Photoluminescence (PL) spectroscopy of individual semiconductor nanocrystals (NCs) is a powerful method for understanding the intrinsic optical properties of these materials. Here, we report the temperature dependence of the PL spectra of single perovskite FAPbBr3 and CsPbBr3 NCs [FA = HC(NH2)2]. The temperature dependences of the PL linewidths were mainly determined by the Fröhlich interaction between excitons and longitudinal optical phonons. For FAPbBr3 NCs, a redshift in the PL peak energy appeared between 100 and 150 K, which was because of the orthorhombic-to-tetragonal phase transition. We found that the phase transition temperature of FAPbBr3 NCs decreases with decreasing NC size.

This paper is part of the Journal of Chemical Physics’s (JCP) Special Topic on 40 Years of Colloidal Nanocrystals. Since the first report of quantum confinement in colloidal nanocrystals (NCs) in JCP in 1983,1 many excellent papers on the photophysics of NCs have been published in the journal. In particular, Brus and his colleagues have greatly contributed to the research field of semiconductor NCs.2,3 Semiconductor NCs, such as CuCl and CdS doped in glass or crystalline matrices, were studied in the early days of research.4–6 Besides NCs composed of compound semiconductors, NCs formed from group-Ⅳ semiconductors, such as Si and Ge, were studied in the 1990s.7–10 Later, it was found that colloidal NCs synthesized by solution chemistry have outstanding optical and electronic properties, because their size, core–shell structure, and shape can be precisely controlled.11–17 In particular, CdSe-based II–VI NCs have been studied in most detail because of their efficient and sharp photoluminescence (PL), photostability, and high optoelectronic device performance.17 In fact, colloidal II–VI semiconductor NCs have been the core materials of nanoscience and nanotechnology for the past three decades.

Recently, metal halide perovskites, new functional semiconductor materials different from II–VI compounds, debuted in the NC research field. All-inorganic halide perovskite NCs were first fabricated in 2015.18–20 Subsequently, perovskite NCs with organic A-site cations were fabricated.21–24 The optical and electronic properties of all-inorganic and organic–inorganic hybrid perovskite NCs have been extensively studied. It was found that APbX3-type lead halide perovskites {A = Cs, MA [CH3NH3], and FA [HC(NH2)2]; X = Cl, Br, and I} are direct-gap semiconductors at room temperature.25 Perovskite NCs have a well-defined cubic shape with a narrow size distribution, extremely high PL quantum yields (PLQYs) without special surface passivation, such as core/shell structures,18–24 and bandgap energies that are tunable over a wide range.26,27 Thus, it is expected that halide perovskite NCs will be used in the next generation of light-emitting diodes, lasers, solar cells, and so on.28,29

Single-dot spectroscopy, which can monitor individual NCs, is one of the most useful methods for understanding the optical properties of these new NCs.30 Most of the studies on the optical properties of single perovskite NCs have been done at room temperature or at extremely low temperatures;31–45 there have been few studies examining the optical properties over a wide temperature range.41,46–49 The temperature dependence of the PL spectral shape can be used to study electron–phonon interaction mechanisms in semiconductors. In bulk crystals, the shape is modified by photon reabsorption and/or photon recycling because there is essentially no Stokes shift between the PL peak and the absorption edge in halide perovskites.50,51 The PL spectrum from a single perovskite NC with a high PLQY provides intrinsic information on the broadening mechanism of the exciton PL linewidth. Moreover, single-dot spectroscopy has been used to study size-dependent crystal structures and phase transitions of II–Ⅵ compound semiconductor NCs.52,53 Lead halide perovskites have three main crystal structures (orthorhombic, tetragonal, and cubic),54,55 and some perovskites have many structural phase transitions below room temperature. The stability of the crystal structure and the structural phase transition temperature depend on the A site cation.56 In lead-halide-perovskite single crystals and thin films, the orthorhombic-to-tetragonal phase transition causes a large jump in the bandgap energy and the PL peak energy.57 Some questions about perovskite NCs remain unanswered: for instance, how does the phase transition temperature of perovskite NCs change with the size of the NC and how does the phase transition affect the PL properties of NCs? To address these questions, it is essential to measure the temperature dependence of PL spectra of single NCs, which can eliminate the effect of broad PL spectra due to inhomogeneity in the size of NCs.

