Trap States and Their Dynamics in Organometal Halide Perovskite ...
Supporting Information: Trap States and Their Dynamics in Organometal Halide Perovskite Nanoparticles and Bulk Crystals Kaibo Zheng,†,‡, * Karel Žídek,† Mohamed Abdellah,†,﹟ Maria E Messing,§ Mohammed J. AlMarri,‡ Tõnu Pullerits†,*
†
Department of Chemical Physics, Lund University, Box 124, 22100, Lund, Sweden
‡ Gas Processing Center, College of Engineering, Qatar University, PO Box 2713, Doha, Qatar §
﹟
Department of Solid State Physics, Lund University, Box 118, 22100, Lund, Sweden Department of Chemistry, Faculty of Science, South Valley University, Qena 83523, Egypt
Table of Content S1. Synthesis methods: ......................................................................................................................... 2 S2. Size and morphology of MAPbBr3 microcrystals and nanoparticles.............................................. 2 S3. Calculation of absorption coefficient and excitation density of MAPbBr3..................................... 3 S4. Comparison of fitting PL decays of MAPbBr3 BCs using different models.................................. 4 S5. Fitting parameters of TRPL decay. ................................................................................................. 5 S6. Stability and reproducibility of PL kinetics. ................................................................................... 6 S7. Dependence of relative PL quantum yield of BCs and NPs on the excitation intensities. ............ 7 S8. Detailed model of trap filling and fitting process: .......................................................................... 7 S9. Trap filling via charge accumulation for the limited number of traps ............................................ 9 S10. Uncertainty estimation in modelling of PL kinetics in NPs........................................................ 10 S11. PL kinetics of BCs detected on different spots of the substrates ................................................ 11
1
S1. Synthesis methods: Synthesis of precursors: methylammonium bromide (CH3NH3Br) and octylammonium bromide (CH3(CH2)7NH3Br) were synthesized by reaction of the corresponding amine in water/HBr accordingly to the previously reports. In brief, for (CH3NH3Br) 36.9 ml of HBr and 83.4 ml of CH3NH2 were stirred for two hours in ice bath. The resulting solution was evaporated till the formation of white crystals. The white crystals then were recrystallized from ethanol solution which then used as a precursor for CH3NH3PbBr3 colloidal nanoparticles. The same procedures were repeated in order to prepare (CH3(CH2)7NH3Br) where 33.5 ml of CH3(CH2)7NH2 and 22.6 ml of HBr were stirred for two hours in ice bath. Synthesis of CH3NH3PbBr3 bulk crystals: MAPbBr3 microcrystals were prepared by spin coating MAPbBr3 precursors in DMF onto glass substrates with 2000 rpm of 30 sec. Substrates were then annealed in air at 85 oC for half hour to form orange colored crystals. In order to verify the crystal size, different dilution of precursors (×2, ×4, ×8, ×16, ×25) were used which produced crystals with mean size of 6.2, 4.2, 2.0 and 0.4 µm, respectively. Synthesis of CH3NH3PbBr3 colloidal nanoparticles: CH3NH3PbBr3 colloidal nanoparticles were synthesized via hot injection of MABr/ODABr and PbBr2 precursors in coordinator solvent analogous to previous reports. In brief, 0.5 mmol oleic acid in 10 ml of octadecene was stirred and heated at 80 °C followed by addition of 0.3 mmol ODABr in 1 ml DMF. Then 0.2 mmol of MABr in 1 ml DMF and 0.5 mmol PbBr2 in 1 ml DMF were injected subsequently. The yellow dispersion containing nanoparticels was directly precipitated by acetone. Finally, the nanoparticles were redispersed in toluene for use. Here the ratio between ODABr and MABr is 6:4, we also prepared two more samples with ODABr/MABr of 5:5 and 7:3, which keep the same synthesis procedures except for adding 0.25 mmol ODABr and 0.25 mmol MABr, 0.35 mmol ODABr and 0.15 mmol MABr, respectively.
