Structural phase transitions and photoluminescence mechanism in a layer of 3D hybrid perovskite nanocrystals

Although the structural phase transitions in single-crystal hybrid methyl-ammonium (MA) lead halide perovskites (MAPbX3, X = Cl, Br, I) are common phenomena, they have never been observed in the corresponding nanocrystals. Here we demonstrate that two-photon-excited photoluminescence (PL) spectroscopy is capable of monitoring the structural phase transitions in MAPbX3 nanocrystals because nonlinear susceptibilities govern the light absorption rates. We provide experimental evidence that the orthorhombic-to-tetragonal structural phase transition in a single layer of 20-nm-sized 3D MAPbBr3 nanocrystals is spread out within the 70 - 140 K range. This structural phase instability range arises because, unlike in single-crystal MAPbX3, free rotations of MA ions in the corresponding nanocrystals are no longer restricted by a long-range MA dipole order. The resulting configurational entropy loss can be even enhanced by the interfacial electric field arising due to charge separation at the MAPbBr3/ZnO heterointerface, extending the orthorhombic-to-tetragonal structural phase instability range from 70 to 230 K. We conclude that the weak sensitivity of conventional one-photon-excited PL spectroscopy to the structural phase transitions in 3D MAPbX3 nanocrystals results from the structural phase instability providing negligible distortions of PbX6 octahedra. In contrast, the intensity of two-photon-excited PL and electric-field-induced one-photon-excited PL still remains sensitive enough to weak structural distortions due to the higher rank tensor nature of nonlinear susceptibilities involved. We also show that room-temperature PL originates from the radiative recombination of the optical-phonon vibrationally excited polaronic quasiparticles with energies might exceed the ground-state Frohlich polaron and Rashba energies due to optical-phonon bottleneck.


I. INTRODUCTION
Hybrid methyl-ammonium (MA) lead halide perovskites (MAPbX3, X = Cl, Br, I) represent a class of materials offering an illustrative platform for studying the relaxation dynamics of photoexcited carriers and their transport phenomena in novel highly efficient solar cells for solar energy harvesting technology. [1][2][3][4][5][6][7][8][9][10][11] One of the most important specific features of these hybrid materials is that their crystalline structure can be viewed as two alternating sublattices. Specifically, the inorganic sublattice is composed by cornersharing PbX6 octahedra which are responsible for forming the valence band (VB) maximum and conduction band (CB) minimum of these materials. 7,8 Consequently, the initial relaxation of photoexcited carriers, their recombination and transport phenomena all occur in the inorganic sublattice. Alternatively, the organic MA sublattice acts as a medium modifying the electrostatic potential of the inorganic sublattice, thus contributing less significantly to the charge screening and localization effects, nevertheless, providing an ultralow thermal conductivity being caused by long-range MA dipole order. 12 The structural peculiarities of these materials allow for the three structural phase transitions occurring in the temperature range of T ~140 -240 K, which usually appear in single-crystal MAPbX3 and its polycrystalline thin film, [13][14][15][16][17][18][19][20][21][22][23][24][25] whereas they have never been observed in MAPbX3 nanocrystals. 21 Because arrays of colloidal nanocrystals are known to be promising alternatives to the single-crystal semiconductor based electronics, optoelectronics, and solar energy harvesting applications 26 and because the properties of single-crystal MAPbX3 differ significantly for different structural phases, [13][14][15][16][17][18][19][20][21][22][23][24][25] we comprehensively explored the structural phase transitions in a fully encapsulated single layer of 20-nm-sized 3D MAPbBr3 nanocrystals using one-photon-excited and two-photon-excited PL spectroscopy. The effect of the technologically important MAPbBr3/ZnO heterointerface on this phenomenon has also been studied here. We show that two-photon-excited PL spectroscopy and electric-field-induced one-photon-excited PL spectroscopy are capable of more precisely monitoring the structural phase transitions in 3D MAPbBr3 nanocrystals compared to conventional one-photon-excited PL spectroscopy since nonlinear susceptibilities govern the light absorption rates. Consequently, one can recognize that the orthorhombic-totetragonal structural phase transition in 3D MAPbBr3 nanocrystals, unlike in single-crystal MAPbX3, is spread out over the broad temperature range of T ~70 -140 K. This extension of the structural phase transition defines the structural phase instability range, within which the local field fluctuations arising due to free rotations of MA ions are no longer restricted by long-range polar order. 27,28 The resulting configurational entropy loss and the corresponding liquid-like motion of MA cations 1 can be even enhanced by the interfacial electric field when charge separation at the MAPbBr3/ZnO heterointerface occurs, extending the orthorhombic-to-tetragonal structural phase instability range from T ~70 to 230 K. The latter effect is found to be dependent on the ZnO layer thickness and the photoexcited carrier density. Finally, we conclude that a stepwise shift of the PL band with temperature observed for single-crystal MAPbX3 and assigned to structural phase transitions does not appear anymore in 3D MAPbX3 nanocrystals because of negligible distortions of PbX6 octahedra under the structural phase instability regime. On the contrary, the nearly monotonic blue shift of PL band with increasing temperature in a fully encapsulated single layer of 20-nm-sized 3D MAPbBr3 nanocrystals seems to result rather from the heating effect under TO/LO phonon bottleneck [2][3][4] than that being induced by the progressive PbX6 octahedra distortions. Consequently, room-temperature PL is expected to originate from the radiative recombination of the optical-phonon vibrationally excited polaronic quasiparticles with energies might exceed the ground-state Fröhlich polaron and Rashba energies due to optical-phonon bottleneck. Because of small masses and large radii of these vibrationally excited polaronic quasiparticles, their high mobility and long-range diffusion become possible.

II. EXPERIMENTAL A. Sample fabrication
The size-controlled CH3NH3PbBr3 nanocrystals were synthesized by a ligand-assisted reprecipitation (LARP) technique. 29 The CH3NH3Br precursor was synthesized by adding hydrobromic acid (HBr, 48 wt.% in H2O, 99.99%; Sigma-Aldrich) drop wise to a stirred solution of methylamine (CH5N, 30~33 wt.% in ethanol) at 0 o C followed by stirring for 1 h. Upon drying at 100 °C in air, white CH3NH3Br powder in quantitative yield was formed. After being washed with diethyl ether (Shanghai Lingfeng Chemical Reagents) and recrystallized with ethanol, CH3NH3Br powder was dried for 24 h in a vacuum furnace and along with other precursors was added into the N,N-dimethylformamide (DMF, C3H7NO, anhydrous, 99.8%). Specifically, CH3NH3Br and lead (II) bromide (PbBr2, powder, 98%) were dissolved in 100 μL DMF forming a mixture with a concentration of 0.1 mM and then 200 μL oleic acid (C18H34O2; Aladdin) and 20 μL oleylamine (C18H37N, 80~90%; Aladdin) were added into this mixture. The oleic acid/oleylamine ligand ratio was selected for tailoring the size of the nanocrystals. The 100 μL mixture of various precursors was injected afterwards into 3 mL chloroform (Shanghai Lingfeng Chemical Reagents) as an antisolvent. A yellow-greenish colloidal solution was acquired afterwards. For further purification, 1.5 mL toluene/acetonitrile (CH3CN, anhydrous, 99.8%) mixture with a volume ratio 1:1 was added into the solution and the sediment was dispersed in hexane after centrifuging at 9000 rpm for 2 min.
