Structural effects on the luminescence properties of CsPbI3 nanocrystals

Metal halide perovskite nanocrystals (NCs) are promising for photovoltaic and light-emitting applications. Due to the softness of their crystal lattice, structural modifications have a critical impact on their optoelectronic properties. Here we investigate the size-dependent optoelectronic properties of CsPbI3 NCs ranging from 7 to 17 nm, employing temperature and pressure as thermodynamic variables to modulate the energetics of the system and selectively tune the interatomic distances. By temperature-dependent photoluminescence spectroscopy, we have found that luminescence quenching channels exhibit increased non-radiative losses and weaker exciton–phonon coupling in bigger particles, in turn affecting the luminescence efficiency. Through pressure-dependent measurements up to 2.5 GPa, supported by XRD characterization, we revealed a NC-size dependent solid–solid phase transition from the γ-phase to the δ-phase. Importantly, the optical response to these structural changes strongly depends on the size of the NC. Our findings provide an interesting guideline to correlate the size and structural and optoelectronic properties of CsPbI3 NCs, important for engineering the functionalities of this class of soft semiconductors.

Growth of CsPbI 3 nanocrystals. When the PbI 2 precursor dissolved completely, N 2 flow was introduced into the flask heating it up to the desired temperature (140˚C -220 ˚C). Then 1 ml of the Cs-oleate precursor was swiftly injected into the reaction flask. Within just few seconds from the injection, solution became turbid red. Further crystal growth and nucleation was stopped by immersing reaction flask in an ice bath.
After cooling to room temperature, CsPbI 3 NCs size-selective precipitation and purification was introduced. Methyl acetate (MeOAc) was added in the initial CsPbI 3 NCs solution in a volume ratio of 3 (NCs):1 (MeOAc). After centrifuging at 7500 rpm for 5 min, larger NCs were precipitated. Precipitate was collected and redispersed into 3 ml of n-hexane and supernatant was decanted for the next step (MeOAc) was added again in the same ratio). This second centrifugation produced another batch of NCs with a smaller size, compering to the first one.
This same process was repeated until there was no obvious precipitate of NCs from the supernatant. Average number of batches from one synthesis was three. Some of the final solutions required one more centrifugation (without adding extra MeOac) in order to discard supernatant which sometimes contained some bigger agglomerates or precursor crude leftovers.
All solutions were was filtered through a PVDF/L0.22 μm filter and then kept in a vial inside the fridge (5˚ C). These solutions were stable for a month. For longer stability of the solutions, few months, they were kept in freezer (-21˚C).
Thin film deposition. CsPbI 3 NCs were first deposited as thin films prepared by spin coating the colloidal solution onto a glass substrates and drying it under N 2 flow multiple times, to ensure adequate substrate coverage. The spectra of the films at room temperature are nearly identical with the PL spectra of the NCs in solution, validating the success of the deposition procedure (Fig. S8). Only deviation has been seen for the smallest, 7nm, NCs.

Transmission electron microscopy (TEM)
Transmission electron microscopy (TEM) for size distribution analysis was performed using a JEM-1400Plus (JEOL) equipped with a thermionic source (LaB6) and operated at 120 kV. nm NCs were carried out Bruker APEX-II diffractometer equipped with sealed-tube and CCD detector, using Mo-Kα radiation (λ=0.71073 Å). NC samples were measured at room temperature. Specifically, the 17 nm NCs were load, in silicon oil, on Diamond Anvil Cell (DAC) with diamond anvil type Ia and culet of 0.4 mm. The internal pressure was measured using the ruby fluorescence method [1]. The NCs-loaded DAC was mounted on a standard goniometer head and centered to X-ray beam. The diffraction patterns at different pressures were collected on the CCD detector and the obtained two-dimensional ring patterns were integrated and converted to one dimensional powder profile using CrysAlis Pro program.

Steady -state absorption and photoluminescence
Steady-state absorbance of perovskite solutions, in a quartz cuvette, was measured using a UV-VIS spectrophotometer Shimadzu uv-2700. Photoluminescence of the same solutions was characterized using a NanoLog Fluorometer (Horiba Jobin-Yvon), with excitation wavelength 450 mn and a 2 nm spectral resolution and using an iHR320 detector in the visible range.