S2. Size and morphology of MAPbBr3 microcrystals and nanoparticles The size and morphology of MAPbBr3 microcrystals were characterized by SEM. Fig. SI (a-d) shows the SEM images of 4 MAPbBr3 bulk crystals samples synthesis via different concentration of precursors. The histogram in the insets show the size distribution of the crystals calculated from the SEM pics, the mean size of the crystal was obtained by fitting with Gaussian distribution. Fig. SI (e) exhibits the HRTEM image of CH3NH3PbBr3 nanoparticles with MA and ODA ratio of 6:4 with the size distribution histogram shown in the inset.
2
Figure S1. (a-d) SEM images of MAPbBr3 micro crystals with different mean sizes prepared by using precursors with different dilutions (1:1, 1:3, 1:7 and 1:20, respectively), (e) MAPbBr3 nanoparticles synthesized using MA:ODA ratio of 6:4. The insets in all figures illustrate the size distribution of the crystals and nanoparticles. (f) HR-TEM image of individual MAPbBr3 NP with well-defined lattice fringes. The size of the NP is about 8.5 nm for this NP.
S3. Calculation of absorption coefficient and excitation density of MAPbBr3 Due to incomplete coverage of the BCs on the substrate, the absorption spectra need to be corrected to obtain the accurate absorption coefficient of the samples.1 Absorption coefficient of MAPbBr3 was evaluated by absorption spectrum of 400 nm crystal film as shown in Fig. S2. The optical density (O.D.) at 438 nm (the excitation wavelength for TRPL measurement) is 0.015. A=log(I0/I1)
(1)
The morphology of our crystals is disk as shown in fig. 1 in main text, which can be considered as discontinues film. As shown in fig. S1e, we have such film consisting of discrete crystals with about 12.5% coverage, in order to increase the accuracy of the coverage calculation, we averaged the results from 5 SEM images from different area of the same sample to obtain decent statistics. The OD of a continuous film with the same thickness would be then given as: A
(2)
Here I1conti is the intensity of light after a continuous film, and it can be calculated from the intensity of light after a discontinues film with 12.5% coverage in our case (I1): I 3
. %
(3)
Then we can get Aconti as: A
/.
"
# % $
&
(4)
Taking A=0.015, Aconti can be calculated as 0.14. The absorption coefficient ε= A/l, where l is the path length of the light which equals to the thickness of the film 40 nm. We obtain ε=3.5×104 cm-1. The excitation density n can be calculated as photon flux f in photons/cm2 multiplied by absorption coefficient ε: n= fε, table SI summarizes the corresponding excitation density at different laser photon flux in TRPL measurements: Table S1. Excitation density with different laser photon flux Power density (nJ/cm2)
Photon flux (ph/cm2)
Excitation density (cm-3)
0.51
1×109
3.5×1013
5.1
1×1010
3.5×1014
17
3.3×1010
1.2×1015
51
1×1011
3.5×1015
Figure S2. Absorption spectrum of MAPbBr3 nanocrystal film with mean diameter of 400 nm.
S4. Comparison of fitting PL decays of MAPbBr3 BCs using different models. In order to give further support to the used tri-exponential fitting model for the PL decays of BCs samples, we also fit the decays using stretched exponential decays: It I0 ) exp-.// 0 1, where βis the 4
dispersion factor. Such model is widely used for disordered system where there is a distribution of lifetimes. However, as shown in Fig. S3, the fitting by the stretched exponential is obviously much worse than tri-expoential decays. We also extend such stretched exponential decays to three components: 0
0
9 09
It I1 ) exp 3 4 5 6 I2 ) exp 3 4 5 6 I3 ) exp 3 4 5 . The fitting result
shows very similar lifetimes of the three components which similar to the single component fitting as shown in the figure.
Fig. S3 tri-exponential and stretched exponential fitting (single component and three components) of PL decays for BCs with 6.2 um sizes.