In this study, we examined the PL spectra of single NCs of two different lead halide perovskites, FAPbBr3 and CsPbBr3, over a wide temperature range. The FAPbBr3 NCs showed a PL energy shift between 100 and 150 K that was caused by the orthorhombic–tetragonal crystal structure transition, while the CsPbBr3 NCs showed no phase transition in the same temperature range. However, there were no changes in the exciton PL linewidth at the phase transition, and the exciton–phonon couplings could be determined from the Fröhlich interaction between excitons and longitudinal optical (LO) phonons for both FAPbBr3 and CsPbBr3 NCs. We found that the phase transition temperatures of FAPbBr3 NCs shift toward lower temperatures with decreasing NC size.

Solutions of FAPbBr3 and CsPbBr3 NCs were synthesized using the hot-injection method.18,22 Information on the synthesis methods and samples can be found in our previous work.43,44 For comparison, a solution of FAPbBr3 microcrystals (MCs) (whose average particle size is larger than 100 nm) was also synthesized. For the synthesis of MC solutions, FA acetate (39 mg), Pb acetate (38 mg), oleic acid (1 ml), and 1-octadecene (4 ml) were added to a three-neck flask, and the mixture was vacuumed and refilled with N2 at 50 °C. After the flask was heated to 120 °C, oleylammonium bromide (100 mg) dissolved in anhydrous toluene (1 ml) was swiftly injected. After 1 min, the flask was cooled to room temperature by an ice-water bath. The orange products were purified with toluene and acetonitrile by using centrifugation. The supernatant was discarded, and the FAPbBr3 MCs precipitates were dispersed in anhydrous hexane for further use.

The PL spectra of perovskite NCs were measured at different temperatures by using single-dot spectroscopy. A continuous wave semiconductor laser diode with a wavelength of 444 nm was used as the excitation light source. The spin-coated NC samples on sapphire substrates were set in a helium cryostat. For single-dot spectroscopy, we used a long working-distance objective lens with a numerical aperture of 0.67, a magnification of 50 times, and a glass thickness compensation of 0.7 mm. The PL spectra of the single NCs were measured using a confocal system with a pinhole of 100 µm in diameter and a spectrometer with a resolution of ∼0.5 meV. For the measurements of ensemble MCs, the solution was drop-cast onto a sapphire substrate. Here, all PL spectra were measured from low to high temperatures. The NC sizes were estimated by using the relationship between the PL peak energy and NC size at a cryogenic temperature (5.5 K), which was derived in our previous work.43,44

To avoid spectral diffusion,33,58 the PL of exciton complexes,43,59 and the sample photodegradation, the excitation fluence was adjusted between 4.4 and 38.9 W/cm2 with a neutral density filter, by considering the NC size. As shown in the  Appendix (Fig. 6), we did not observe the formation of trions and biexcitons at the low energy region below the strong exciton PL and no spectral diffusion of the exciton PL under our experimental conditions. Moreover, sharp PL is a good indicator for the phase transition of NCs. In the x-ray diffraction (XRD) spectra, at the tetragonal-to-orthorhombic phase transition, spectral changes are very small even in bulk single crystals because of the similar structures of the two phases.60,61 In addition, for NCs, the size and strain effects cause the broadening of the XRD peaks. On the other hand, it is known that a large change in the bandgap energy appears at the orthorhombic–tetragonal phase transition.57,62 Therefore, the temperature dependence of the PL spectrum of a single NC provides essential information for the phase transition of halide perovskite NCs.

We measured the temperature dependences of the PL spectra in single FAPbBr3 and CsPbBr3 NCs. Figures 1 and 2 show their PL spectra, peak energy, and linewidth as a function of the measurement temperature. In both samples, the PL peak energy is blueshifted and linewidth broadens with temperature. To determine the PL peak energy and linewidth of free excitons, a spectral fitting was performed on the results of both samples by using multiple Gaussian or Lorentzian functions. Up to 40 K, the exciton peak and LO phonon replicas were fitted using multiple Gaussian functions.43,47 At high temperatures above 50 K, a tail appears on the low energy side of the PL spectra and the spectra were fitted using two Lorentz functions.47,49 The peak energy and linewidth (full width at half maximum) were obtained after deconvoluting the spectral resolution of the measurement system.