To prepare the fully encapsulated layer of 3D CH3NH3PbBr3 nanocrystals, the sapphire plates (10×10×0.3 mm; Jiangsu Hanchen New Materials) were cleaned by successively soaking them in an ultrasonic bath with deionized water, acetone, and isopropanol for 10 min each and dried with nitrogen. The sapphire substrates were transferred afterwards into the atomic layer deposition (ALD) system (PICOSUN™ R-200) to grow a ZnO film. Diethyl zinc (DEZn, Zn(C2H5)2) and H2O were used as precursors. High purity nitrogen with dew point below -40 o C was used as a purging and carrier gas. The reactor chamber pressure was set as 1000 Pa during the growth. When the growth temperature of 200 °C was reached, DEZn was introduced to the reactor chamber with a flow rate of 150 sccm followed by purging with nitrogen to remove the residues and byproducts. The precursor of H2O with a flow rate of 200 sccm was introduced afterwards into the reactor chamber to start with the ZnO layer growth. The number of ALD growth cycles was selected to grow a ZnO layer with thicknesses of 30 and 100 nm, which were also verified by other methods.
Closely packed and uniformly distributed CH3NH3PbBr3 nanocrystals were spin-coated afterwards by optimizing the spin speed to 1500 rpm to either the clean sapphire (Sa) plate or to those initially ALD-coated with a ZnO layer of 30 nm and 100 nm thickness. The resulting structure was covered by another sapphire plate, leaving the air gap above the nanocrystal array of ~1 m and gluing sapphire plates on sides by UV adhesive. The obtained samples will be referred further below as MAPbBr3/Sa, MAPbBr3/ZnO(30nm) and MAPbBr3/ZnO(100nm), respectively.

B. Scanning electron microscopy (SEM) imaging.
The cross-sectional SEMs images of the sandwiched samples were acquired using a ZEISS Gemini 300 field emission scanning electron microscope in a secondary electron mode after cleaving the samples with a diamond scriber.

C. Transmission electron microscopy (TEM) imaging
The crystallinity of the synthesized CH3NH3PbBr3 nanocrystals was confirmed by TEM imaging (Tecnai F30 field-emission TEM) operated at 300 kV and at room temperature.

D. X-ray diffraction (XRD) characterization
The XRD patterns of the synthesized CH3NH3PbBr3 nanocrystals were measured using a Rigaku SmartLab X-ray diffractometer, equipped with a Cu KR radiation source (wavelength at 1.542 Å). The samples were scanned from 10 o < 2θ < 60 o at an increment of 10 o /min.

E. Conventional ultraviolet-visible absorption and PL characterization
The conventional absorption spectra were measured at room temperature using the Beijing Spectrum Analysis 1901 Series spectrometer. To study PL spectra, the Ocean Optics QE 65 Pro spectrometer equipped with a 365 nm excitation source was used with a spectral resolution of ~1.0 nm.

F. Temperature-dependent PL measurements
To study temperature-dependent PL spectra, the commercially available temperature controller (Lakeshore 336) with a temperature range of 20 -295 K was used. The PL spectra were measured using the Andor Shamrock SR750 spectrograph equipped with a CCD detector. Figure 1a shows a sketch of the experimental setup for measuring the temperature dependent PL from a layer of 3D MAPbBr3 NCs. Three laser wavelengths were used to excite PL: 325, 442, and 800 nm, which were emitted from the CW He-Cd laser (325 and 442 nm) and the femtosecond laser (Astrella-Tunable-V-F-1K) with the pulse width of 100 fs and a repetition rate of 1.0 KHz (800 nm). The laser beam incidence angle was 30°. The sample holder was designed to allow the excitation laser light to pass through the sample and the cryostat windows, being blocked afterwards outside the cryostat. Such an arrangement eliminates any additional spectroscopic features associated with the scattering and reabsorption of laser light from the sample holder to appear in PL spectra. The laser spot diameter was ~250 m for all the three excitation wavelengths. The excitation power was changed by a variable neutral density filter (Thorlabs). The averaged laser power varied from 0.03 to 20 mW for the CW He-Cd laser and from 2.0 to 30 mW for the pulsed laser. For the experimental conditions applied, 1.0 mW average laser power corresponds to the laser light intensity (power density) of 2.04 W/cm 2 for the CW laser and 20.5 GW/cm 2 for the pulsed laser. Taking into account the measured one-photon absorption coefficient (~4.0 × 10 4 cm -1 and ~1.9 × 10 4 cm -1 for 325 and 442 nm laser light, respectively) and the two-photon absorption coefficient of ~8.6 cm/10 9 W, 30 the reflectance coefficient of 0.37 and estimating afterwards the power density absorbed within the CH3NH3PbBr3 nanocrystal array, 31 the corresponding photoexcited carrier densities were calculated to be ~7.5 × 10 17 cm -3 ( ~7.5 × 10 -4 nm -3 ), ~4.9 × 10 17 cm -3 ( ~4.9 × 10 -4 nm -3 ), and ~1.7 × 10 18 cm -3 (~1.7× 10 -3 nm -3 ) for 325, 442, and 800 nm laser light, respectively. Assuming the nanocrystal cubic shape of the same edge length of ~20 nm (the corresponding volume is ~8 × 10 3 nm 3 ), the average electron-hole pair occupancy per nanocrystal can be estimated as ~6.0, ~3.9, and ~13.6, respectively. However, multiple excitons photoexcited in a nanocrystal is believed to be non-interactive since their small effective exciton Bohr radius in MAPbX3 perovskite materials (2.0 -4.0 nm), compared, for example, to GaAs (~12 nm), 32 as will be discussed further below in details. Figure 2(a) shows the TEM image of the as-grown colloidal cubic-shaped MAPbBr3 nanocrystals together with the corresponding histogram presenting the nanocrystal size distribution which is maximized at ~19.8 ± 1.7 nm. The highresolution TEM image [ Fig. 2 thus suggesting that no more than one layer of the closely packed MAPbBr3 nanocrystals was deposited. Because 3D MAPbX3 nanocrystals are known to be the basic building blocks for growing the corresponding nanoplates and nanowires, that is, 2D and 1D structures, 35,38 our samples can also be identified as quasi-2D arrays of 3D CH3NH3PbBr3 nanocrystals to distinguish them from the 2D layered counterpart of hybrid perovskites [(C4H9NH3)2PbBr4]. 38 Figure 2(h) and (i) shows the room-temperature conventional absorption and PL spectra of the MAPbBr3/Sa, MAPbBr3/ZnO(30nm), and MAPbBr3/ZnO(100nm) samples identified in Fig. 2(d)-(f). The absorption spectrum of the MAPbBr3/Sa sample reveals two contributions associated with electronic transitions from VB to two CBs. 40,41 The ZnO layer additionally contributes to absorption spectra in the UV range for the MAPbBr3/ZnO samples [ Fig. 2(h)]. 