Photoluminescent Spectral Broadening of Lead Halide Perovskite Nanocrystals Investigated by Emission Wavelength Dependent Lifetime - MDPI

molecules
Article
Photoluminescent Spectral Broadening of Lead
Halide Perovskite Nanocrystals Investigated by
Emission Wavelength Dependent Lifetime
Jinlei Zhang 1 , Jiuyang He 2 , Lun Yang 3, * and Zhixing Gan 4,5, *
 1 Jiangsu Key Laboratory of Micro and Nano Heat Fluid Flow Technology and Energy Application,
 School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
 zhangjinlei199119@126.com
 2 College of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi 830054, China;
 hejiuyang@sina.com
 3 Institute for Advanced Materials, Hubei Key Laboratory of Pollutant Analysis & Reuse Technology,
 Hubei Normal University, Huangshi 435002, China
 4 Jiangsu Key Laboratory of Optoelectronic Technology, School of Physics and Technology,
 Nanjing Normal University, Nanjing 210023, China
 5 College of Materials Science and Engineering, Qingdao University of Science and Technology,
 Qingdao 266042, China
 * Correspondence: yanglun@hbnu.edu.cn (L.Y.); zxgan@njnu.edu.cn (Z.G.)

 Academic Editors: Mirosław Maczka
 ˛ and Maciej Ptak 



 

 Received: 3 February 2020; Accepted: 25 February 2020; Published: 4 March 2020

 Abstract: Despite intensive efforts, the fluorescence of perovskite nanocrystals (NCs) still suffers
 from a poor color purity, which limits the applications in light emitting and multicolor display.
 A deep understanding on the fundamental of the photoluminescent (PL) spectral broadening is
 thus of great significance. Herein, the PL decay curves of the CsPbClx Br3-x NCs are monitored at
 different wavelengths covering the entire PL band. Moreover, energy relaxation time τ and radiative
 recombination time β are obtained by numerical fittings. The dependences of τ and 1/β on the detection
 wavelength agree well with the steady-state PL spectrum, indicating the observed PL broadening is
 an intrinsic effect due to the resonance and off-resonance exciton radiative recombination processes.
 This work not only provides a new analysis method for time-resolved PL spectra of perovskites,
 but also gains a deep insight into the spectral broadening of the lead halide perovskite NCs.

 Keywords: perovskite nanocrystals; photoluminescence; bandwidth; lifetime

1. Introduction
 The lead halide perovskites nanocrystals (NCs) have attracted extensive interest due to their
potential applications for low-cost and high-efficiency photovoltaic, light-emitting diodes (LEDs),
and photo-detectors [1–13]. In particular, the mixed halide perovskite NCs, of which semiconductor
bandgaps can be regulated by halide compositions and sizes, have attracted tremendous attention
for flexible optoelectronic applications [14–16]. The optical response and emission wavelength
can be tuned between ~ 1.5 and 3 eV, which enable the harvest of full solar spectrum and light
emitting covering the entire visible range [1–13]. Thus, the colloidal perovskite NCs exhibiting high
photoluminescence quantum yields (PLQYs) and the broad spectral tuneability have been widely
reported [1,2]. For example, the all inorganic CsPbX3 (X = Cl, Br or I, or mixture) NCs with PL
covering the entire visible spectral region of 410−700 nm were synthesized via compositional bandgap
engineering and size effect [1].

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Molecules 2020, 25, 1151 2 of 11