S5. Fitting parameters of TRPL decay. Table S2 summarized all the parameters in multi-exponential fitting of TRPL decays. Table S2. Multi-exponential fitting parameters for PL decays of MAPbBr3 microcrystals (MC) and nanoparticles. Sample
Exc. (ph/cm2)
A1
τ1 (ns)
A2
τ2 (ns)
MC 6.2 µm
1E9
0.97
0.39±0.01
0.03
5.86±0.05
1E10
0.90
0.49±0.01
0.06
3.3E10
0.78
0.63±0.01
1E11
0.59
1E9
MC 4.2 µm
MC 2.1 µm
A3
τ3 (ns)
3.88±0.03
0.04
14.58±0.05
0.10
3.90±0.02
0.12
14.83±0.03
1.27±0.02
0.25
5.39±0.01
0.19
16.79±0.01
0.99
0.30±0.01
0.01
4.11±0.10
1E10
0.94
0.50±0.01
0.05
3.44±0.03
0.01
15.70±0.11
3.3E10
0.87
0.75±0.01
0.10
4.75±0.03
0.03
21.15±0.13
1E11
0.79
1.03±0.01
0.18
4.86±0.03
0.03
15.52±0.11
1E9
0.98
0.58±0.03
0.02
6.99±0.21
5
MC 0.4 µm
NPs
1E10
0.96
0.46±0.01
0.03
3.57±0.06
0.01
18.18±0.19
3.3E10
0.88
0.72±0.01
0.09
5.13±0.04
0.03
24.37±0.15
1E11
0.84
1.09±0.01
0.13
5.12±0.03
0.03
22.35±0.13
1E9
0.94
0.68±0.01
0.06
6.43±0.03
1E10
0.92
0.62±0.01
0.07
5.33±0.08
0.01
77.07±1.40
3.3E10
0.91
0.62±0.05
0.07
4.62±0.04
0.02
35.3±0.26
1E11
0.85
1.04±0.01
0.11
5.15±0.04
0.03
24.87±0.20
1E9
0.67
1.03±0.06
0.14
9.19±0.44
0.19
122.37±2.67
1E10
0.41
1.55±0.06
0.16
11.84±0.49
0.40
119.14±1.33
3.3E10
0.26
1.90±0.06
0.18
14.66±0.44
0.56
96.37±0.70
1E11
0.16
2.81±0.08
0.31
18.67±0.44
0.53
78.69±0.80
S6. Stability and reproducibility of PL kinetics. In order to verify that there is no long-term photochemical reaction which affected the PL dynamics the following test was conducted for the NC sample. The PL kinetics was first measured at flux of 50 nJ/cm2, and then the sample was continuously excited at the same excitation intensity for 1h. A PL kinetics at low flux of 5 nJ/cm2 was measured. After continuous excitation for another 1 h, such cycle was repeated once more. As shown in Fig. S4, the PL decay curves are almost identical at both high and low excitation flux. All the experiments are conducted under ambient atmosphere with constant humidity (RH=30%) This proves that no long-term photochemical reaction related to oxygen and water occurs for our samples and the dynamics we observe is reproducible and transient.
Figure S4. TRPL kinetics of NCs at excitation flux of 50 nJ/cm2 and 5 nJ/cm2 measured at different times within a continuous laser excitation (50 nJ/cm2) in between. 6
S7. Dependence of relative PL quantum yield of BCs and NPs on the excitation intensities. The relative PL quantum yield of BCs and NPs was evaluated by calculating the integrated-PL intensity of the PL decays, which is proportional to the number of emitting photons after each excitation pulse. The QY is then proportional to the integrated PL decays divided by the excitation concentration (Nc), which represents the number of incident photon per volume. (QY ∝ I =>?.@A /C ) As optical configuration
(i.e sample position, optical alignment) is the same for measurement with different excitation intensity, the spatial collection efficiency of the emission light should also keep the same. Therefore we can normalize the QY data with the value under lowest excitation intensity to plot the intensity dependence QY as shown in Fig. S5. For both BCs and NPs, the QY increase with the increasing excitation intensity. The QY of BCs can be increased several times while in NPs the enhancement is much less indicated less trapping filling would occur, which is consistent with the discussion in section 3.4 in the main text.
Fig. S5 Evolution of the relative PL quantum yield of BCs and NPs under different excitation intensity.
S8. Detailed model of trap filling and fitting process: The detailed calculation procedures of the model have been described in the reference. 2 In brief, the equilibrium between free carriers and excitons can be described using the Saha equation.
