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Electronic Structure and Optical Properties of α‑CH3NH3PbBr3 Perovskite Single Crystal Ji-Sang Park, Sukgeun Choi,* Yong Yan, Ye Yang, Joseph M. Luther, Su-Huai Wei, Philip Parilla, and Kai Zhu National Renewable Energy Laboratory, Golden, Colorado 80401, United States

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S Supporting Information *

ABSTRACT: The electronic structure and related optical properties of an emerging thin-film photovoltaic material CH 3 NH 3 PbBr 3 are studied. A block-shaped α-phase CH3NH3PbBr3 single crystal with the natural ⟨100⟩ surface is synthesized solvothermally. The room-temperature dielectric function ε = ε1 + iε2 spectrum of CH3NH3PbBr3 is determined by spectroscopic ellipsometry from 0.73 to 6.45 eV. Data are modeled with a series of Tauc−Lorentz oscillators, which show the absorption edge with a strong excitonic transition at ∼2.3 eV and several above-bandgap optical structures associated with the electronic interband transitions. The energy band structure and ε data of CH3NH3PbBr3 for the CH3NH3+ molecules oriented in the ⟨111⟩ and ⟨100⟩ directions are obtained from first-principles calculations. The overall shape of ε data shows a qualitatively good agreement with experimental results. Electronic origins of major optical structures are discussed.

T

electronic interband transitions. The energy band structure and ε data are obtained for CH3NH3PbBr3 with the CH3NH3+ molecules oriented in the ⟨111⟩ and ⟨100⟩ directions from the first-principles calculations. Overall, the calculated ε data are in good agreement with the SE-determined spectrum. Electronic origins of the observed major optical structures are discussed based on the results from calculations. Formation of a single-crystal of CH3NH3PbBr3 is confirmed by an X-ray diffraction (XRD) scan as shown in Figure 1. The 00l (l = 1, 2, 3, and 4) reflections are clearly seen and their angular positions all match well with the results from a simulated XRD curve (not shown), which indicates that the crystal formed in the cubic phase and its surfaces are {001} planes. Details of the XRD analyses are presented in ref 18. Ellipsometry in its most general form studies the changes of the polarization state of light due to interaction between the light and a material. If the light is neither s nor p polarized, then the s- and p-polarizations experience a different attenuation and phase shift upon reflection. The two SE parameters Ψ and Δ are respectively the amplitude component and the phase difference of the complex reflectance ratio ρ. The two parameters are related to ρ by

he organic−inorganic hybrid compounds with the perovskite structure CH3NH3PbX3 (X = Cl, Br, I) are of great interest for their potential applications in high-performance photovoltaic (PV) devices.1−4 In less than 2 years of intense studies, the power-conversion efficiency (PCE) of CH3NH3Pb(I1−xBrx)3-based solar cells has already reached as high as 20.1%.5 Knowledge of optical properties plays a critical role in better understanding a material’s electronic structure and optimizing PV device structures, and therefore further improves the device performance.6,7 Despite rapid progress in CH3NH3Pb(I1−xBrx)3 perovskite solar cell technology; however, the material’s fundamental properties are still largely unknown. Spectroscopic ellipsometry (SE) is recognized8 as a highly suitable method of determining a material’s optical functions, such as complex dielectric function ε(E) = ε1(E) + iε2(E) and complex refractive index N(E) = n(E) + ik(E) over a wide photon-energy range. Therefore, SE has been used to characterize a wide variety of PV materials. 9−13 For CH3NH3Pb(I1−xBrx)3, the ε and N spectra of one end point x = 0.0 (CH3NH3PbI3) have recently been obtained by SE.14−16 However, no systematic optical study of the other end point x = 1.0 (CH3NH3PbBr3) has been reported yet. Here we apply SE to determine the room-temperature ε spectrum of bulk single-crystalline α-phase CH3NH3PbBr3 from 0.73 to 6.45 eV. SE data modeled with the sum of eight Tauc−Lorentz (T−L) oscillators17 clearly show the absorption edge with a strong excitonic transition at around 2.3 eV and several above-bandgap optical structures associated with the © 2015 American Chemical Society