 However, the limited emission color purity due to the broad spectral width, have hindered the
further development of high-performance perovskite LEDs [17–19]. Almeida et al. devised a general
synthesis scheme for cesium lead bromide NCs which allows control over size, size distribution, shape,
and phase (CsPbBr3 or Cs4 PbBr6 ) by combining key insights on the acid−base interactions [19]. The PL
full width at half maximum (FWHM) for CsPbBr3 nanocubes synthesized at different conditions are
as large as 69–170 meV. Dong et al. developed a new synthesis approach to precisely control the
size and improve the ensemble uniformity. [17] However, the FWHM of the ensemble PL is still as
large as 94 meV for 6.2 nm NCs, 109 meV for 5.3 nm NCs, 117 meV for 4.1 nm NCs, and 142 meV for
3.7 nm NCs [17]. The challenge of producing fluorescent perovskite NCs with narrow bandwidth has
been one of the major obstacles impeding the utilization of perovskite NCs. Such a broad emission
band is commonly attributed to the size distribution in Cd- and Pb-based chalcogenide NCs [20,21].
Current efforts are focused on exploring of colloidal solutions of perovskite NCs with narrow size
distributions to address this issue. Despite intensive efforts, these perovskite NCs are still suffering from
a broad bandwidth. In fact, in addition to the size distribution, the PL spectral width could be attributed
to complex factors, including intrinsic broadening, electron-phonon coupling, and inhomogeneous
surface [22–25]. Moreover, the ion migration induced phase segregation also may lead to spectral
broadening of mixed halide perovskite NCs [26–29]. Therefore, a fundamental exploration on the PL
spectral broadening of the mixed-halide perovskite NCs is of great importance.
 In this work, CsPbCl1.32 Br1.68 NCs were synthesized by Protesescu’s method. The mixed
halide perovskite NCs were selected to include the contribution of phase segregation. The colloidal
CsPbCl1.32 Br1.68 NCs solution shows excitation-independent emission centered at 465 nm. Transmission
electron microscopy (TEM) shows the most probable size is 9.71 nm with a standard deviation of
2.94 nm. The PL decay curves of different emissions (450 to 485 nm) excited at the fixed wavelength
(375 nm) are systematically measured. Also, energy relaxation time τ and radiative recombination
time β are obtained by numerical fitting of the time-resolved PL decay curves. The β decreases firstly
and then increases with the emission wavelengths and shows a maximum at emission of ca. 465 nm.
The results indicate that the PL broadening is an intrinsic effect due to the resonance and off-resonance
exciton radiative recombination processes.

2. Results and Discussion
 A representative TEM image of the perovskite NCs is shown in Figure 1a. The shapes of the
perovskite NCs are cubic. The edge lengths’ distribution of the perovskite NCs calculated from the TEM
image is plotted in Figure 1b, which is fitted by a Gaussian function. The most probable edge length of
our perovskite NCs is 9.71 nm and the standard deviation is 2.94 nm. The uniformity of the perovskite
NCs in this work is better than general preparation [30], while it is inferior to perovskite NCs with
precise control, [19] representing a general situation. As is well known, size inhomogeneity is expected
to be a main contribution to the PL broadening. Thus, in order to ensure the broad applicability of
the conclusion and to include the possible contribution from size inhomogeneity, the synthesis in this
work has not been optimized to eliminate the size in-homogeneity.

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 (a)

 20 nm

 8
 (b) 9.71 nm
 7
 6
 5
 Count

 4 2.94 nm

 3
 2
 1
 0
 8 9 10 11 12 13 14
 Edge length (nm)

 Figure
 Figure 1. (a) TEM
 1. (a) TEM image
 image of
 of the
 the perovskite
 perovskite nanocrystals
 nanocrystals (NCs)
 (NCs) (b)
 (b) Size
 Size distributions
 distributions of
 of the
 the perovskite
 perovskite
 NCs
 NCs calculated
 calculated from
 from the
 the TEM
 TEM image.
 image.