2
When
photodoping (i.e accumulated trap filling) is present, the Saha equation can be generalized as the following equation expressing the concentrations of electrons (ne), holes (nh) and excitons (nx) corresponding to the overall untrapped photogenerated species density N: DE
FG
6 HI 6 CJ 6 4IC, 7
(5)
LM PQRSTU /VW XY N LO
where I L
D= DE D J ,
(6)
and νi = λi3, λi is the thermal wavelength of the species i. nT is
concentration of filled traps and NT is the concentration of total traps. Here we assume that nT varies little and is only dependent on average concentration of electrons
D= .
Z D= .
during the PL recording time t0 among the repetition pulses. Then we can get the
following rate equations: [G [
\]] CJ D J D= . \[=] CJ 6 D J D= . 0,
(7)
where Rpop and Rdep are the recombination rates of trap population and depopulation, respectively. Taking equations (5)&(6) we can obtain the average concentration of electrons as: Z D= .
D= .
≈ _I 6 D J , _ a
ln d1 6 e
Fe
G ∙FgeG
h,
(8)
Here N(0) can be simplified as initial excitation density Nc. γ0 is the total rate of electronic decay not involving traps. Substitution of equation (8) into (7) gives:
D J i 6 Hi 6 4jCJ , i j
(9)
SFgkFeG Y l
g gk kF l
g gk
_a
,
(10)
,
(11)
ln d1 6 e
Fe
G FgeG
h , \ \]] /\[=] ,
(12)
which are the equations 2~5 in the main text. During the fitting of the trapping model, we first assume that both traps exhibit filling but due to different trap population and depopulation rates, the ratio of unoccupied trap densities between two type of traps varies with different excitation intensity. Therefore we can plot A1/(A1+A2)~Nc data and fit with the expression combination equation 1,7&8 in the main text: F F gFm
nG nG gnGm
eG g o Hom gp0eG m m eG g o Hom gp0eG geGm g o Ho m gp0 eGm m m m m
,
(13)
Here nuncT1 and nuncT2 are the concentration of filled traps 1 and 2, respectively. NT1 and NT2 are the concentrations of original concentration of trap 1 and trap 2, respectively. In the fitting, A was calculated as 7×1015 cm-3, PL recording time t0 was 2.5×10-7 s, and γ0 was taken as the rate of the charge 8
recombination not contributing to the trap filling process (i.e. the slow component in PL kinetics). We first set all the four fitting parameters (NT1, NT2, R1, and R2) while analyzing the largest 6.2 µm BCs. The best fitting results give the R2 to be 35.8 as shown in table SIII. Considering R is the ratio between trap population and depopulation rates, we can then roughly estimate the depopulation time of trap 2 using the trap population time obtained in PL kinetics (lifetime of the second component ~4 ns) to be 143 ns. This depopulation time is significantly shorter than the interval between the pulses in our measurement (250 ns). Therefore we conclude that no considerable trap filling should occur in trap 2 since the depopulation rate is too fast. The model is then modified for the case that trap filling occurs only in trap 1 as follows: F F gFm
nG nG geGm
m
m
eG g o Hom gp0eG m
m
eG g o Ho m gp0eG geGm
.
(13)
Here the A1/(A1+A2) represents the ratio between unoccupied density of trap 1 and original density of trap 2. Again we first set all the three fitting parameters (NT1, NT2, and R) free for the largest 6.2 µm BCs as shown in table S3. The R value obtained was then fixed to fit the other two parameters in the rest of the samples. Table S3. Fitting parameters for trap filling processes using different models. Model
I DqJ I 6 I DqJ 6 DqJ I DqJ I 6 I DqJ 6 CJ
Sample
R1
R2
NT1 (1015 cm-3)
NT2 (1015 cm-3)
BC 6.2 µm
4.2×104
35
10.6
0.2
BC 6.2 µm
1.4×105
/
63.9
1.1
BC 4.2 µm
1.4×105
/
84.7
1.7
BC 2.1 µm
1.4×105
/
133.0
3.3
BC 0.4 µm
1.4×105
/
325.6
20.4
S9. Trap filling via charge accumulation for the limited number of traps During a short time of sample irradiation is formed a steady-state equilibrium between charges being trapped (G, as generating term) and trapped charges recombining into their ground state (R, as recombination term). Analogously to equation (10) in the main text we can express the number of trapped carriers after excitation: t r s1 u 〈C〉. (14) The number of trapped carriers will depend on the mean number of excited carriers in NP 〈C〉, maximum number of available traps M, mean number of already trapped carriers Θ, and finally also on the trapping 9
efficiency s V Jk /V Jk 6 Vkyz . The trapping efficiency takes into account that not every charge will get trapped (with rate V Jk ) as there is a competing recombination channel (Vkyz ). The recombination of trapped carriers over an excitation cycle (.z{zAy ) can be expressed by integrating a single-exponential decay with the lifetime of \ Θ d1 exp
|}|~ h 4
≈Θ∗
|}|~ 4
t
>4.