42 The Stokes shift was estimated as ∆ Stokes = + ℎ = ~60 meV, where  is the reduced Planck constant, ∆ Stokes is the frequency difference between the 1s free exciton (FE) peak in absorption spectra and the PL peak, and and ℎ are the corresponding reorganization The Stokes shift was estimated as a photon energy difference between the FE peak in absorption spectra and the PL peak. energies 43 for electrons and holes, respectively. The latter quantities characterize hence the band gap renormalization appearing as the energetic difference between the unrelaxed (non-equilibrium) and relaxed (equilibrium) carriers, which can be estimated in the frame of the Fröhlich large polaron model 9,44 as = ~32.6 meV and ℎ = ~39.2 meV for the longitudinaloptical (LO)-phonons contribution. The intensity of the 1s FE absorption peak decreases in MAPbBr3/ZnO due to the interfacial-electric-field-induced FE dissociation, the process which balances the relative densities of free carriers and FEs. 19 The more prominent suppression of the 1s FE absorption peak in the MAPbBr3/ZnO(30nm) sample compared to the MAPbBr3/ZnO(100nm) sample suggests that the interfacial electric field in the former is stronger than that in the latter. The exciton dissociation process is also accompanied by a blue-shift of PL-peak (~10 meV), which is greater in the MAPbBr3/ZnO(30nm) sample as well [ Fig. 2(i)]. These facts together with good coincidence between reorganization energies and the Stokes shift all confirm the FE nature of the band-edge light emission at room temperature. The latter statement is also well consistent with the large polaronic exciton binding energy in MAPbBr3 (~35 meV), 17,23 thus exceeding substantially the room temperature = 25.7 meV, where kB in the Boltzmann constant and T is the temperature. We also note that because the size of MAPbBr3 nanocrystals (~20 nm) substantially exceeds the exciton Bohr radius (~2.0 nm), 45 any quantum-confinementinduced effects are expected to be negligible. The typical phonons contributing to the temperaturedependent dynamics include the PbBr6 octahedra twist mode (TO-type) with frequency ~40 cm -1 (~5 meV) and the distortion mode (LO/TO-type) with frequency ~58 cm -1 (~7.2 meV). 46,47 The interaction between MA cations and PbBr6 anions results in a broad MA torsional (MAT) mode peaked at ~300 cm -1 (~37.2 meV), which governs the orientation dipole order of MA cations in the whole crystal. 46 MA internal (MAI) modes have much higher frequencies of ~900 -3200 cm -1 (112 -397 meV). 46,47 However, owing to a global lattice compression in nanocrystals, 36 the frequency of the LO-phonon mode observed for MAPbBr3 nanocrystals increases to ~150 cm -1 (~18.6 meV). 48,49 Because the lattice compression varies with the nanocrystal size, TO/LO-phonon energy is expected to be spread over a few meV. 49 Consequently, we will refer further below to the following low-energy lattice vibrations: (i) the TO-phonon mode with averaged energy 〈 〉 ~5.0 meV, (ii) the LOphonon mode with averaged energy 〈 〉 ~18.6 meV, (iii) the MAT-phonon modes with averaged energy 〈 〉 ranging between ~35 and ~90 meV, and (iv) the MAI-phonon modes and their combinations with averaged energy 〈 〉 ranging between ~100 and ~700 meV.

B. Structural phase transitions in 3D MAPbBr3 nanocrystals
The structural phase transitions in MAPbX3 have been monitored for single-crystal MAPbBr3 13-18,20,21 and MAPbI3 16,19,20 using the XRD, 13,14,18 absorption, 16 reflection, 17 one-photon excited PL, 13,14,18,19,21 two-photon excited PL, 15 and dielectric response 20 techniques. Polycrystalline films, 21,22,23 microplate crystals 24 and nanowires 25 of MAPbBr3 23 and MAPbI3 21-25 have also been studied using the XRD, 22 absorption, 21,23 charge transport 24 and one-photon excited PL 21,22,24,25 techniques to recognize the structural phase transitions on the nanoscale. The structural phase transition in MAPbX3 usually appears as the stepwise shift of the corresponding spectral band [13][14][15][16][17][18][19][20][21][22][23][24][25] whereas its intensity is less suitable for this purpose. 18,19,21,22,24 Three structural phase transitions were found to occur at T ~145 K [orthorhombic(O)to-tetragonal(T1)], at T ~155 K [tetragonal(T1)-totetragonal(T2)], and at T ~237 K [tetragonal(T2)-to-cubic(C)], which usually appear in single-crystal MAPbX3 and its polycrystalline thin film. 13,15 However, even a shift of the absorption and PL bands was incapable for recognizing the structural phase transition in MAPbX3 nanocrystals. 21 The reason that a stepwise shift of the absorption and PL bands is no longer observable in MAPbX3 nanocrystals has been suggested to arise from the configurational entropy loss upon suppressing long-range MA polar order. 21,27,28 To study the structural phase transition in a layer of 3D MAPbBr3 nanocrystals, we measured the temperature dependences of PL from the aforementioned three samples using the three laser excitation regimes of photon energy (i) 3.81 eV (exc = 325 nm) being above ZnO and MAPbBr3 band gaps ( = ~3.37 and ~2.3 eV, respectively); (ii) 2.81 eV (exc = 442 nm) being below ZnO band gap but above MAPbBr3 band gap; (iii) 1.55 eV (exc = 800 nm) being below ZnO and MAPbBr3 band gaps [ Fig. 1 Figure 3 shows PL spectra measured as a function of temperature using the three different laser excitations, as indicated for each of the panels. Additionally, Figure 4 shows PL spectra measured at temperatures T = 50, 150, and 285 K, which correspond to the orthorhombic, tetragonal, and cubic structural phases of single-crystal MAPbBr3, respectively. All PL spectra demonstrate a characteristic ≤100 meV blue-shift with increasing temperature from T ~20 to 295 K ( Fig. 3 and Fig. 4). The position of PL peak in low-temperature spectra (T = 50 K) slightly vary with excitation photon energy in the range of ~30 -40 meV. This variation sets up the range of inhomogeneous broadening, which is believed to be due to the nanocrystal structural imperfectness since the MAPbBr3/ZnO heterointerface does not affect significantly the position of PL bands and their full width at half maximum (FWHM). Moreover, the LO-phonon sideband 48 is red-shifted from PL peak by ~18 meV for the MAPbBr3/Sa sample when two-photon excitation is applied (exc = 800 nm) (Fig. 4). As temperature increases, both the PL peak position variations and the LO-phonon sideband peak are masked by homogeneous broadening due to dominant carrier scattering with optical phonons. The bandwidth of the room-temperature PL bands (FWHM) reaches ~90 meV, indicating that homogeneous and inhomogeneous broadenings are somewhat comparable. The PL broadening dynamics with increasing temperature will be discussed in detail in the next section.