ρ=

rp rs

= tan Ψ·exp[iΔ]

(1)

Received: August 5, 2015 Accepted: October 13, 2015 Published: October 13, 2015 4304

DOI: 10.1021/acs.jpclett.5b01699 J. Phys. Chem. Lett. 2015, 6, 4304−4308

Letter

The Journal of Physical Chemistry Letters

Figure 2. Data (dashed color lines) and the best-fit curves (solid gray lines) for (a) Ψ and (b) Δ of CH3NH3PbBr3, respectively, for the incident angles of 55°, 65°, and 75°. Figure 1. X-ray diffraction curve measured from the top surface of the CH3NH3PbBr3 single crystal. The data were obtained by integrating the diffraction intensity between 85° and 95° for the angle formed by the crystal surface and the plane of incidence. Inset: A photograph of the crystal.

Table 1. Best-Fit Parameters for the Eight Tauc−Lorentz Oscillators Used to Construct the ε2 Spectrum of CH3NH3PbBr3a osc. no. 1 2 3 4 5 6 7 8

where rp and rs are the complex reflectance coefficients for pand s-polarized light, respectively. The fundamental optical function spectra can be obtained by modeling the two parameters Ψ and Δ, and the result with the minimum discrepancy between the model and the experimental data provides accurate optical information on a material. In this study, the SE data were analyzed with the three-phase model consisting of the ambient, a surface overlayer, and the CH3NH3PbBr3 crystal. A surface overlayer is presumably composed of microscopic roughness and native oxides, whose optical response can be represented by the Bruggeman effective medium approximation (BEMA)19 using a 50−50 mix of the underlying material and void. The best result was achieved with a 3.63 nm-thick BEMA layer. As pointed out by Nelson et al.,20 the contributions from microscopic roughness and native oxides to a thin BEMA layer are practically indistinguishable. The ε spectrum of CH3NH3PbBr3 was constructed by the sum of eight T−L oscillators. The ε2(E) of an individual T−L oscillator is expressed by17 ⎧ AE C(E − E )2 1 0 g ⎪ · (E > Eg ) ⎪ 2 2 2 2 2 ε2 = ⎨ (E − E0 ) + C E E ⎪ ⎪ 0 (E ≤ Eg ) ⎩

A [eV] 70.13 30.02 8.69 2.76 5.03 11.13 4.70 18.53

± ± ± ± ± ± ± ±

20.01 50.31 13.97 4.04 1.07 1.00 0.38 0.65

C [eV] 0.09 0.60 0.83 0.47 0.58 0.90 1.41 0.77

± ± ± ± ± ± ± ±

0.01 0.23 0.63 0.21 0.06 0.03 0.06 0.32

E0 [eV] 2.33 2.34 3.10 3.42 3.92 4.36 5.88 9.65

± ± ± ± ± ± ± ±

0.00 0.37 0.10 0.03 0.01 0.01 0.01 0.11

The Tauc gap Eg in eq 1 was determined to be 2.25 ± 0.01, which was obtained from oscillator no. 1 and was kept the same for all the oscillators. The ε1(∞) is set to 1.0.

a

(2)

where A is the oscillator strength, C is a broadening parameter, E0 is the resonance energy, and Eg is the Tauc gap (the onset of absorption). The Eg was set to be the same for all T−L oscillators and constrained to be smaller than the E0 by definition. The mathematical expression for the corresponding ε1 can be calculated by the Kramers−Krönig (K−K) transformation of ε2. The two SE parameters Ψ and Δ taken at three incident angles and their best-fit curves are displayed in Figure 2a and Figure 2b, respectively. The experimental data and model are in excellent agreement. The fit-determined parameters A, C, and E0 for all eight T−L oscillators are listed in Table 1. We note that the E0 of oscillator no. 8 situates outside the spectral range of our data, which serves mainly as the background correction. The real (ε1) and imaginary (ε2) parts of the resulting ε spectrum are shown as solid red and solid blue curves, respectively, in Figure 3. The ε2 spectrum exhibits the absorption edge at ∼2.3 eV accompanied by a strong exciton