 PL
 PL spectra
 spectra excited
 excited atat 375
 375 to
 to 415
 415 nm
 nm with
 with anan interval
 interval of
 of 10
 10 nm
 nm are
 are shown
 shown in in Figure
 Figure 2a.2a. The
 The PL
 PL
peak
peak isis ascribed
 ascribed to to bandgap
 bandgap (2.65
 (2.65 eV)
 eV) emission
 emission.[31,32]. Except for
 [31,32] Except for different
 different intensities,
 intensities, all
 all the
 the spectra
 spectra
almost
almost keep
 keep thethe same
 same peak
 peak position
 position and
 and spectral
 spectral profiles. The FWHM
 profiles. The FWHM is is about
 about 144
 144 meV
 meV (25 (25 nm),
 nm),
which
which is is aareasonable
 reasonablevaluevaluecompared
 comparedwith withother
 otherreports [17–19].
 reports. [17–19]It is
 It worth
 is worth noting thatthat
 noting redshift of PL
 redshift of
spectra with increasing excitation wavelength is a fundamental feature of radiative
PL spectra with increasing excitation wavelength is a fundamental feature of radiative recombination recombination
dominated
dominated by by the
 the size
 size effect
 effect.[31,32].
 [31,32] According
 According to to quantum
 quantum confinement
 confinement effect,
 effect, the
 the size
 size distribution
 distribution
induces a corresponding distribution of the energy gaps. When excitation wavelength
induces a corresponding distribution of the energy gaps. When excitation wavelength increases, increases, more
NCs with big sizes and narrow bandgaps are selectively excited, resulting
more NCs with big sizes and narrow bandgaps are selectively excited, resulting in PL spectral in PL spectral redshift,
which
redshift,haswhich
 been has
 extensively observed observed
 been extensively in Si quantumin Si dots, SiC NCs,
 quantum dots, carbon
 SiC NCs, nanoparticles, graphene
 carbon nanoparticles,
quantum
graphenedots, and MoS
 quantum 2 quantum
 dots, and MoS2dots [31–33].
 quantum Here,
 dots. the PL
 [31–33] peaks
 Here, theofPL
 perovskite
 peaks ofNCs that hardly
 perovskite NCsshift
 that
tend to imply minor contribution from size effect. PL excitation (PLE) spectra monitored
hardly shift tend to imply minor contribution from size effect. PL excitation (PLE) spectra monitored at emission
wavelengths of 455, 465, of
at emission wavelengths and 475465,
 455, nmand
 are 475
 alsonmacquired.
 are alsoSimilarly,
 acquired.the PLE spectra
 Similarly, do spectra
 the PLE not shiftdowith
 not
the emission wavelengths. In addition, PL spectra excited at different wavelengths
shift with the emission wavelengths. In addition, PL spectra excited at different wavelengths are normalized are
(Inset of Figure
normalized 2a).
 (Inset of The
 FigurePL2a).
 spectral
 The PLshape and FWHM
 spectral shape and almost
 FWHM keep the same
 almost keepwhen the excitation
 the same when the
wavelength changes. changes.
excitation wavelength

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 (a)

 PL intensity (a.u.)
 375

 PL intensity (a.u.)
 385
 395
 405
 415
 λExcitation
 nm 450 500 550
 Wavelength (nm)

 400 450 500 550 600
 Wavelength (nm)

 (b)
 455
 PLE intensity (a.u.)

 465
 475
 λEmission
 nm

 300 320 340 360 380 400 420 440
 Wavelength (nm)

 Figure 2. (a)
 Figure 2. (a) Photoluminescent
 Photoluminescent(PL)(PL)spectra
 spectraexcited
 excitedatat
 375 toto
 375 415 nmnm
 415 with an an
 with interval of 10
 interval ofnm. Inset:
 10 nm. PL
 Inset:
 spectra excited at different wavelengths are normalized. (b) Excitation spectra monitored
 PL spectra excited at different wavelengths are normalized. (b) Excitation spectra monitored at at emission
 wavelengths of 455, 465,
 emission wavelengths ofand
 455,475
 465,nm.
 and 475 nm.

 To explore the origins of the FWHM of colloidal perovskite NCs, we quantitatively study the
 To explore the origins of the FWHM of colloidal perovskite NCs, we quantitatively study the
time-resolved fluorescence decay spectrum of colloidal NCs as a function of the detection wavelength.
time‐resolved fluorescence decay spectrum of colloidal NCs as a function of the detection
The bandpass of the detector is fixed as small as 1 nm so that we collected only the fluorescence signals
wavelength. The bandpass of the detector is fixed as small as 1 nm so that we collected only the
from NCs of one size, if NC size distribution is the sole cause of the broad FWHM. The emission
fluorescence signals from NCs of one size, if NC size distribution is the sole cause of the broad
wavelength dependent PL lifetimes are quantitatively analyzed by a model developed by Xu et al. [25].
FWHM. The emission wavelength dependent PL lifetimes are quantitatively analyzed by a model
This model was validated by both numerical simulations and experiments. In order to avoid repetition,
developed by Xu et al. [25] This model was validated by both numerical simulations and experiments.
this article does not go into too much detail. As schemed in Figure 3, the electron energy levels in a NC
In order to avoid repetition, this article does not go into too much detail. As schemed in Figure 3, the
is characterized by quantized exciton levels. Upon photoexcitation, the photogenerated exciton is in
electron energy levels in a NC is characterized by quantized exciton levels. Upon photoexcitation, the
an excited exciton state ψn . The excited exciton relaxes to the ground exciton state ψ1 via nonradiative
photogenerated exciton is in an excited exciton state ψn. The excited exciton relaxes to the ground
interactions, and then radiatively recombines to emit a photon. After that, the NC returns to its vacuum
exciton state ψ1 via nonradiative interactions, and then radiatively recombines to emit a photon. After
state ψ0 . Before excitation, the NC is initially at its vacuum state. Once a pulsed excitation excites the
that, the NC returns to its vacuum state ψ0. Before excitation, the NC is initially at its vacuum state.
QD at t = 0 so that nn = 1 and n1 = n0 = 0. nn , n1 , and n0 are populations of the state ψn , ψ1 , and ψ0 ,
Once a pulsed excitation excites the QD at t = 0 so that nn = 1 and n1 = n0 = 0. nn, n1, and n0 are
respectively. When ψn -exciton nonradiatively relaxes to ψ1 at a rate of 1/τ while ground-state exciton
populations of the state ψn, ψ1, and ψ0, respectively. When ψn‐exciton nonradiatively relaxes to ψ1 at
radiatively transits to ψ0 at a rate of 1/β. The following rate equations can be acquired to describe the
a rate of 1/τ while ground‐state exciton radiatively transits to ψ0 at a rate of 1/β. The following rate
PL decay processes Equation (1):
equations can be acquired to describe the PL decay processes (Equation 1):
 n n (1−n
 1 ) 
 