There are two general tendencies characterizing the temperature-dependent dynamics of one-photon-excited PL (exc = 325 nm or 442 nm). Specifically, PL peak intensities [ Fig. 3 photoexcited carrier density, since at least 10-fold higher carrier density was photoexcited in this case compared to one-photonexcited PL. The temperature dependences of PL peak position for the MAPbBr3/ZnO(30nm) sample also demonstrate the minor features when approaching room temperatures [ Fig. 5(d) -(f)], pointing to more complicated dynamics in this case. The fairly monotonic blue-shift with increasing temperature is well consistent with that reported for MAPbI3 nanocrystals and suggested to provide evidence that MAPbI3 nanocrystals do not undergo the bulk phase transitions. 21 Alternatively, we show that although the temperature dependences of PL peak position reveal a fairly monotonic behaviour, the temperature dependences of PL intensity can be either monotonic or non-monotonic depending on the PL excitation regime applied. Figure 5(a)-(c) clearly demonstrates this dual behaviour for the MAPbBr3/Sa sample. Specifically, although one-photonexcited PL decays with increasing temperature nearly monotonic, there are two distinct peaks for two-photon-excited PL, the positions of which (T ~140 K and ~245 K) closely match those known for the orthorhombic-to-tetragonal and tetragonalto-cubic phase transitions in single-crystal MAPbBr3. [13][14][15][16][17][18][19][20][21] The temperature dependences of the integrated PL intensity can be fitted using the multiple Mott equation, 50 which for one-photonexcited PL, takes into consideration phonon-assisted PL quenching in all the structural phases (three terms), as well as in the phase transition regions (two terms), where (0) is PL intensity at T = 0 for each of the terms, is the pre-exponential factors characterizing the relative probabilities of non-radiative decay, and is the corresponding activation energies. We note that all 5 terms in Eq. (1) are positive for one-photon-excited PL, thus characterizing the overall phonon-assisted PL quenching, while partial contributions from the specific components can be weakly recognized [ Fig. 6(c)]. However, the situation changes dramatically when switching to two-photon excited PL. Consequently, phonon-assisted PL quenching in each of the structural phases (three positive terms) still contribute into the temperature-dependent dynamics, however, together with PL intensity increase when the structural phase changes towards the higher symmetry one (two negative terms) [ Fig. 6(a) -(c)]. This observation demonstrates a higher sensitivity of the nonlinear absorption coefficient to the crystalline lattice symmetry and suggests that the specific phonon modes participate in the structural phase transitions 51 similarly to PL non-radiative decay. 50 Consequently, temperature dependences of both onephoton-excited and two-photon-excited PL intensities can be fitted using the same and parameters, nevertheless, the intensity (0) of two terms governing the structural phase transition dynamics change sing when switching to two-photonexcited PL. Specifically, PL quenching in the orthorhombic phase involves TO-phonons ( 1 ~5 meV). In contrast, PL quenching in the tetragonal/cubic phase involves MAI-phonons ( 3 ~204 meV, 5 ~413 meV). The orthorhombic-totetragonal phase transition is a phonon-assisted process which occurs owing to MAT-phonon activation ( 2 ~45 meV) whereas the tetragonal-to-cubic phase transition involves MAIphonons ( 4 ~615 meV). We note also that the orthorhombicto-tetragonal structural phase transition in 3D MAPbBr3 nanocrystals is spread out over the T ~70 -140 K range, which is believed to be due to the configurational entropy loss and the corresponding structural phase instability when, unlike in singlecrystal MAPbX3, free rotations of the MA ions are no longer restricted strongly by long-range polar order. 27,28 The resulting local field fluctuations in MAPbX3 nanocrystals and the liquidlike motion of MA cations 1 weaken and smooth distortions of PbX6 octahedra which are responsible for the band-edge electronic transitions, thus eliminating the stepwise shift of the corresponding absorption and PL bands.
Although the temperature dependences of the integrated PL intensity for the MAPbBr3/ZnO(100nm) sample are quite similar to those of the MAPbBr3/Sa sample, they differ significantly for the MAPbBr3/ZnO(30nm) sample [ Fig. 5(a)-(c)]. The dynamics can be associated with that being caused by the interfacial electric field. 19 Specifically, one should distinguish between the two principally different PL excitation regimes. One of them (exc = 325 nm) deals with the excitation of carriers in both MAPbBr3 and ZnO. The charge separation process at the MAPbBr3/ZnO heterointerface in this case is not efficient enough because although the photoexcited holes in both materials tend to reside in MAPbBr3, the majority of photoexcited electrons in MAPbBr3 do not leave it since the edge of the ZnO CB is filled by electrons photoexcited in ZnO [ Fig.  1(b)]. The second regime involves the excitation of carriers exclusively in MAPbBr3 (exc = 442 and 800 nm) and hence the interfacial electric field at the MAPbBr3/ZnO heterointerface is formed with high efficiency since electrons can freely move to the CB of ZnO whereas holes remain in MAPbBr3 [ Fig. 1(b)]. One can hence vary the strength of the interfacial electric field by varying the photoexcited carrier density and exc.
The thickness of the ZnO layer also significantly affects the interfacial electric field strength. Specifically, the interfacial electric field in the MAPbBr3/ZnO(30nm) sample is expected to be much stronger compared to that in the MAPbBr3/ZnO(100nm) one. This statement can be clarified in the framework of the two effects that can potentially occur at the MAPbBr3/ZnO heterointerface: (i) the strain-induced effect and (ii) the charge-separation-induced effect. The first one takes into consideration that the ZnO layer was grown on the sapphire substrate and hence the thicker the ZnO layer, the stronger the residual strain should act on MAPbBr3 nanocrystals. 51 The second effect also depends on the ZnO layer thickness, but in the opposite way. Because the strength of the interfacial electric field is proportional to the carrier density separated at the MAPbBr3/ZnO heterointerface, the thicker the ZnO layer, the lower the carrier density in it and hence the weaker the interfacial electric field. This principal difference between the strain and electric field induced effects can be distinguished by testing two samples of different ZnO layer thicknesses, as it has been done in the current study. Specifically, the non-monotonic behaviour observed for the MAPbBr3/ZnO(30nm) sample with one-photon excitation (exc = 325 and 442 nm) points to the stronger interfacial electric field being involved in this sample. Moreover, as the strength of the interfacial electric field increases (exc = 442 nm), the shift of the structural phase transition towards the higher temperature range also progresses. Alternatively, the temperature dependences of the MAPbBr3/Sa and MAPbBr3/ZnO(100nm) samples demonstrate a similar monotonic behaviour, suggesting that the interfacial electric field in MAPbBr3/ZnO(100nm) sample is as weak as that in the MAPbBr3/Sa sample and proving that the strain-induced effect is negligible [ Fig. 5(a) and (b)]. This tendency is also confirmed using two-photon-excited PL (exc = 800 nm), despite the nonmonotonic temperature dependences for all the samples. Specifically, the temperature dependence of two photon-excited PL intensity for the MAPbBr3/ZnO(100-nm) sample looks more like that for the MAPbBr3/Sa sample [ Fig. 5(c)].