Figure 3. Real (solid red line) and imaginary (solid blue line) parts of the modeled ε spectrum of CH3NH3PbBr3. For comparison, real (dotted red line) and imaginary (dashed blue line) of the ε spectrum of CH3NH3PbI3, obtained from ref 14, are also shown.

peak and several above-bandgap optical structures associated with the electronic interband transitions. For comparison, the ε spectrum of CH3NH3PbI3 obtained from ref 14 is also included. The overall ε spectra shapes of these two materials look similar. However, CH3NH3PbBr3 shows a larger bandgap as expected21,22 and lower ε values. For many semiconducting materials, the materials with larger bandgap generally possess smaller ε values.23 Thus, it is not surprising to see that CH3NH3PbBr3 with the bandgap of ∼2.3 eV exhibits ε values smaller than those for CH3NH3PbI3 with a bandgap of ∼1.5 eV. The smaller ε in turn results in the larger oscillator strength of 4305

DOI: 10.1021/acs.jpclett.5b01699 J. Phys. Chem. Lett. 2015, 6, 4304−4308

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The Journal of Physical Chemistry Letters the excitons in CH3NH3PbBr3 than that for CH3NH3PbI3,24 which is clearly seen in Figure 3. Electronic origin of optical structures observed in the ε spectrum can be identified by comparing the experimental data and the results from the first-principles calculations. In this study, two different geometries of α-phase CH3NH3PbBr3 are considered. The calculations were performed for the CH3NH3+ molecules aligned in the ⟨111⟩ and ⟨100⟩ directions as depicted in Figure 4a and Figure 4b, respectively. Our calculations

aligned with the bond direction. When the CH 3 NH 3 + molecules are oriented to the ⟨111⟩ direction, Pb-p orbitals rotate with respect to the bond direction, which makes the interaction weaker. Overall, the band structures look similar for both molecular orientations. However, a few small differences are found. While the structure with ⟨111⟩ orientation has a direct bandgap located at the R point of Brillouin zone (BZ), the conduction-band-minimum for the structure with ⟨100⟩ orientation appears at a position that is slightly off the R point toward the Γ point. Thus, CH3NH3PbBr3 exhibits the indirect bandgap characteristic when the CH3NH3+ molecules are aligned in the ⟨100⟩ direction. Our calculations show that the energy difference between the direct and indirect bandgap, ΔE ≡ Edir − Eind for the ⟨100⟩ configuration, is 24 meV. A similar result was obtained for CH3NH3PbI3, and the calculated ΔE is 25 meV.29 The calculated ε spectra of CH3NH3PbBr3 for the CH3NH3+ molecules oriented in the ⟨111⟩ and ⟨100⟩ directions are displayed in Figure 6a and Figure 6b, respectively. Even though

Figure 4. Atomic structures of the cubic phase CH3NH3PbBr3 with the CH3NH3+ molecules aligned in the (a) ⟨111⟩ and (b) ⟨100⟩ directions. The view is in the y−z plane. (Purple: Pb; Green: Br; Red: C; Blue: N).

suggest that CH3NH3+ molecules prefer to align in the ⟨100⟩ direction, although the energy difference between the two configurations is small. The difference in the total energy between the ⟨100⟩ and ⟨111⟩ orientations is estimated to be only 33 meV/unit-cell (12 atoms). A similar conclusion has been drawn from recent density functional theory calculations for CH3NH3PbI3.25 The absence of a large energy barrier to rotation is likely to result in a labile movement of CH3NH3+ molecules at room temperature.26,27 We note that a formation of ferroelectric domain wall has not been considered in our calculations because the energetically favorable domains seem not to change the bandgap much.28 The calculated energy band structures of CH3NH3PbBr3 for the two molecular orientations are shown in Figure 5. Charge density analysis shows that the valence band maximum has Pb-s and Br-p antibonding characteristics, while the lowest three conduction band states have Pb-p and Br-s orbital characteristics. The antibonding character of the conduction band state is more clearly observed when the CH3NH3+ molecules are oriented to the ⟨100⟩ direction because Pb-p orbitals become