 dn n
 ⎧ dt = −
 
 τ
 
 
 ⎪
 
 dn1 (
 n 1−n ) n 1−n )
 (
 ⎪ = n τ 1 − 1 β 0 
 
 
  
 dt (1)
 
 dn n ( 1−n ) (1)
 ⎨ 
 1 0
  0
 dt =
 
 β
 ⎪
 ⎪ 
 ⎩ 

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 Excited exciton ψn nn
 En

 τ Stage 1

 Exciton ψ1 n1

 E1

 β
 Stage 2
 Excitation 450 nm
 465 nm
 Emission

 480 nm
 ψ0 n0
 E0

 Figure 3.3.Schematic
 Figure Schematicillustration of excitation,
 illustration energy relaxation
 of excitation, time τ and time
 energy relaxation radiative recombination
 τ and radiative
 time β of an exciton
 recombination timeinβthe perovskite
 of an exciton NCs.
 in the perovskite NCs.

 Considering the
 Considering the Pauli
 Pauli exclusion
 exclusion principle,
 principle, the
 the transition
 transition efficiency
 efficiency of
 of an
 an exciton
 exciton from
 from an
 an initial
 initial
exciton level to a final exciton level is determined by both the occupation of the initial level
exciton level to a final exciton level is determined by both the occupation of the initial level and the and the
un-occupation of the final level. For a very short time directly after the optical excitation,
un‐occupation of the final level. For a very short time directly after the optical excitation, assumingassuming ψ1 ,
and
ψ ψ0 are
 1, and
 empty,
 ψ0 are empty,the the
 PL PL
 intensity f1 (t)f1is
 intensity (t)well characterized
 is well characterizedby by
 a single decay
 a single term
 decay Equation
 term (2): 2):
 (Equation
 / 
 f 1 (t ) ∝∝ e −t/τ0 (2)
 (2)
 The subscript ‘‘1’’ in is assigned for the stage 1. ′ depends on both and . As
decay proceeds,
 The subscriptwhen nnf1is(tnegligibly
 “1” in small,
 ) is assigned for the thestage 1. τ0 depends
 rate equations become τ and β.
 (Equation
 on both 3):As decay
proceeds, when nn is negligibly small, the rate equations
 become Equation (3):
 ⎧ 
 ⎪ 
 dn1 n1 (1−n0 ) (3)
 
 
 ⎨ dt 
 
  = −
 β 
 (3)
 
 ⎪ 
 ⎩ dt0 = 1 β 0
 
 
  dn n (1−n )

 The solution for the above equation is hardly exponential and needs many exponential
decays
 Thetosolution
 numerically
 for the fit it. However,
 above equation isathardly
 a special time stage
 exponential and needs , 1exponential
 ∈ ,many decays
 .
The solution for
to numerically fit above equation
 it. However, at a can be acquired
 special time stage(Equation
 t ∈ (t1 , t2 ),4): 0
 (1 − n0 ) = n1 = n0 . The solution for
above equation can be acquired Equation (4): 1 1 
 (4)
 