The orthorhombic-to-tetragonal phase transition in the MAPbBr3/ZnO(30nm) sample reaches the extremely broad temperature range of T ~70 -230 K [ Fig. 5(a)-(c) and Fig. 6(d)], confirming once again that the interfacial electric field in this sample is enhanced. The dynamics also demonstrate more clearly the existence of T1 and T2 subphases. The corresponding activation energies are in the range of MAT-and MAI-phonons [ Fig. 6(d)], confirming that the structural phase instability results from the MA dipole order suppression. Additionally, if the exc = 800 nm excitation regime is applied, the cubic structural phase feature is not observed for the MAPbBr3/ZnO(30nm) sample even for temperatures ranging up to T ~ 295 K [ Fig. 5(a)-(c)], suggesting that the room-temperature structural phase in this case most likely is also instable, being the mixture of the orthorhombic and tetragonal phases.
To estimate how far the interfacial electric field is extended inward towards the MAPbBr3 nanocrystal core, we calculated the Thomas-Fermi screening length for the photoexcited carrier densities = 1.0 × 10 19 cm -3 , = 1.0 × 10 18 cm -3 and = 1.0 × 10 17 cm -3 (see the Experimental Methods section) as 1⁄ = ~2.7 nm, ~3.9 nm and ~5.8 nm, respectively, with being the Thomas-Fermi wavevector defined as 2 = ( 19,53 where * is the carrier effective mass ( * = 0.13 0 and ℎ * = 0.19 0 for electrons and holes, respectively, with m0 being the free-electron mass), e is the electron charge, = 21.36 is the static dielectric constant, and 0 is the permittivity of free space. 9 Consequently, the Thomas-Fermi screening length naturally decreases with increasing carrier density, indicating that the interfacial electric field tends self-consistently to be confined at the heterointerface when the photoexcited carrier density increases. Because the range of the orthorhombic-to-tetragonal structural phase transition also extends with increasing photoexcited carrier density, the latter behaviour implies that the strength of the interfacial electric field mainly governs the structural phase instability in the whole MAPbBr3 nanocrystal rather than the field extension inward towards the nanocrystal core. The short-range Thomas-Fermi screening length also suggests that the long-range MA dipole order which was suppressed substantially in the whole MAPbBr3 nanocrystal cannot be restored by the interfacial electric field.
We also note that the temperature dependences of PL peak position observed for the MAPbBr3/ZnO(30nm) sample demonstrate some additional features when approaching room temperature [ Fig. 5(d) -(f)]. We associate these features with FE dissociation because of stronger interfacial electric field in this sample. 19 Specifically, the interfacial electric field dissociates FEs in the tetragonal phase, giving rise to the blue-shift of the PL band because of progressive switching from FE to band-to-band recombination. The rate of this process strongly depends on the electric field strength, thus being maximised for the exc = 442 nm and exc = 800 nm excitation regimes. Once the tetragonalto-cubic structural phase transition occurs, the FE dissociation process weakens, giving rise to the red-shift of the PL band since FE binding energy in the cubic structural phase is higher compared to that in the tetragonal phase. 54 It should be noted that applying exc = 800 nm excitation, one can observe only the initial blue-shift of the PL band because the tetragonal-to-cubic structural phase transition in this case occurs at temperatures higher than room temperature [ Fig. 5(f)].

C. PL excitation mechanisms
The formation of the interfacial electric field of different strengths is also one of the key circumstances of why PL technique becomes sensitive enough to negligible structural distortions in 3D MAPbBr3 nanocrystals. Specifically, this behaviour is realized because PL excitation involves the absorption rates governed by the second-order and third-order nonlinear susceptibilities, which owing to their higher rank tensor nature compared to the first-order susceptibilities, are known to demonstrate a higher spatial sensitivity to the lattice symmetry. [55][56][57][58] The situation emerging is known as electric-fieldinduced one-photon-excited PL and two-photon-excited PL, both involving nonlinear susceptibilities. 55 This behaviour is in stark contrast to the conventional one-photon-excited PL which loses sensitivity to the structural phase transition in 3D MAPbX3 nanocrystals because of structural phase instability and the corresponding negligible distortions of PbX6 octahedra responsible for light-emitting process. It is worth noting that all three structural phases in MAPbX3 materials are centrosymmetric. 59,60 This statement significantly distinguishes between PL excitation regimes through the light absorption rate. Specifically, PL intensity can be expressed as 61 where ∝ ℎ is the emission rate caused by carrier radiative recombination with and ℎ being the density of electrons and holes, respectively. The latter process is known as bimolecular recombination and mainly appears through electroluminescence (EL), when and ℎ , in general, can be different as a consequence of the specific structure of the samples, their doping type, as well as the carrier injection level. Additionally, for highly efficient light-emitters, and ℎ should be low enough to guarantee the carrier wavevector conservation in the recombination process. 61 In contrast, in PL experiments one always excites equal numbers of electrons and holes, = = ℎ (each photon with energy exceeding band gap energy excites two particles, electron and hole), with energies equal to one half of the difference between photon and band gap energies. The density of photoexcited carrier is usually much higher compared to the intrinsic carrier density (the doping level). Furthermore, PL resulting from recombination between nonthermalized (hot) carriers (hot PL) should also be negligible since the wavevector is not strictly conserved for them. However, if wavevector conservation is not necessary, the situation which may happen due to the trapping of carriers by defects or carrier interaction with phonons (including the polaron formation as well), the rate ∝ (monomolecular recombination) if the photoexcited carrier density exceeds the intrinsic carrier density. 61 The latter proportionality indicates that two-particle recombination is a highly probable process emitting a single photon. The monomolecular recombination is hence a direct opposite of the PL excitation process and its rate is known to be significantly enhanced as compared to that of bimolecular recombination. 61 Because ∝ , where and are rates of light absorption and carrier relaxation to the light-emitting states, respectively, 61 and because is expected to be a constant for the fixed incident photon energy, as that occurs in our case, PL intensity can be expressed as that is, being predominantly governed by the absorption rate (in units of s -1 ), which, in general, is a sum of several contributions associated with one-photon absorption (1) , twophoton absorption (2) if the excitation light intensity ( ) is strong enough, and one-photon electroabsorption (1) if an external or internal electric field is applied, so that where  is the excitation photon energy, (1) , (1) and (2) are the corresponding one-photon and two-photon cross sections. 55 If  > , then the (1) and (1) terms dominate the PL excitation dynamics. On the contrary, if  < , then the (2) term completely governs the PL excitation mechanism. Consequently, the following proportionalities ~ and ~ 2 correspond to onephoton-excited and two-photon-excited PL, respectively. [62][63][64][65] These relations can be confirmed experimentally when analyzing the slope of the power dependences of presented in a log-log plot (Fig. 7).