Figure 6. Real (gray solid lines) and imaginary (black solid lines) parts of calculated ε spectra for the cubic phase CH3NH3PbBr3 with the CH3NH3+ molecules oriented in the ⟨111⟩ and ⟨100⟩ directions. Contributions to ε2 from the M, R, Γ, and X points of BZ are shown as colored dashed lines.

the overall shapes of ε spectra do not show a strong dependence on the molecular orientation, the optical structures in the ⟨111⟩ data appear to be sharper than those in the ⟨100⟩ data. This is because the crystal with the ⟨111⟩ molecular orientation has high symmetry, so there are more degenerate states that lead to sharp peaks in the ε spectra. For the ⟨100⟩ orientation, the lower symmetry leads to band splitting, so the optical spectrum is broadened. However, as discussed earlier, it is unlikely that the SE-determined ε spectrum can be unambiguously matched to either of the calculated ε spectra because the CH3NH3+ molecules could be randomly oriented at room temperature due to the small orientation energy. Therefore, the experimental ε spectrum shown in Figure 3 can be regarded as an average of the two calculated data sets in practice. To understand the electronic origin of each major optical structure, we resolved the contributions from four high symmetric points of BZ. The ε2 data associated with the M, R, Γ, and X points are shown in colored dashed lines. As shown in the energy band structure diagram (Figure 5a,b), the lowenergy structures including the band edge are formed by the transitions at the R point. The transitions occurring at the M and X points have their major peaks at ∼3.5 and ∼4.0 eV, respectively. The contributions from the Γ point appear at the high-energy region (>5 eV). The major peak spanning from

Figure 5. Energy band structures of the cubic phase CH3NH3PbBr3 for the CH3NH3+ molecules oriented in the (a) ⟨111⟩ and (b) ⟨100⟩ directions. Percentage of red, blue, and green color represents relative contribution of CH3NH3+ molecule, Pb atom, and Br atom to the charge density of a given state, respectively. 4306

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The Journal of Physical Chemistry Letters ∼4.0 to ∼4.5 eV in the experimental spectrum seems to have multiple contributions−transitions at the M, R, and X points, while the shoulder structure at ∼3.5 eV can be attributed mainly to the transition at the M point. In conclusion, the electronic structure and related optical properties of a bulk single crystal of α-CH3NH3PbBr3 were studied both experimentally and theoretically. Spectroscopic ellipsometry was used to determine the room-temperature dielectric function ε = ε1 + iε2 spectrum of CH3NH3PbBr3 from 0.73 to 6.45 eV. Data are modeled with a total of eight T−L oscillators, which show the absorption edge with a strong excitonic transition at ∼2.3 eV and several above-bandgap optical structures associated with the electronic interband transitions. The energy band structure and ε data of CH3NH3PbBr3 for the CH3NH3+ molecules oriented in the ⟨111⟩ and ⟨100⟩ directions are obtained from first-principles density functional calculations. Results from the calculations suggest that the crystal with the CH3NH3+ molecules oriented in the ⟨100⟩ direction is energetically more favored than the one in the ⟨111⟩ direction, although the energy difference is rather small at 33 meV/unit-cell. In addition, the ⟨100⟩ molecular orientation makes the crystal become a slightly indirect bandgap material. The energy difference between the indirect and direct bandgap is estimated to be 24 meV. Overall, the shape of calculated ε data shows a qualitatively good agreement with experimental results. Owing to the small energy barrier between the ⟨111⟩ and ⟨100⟩ molecular orientations, the actual crystal is believed to have CH3NH3+ molecules in random orientations at room temperature. Electronic origins of major optical structures have been identified.

molecules oriented in the ⟨111⟩ and ⟨100⟩ directions were obtained from first-principles calculations using the generalized gradient approximation (GGA)31 for the exchange-correlation potential within the density functional theory framework and projector-augmented wave (PAW) potentials,32 as implemented in the Vienna Ab-initio Simulation Package (VASP) code.33 In the calculations, the lattice parameter is fixed to the experimentally determined value of 5.9312 Å. The internal atomic positions are fully relaxed until the residual forces on the atoms are smaller than 0.05 eV/Å, and a 6 × 6 × 6 k-point grid was used for BZ integration. For the calculation of ε, 3 × 3 matrix representation of the ε2 was calculated first, which is given as ⎛ 4π 2e 2 ⎞ 1 ϵ2, αβ (ω) = ⎜ ⎟ limq → 0 2 ⎝ Ω ⎠ |q|

