Large polarons in lead halide perovskites

Abstract

Lead halide perovskites show marked defect tolerance responsible for their excellent optoelectronic properties. These properties might be explained by the formation of large polarons, but how they are formed and whether organic cations are essential remain open questions. We provide a direct time domain view of large polaron formation in single-crystal lead bromide perovskites CH₃NH₃PbBr₃ and CsPbBr₃. We found that large polaron forms predominantly from the deformation of the PbBr₃^- frameworks, irrespective of the cation type. The difference lies in the polaron formation time, which, in CH₃NH₃PbBr₃ (0.3 ps), is less than half of that in CsPbBr₃ (0.7 ps). First-principles calculations confirm large polaron formation, identify the Pb-Br-Pb deformation modes as responsible, and explain quantitatively the rate difference between CH₃NH₃PbBr₃ and CsPbBr₃. The findings reveal the general advantage of the soft [PbX₃]^- sublattice in charge carrier protection and suggest that there is likely no mechanistic limitations in using all-inorganic or mixed-cation lead halide perovskites to overcome instability problems and to tune the balance between charge carrier protection and mobility.

Fig. 1. TR-OKE transients from a CH₃NH₃PbBr₃ crystal.

(A) OKE transients from CH₃NH₃PbBr₃ as a function of pump energy (1.85 to 2.30 eV). As it moves from nonresonant to preresonant condition, contribution from low-frequency motions coupled to electronic excitation is enhanced. As it reaches the carrier injection regime, additional subpicosecond dynamics manifest itself. (B) Fourier component of each OKE transient. The inset is the crystalline structure of CH₃NH₃PbBr₃. Black ticks at the top show calculated frequencies of normal modes, and sticks represent projections of the displacement vector on the normal modes upon large polaron formation (see fig. S4). FFT, fast Fourier transform.

Fig. 2. TR-OKE transients from a CsPbBr₃ crystal.

(A) OKE transients from CsPbBr₃ as a function of pump energy (1.83 to 2.43 eV). At the preresonant regime, low-frequency modes that are coupled to band-edge excitation are enhanced. At the carrier injection regime, additional subpicosecond dynamics, as well as long-lived polarization, manifest itself. (B) Fourier spectra of selected transients in nonresonant regime (1.83 and 2.00 eV), preresonant regime (2.21 and 2.25 eV), and carrier injection regime (2.43 eV). The inset is the crystalline structure of CsPbBr₃. Black ticks at the top show calculated frequencies of normal modes, and sticks represent projections of the displacement vector on the normal modes upon large polaron formation (see fig. S5).

Fig. 3. Comparison of transient reflectance and TR-OKE with above-gap excitation.

(A) Pseudocolor (Δα) representation of transient absorbance spectra of a CH₃NH₃PbBr₃ single crystal retrieved from transient reflectance (ΔR/R) pumped by 2.92 eV at 100 μW. (B) Dynamics of screening extracted from transient reflectance probed at 2.31 eV for CH₃NH₃PbBr₃ (blue) and at 2.38 eV for CsPbBr₃ (red) as a function of pump-probe delay. The lines are monoexponential fits convoluted with a Gaussian function, which describes the cross-correlation between pump and probe pulse [full width at half maximum (FWHM), 100 fs]. (C) The structural dynamics triggered by photo-carrier injection as a function of pump-probe delay observed by TR-OKE with across-gap excitation. CH₃NH₃PbBr₃ (blue) and at 2.38 eV for CsPbBr₃ (red) as a function of the pump-probe delay. The lines are double-exponential fits convoluted with a Gaussian function, which describes cross-correlation between the pump and probe pulse (FWHM, 70 fs).

Fig. 4. Hybrid DFT calculations.

(A) Relaxed structures of CH₃NH₃PbBr₃ with positive and negative charge injection. Changes in Pb-Br-Pb bending and Pb-Br length are shown. (B to E) Potential energy surfaces for relaxation of the CH₃NH₃PbBr₃ (B and C) and CsPbBr₃ (D and E) unit cell (four formula units) upon positive (B and D; red curve) and negative (C and E; blue curve) charge injection. The neutral state energy (black) along the distortion coordinate is also shown.

Fig. 5. Estimation of polaron size from first principle.

(A) Distribution of Pb-Br distances (Å; top) of the positive polaron state for a pseudocubic 2 × 2 × 8 CsPbBr₃ model made by 32 formula units. (B) Distribution of the excess positive charge (red isosurface) following the pattern of Pb-Br distances. The figure has been centered at the maximum of hole localization.