However, the absorption rates of the one-photon and twophoton absorption processes are known to be proportional to the imaginary part of the first-order and third-order optical susceptibilities (   55 Consequently, this approach is well consistent with the aforementioned centrosymmetry restriction applied to MAPbBr3 crystals, according to which the second-order nonlinear process [ χ (2) ] is not allowed, whereas the linear [χ (1) (− ; )] and third-order nonlinear [χ (3) (− ; , , − )] processes should completely govern the one-photon and two-photon absorption in these materials, appearing through onephoton-excited and two-photon-excited PL, respectively. However, once the crystalline lattice is getting distorted by an external or internal electric field, for example, the centrosymmetry breaking allows the second-order nonlinear process to appear through the linear electro-optic effect  [55][56][57][58] We note that PL excitation involving χ (2) (− ; , 0) and χ (3) (− ; , 0,0) still produces a one-photon-excited PL response, although the light absorption rates are characterized by nonlinear electro-optic susceptibilities. This brief discussion of nonlinear optics highlights an advantage of the electric-fieldinduced one-photon-excited and two-photon-excited PL for monitoring structural phase transitions in hybrid perovskite nanoscale materials. This behaviour results from the fact that these techniques exploit the higher sensitivity of nonlinear optical and electro-optical susceptibilities to the crystalline lattice distortions compared to the conventional linear optical processes. [55][56][57][58] Specifically, χ (1) (− ; ) is a second rank tensor containing 9 elements, whereas χ (2) (− ; , 0) and χ (3) (− ; , 0,0), χ (3) (− ; , , − ) are the third and fourth rank tensors containing 27 and 81 elements, respectively. 55 This principal difference also indicates that both (1) and (2) mainly characterize PL excitation in the nanocrystal core, contrary to (1) which characterizes PL excitation in both the nanocrystal core and the nanocrystal surface. Consequently, because the ratio of the surface-to-core PL contributions for nanocrystals is large enough and because the surface states are less sensitive to the structural phase transitions in the core, the structural phase transitions in MAPbX3 nanocrystals can be significantly masked by PL from the surface states when conventional one-photon excitation is applied. This circumstance together with the structural phase instability occurring within the broad temperature range seems to be a reason why the structural phase transitions in MAPbX3 nanocrystals have never been observed. It is worth noting that PL peak position remains almost unchanged with increasing laser power for all the samples and

D. PL broadening dynamics
To gain deeper understanding through the phonon-assisted structural phase transitions in 3D MAPbBr3 nanocrystals, the temperature dependences of the PL band FWHM for all the samples were analysed (Fig. 8). All the dependences clearly demonstrate the two-stage homogeneous broadening process appearing at low (T ~20 -140 K) and moderate (T ~140 -295 K) temperatures. These two temperature intervals closely match those corresponding to the orthorhombic and tetragonal-cubic phases in single-crystal MAPbBr3, respectively. However, PL broadening dynamics with temperature is expected to be governed rather by various phonons being involved than the structural phase transitions. The temperature dependences of the PL band FWHM also reveal additional features for the MAPbBr3/ZnO(30nm) sample when approaching room temperature. These features are due to the interfacial-fieldinduced FE dissociation, which additionally to the blue-shift of the PL band [ Fig. 5(d) -(f)] is accompanied by its narrowing. 19 Further broadening of the PL band with increasing temperature occurs when the tetragonal phase transforms to the cubic one, at which FE binding energy is increased and hence the FE dissociation process is slowed down, as discussed in the preceding section for the PL peak position dynamics.
To analyze the PL band FWHM variations with temperature, we use a phenomenological approximation for phonon-induced broadening 19,66,67 = γ 0 + γac + where 0 is inhomogeneous broadening, γac is the electron (hole)acoustic-phonon coupling strength, γTO/LO is the electron (hole)-TO/LO-phonon coupling strength, γMAT is the electron (hole)-MAT-phonon coupling strength. Consequently, the electron (hole)-acoustic-phonon coupling strength (γac ~3×10 -5 eVK -1 ) is negligible [ Fig. 8(a)-(c)], being of the same order as that previously reported. 19,66 The first stage of PL band broadening is due to the scattering of carriers with TO/LO-phonons, whereas the second stage can be attributed to the MAT-phonons effect. It should be especially stressed here that the MAT-phonon contribution becomes significantly enhanced for the MAPbBr3/ZnO(30nm) sample [ Fig. 8(b)]. This behaviour confirms the stronger interfacial electric field in this sample to occur and its significant effect on the suppression of the MA cation dipole order in the whole nanocrystal. 45 We note that the fits are not necessarily unique, thus allowing one to determine the effective energy ranges of TO/LO-phonons as 〈 LO/TO 〉 ~4.0 -17 meV and MAT-phonons as 〈 MAT 〉 ~55 -92 meV, which well match those discussed above in the sample characterization section.
We also found that the electron (hole)-MAT-phonon coupling strength (γMAT ~245 -679 meV) is ~100-fold greater than the electron (hole)-TO/LO-phonon coupling strengths (γTO/LO ~2.5 -8.4 meV). This strong coupling of electrons (holes) to MAT-phonons highlights the main specific feature distinguishing the carrier relaxation in MAPbX3 compared to conventional semiconductors. Specifically, the photoexcited carriers relax down not only through the TO/LO-phonon cascade, but also through the MAT-phonon excitation. This behaviour is the reason why TO/LO-phonon bottleneck occurs in MAPbX3. Specifically, because of the ultralow thermal conductivity between the sublattices, the organic sublattice heated during carrier relaxation keeps TO/LO-phonons in the inorganic sublattice at the temperature of the former, thus blocking their decay through acoustic phonons (Klemens-Ridley anharmonic process) and allowing carriers to reabsorb TO/LOphonons. [2][3][4] This process is expected to be enhanced in nanocrystals as a consequence the additional reduction of thermal conductivity through the nanocrystal boundaries. Consequently, the nearly monotonic blue shift of PL band with increasing temperature seems to result rather from the heating effect under TO/LO-phonon bottleneck than that being induced by a progressive distortion of PbX6 octahedra. This conclusion is also well consistent with the structural phase instability in MAPbX3 nanocrystals due to the configurational entropy loss. 21,27,28

E. PL mechanism
PL mechanism in MAPbX3 is not trivial mainly due to a polar crystal lattice and the ultralow thermal conductivity between the sublattices. The observed dominant PL blue-shift with increasing lattice temperature (T) [Fig. 5(d)-(f)] is opposite to that usually predicting the band gap ( ) variation in conventional semiconductors 61,68,69 where a and b are fitting parameters and is the mean temperature of phonons taking part in the scattering process with carriers. It has recently been suggested that ( ) can show either a decrease (red-shift) or an increase (blue-shift) depending on whether derivative ⁄ (slope) is positive (phonon emission) or negative (phonon reabsorption), respectively. 18 The latter behavior points to the non-equilibrium dynamics, being equivalent to the introduction of the negative absolute temperature. 70 To adapt this situation to TO/LO-phonon bottleneck, we consider the Bose-Einstein phonon occupation numbers for spontaneous TO/LO-phonon emission and for TO/LO-phonon reabsorption where denote the temperature at which TO/LO-phonon bottleneck occurs. This approach implies that upon photoexcitation, electrons and holes (also FEs) cool down through the TO/LO/MAT-phonon cascade. Consequently, free carriers and FEs relax down at least within a few ps timescale and their temperature in the light-emitting states prior to emission ( ) is determined by the decay of TO/LO-phonons in the inorganic sublattice through the Klemens-Ridley anharmonic process [2][3][4]30,31 , which however is controlled by the organic sublattice temperature ( ). Because the further cooling of the organic sublattice through acoustic phonons is slower than that of the inorganic sublattice due to the more energetic optical phonons involved in the organic sublattice, TO/LO-phonon bottleneck in the inorganic sublattice occurs at = > and allows carriers in the latter to reabsorb TO/LO-phonons. The effect progresses with increasing , since the organic sublattice cooling rate is reduced. Consequently, TO-phonon bottleneck occurs predominantly in the orthorhombic phase whereas LOphonon bottleneck dominates in the tetragonal/cubic phase. The resulting TO/LO-phonon-dressing process hence lowers the electron (hole, exciton) energies by the polaron (reorganization) energy 1,7,10,71-73 . Consequently, the stronger the electron (hole, exciton)-phonon coupling, the larger the number of TO/LOphonons contribute to the polaronic effect.
