Static Disorder in Lead Halide Perovskites

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.


S2
Temperature dependent external quantum efficiency (EQE): Sensitive EQE spectra were obtained using a PerkinElmer spectrophotometer (Lambda950) as a light source. The monochromator output light was physically chopped at 273 Hz (Thorlabs MC2000B) and focused on the device under test (DUT) using different optical components. Prior to analyzing the DUT photocurrent response with a Standford Research lock-in amplifier (SR860), the DUT photocurrent was fed into a Femto current pre-amplifier (DCLPCA-200). The EQE system was pre-calibrated using NIST-calibrated silicon and germanium photodiode sensors from Newport (818-UV, 818-IR). A detailed description of the EQE apparatus is provided elsewhere. 1 For temperature dependent EQE measurements, the DUT was mounted in an electrically shielded sample holder (Linkam LTS420 thermal stage) connected to the Linkam T96 temperature controller with integrated LNP96 liquid nitrogen pump.
Current-voltage (J-V) characteristics: J-V curves were obtained in a 2-wire source-sense configuration with a Keithley 2400. An Oriel class AAA Xenon lamp-based solar simulator was used for illumination providing approximately 100 mW cm -2 of AM 1.5G irradiation and the intensity was monitored simultaneously with a Si photodiode. The exact illumination intensity was used for efficiency calculations, and the simulator was calibrated with a KG5 filtered silicon solar cell (certified by the Fraunhofer ISE). The obtained short-circuit current density ( SC ) was checked by integrating the product of the corresponding external quantum efficiency (EQE) and the AM 1.5G solar spectrum which matches the obtained SC within less than 5 %. The temperature of the cell was fixed to 25 °C and a voltage ramp (scan rate) of 67 mV/s was used. Perovskite film fabrication: The triple cation perovskite was deposited by spin-coating at 5000 rpm for 35 s and 10 s after the start of the spinning process, the spinning substrate was washed with 300 L ethylacetate for approximately 1 s (the anti-solvent was placed in the center of the film). We note, that by the end of the spinning process the perovskite film turned dark brown.

Device fabrication of p-i-n-type cells:
The perovskite film was then annealed at 100 °C for 1 h on a preheated hotplate where the film turned slightly darker. The MAPI solution (80 L) was spin-coated at 1000 rpm for 5 s followed by 3000 rpm for 80 s. 100 L toluene was added dropwise after 40 s to form a transparent perovskite film. After the spin coating, the films were dried for 2 min in the glovebox at room temperature until the films changed their color from yellow to light brown. The MAPI perovskite layers were then subsequently annealed at 100 °C on a hotplate where the films turned black immediately. For the double cation perovskite, a 2-step interdiffusion method was employed. The first step was the deposition of the PbI2 layer. This was achieved by dropping 150 L of the lead iodide solution in a N2-filled glovebox and spin-coating at 1500 rpm for 30 s, the films were then annealed at 70 °C for 1 min resulting in a yellow-transparent layer. We note that if the PbI2 layers are left for too long before proceeding to the next step, the lead S4 iodides appearance would change to a rougher yellow color and the performance of the complete devices would be substantially lower. Afterwards the formation of the perovskite was achieved by dropping 150 L of the cation solution on top of the lead iodide layer which turned the film into a brown-transparent layer, then rapidly starting the spin-coating at 2500 rpm for 30 s, which resulted in a red film. This was followed by an annealing step at 150 °C for 15 min outside of the glovebox under ambient conditions (at a relative humidity of 25%) which resulted in a dark brown or black perovskite film. For the second-annealing step, a transportbox was used to transfer the samples out of the glovebox and in order to keep the layers in a nitrogen atmosphere immediately before the annealing on a preheated plate (150 °C). We note that as soon as the perovskite layers get into contact with air, the crystallization and a phasechange process starts, and we noticed that a rapid transfer to the hotplate directly after opening the transport-box was beneficial for the cell performance. A Supplementary Video is available on the publishers webpage of ref. 2 that shows the critical fabrication steps. in the exponential region calculated using Equation (2) provided in the main text. A thickness dependence is seen leading to an uncertainty in Urbach energy ( U ) determination of ±1 meV. Note that these devices were fabricated from the same precursor with the same recipe and in the same fabrication round as devices shown in Figure 1b in the main text.

Figure S4
External quantum efficiency (EQE) spectrum of (a-c) single, double, and triple cation perovskite solar cell plotted as a function of photon energy and compared for different temperatures.
(d-f) Repetition of panel (a-c), but apparent Urbach energy spectra plotted as a function of photon energy and compared for different temperatures. The Urbach energy spectra were calculated according to Equation (2) shown in the main text.