 1 1 t+a
 where a is a constant. The long‐time=fluorescence
 = decay, , at the second stage (4)
 ∈
 n1 n00 β
 , is (Equation 5)
where a is a constant. The long-time fluorescence 1 decay, f2 (t), at the second stage t ∈ (t1 , t2 ) is
 ∝ (5)
Equation (5) 
 β time duration. The time‐resolved
 Z t2
 since the variations of n1 and (1‐n0) in tnis 1 (very
 1 − n0small
 ) in the
 f (t) = dt ∝ (5)
PL decays of the perovskite NCs 2at different t1 β
 detection wavelengths
 (t + a)2 (450–485 nm) excited at a fixed
wavelength (375 nm) are obtained and shown in Figure 4. According to the model above, two
since the variations of n1 and (1-n0 ) in t is very small in the time duration. The time-resolved PL decays
different stages are defined in the PL decay curves (Figure 4b). The relaxation value τ is fitted by a
of the perovskite NCs at different detection wavelengths (450–485 nm) excited at a fixed wavelength
single exponential function from the first stage of the PL decay function in the photon count range
(375 nm) are obtained and shown in Figure 4. According to the model above, two different stages are
between 1 × 104 and 0.5 × 104. As shown in Figure 4c, the time‐resolved PL decay curves are
defined in the PL decay curves (Figure 4b). The relaxation value τ is fitted by a single exponential
transformed to 1⁄ , where is the fluorescence intensity as a function of decay time.4 The
function from the first stage of the PL decay function in the photon count range between 1 × 10p and
second‐stage time window is found in the range of 30 and 60 ns, since 1⁄ is well approximated
0.5 × 104 . As shown in Figure 4c, the time-resolved PL decay curves are transformed to 1/ F(t),
as linearly related to time t.
where F(t) is the fluorescence intensity as a function
 p of decay time. The second-stage time window is
found in the range of 30 and 60 ns, since 1/ F(t) is well approximated as linearly related to time t.

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 (a) 10000

 480

 Wavelength (nm)
 1000
 470

 460 100.0

 450
 0 20 40 60 80
 Time (ns)

 10000 0.10
 (b) 450 (c) 450
 Stage 1 455
 455
 460 0.08 460
 465 465
 470 470

 1/sqrt(F)
 475 0.06 475
 480
 F(t)

 480
 Stage 2 485 485
 1000 0.04

 0.02

 0.00
 0 20 40 60 80 100 0 20 40 60 80 100
 Time (ns) Time (ns)

 Figure4. 4.(a)(a)
 Figure TheThe
 time-resolved
 time‐resolvedPL decay
 PL mapping monitoredmonitored
 decay mapping at differentatdetection wavelengths
 different detection
 (450–485 nm) excited
 wavelengths at a fixed
 (450–485 nm) wavelength
 excited at a (375 nm).wavelength
 fixed (b) The time-resolved
 (375 nm). fluorescence decay spectra
 (b) The time‐resolved
 at different emissions
 fluorescence decay (420, 460, at
 spectra 500,different
 540, and emissions
 600 nm). The detection
 (420, bandpass
 460, 500, 540, was
 andfixed
 600 tonm).
 be 1 The
 nm.
 p
 Two stages are selected. (c) The time-resolved fluorescence decay curves are transformed
 detection bandpass was fixed to be 1 nm. Two stages are selected. (c) The time‐resolved to 1/ F (t)
 versus t.
 fluorescence decay curves are transformed to 1⁄ versus t.

 The
 Thefittings
 fittingsofofthethe
 two different
 two stages
 different are presented
 stages in Figure
 are presented 5a,b, respectively.
 in Figure The acquired
 5a,b, respectively. The
parameters as a function of detection wavelength are plotted in Figure 5c. The
 acquired parameters as a function of detection wavelength are plotted in Figure 5c. The standard errors of fitting
of τ are alsoerrors
 standard presented. The results
 of fitting reveal
 of τ are alsothat both τ andThe
 presented. β depend
 resultsstrongly
 reveal on theboth
 that detection
 τ andwavelength.
 β depend
 is minimal
βstrongly on the detection wavelength. β is minimal while τ is approximately maximum atof
 while τ is approximately maximum at the PL peak wavelength. The dependences τ
 the
and 1/β onwavelength.
 PL peak the detection The wavelength agree well
 dependences of τwith
 andthe steady
 1/β on thestate PL spectrum.
 detection Very similar
 wavelength agreeresults
 well
have been observed for the conventional CdSe QDs [25]. According to
 with the steady state PL spectrum. Very similar results have been observed for the the generalized Fermi golden
rule, the decay CdSe
 conventional (}ω) of
 rate r1 QDs. exciton
 [25] state ψ1toisthe
 According given as [25]:
 generalized Fermi golden rule, the decay rate
 ℏ of exciton state ψ1 is given as*[25]: +2
 2π X Γ1
 r1 (}ω) = 2 ψ0 V ψ Γ (6)
 ℏ }ℏ |⟨ | ∑ i| 1⟩| Γ2 + (E1 − E0 − }ω)2 Γ1 ℏ 
 (6)
 i