According to this model, the resulting polaronic electron (pe), polaronic hole (ph) and polaronic exciton (PE) quasiparticles are involved into their further recombination in MAPbBr3 nanocrystals, thus completely governing their PL and transport properties. Moreover, upon TO/LO-phonon bottleneck, polaronic quasiparticles can reabsorb TO/LOphonons to form the TO/LO-phonon vibrationally excited polaronic quasiparticles with reduced ground-state polaron energy. Consequently, polaronic quasiparticle recombination may occur in either the ground or vibrationally excited polaron states [ Fig. 9(a)]. This behavior gives rise to the ~100 meV blueshift of PL-peak with increasing temperature, unlike a red-shift in conventional semiconductors. Because the blue-shift is observed for the entire temperature range applied, one can assume that > 300 K whereas it should apparently be less than the material melting point of < 450 K. Owing to screening from other carriers and defects, polaronic quasiparticles possess a very small recombination rate (PL decay-time is very long), thus being expected to demonstrate high mobility and long-range diffusion.
To treat the experimental results, we first consider the single electron (hole) polaron energy. The polaronic band gap renormalization is known to narrow the band gap by reorganization energy, introducing the ground-state Fröhlich polaron energy for electrons and holes which can be given as 71,74 ,ℎ = 〈 TO/LO 〉〈 ,ℎ 〉, where 〈 ,ℎ 〉 = Using 〈 〉 = 5 meV and 〈 〉 = 18.6 meV, one can obtain the following Fröhlich polaron coupling coefficients 〈 〉 = 3.37, 〈 ℎ 〉 = 4.07 and 〈 〉 = 1.75, 〈 ℎ 〉 = 2.11 for TO and LO phonons, respectively, which are well consistent with those calculated using the Feynman-Osaka model 9 . The ground-state Fröhlich polaron energy for electrons and holes is hence temperature independent and can be calculated as = ~16.9 meV and ℎ = ~20.35 meV for TOphonons and = ~32.6 meV and ℎ = ~39.2 meV for LOphonons. These estimates imply that LO-phonons might govern the room-temperature ~60 meV Stokes shift ( + ℎ ) discussed above in the sample characterization section. Specifically, assuming that the absorption and PL spectra manifest the unperturbed and BGR-induced dynamics, respectively, the corresponding band gap narrowing is and the Stokes shift is hence equal to + ℎ . To introduce the temperature effect into the dynamics, we use the Bose-Einstein phonon occupation numbers defined above, so that We note that Eq. (12) completely describes the variation of the polaronic band gap energy of MAPbX3 nanocrystals, depending on whether TO/LO-phonon bottleneck occurs. To use this approach to PEs, one should consider the PE binding energy ≡ . . − − ℎ , where . . is the PE ground-state energy [ Fig. 9(a)]. 77 Because for MAPbBr3 is similar to the exciton binding energy ( ≈ ) and because = 35 meV is higher than the room temperature = 25.7 meV, 16,77 we consider PEs as those dominantly contributing to PL in the temperature range of 20 -295 K. Consequently, the exciton peak energy in absorption and PL spectra varies as follows ) term dealing with the equilibrium relaxation dynamics and governing the PL peak red shift. As a result, the PE absorption and PL peaks both tend to blue shift with temperature in the broad temperature range of = 20 -100 K, indicating a strong TO/LO bottleneck effect to occur. However, this general trend is gradually weakened for the PL peak when temperature approaches to that at which the crystalline lattice is getting unfrozen enough to initiate the anharmonic three-phonon TO/LO-phonon decay process involving acoustic phonon branches (Klemens/Ridley process). The resulting deviation of the PL peak temperature dependence from that of the PE absorption peak is hence coming from the weakening of TO/LO-phonon bottleneck, which mainly appears for the PL peak since PE relaxation (cooling) towards their ground state is required prior to light emission. Alternatively, the PE absorption peak temperature dependence mainly reflects the non-equilibrium dynamics, which ignores any relaxation processes. The resulting Stokes shift progresses with increasing temperature, reaching ~60 meV at room temperature. the value which presents the energetic difference between the polaronic band gap and PE ground-state energy. To verify whether Eq. (12) is relevant to the experimental observations, we re-plotted the temperature dependences of PLpeak position as ( ) − (20 ) , where the lowest temperature data taken at = 20 K is applied instead of that at = 0 K (Fig. 5(d)-(f)), Alternatively, neglecting the spontaneous TO/LO-phonon emission, Eq. (12) describes the PL-peak energy increase with increasing temperature [ Fig. 9(a)]. Figure 5(f) confirms the latter tendency by numerically simulated results under = 450 K obtained without any fitting parameters. One can clearly see that TO-phonon bottleneck dominates in the orthorhombic phase whereas LO-phonon bottleneck controls the dynamics in the tetragonal/cubic phase. The inflection point is hence a signature of switching between these two regimes.
It is worth noting that the band gap modification energy ( ) − (0 ) varies in the range of ~60 -100 meV, which closely matches the polaronic band-edge energy ( + ℎ ) ~ 70 meV for LO-phonons, thus suggesting that the blue shift of PL band can be associated with the LO-phonon vibrationally excited polaronic quasiparticles. We note that this mechanism, which is applied to a layer of MAPbBr3 nanocrystals clearly demonstrating a single PL peak, is completely different to that proposed for thick films demonstrating dual emission features like in bulk single-crystals. 19,78 Consequently, the proposed mechanism was associated with the thermal expansion of the lattice, 78 which seems to be irrelevant for nanocrystals where the lattice is flexible enough due to structure phase instability. Furthermore, because and ℎ for LO-phonons are of the same order as Rashba energies ( ~40 meV), 79 the polaronic nature of the edge states in MAPbX3 materials at room temperature should dominate over that associated with the Rashba effect.
