Static Disorder in Lead Halide Perovskites

Abstract

In crystalline and amorphous semiconductors, the temperature-dependent Urbach energy can be determined from the inverse slope of the logarithm of the absorption spectrum and reflects the static and dynamic energetic disorder. Using recent advances in the sensitivity of photocurrent spectroscopy methods, we elucidate the temperature-dependent Urbach energy in lead halide perovskites containing different numbers of cation components. We find Urbach energies at room temperature to be 13.0 ± 1.0, 13.2 ± 1.0, and 13.5 ± 1.0 meV for single, double, and triple cation perovskite. Static, temperature-independent contributions to the Urbach energy are found to be as low as 5.1 ± 0.5, 4.7 ± 0.3, and 3.3 ± 0.9 meV for the same systems. Our results suggest that, at a low temperature, the dominant static disorder in perovskites is derived from zero-point phonon energy rather than structural disorder. This is unusual for solution-processed semiconductors but broadens the potential application of perovskites further to quantum electronics and devices.

Origin of Photoluminescence, Exciton Binding Energy, Exciton-Phonon interaction, and Urbach Energy in γ-CsPbI3 Nanoparticles.

“…The fitting of the model to the experimental data gives that 𝐸 𝑝ℎ = 20 ± 2 𝑚𝑒𝑉, which is within the same order of magnitude of the value calculated for LO phonons using the Segall's expression. On the other hand, 𝐸 𝑈 (0) = 8 ± 2𝑚𝑒𝑉 which is very close to the results in thin films of different composition recently reported 67,96,98 , although a bit higher as expected for nanoparticles. In the work by Zeiske and collaborators it is also argued that the very low values for 𝐸 𝑈 (0) obtained in perovskites are produced by the excellent quality of the crystal structure and that the static contributions to Urbach energy are dominated by zero-point phonon energy.…”

“…𝐸 𝑈 monotonically increases from 7 meV at 10 K to 21 meV at 290 K as shown in Figure 6 b, which is a consequence of an increased carrier-phonon interaction 96 . This behavior can be modeled using equation (9) 96,97 𝐸 𝑈 (𝑇) = 𝐸 𝑈 (0) coth ( 𝐸 𝑝ℎ 2𝑘 𝐵 𝑇 )…”

“…In this expression 𝐸 𝑈 is called Urbach Energy and is related to lattice disorder 96 and 𝐸 0 is the Urbach Focus which is one of the characteristics of the Urbach like absorption. For regular semiconductors 𝐸 0 has a value that is above the bandgap but in lead halide perovskites, due to the atypical dependence of the bandgap with energy, this parameter takes values below the bandgap.…”

“…high crystalline quality) and hence it also determines the electronic properties of the material. This parameter is related with carrier mobility and determines the voltage deficiency (defined as the difference between bandgap voltage 𝐸 𝑔 /𝑞 and open circuit voltage) in solar cells 96,98 .…”

The Electronic Disorder Landscape of Mixed Halide Perovskites

“…Figure d shows the extracted Urbach energies: they are in broad agreement with previously reported values in the literature. ,,− The values of the measured Urbach energies are all above 10 meV, much larger than our modeled values. This discrepancy has been attributed to the strong temperature dependent contribution to the Urbach energy that has been previously noted and assigned to dynamic disorder due to thermal occupancy of vibrational modes. , Some studies using temperature dependent photoluminescence measurements have indicated that extrapolation to low temperatures takes the Urbach energies down to a few meV . We note that our direct measurements of optical absorption are performed at room temperature, and we emphasize that our computational model introduces disorder only through the compositional alloying of the halides.…”