wherewhere ℏ photon
 }ω is the is the photon Vi is the ithisinteraction
 energy, energy, the ith interaction
 between ψ between ψ1 and ψ0, and Γ is the
 1 and ψ0 , and Γ1 is the relaxation
 relaxation energy of ψ due to interactions with ψ . According
energy of ψ1 due to interactions Vi with ψ0 . According to Equation (6), resonance
 1 0 to Equation 6, resonance
 fluorescence with
Efluorescence
 1 − E 0 = } ω with
 exhibits a 
 shortest ℏ exhibits
 lifetime whilea shortest lifetime
 off-resonance while off‐resonance
 fluorescence ( E1 − E 0 , } ω)
 fluorescence
 possesses (
 ℏ ) possesses a long lifetime. As displayed in Figure 5d, Equation
a long lifetime. As displayed in Figure 5d, Equation (6) is used to fit relationship between 1/β (blue 6 is used to fit
 relationship
star) and photonbetween
 energy.1/βThe(blue star)dependence
 strong and photonofenergy.1/β on The strong dependence
 the detection photon energy of 1/β
 andontheir
 the
 detectionwith
symmetry photon energy
 respect to theand their symmetry
 emission wavelengthwith respect
 indicate that tothethe emission
 large FWHM wavelength indicate
 of the perovskite NCs
 that the large FWHM of the perovskite NCs is most probably caused by
is most probably caused by intrinsic broadening rather than being dominated by the size distribution. intrinsic broadening
 rather than
Moreover, thebeing dominated
 steady-state by the
 spectrum (redsize
 line)distribution.
 is also addedMoreover,
 for comparison.the steady‐state
 The FWHM spectrum
 of the 1/β
 (red line) ispeak
distribution alsoisadded
 about for140 comparison.
 meV, which isThe veryFWHM of the
 close to the FWHM1/β distribution peak PL
 of the steady-state is about 140
 spectrum
 meV, which is very close to the FWHM of the steady‐state PL spectrum
(~144 meV). On the contrary, as reported previously, for PL of SiC NCs caused by size effect, both (~144 meV). On the
 τ
 contrary,
and as reported
 β are hardly dependentpreviously, for PL wavelength
 on the detection of SiC NCs[33]. caused bycase,
 In that size the
 effect, both τ PL
 ultra-broad andwidths
 β are
 hardly
with dependent
 FWHM>600 meVonaretheoriginated
 detectionfromwavelength. [33] In that
 the size distribution of case,
 the NCs.the ultra‐broad PL widths
 with FWHM>600 meV are originated from the size distribution of the NCs.

Molecules 2020, 25, x FOR PEER REVIEW 7 of 11

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Molecules 2020, 25, 1151 7 of 11

 Figure 5. (a) The first stage of the PL decay curves fitted by simple exponential functions. (b).
 Linear fittings of 1⁄ versus t at the first stage area. (c) Fitting parameters as a function of
 Figure 5. (a) The first stage of the PL decay curves fitted by simple exponential functions. (b) Linear
 Figure 5. (a)
 detection pThe first stage
 wavelength. of squares:
 Black the PL decay
 τ; redcurves fitted
 circles: byThe
 β. (d) simple exponential
 relationship functions.
 between (b).
 1/β (blue
 fittings of 1/ F(t) versus t at the first stage area. (c) Fitting parameters as a function of detection
 Linear fittings
 star) and photon ⁄ isversus
 of 1energy fitted tbyatequation
 the first stage area.
 6 (blue (c) The
 line). Fitting parameters
 steady as a function
 sate spectrum of
 (red line)
 wavelength. Black squares: τ; red circles: β. (d) The relationship between 1/β (blue star) and photon
 detection wavelength.
 is added for Black squares: τ; red circles: β. (d) The relationship between 1/β (blue
 comparison.
 energy is fitted by Equation (6) (blue line). The steady sate spectrum (red line) is added for comparison.
 star) and photon energy is fitted by equation 6 (blue line). The steady sate spectrum (red line)
 Asadded
 is
 As found
 found forpreviously,
 comparison.
 previously, thePL
 the PLlifetime
 lifetimeofofperovskite
 perovskiteNCs NCsisisstrongly
 stronglydependent
 dependenton onthe
 thehalide
 halide
 composition,with
composition, withClCl