(15)
≪ 1, which can be used in our case because we observe a huge We employ here the approximation |}|~ 4 accumulation of trapped carriers in our experiments, implying that the trap recovery time must be much longer than the used excitation cycle. In the end, we used the laser repetition rate in expression r. A simplification of G=R, which has to be fulfilled for the steady-state equilibrium, leads to equation (14) in the main text: u (16) g
. .〈〉.
S10. Uncertainty estimation in modelling of PL kinetics in NPs The model used to fit the PL decay of perovskite QDs (equations (1) – (6)) experimental data features three unknown parameters, where two of them (number of traps per QD and trap recovery time) can to some extent compensate each other. This brings an uncertainty to determine these parameters. To illustrate reliability of the fit, we provide two examples in Figure S6, where we found the best fit for two fixed numbers of available traps M (namely we assume that 30% of QDs have no traps and 70% of QDs have 1 or 4 traps, respectively).
PL data
M =1
100 kHz 1E11 3.3E10 1E10 3.3E9 2.5 MHz 1E9
M=4
2.0
2.0
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0 0
20
40
60
80
100
0
delay (ns)
20
40
60
delay (ns) 10
80
100
Figure S6. Best fit of normalized PL decays of perovskite QDs for two fixed values of M. In both cases we assume that 30% of QDs are without traps. For the case of M=1 we obtain a better overall agreement - compare especially the low intensities. Note that a vertical offset (0.2) is applied for each dataset for the sake of clarity.
S11. PL kinetics of BCs detected on different spots of the substrates
Figure S7. PL decays for BCs (6.2 µm) measured at different spots of the same samples on the substrates. The almost overlapped curves indicate the spatial homogenous kinetics of the BCs.
Reference: (1)
Tian, Y.; Merdasa, A.; Unger, E.; Abdellah, M.; Zheng, K.; McKibbin, S.; Mikkelsen, A.; Pullerits, T.; Yartsev, A.; Sundström, V.; Scheblykin, I. G. Enhanced Organo-Metal Halide Perovskite Photoluminescence from Nanosized Defect-Free Crystallites and Emitting Sites. J. Phys. Chem. Lett. 2015, 6, 4171–4177.
(2)
Stranks, S. D.; Burlakov, V. M.; Leijtens, T.; Ball, J. M.; Goriely, A.; Snaith, H. J. Recombination Kinetics in OrganicInorganic Perovskites: Excitons, Free Charge, and Subgap States. Phys. Rev. Appl. 2014, 2, 034007.
