixels, as demonstrated by the correlation between the PL intensity and Mem measured in the same pixel of the image (Figure 4c). A similar result was obtained for Mex (not shown).

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2D POLIM can be also used to assess the excitation energy transfer processes occurring between the initially excited transition dipoles of CH3NH3PbI3 and those later responsible for the PL

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emission.33 To this end, a so-called single-funnel approximation is employed in analyzing the full polarization portrait, as described in detail elsewhere.33,34 The energy funneling efficiency parameter ε thus obtained ranges from zero, meaning a complete absence of energy funneling and a strong photo-selection, to unity, meaning 100% energy funneling and no photo-selection. For all the nanocrystals investigated, values of ε larger than 0.95 were obtained. The implications of this will be discussed later.

Figure 5: PL spectra of individual perovskite crystals NW3 (a) and NW5 (b), as shown in Figure 1, at 77K, 150K and 295K. The spectra were measured at the same excitation power 10


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and under the same detection conditions, enabling the comparison of PL intensities at different temperatures.

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PL spectra were obtained for several of the nano-objects investigated by 2D POLIM (Figure 5 shows two examples). The PL spectra of the nano-objects at room temperature show a broad band peaking at λ≈760 nm, in agreement with results reported in literature.29,35,36 At 152K, which is within the range of the phase transition temperature from the tetragonal to orthorhombic phase, the PL spectra can contain contributions of both phases. Below this phase transition, at T=77K, the PL spectra contain two peaks, a narrow peak at λ≈750 nm, related to the band-to-band recombination and a broad feature at λ>760 nm, related to defect-assisted PL.36 The intensity ratio of the PL that originates from the band-to-band recombination to that from the defectassisted one varies dramatically for different nano-objects; compare Figure 5a and b.

3. DISCUSSION 3.1 Can the antenna effect account for the observed PL polarization? The PL emission and PL excitation polarizations for regularly-shaped elongated objects having dimensions comparable with the wavelength of light may be caused by the so-called antenna effect37,38 which is often used to explain the PL polarization of metal and semiconductor NWs.38– 40

The origin of the antenna effect is in the mismatch between the refractive index of the NW

material and the surroundings, resulting in a redistribution of the electric field inside the NW,37,38 and implying the appearance of “selection rules” for the electric field modes. For thin NWs (d < 0.1 µm), PL excitation as well as PL emission can be expected to be polarized parallel to the long axis of the NW, due to this effect.38 This matches our observations for PL emission 11


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polarization (see Figure S1 in SI). However, the PL excitation polarization was generally much weaker, and no preferential orientation with respect to the NW geometry was found; see Figure

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S1 in SI. Yet these calculations for thin NWs might not be quantitatively valid for our thicker and not ideally shaped NWs. For thicker NWs, Ruda et al. reported an oscillatory dependence of the degree of polarization and of the orientation of PL emission and PL excitation on the NW radius and on the wavelength of light.39 The authors calculated the dependence of the PL emission and the PL excitation polarization upon the light frequency ω (which is either the frequency of the excitation light or the frequency of the PL emission) and the NW radius (d/2) for a material with dielectric constant of ≈ 9.39 This matches the situation for CH3NH3PbI3, since the refractive index here is n ≈ 3, meaning that the dielectric constant ≈ 9.41 These calculations showed a switch in the orientation of the PL emission polarization from parallel to perpendicular to the NW long axis with an oscillatory period of dω/(2c2).39 At 295K the PL spectra of our nano-objects revealed only negligible (< 10 nm) differences in the peak position, so that the PL frequency can be considered to be constant. Thus, we would expect a 25% change in d (d/4 is the half of the oscillation period) to result in a change from a parallel to a perpendicular PL emission polarization. However, despite the large variation in d for the studied nano-objects, a clear preference for PL emission that was polarized parallel to the long axis of the NW was found. A perpendicular orientation was only observed once, for a weakly polarized object (Mem = 0.13) that might well be a platelet standing on its edge; see Figure S1 in SI.

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Thus the set of the experimental data as a whole allows us to conclude that the antenna effect alone cannot explain the PL polarization properties of perovskite NWs that were observed.

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Figure 6: Schematic representation of the perovskite crystal structures and of the suggested transition dipole moment orientations in relation to the orbital hybridization directions. Crystal structure of the tetragonal (a) and the orthorhombic (b) phases42 highlighting the Pb-I bond lengths22 and the Pb-I-Pb bond angles of the equatorial (Ieq) and the apical (Iap) iodide.22 (c) Cartoon showing the idea of correlations between the dipole moment orientations and excited state energy predicting polarized PL emission and unpolarized PL excitation. 14


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3.2 The crystal unit cell structure defines the degree of PL polarization

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structure of the semiconductor, which in turn is related to the chemical composition and the crystal structure of the material.23,43 Note that, contrary to the antenna effect, the geometrical shape of the crystal in this case is not critical for its polarization properties. For the experimental detection of any PL polarization that is related to the crystal structure we should avoid ensemble-averaging. Measuring individual crystals is necessary but not sufficient. This is because even sub-wavelength crystals can in fact be poly-crystals for which the directions of the crystal axes differ rendering their overall polarization random. Thus, the degree of polarization should be highest for mono-crystals and should decrease with an increase in polycrystallinity. In addition, the material properties should be taken into account in the choice of the excitation wavelength, since the polarization properties may also depend on it. At room temperature CH3NH3PbI3 has a tetragonal structure,22,44–46 whereas at low temperatures (

Exploring the Electronic Band Structure of Organometal Halide

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