Molecules 2020, 25, x FOR PEER REVIEW 8 of 11

 The colloidal CsPbX3 NCs solutions were synthesized by a method developed by
Protesescu
Molecules et al.
 2020, 25, 1151[1]
 Cs‐oleate was prepared by dissolving 0.814 g Cs2CO3 into 100 mL 3‐neck 8 of 11
flask containing 40 mL octadecene (ODE) and 2.5 mL oleic acid (OA), dried at 120 °C for one
hour, and then heated to 150 °C under protection of nitrogen gas until all Cs◦ 2CO3 reacted with
flask containing 40 mL octadecene (ODE) and 2.5 mL oleic acid (OA), dried at 120 C for one hour, and
OA. Then, 5 mL ODE and 0.188 mmol mixtures of PbBr2 and PbCl2 (0.052 g) were added into
then heated to 150 ◦ C under protection of nitrogen gas until all Cs2 CO3 reacted with OA. Then, 5 mL
a 3‐neck flask and dried under vacuum for 1 h at 120 °C. Dried oleylamine (0.5 mL, OLA) and
ODE and 0.188 mmol mixtures of PbBr2 and PbCl2 (0.052 g) were added into a 3-neck flask and dried
dried OA (0.5 mL) were injected at 120 °C under N2. The temperature was raised to 140–200
under vacuum for 1 h at 120 ◦ C. Dried oleylamine (0.5 mL, OLA) and dried OA (0.5 mL) were injected
°C, after complete solubilization of the PbX2. The Cs‐oleate solution prepared earlier (0.4
at 120 ◦ C under N2. The temperature was raised to 140–200 ◦ C, after complete solubilization of the PbX2 .
mL,0.125M in ODE) was quickly injected. Five seconds later, the reaction mixture was cooled
The Cs-oleate solution prepared earlier (0.4 mL,0.125M in ODE) was quickly injected. Five seconds
by the ice‐water bath. Higher temperature of 150 °C and 1 mL of trioctylphosphine were
later, the reaction mixture was cooled by the ice-water bath. Higher temperature of 150 ◦ C and 1 mL of
required to solubilize PbCl2 for the synthesis of CsPbCl3. Finally, the aggregated NCs in the
trioctylphosphine were required to solubilize PbCl2 for the synthesis of CsPbCl3. Finally, the aggregated
crude solution was separated by centrifuging. After centrifugation, the supernatant was
NCs in the crude solution was separated by centrifuging. After centrifugation, the supernatant was
discarded and stable solutions of colloidal CsPbX3 NCs were obtained by redispersing the
discarded and stable solutions of colloidal CsPbX3 NCs were obtained by redispersing the particles
particles in hexane. The concentration of the final CsPbX3 NCs solution is about 1 mg/mL.
in hexane. The concentration of the final CsPbX3 NCs solution is about 1 mg/mL. According to the
According to the Vegard’s law, [29] the chemical formula is estimated to be CsPbCl1.32Br1.68.
Vegard’s law, [29] the chemical formula is estimated to be CsPbCl1.32 Br1.68 .
 TEM images were captured by a JEOL JEM‐2100F transmission electron microscope
 TEM images were captured by a JEOL JEM-2100F transmission electron microscope (TEM)
(TEM) (JEOL, Japan). The optical absorption spectra were obtained using a Shimadzu UV‐2600
(JEOL, Japan). The optical absorption spectra were obtained using a Shimadzu UV-2600 spectrometer
spectrometer (Shimadzu, Japan). Both steady‐state and time‐resolved PL (TRPL)
(Shimadzu, Japan). Both steady-state and time-resolved PL (TRPL) measurements were performed
measurements were performed on an Edinburgh FLS‐920 fluorescence spectrometer (
on an Edinburgh FLS-920 fluorescence spectrometer ( Edinburgh Instruments, UK). As illustrated in
Edinburgh Instruments, UK). As illustrated in Scheme 1, a 375 nm picosecond pulse laser was
Scheme 1, a 375 nm picosecond pulse laser was used as the excitation light (2 MHz, 0.5 mW) for TRPL
used as the excitation light (2 MHz, 0.5 mW) for TRPL measurements. The emission
measurements. The emission bandwidth was fixed at 1 nm by a monochromator equipped on FLS-920
bandwidth was fixed at 1 nm by a monochromator equipped on FLS‐920 spectrometer and
spectrometer and the detection wavelength was modified from 450 to 485 nm to cover the fluorescence
the detection wavelength was modified from 450 to 485 nm to cover the fluorescence peak.
peak. Photon counting was stopped when the maximal number of photon counts reached a pre-set
Photon counting was stopped when the maximal number of photon counts reached a pre‐set
maximal value of 104 in order to reach a high signal-to-noise ratio.
maximal value of 104 in order to reach a high signal‐to‐noise ratio.