FIG. 1.

(a) Temperature dependence of the PL spectrum of a single FAPbBr3 NC. The PL spectrum just before the redshift is indicated by the red arrow. The fitting results are shown as solid lines. (b) Temperature dependence of the PL peak energy, which is redshifted from around 130 K and then blueshifted around 170 K. The temperature just before the redshift is indicated by the red arrow. (c) Temperature dependence of PL linewidth. Here, the solid line is the fitting result with ELO = 16.0 meV.

FIG. 1.

(a) Temperature dependence of the PL spectrum of a single FAPbBr3 NC. The PL spectrum just before the redshift is indicated by the red arrow. The fitting results are shown as solid lines. (b) Temperature dependence of the PL peak energy, which is redshifted from around 130 K and then blueshifted around 170 K. The temperature just before the redshift is indicated by the red arrow. (c) Temperature dependence of PL linewidth. Here, the solid line is the fitting result with ELO = 16.0 meV.

Close modal
FIG. 2.

(a) Temperature dependence of the PL spectrum of a single CsPbBr3 NC. The fitting results are shown as solid lines. (b) Temperature dependence of the PL peak energy. There is no shift in PL peak energy. (c) Temperature dependence of PL linewidth. Here, the solid line is the fitting result with ELO = 16.0 meV.

FIG. 2.

(a) Temperature dependence of the PL spectrum of a single CsPbBr3 NC. The fitting results are shown as solid lines. (b) Temperature dependence of the PL peak energy. There is no shift in PL peak energy. (c) Temperature dependence of PL linewidth. Here, the solid line is the fitting result with ELO = 16.0 meV.

Close modal

Figure 1(a) shows the PL spectrum of a single FAPbBr3 NC; the solid curves are the fittings made with the above-mentioned procedure. Figure 1(b) shows the temperature dependence of the PL peak energy; a clear redshift appears at around 130 K, whereas a blueshift reappears at around 170 K. This spectral change corresponds to the phase transition from orthorhombic to tetragonal. The fitting error is negligibly small compared with the shift in peak energy between 130 and 170 K.

On the other hand, for CsPbBr3 NC, the PL peak energy blueshifts monotonically, and no redshift appears in Figs. 2(a) and 2(b). These results indicate that there is no phase transition in the CsPbBr3 NC in the observed temperature range and that the crystal structure remains orthorhombic.54 This is because the FA cation has a much larger ionic radius than the Cs cation, resulting in a smaller distortion of the PbBr6 octahedra and a lower phase transition temperature for FAPbBr3.56 Thus, the phase transition (orthorhombic to tetragonal) can be clearly observed in the low temperature region for FAPbBr3 NCs. In Sec. III B, we will discuss the NC size dependence of the transition temperature for FAPbBr3 NCs by analyzing the temperature dependence of the PL peak energy.

Next, let us examine the temperature dependences of the linewidths shown in Figs. 1(c) and 2(c). The linewidth of the exciton PL in a single NC is determined by inhomogeneous broadening, the exciton-fine structure, spectral diffusion, and the exciton–phonon couplings. The temperature T dependence of the PL linewidth of semiconductors is usually expressed by the following equation:63,
(1)
where Γ0 is the linewidth at T = 0, γac is the acoustic phonon coupling constant, ΓLO is the LO phonon coupling constant, ELO is the effective LO phonon energy, and kB is the Boltzmann constant. For a single NC, Γ0 includes the inhomogeneous broadening due to defects and traps in the NC interior and on the NC surface, spectral diffusion due to local electronic field fluctuations, and the exciton-fine structure. For lead halide perovskites, many LO phonon modes exist. Here, for simplicity, γac is set to zero because the interaction between excitons and acoustic phonons is negligibly small around the phase transition temperature and the value of γac is not sensitive to the curve fitting. First, we performed the fitting with all parameters free, and it was found that ELO varied between 10 and 20 meV. The average value of obtained ELO is ∼16 meV. This value agrees with previous studies.41,46,62 Next, we fixed ELO to 16 meV for all NCs and recalculated the linewidths. The calculated curves explain the observed temperature dependence as shown in Figs. 1(c) and 2(c). There are no abrupt changes in PL linewidth around the phase transition temperature (130–170 K), indicating that the phase transition does not change the exciton–phonon couplings in the orthorhombic and tetragonal crystal phases. These results are in good agreement with the PL linewidth dependence of bulk MAPbBr3 single crystals, which is described by the same effective LO phonon energy in both crystal phases.64 