Absolute PLQY
Absolute values of PLQY were obtained from measurements performed in an integrating sphere (Labsphere). Excitation was provided by a 405 nm c.w. diode laser and spectra acquired through an optical fiber coupled from the sphere to a spectrometer (Ocean Optics Maya Pro 2000) with an intensity of 10 mW. PLQY values were calculated employing the method proposed by deMello et al. [3]

Temperature dependent steady state absorption and photoluminescence
All temperature dependent measurements were performed under vacuum using a Linkam Stage cooled with liquid nitrogen. Steady state absorption spectra was measured on perovskite thin films deposited on quartz using a UV/VIS/NIR spectrophotometer Lambda 1050, Perkin Elmer.
Photoluminescence was excited using a 405 nm Oxxius laser focused on the sample with a 10 cm lens. PL was detected using a Maya1000 visible spectrometer.

Pressure-dependent measurements
All pressure-dependent measurements were performed on a Diamond Anvil Cell (One20DAC) with diamond anvil type Ia and culet of 0.4 mm. Stainless still gasket, with the pre-indented hole, was centered on one of the diamonds. Sample was loaded by drop casting several times and drying under a nitrogen flux between the depositions. When the sample was dried, pressure marker (ruby powder) and pressure transmitting medium (silicon oil) were placed into the hole in the gasket. Silicon oil was applied as a pressure-transmitting medium in order to establish hydrostatic conditions. The pressure was measured by using the ruby fluorescence method. [1] With applying pressure ruby photoluminescence peaks are shifting toward higher wavelengths ( Fig. S9) and by fitting peaks with Lorentzian profiles it is possible to determinate the exact pressure. [2] The high-pressure evolution of steady-state photoluminescence spectra was collected using a micro Raman confocal microscope (via Raman Microscope Renishaw, 50 x objective, 532 nm excitation wavelength).

Time-resolved PL (tr -PL)
TRPL in the ps range was performed using a Hamamatsu streak camera and a Coherent Chameleon oscillator (pulse duration 30 fs, repetition rate 80 MHz) as a pump, using a pump wavelength λ = 400 nm obtained by frequency doubling the fundamental at 800 nm in a BBO crystal. An acousto-optic modulator (AOT) was used to reduce the laser repetition rate to 2 MHz. The measurements were performed using a measurement window of 50 ns for pressures up to 1 GPa, and a 100 ns widow for higher pressure (respectively 0.5 ps and 1 ns temporal resolution). The sample was pressurized in a DAC, on the previously described way, and light was focused on NCs clusters through a 50x long working distance microscope objective, (r = 2 m), corresponding to a typical of pump fluence of 150 mW/cm 2 .

Calculation of radiative and non-radiative decay rates
The radiative and non-radiative decay rates, respectively k rad and k nonrad , are calculated by combining tr-PL results with absolute PLQY. First we note that the total decay rate k tot = k nr + k rad = 1/ is the inverse of the effective decay time , which for this simple model can be retrieved from fitting the tr-PL decay with a single exponential. Furthermore, the absolute PLQY is the ratio of radiative recombination processes with all decay paths, namely PLQY = k rad / k tot . Hence, the radiative decay rate can be retrieved from the experimental data as k rad = PLQY* k tot = PLQY/ Subsequently, the non radiative decay rate can be found as k nonrad = k tot -k rad = (1-PLQY)/. Table S1. Parameters obtained from the temperature-dependent PL peak fitting    Energy (eV) Figure S2. Temperature dependent PL spectra, for the 9 nm NCs (7 and 17 nm are found in Fig.3a,b): the graph indicates three main phenomena with decreasing temperature: anomalous blue band gap shift (but characteristic for perovskite), narrowing of the PL and a variation in PL intensity, with inflection points are observed at around 200 K. Figure S3. Change of PL peak position with temperature. The PL peak energy E g (T) is blue shifted as the temperature increases across all particle sizes.
The relative shift is related to electron-phonon (EP) interaction and lattice thermal expansion through a single oscillator model , [5] where is the un-renormalized bandgap, and are the weight of the thermal expansion and carrierphonon interaction, respectively, and represents the average optical phonon energy. Results ℏ are reported in Table S1. As expected, due to quantum confinement the normalized band gap decreases with NC size. The thermal expansion A TE on the other hand ( = 0) = 0 + is increased. The value of the average optical phonon energy was fixed to the values obtained in the fitting of the temperature dependence of the PL FWHM (see Fig. 3 and Table 2  Energy (eV) Figure S4. Temperature dependent absorbance of the 17 nm NPs: no phase transition is observed between 77 K and 300 K.

Wavelength (nm)
Before pressurization After pressurization Energy (eV) Figure S5. PL spectra recorded for 17 nm NCs at atmospheric, before a pressurization cycle (black line) and after release of the highest applied pressure (red line). During the whole pressurization cycle, the PL intensity is gradually quenched before finally disappearing, but the pressure-induced change is fully reversible in the investigated range of pressures.   Only deviation has been seen for the smallest, 7 nm, NCs.