To recognize TO/LO-phonon bottleneck on the pe/ph and PE masses, we consider again the process of TO/LO-phonon emission/reabsorption by hot carriers. LO-phonon emission influences the pe/ph masses as show the numerically simulated results which point out that if TO/LO-phonon bottleneck is neglected ( = 0), the polaron masses increase with increasing temperature in all the structural phases, that is, the electron (hole, exciton)-phonon coupling is enhanced. TO-phonon bottleneck significantly increases the polaron masses at = 0 K followed by their slight decrease with increasing temperature. This behavior indicates that the polaronic quasiparticles are strongly localized in the orthorhombic phase. Alternatively, LO-phonon bottleneck dominating in the tetragonal/cubic phase decreases the polaron masses, making them be almost temperature independent. We note that the pe/ph masses in the latter case are only slightly above the electron and hole effective masses, whereas the PE mass is less than those.
The effect of TO/LO-phonon bottleneck on the polaron radii can be considered using the polaron radii of Fröhlich polarons at = 0 K 71 , We use the aforementioned parameters to obtain the following equilibrium polaron radii at = 0 K when TO-phonons are involved 〈 〉 = 7.66 nm, 〈 ℎ 〉 = 6.35 nm, 〈 〉 = 9.95 nm and when LO-phonons are involved 〈 〉 = 3.97 nm, 〈 ℎ 〉 = 3.29 nm, and 〈 〉 = 5.16 nm. These values well match those calculated using the Feynman-Osaka model 9 . The polaron radii are at least three times greater than the exciton Bohr radius 80 =  2 0 2 = 1.17 nm, which in turn is about twice the lattice constant (~0.59 nm) 9 . These estimates prove the large polaron nature (Fröhlich polaron) 71 of quasiparticles in MAPbBr3 and imply that the lattice distortions spread over many lattice sites, thus allowing Fröhlich polarons to travel through the lattice as free quasiparticles. We note that the PE radius 〈 (0)〉 only slightly greater than 〈 , ℎ (0)〉 because the overlapped polarization clouds of pe and ph partially cancel each other. 81 The temperature effect on the polaron radii can be treated following the general consideration for polaronic quasiparticles in quantum dots 81 (18)], the polaron radii shorten with increasing temperature in all the structural phases, thus agreeing with the corresponding increase of the polaron masses. 71 TO-phonon bottleneck slightly increases the polaron radii at = 0 K [Eq. (19)], nevertheless, they significantly decrease with increasing temperature in the orthorhombic phase. Once LO-phonon bottleneck begins contributing to the dynamics in the tetragonal/cubic phase, the polaron radii become longer and significantly elongate with increasing temperature. The latter behavior demonstrates the weakening of the electron (hole, exciton)-phonon coupling. The resulting polaron diameters at room temperature exceed the MAPbBr3 nanocrystal size. This tendency allows the LO-phonon vibrationally excited polaronic quasiparticles to travel through a layer of 3D MAPbBr3 nanocrystals without scattering on the electrostatic potential fluctuations associated with structural imperfections. Accordingly, the mobility and diffusion of polaronic quasiparticles in a layer MAPbX3 nanocrystals at room temperature should be significantly enhanced due to LO-phonon bottleneck.

IV. CONCLUSIONS
In this article we highlight several basic approaches which would be interesting to a broad audience of scholars exploring unique PL and transport properties of MAPbX3 materials. One of them suggests that two-photon-excited PL spectroscopy and electric-field-induced one-photon-excited PL spectroscopy are required to study the structural phase transitions in 3D MAPbX3 nanocrystals. These techniques are capable of more precisely monitoring the structural phase transitions because the secondorder and third-order nonlinear susceptibilities govern the light absorption rates.
Consequently, one can recognize that the structural phase transitions in 3D MAPbBr3 nanocrystals may occur at about the same temperatures as those in single-crystal MAPbBr3. However, the orthorhombic-to-tetragonal structural phase transition in 3D MAPbBr3 nanocrystals, unlike in single-crystal MAPbX3, is spread out over the broad temperature range of T ~70 -140 K due to the structural phase instability induced by local field fluctuations when free rotations of MA ions are no longer restricted strongly by long-range polar order. The resulting configurational entropy loss and the liquid-like motion of MA cations in 3D MAPbBr3 nanocrystals can be even enhanced by the interfacial electric field arising due to charge separation at the MAPbBr3/ZnO heterointerface, extending the range of the orthorhombic-to-tetragonal structural phase instability from T ~70 to 230 K and significantly shifting the tetragonal-to-cubic phase transition towards higher temperatures exceeding room temperature.
The latter effect is found to be dependent on the ZnO layer thickness and the photoexcited carrier density, thus allowing one to control the structural phase instability range in 3D MAPbBr3 nanocrystals. Finally, we conclude that a stepwise shift of the PL band with temperature observed for single-crystal MAPbX3 is no longer an indication of the structural phase transition in 3D MAPbBr3 nanocrystals because of negligible distortions of PbX6 octahedra under the structural phase instability regime. On the contrary, the nearly monotonic blue shift of PL band with increasing temperature in a fully encapsulated single layer of 20nm-sized 3D MAPbBr3 nanocrystals seems to result rather from the heating effect under TO/LO phonon bottleneck than that being induced by the progressive PbX6 octahedra distortions.
Furthermore, we point out that two-photon-excited PL spectroscopy and electric-field-induced one-photon-excited PL spectroscopy mainly characterize PL excitation in the nanocrystal core, contrary to conventional one-photon-excited PL spectroscopy dealing with PL excitation in both the nanocrystal core and the nanocrystal surface. Consequently, because the ratio of the surface-to-core PL contributions for nanocrystals is large enough and because the surface states are less sensitive to the structural phase transitions in the core, the structural phase transitions in MAPbX3 nanocrystals can be significantly masked by PL from the surface states when conventional one-photon excitation is applied. This circumstance together with the structural phase instability occurring within the broad temperature range seems to be a reason why the structural phase transitions in MAPbX3 nanocrystals have never been observed.
We also confirmed that the photoexcited carriers responsible for the light-emitting and transport properties of a layer of 3D MAPbBr3 nanocrystals are the polaronic quasiparticles, which can be TO/LO-phonon vibrationally excited to the higher-energy states owing to TO/LO-phonon bottleneck. Consequently, PL from MAPbBr3 nanocrystals results from the recombination of PEs, which can emit light either in the ground or TO/LO-phonon vibrationally excited states, thus giving rise to the ~100 meV blue-shift of PL-peak usually appearing in MAPbBr3 nanocrystals with increasing temperature. We note that this polaronic nature of the edge states in MAPbX3 nanocrystals becomes dominant exclusively at higher temperatures (including room temperature) just because energies of the TO/LO-phonon vibrationally excited polaronic quasiparticles (~100 meV) significantly exceeds the groundstate polaron ( , ℎ ≤ ~40 meV) and Rashba energies ( ~40 meV). Alternatively, the Rashba spin-split nature of the edge states in MAPbX3 nanocrystals is expected to be dominant only at low temperature when the Rashba energy might exceed energies of the TO/LO-phonon vibrationally excited polaronic quasiparticles.
Additionally, we showed that at room temperature owing to LO-phonon bottleneck, the polaron masses diminish and polaron radii increase. This behavior creates unique conditions for the TO/LO-phonon vibrationally excited polaronic quasiparticles to travel long distances without scattering on electrostatic potential fluctuations governed by structural imperfections.