Since the PL linewidths at elevated temperatures are determined by the exciton–LO-phonon interactions, we plot the obtained PL linewidth at a low-temperature of 5.5 K and at a high-temperature of 130 K just below the phase transition point and the exciton–phonon coupling constant ΓLO as a function of the FAPbBr3 NC size, where L is the edge length of cubic NCs. In Figs. 3(a) and 3(b), the observed PL linewidth and the obtained ΓLO show no clear size dependence. The broadening of zero-phonon line occurs via various mechanisms with different types of phonons. Usually, the overlap between the electron and hole wave functions determines the exciton–phonon coupling in NCs.65 In our NC samples, the NC length is larger than the exciton Bohr radius (3.87 nm).66 Therefore, no clear size dependence of the exciton–phonon coupling constant is observed. In previous studies on single crystals and thin films of MAPbBr3, the effective LO phonon energies showed no dependence on the crystal structure.64,67 The temperature dependence of the PL linewidth can be mainly determined from the Fröhlich interaction between excitons and LO phonons in the temperature range across the phase transition.64,68 The effective LO phonon energy and the LO phonon coupling constant in NCs are not sensitive to the orthorhombic–tetragonal phase transition.

FIG. 3.

(a) PL linewidth of FAPbBr3 NCs at 5.5 K (red) and 130 K (blue) plotted against NC size. (b) ΓLO of FAPbBr3 NCs plotted against NC size (ELO = 16.0 meV).

FIG. 3.

(a) PL linewidth of FAPbBr3 NCs at 5.5 K (red) and 130 K (blue) plotted against NC size. (b) ΓLO of FAPbBr3 NCs plotted against NC size (ELO = 16.0 meV).

Close modal

To discuss the size dependence of the phase transition temperature, drop-cast films of FAPbBr3 MCs (L > 100 nm) were prepared and the phase transition temperature in bulk-like large crystals was determined under the same experimental conditions. Figure 4(a) shows the temperature dependence of the PL spectrum of FAPbBr3 MC thin films. Here, multiple Gaussian functions were used to determine the zero-phonon PL linewidths of the thin films at all temperatures. The PL peak energy begins to redshift at around 150 K due to the phase transition but then begins to blueshift again at around 170 K. The temperature dependence of the peak energy is shown in Fig. 4(b). The phase transition temperature of the FAPbBr3 single crystals was determined to be around 150 K by using XRD and thermal analyses60,61 and is in good agreement with our MC results. The temperature dependence of the linewidth in Fig. 4(c) shows no abrupt change at the phase transition, which is consistent with there being one effective LO phonon energy and one LO phonon coupling constant. This behavior is similar to the case of NCs.

FIG. 4.

(a) Temperature dependence of the PL spectrum of a FAPbBr3 film of MCs (L > 100 nm). The PL spectrum just before the redshift is indicated by the red arrow. The fitting results are shown as solid lines. (b) Temperature dependence of the PL peak energy, which is redshifted from around 150 K and then blueshifted around 170 K. The temperature just before the redshift is indicated by the red arrow. (c) Temperature dependence of PL linewidth. Here, the solid line is the fitting result with ELO = 16.0 meV.

FIG. 4.

(a) Temperature dependence of the PL spectrum of a FAPbBr3 film of MCs (L > 100 nm). The PL spectrum just before the redshift is indicated by the red arrow. The fitting results are shown as solid lines. (b) Temperature dependence of the PL peak energy, which is redshifted from around 150 K and then blueshifted around 170 K. The temperature just before the redshift is indicated by the red arrow. (c) Temperature dependence of PL linewidth. Here, the solid line is the fitting result with ELO = 16.0 meV.