∑ 2ωk δ(ϵc ,k − ϵv ,k − ω) c ,v ,k

× ⟨uc , k + eαq|uv ,k ⟩⟨uc , k + eβq|uv ,k ⟩*

(3)

where Ω is volume of the primitive cell and ωk is the k-point weight. The variable q represents the Block vector, and ϵc(v)k is the eigenvalue of conduction (valence) band at a given k-point. The cell periodic part of the wave function is denoted as u. The vectors eα(β) are unit vectors for the three Cartesian directions. Details of the computational method are explained in ref 34. The ε2 is obtained by averaging the diagonal components. For the calculation of ε2 data, a denser k-point grid of 10 × 10 × 10 was used. The ε1 was consequently calculated by the K−K transformation of the ε2 with a small complex shift of 0.1 eV to make the spectrum smooth for the given k-point meshes. Using the converged charge density, we also performed nonselfconsistent-field (NSCF) calculations for subsets of k-points to obtain the contribution from k-points close to one of four high symmetric points of the BZ. In Figure 6, the sum of the contributions is equal to the total ε2 obtained using all the kpoints in the mesh. We note that the GGA functional tends to underestimate the bandgap energy of semiconducting materials, but it describes the bandgap of CH3NH3PbBr3 quite well due to the error cancelation of “exchange-correlation” and “relativistic” effects. However, it will be desirable to use more advanced but also computationally demanding techniques such as the GW method to calculate the electronic structure and related physical properties with higher accuracy.

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EXPERIMENTAL SECTION Preparation of CH 3NH 3PbBr3 Crystalline Perovskite. We dissolved 0.5 mmol PbBr2 (183 mg) and 0.5 mmol CH3NH3Br (56 mg) in 5 mL of dimethylformamide (DMF) solution. This mixed suspension was slightly heated on a hot plate to obtain a transparent solution. The solution was filtered through a compacted Celite column. The filtrate was collected, and 2 mL of this solution was transferred into a 5 mL inner vial (total vial volume). To the outer vial, 5 mL of toluene was added before the transfer of the inner vial. Finally, the outer vial was carefully capped, sealed, and placed in a light-free benchtop. The diffusion of toluene from the outer vial into the inner vial was slow, and the crystallization process was maintained in a dark and undisturbed environment for at least 3 days. An orange, block-shaped (1.4 × 1.4 × 0.7 mm3) single crystal was obtained. Details of the crystal growth are given elsewhere.30 In a separate study, we characterized the structural properties of CH3NH3PbBr3 crystal by single-crystal XRD scans using a Bruker Apex II CCD-based X-ray diffractometer equipped with Mo Kα radiation (λ = 0.7107 Å).18 Spectroscopic Ellipsometry. SE measurements were carried out from 0.73 to 6.45 eV with the sample maintained at room temperature using a spectroscopic rotating compensator-type ellipsometer (J.A. Woollam, Inc., M2000-DI model). To accommodate a small-sized sample, the focusing optics unit was employed, which reduces the beam diameter down to a few hundred micrometers. The incident angle varied from 55° to 75° with an increment of 10°. Data were recorded after averaging 2000 cycles of the compensator (2000 revolutions per measurement) to improve the signal-to-noise ratio. First-Principles Calculations. The electronic structure and related optical properties of CH3NH3PbBr3 for the CH3NH3+

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.5b01699. Spectra and tabulated data for modeled optical functions, complex refractive index N = n + ik, normal-incidence reflectivity R, and absorption coefficients α, of CH3NH3PbBr3 in the spectral range of 0.74 to 6.40 eV (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Electronic mail: [email protected]. Notes

The authors declare no competing financial interest. 4307

DOI: 10.1021/acs.jpclett.5b01699 J. Phys. Chem. Lett. 2015, 6, 4304−4308

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ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08-GO28308. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes.

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