 Scheme1.1.The
 Scheme The optical
 optical set‐up
 set-up for measurements
 for measurements of time‐resolved
 of time-resolved PL TCSPC=
 PL curves. curves. TCSPC= time‐
 time-correlated
 single photon
 correlated counting
 single photonsystem, APD=system,
 counting avalanche photodiode.
 APD= avalanche photodiode.

4. Conclusions
4. Conclusions
 In
 In summary,
 summary,colloidal
 colloidal CsPbX
 CsPbX 3 perovskite NCs emitted at 465 nm with a bandwidth of 144 meV
 3 perovskite NCs emitted at 465 nm with a bandwidth of 144
are
meV synthesized. The all inorganic
 are synthesized. The all perovskite
 inorganic NCsperovskite
 solution shows NCsexcitation-independent
 solution shows excitation‐ emission
and emission-independent excitation, implying a negligible contribution
independent emission and emission‐independent excitation, implying a negligible from inhomogeneous size.
TEM image shows the size distribution of our perovskite NCs centering
contribution from inhomogeneous size. TEM image shows the size distribution of our at 9.71 nm with a standard
deviation
perovskite of NCs
 2.94 nm. The PL
 centering atdecay
 9.71 nmcurves
 with of adifferent
 standard emissions
 deviation(fromof 450
 2.94tonm.485 The
 nm) PLexcited at
 decay
the fixed wavelength (375 nm) are systematically measured. Moreover, energy
curves of different emissions (from 450 to 485 nm) excited at the fixed wavelength (375 nm) relaxation time τ and
radiative recombination
are systematically time βMoreover,
 measured. are obtained by numerical
 energy relaxationfitting.
 timeThe
 τ andτ and β strongly
 radiative depend on
 recombination
the detection wavelength. The β decreases firstly and then increases with
time β are obtained by numerical fitting. The τ and β strongly depend on the detection the emission wavelengths,
showing
wavelength.a maximum
 The β atdecreases
 PL peak position.
 firstly andThe results further suggest
 then increases with that
 the the FWHM wavelengths,
 emission of 144 meV of
the perovskite
showing NCs is most
 a maximum probably
 at PL peak caused
 position. by The
 the intrinsic
 results broadening instead
 further suggest of inhomogeneous
 that the FWHM of size 144
distribution. We have further checked
meV of the perovskite NCs is most probably the CsPbBr NCs. Also, similar conclusion
 3 caused by the intrinsic broadening is also acquired.
 insteadThis
 of
work not only provides a new analyses of time-resolved fluorescence spectra
inhomogeneous size distribution. We have further checked the CsPbBr3 NCs. Also, similar of perovskites, but also
gains a deep is
conclusion insight
 also into the PL This
 acquired. spectral
 workbroadening
 not onlyofprovides
 the lead halide
 a new perovskite
 analysesNCs. Based on this
 of time‐resolved
work, we now know that if FWHM is much larger than 144 meV, the broad PL and poor color purity

Molecules 2020, 25, 1151 9 of 11

may suffer from a poor size distribution. However, when the FWHM is even smaller than 144 meV,
controlling on the uniformity of the NC size shows a limited ability to narrow the bandwidth.

Author Contributions: L.Y. and Z.G. conceived the concept for the manuscript. J.Z., J.H., and Z.G. conducted the
experiments. Z.G. and L.Y. analysed the data, Z.G wrote manuscript with assistance of all co-authors. All authors
have read and agreed to the published version of the manuscript
Funding: This work was jointly supported by National Natural Science Foundation of China (No. 51801059),
Taishan Scholars Program of Shandong Province (No. tsqn201909117) and Jiangsu Key Disciplines of the Thirteenth
Five-Year Plan (No. 20168765).
Conflicts of Interest: The authors declare that there are no conflicts to declare.

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Sample Availability: Not available.

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