Close modal

Figure 5 shows the orthorhombic-to-tetragonal phase transition temperature (TOT) of FAPbBr3 NCs plotted vs NC size, L (7–14 nm). Here, the measured TOT obtained in the previous study is also plotted as an open circle49 (the exciton peak energies at cryogenic temperatures for these data are ∼2.265 eV, and the estimated NC size is ∼8.2 nm). There is a shift toward lower temperatures as the NC size decreases. Here, TOT is defined as the temperature just before the redshift. For large NCs (>10 nm), TOT is almost the same as that for MCs (red dashed line), while for small NCs (<10 nm), TOT is more shifted to lower temperatures.

FIG. 5.

NC size dependence of the phase transition temperature TOT for a single FAPbBr3 NCs. Here, the NC sizes are estimated from the PL peak energy at 5.5 K. The red dashed line is the bulk phase transition temperature obtained in Fig. 4(b). The TOT reported in the previous work is also plotted as a red open circle.49 The black dashed line is a guide for the eye.

FIG. 5.

NC size dependence of the phase transition temperature TOT for a single FAPbBr3 NCs. Here, the NC sizes are estimated from the PL peak energy at 5.5 K. The red dashed line is the bulk phase transition temperature obtained in Fig. 4(b). The TOT reported in the previous work is also plotted as a red open circle.49 The black dashed line is a guide for the eye.

Close modal

Here, we briefly comment on the observed NC size dependence of the phase transition temperature. In general, the Gibbs free energy of the crystal increases as the ratio of the surface area to the volume increases with decreasing NC size. The Gibbs free energy for the entire NC is inversely proportional to the NC size.52,53,69 This means that below a certain NC size, the tetragonal free energy is smaller than the orthorhombic free energy, and the tetragonal crystal is more stable. Small FAPbBr3 NCs do not become orthorhombic but rather remain tetragonal even at low temperatures. It is pointed out that the transition temperature becomes lower as the size of the NC decreases.70 Moreover, it is known that perovskite NCs have a crystal structure different from that of the bulk crystal even at room temperature.71–74 Structural phase transitions are sensitive to defects in the NC interior and at the NC surface and the quality of the crystals due to their size. Although our data show that the phase transition point from the orthorhombic to tetragonal crystals clearly shifts to lower temperatures with decreasing NC size, further experimental and theoretical studies are needed for a quantitative evaluation of the phase transition of perovskite NCs.

We studied the temperature dependences of the PL spectra of single perovskite FAPbBr3 and CsPbBr3 NCs. The temperature dependences of the PL peak energy for the FAPbBr3 NCs showed an orthorhombic to tetragonal phase transition. The phase transition occurred at lower temperatures compared with the bulk value as the NC size decreased. On the other hand, the temperature dependence of the PL linewidth was mainly determined by the Fröhlich interaction of the LO phonon modes, and the PL linewidth was not affected by the phase transition. The temperature dependence of the PL properties of single NCs is important information for understanding exciton–phonon interactions and for designing single-photon sources.

Part of this work was supported by JST-CREST (Grant No. JPMJCR21B4), JSPS KAKENHI (Grant No. JP19H05465), and JST, the establishment of university fellowships (Grant No. JPMJFS2123).

The authors have no conflicts to disclose.

Kenichi Cho: Data curation (lead); Formal analysis (lead); Investigation (lead); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Takumi Yamada: Formal analysis (supporting); Software (equal); Validation (equal); Writing – review & editing (equal). Masaki Saruyama: Resources (equal); Writing – review & editing (supporting). Ryota Sato: Resources (equal). Toshiharu Teranishi: Funding acquisition (equal); Writing – review & editing (supporting). Yoshihiko Kanemitsu: Funding acquisition (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – original draft (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Figures 6(a) and 6(b) show the PL spectral trajectories of a single FAPbBr3 NC under a photoexcitation of 38.9 W/cm2 and a single CsPbBr3 NC under a photoexcitation of 20.2 W/cm2 at 5.5 K, respectively. These figures indicate no formation of trions and biexcitons at the low energy region below the strong exciton PL and no spectral diffusion of the exciton PL under our experimental conditions.

FIG. 6.

PL spectral trajectories of (a) a single FAPbBr3 NC and (b) a single CsPbBr3 NC at 5.5 K.

FIG. 6.

PL spectral trajectories of (a) a single FAPbBr3 NC and (b) a single CsPbBr3 NC at 5.5 K.

Close modal
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