11
†
Department of Chemical Physics, Lund University, Box 124, 22100, Lund, Sweden
‡ Gas Processing Center, College of Engineering, Qatar University, PO Box 2713, Doha, Qatar §
﹟
Department of Solid State Physics, Lund University, Box 118, 22100, Lund, Sweden Department of Chemistry, Faculty of Science, South Valley University, Qena 83523, Egypt
Table of Content S1. Synthesis methods: ......................................................................................................................... 2 S2. Size and morphology of MAPbBr3 microcrystals and nanoparticles.............................................. 2 S3. Calculation of absorption coefficient and excitation density of MAPbBr3..................................... 3 S4. Comparison of fitting PL decays of MAPbBr3 BCs using different models.................................. 4 S5. Fitting parameters of TRPL decay. ................................................................................................. 5 S6. Stability and reproducibility of PL kinetics. ................................................................................... 6 S7. Dependence of relative PL quantum yield of BCs and NPs on the excitation intensities. ............ 7 S8. Detailed model of trap filling and fitting process: .......................................................................... 7 S9. Trap filling via charge accumulation for the limited number of traps ............................................ 9 S10. Uncertainty estimation in modelling of PL kinetics in NPs........................................................ 10 S11. PL kinetics of BCs detected on different spots of the substrates ................................................ 11
1
S1. Synthesis methods: Synthesis of precursors: methylammonium bromide (CH3NH3Br) and octylammonium bromide (CH3(CH2)7NH3Br) were synthesized by reaction of the corresponding amine in water/HBr accordingly to the previously reports. In brief, for (CH3NH3Br) 36.9 ml of HBr and 83.4 ml of CH3NH2 were stirred for two hours in ice bath. The resulting solution was evaporated till the formation of white crystals. The white crystals then were recrystallized from ethanol solution which then used as a precursor for CH3NH3PbBr3 colloidal nanoparticles. The same procedures were repeated in order to prepare (CH3(CH2)7NH3Br) where 33.5 ml of CH3(CH2)7NH2 and 22.6 ml of HBr were stirred for two hours in ice bath. Synthesis of CH3NH3PbBr3 bulk crystals: MAPbBr3 microcrystals were prepared by spin coating MAPbBr3 precursors in DMF onto glass substrates with 2000 rpm of 30 sec. Substrates were then annealed in air at 85 oC for half hour to form orange colored crystals. In order to verify the crystal size, different dilution of precursors (×2, ×4, ×8, ×16, ×25) were used which produced crystals with mean size of 6.2, 4.2, 2.0 and 0.4 µm, respectively. Synthesis of CH3NH3PbBr3 colloidal nanoparticles: CH3NH3PbBr3 colloidal nanoparticles were synthesized via hot injection of MABr/ODABr and PbBr2 precursors in coordinator solvent analogous to previous reports. In brief, 0.5 mmol oleic acid in 10 ml of octadecene was stirred and heated at 80 °C followed by addition of 0.3 mmol ODABr in 1 ml DMF. Then 0.2 mmol of MABr in 1 ml DMF and 0.5 mmol PbBr2 in 1 ml DMF were injected subsequently. The yellow dispersion containing nanoparticels was directly precipitated by acetone. Finally, the nanoparticles were redispersed in toluene for use. Here the ratio between ODABr and MABr is 6:4, we also prepared two more samples with ODABr/MABr of 5:5 and 7:3, which keep the same synthesis procedures except for adding 0.25 mmol ODABr and 0.25 mmol MABr, 0.35 mmol ODABr and 0.15 mmol MABr, respectively.
S2. Size and morphology of MAPbBr3 microcrystals and nanoparticles The size and morphology of MAPbBr3 microcrystals were characterized by SEM. Fig. SI (a-d) shows the SEM images of 4 MAPbBr3 bulk crystals samples synthesis via different concentration of precursors. The histogram in the insets show the size distribution of the crystals calculated from the SEM pics, the mean size of the crystal was obtained by fitting with Gaussian distribution. Fig. SI (e) exhibits the HRTEM image of CH3NH3PbBr3 nanoparticles with MA and ODA ratio of 6:4 with the size distribution histogram shown in the inset.
2
Figure S1. (a-d) SEM images of MAPbBr3 micro crystals with different mean sizes prepared by using precursors with different dilutions (1:1, 1:3, 1:7 and 1:20, respectively), (e) MAPbBr3 nanoparticles synthesized using MA:ODA ratio of 6:4. The insets in all figures illustrate the size distribution of the crystals and nanoparticles. (f) HR-TEM image of individual MAPbBr3 NP with well-defined lattice fringes. The size of the NP is about 8.5 nm for this NP.
S3. Calculation of absorption coefficient and excitation density of MAPbBr3 Due to incomplete coverage of the BCs on the substrate, the absorption spectra need to be corrected to obtain the accurate absorption coefficient of the samples.1 Absorption coefficient of MAPbBr3 was evaluated by absorption spectrum of 400 nm crystal film as shown in Fig. S2. The optical density (O.D.) at 438 nm (the excitation wavelength for TRPL measurement) is 0.015. A=log(I0/I1)
(1)
The morphology of our crystals is disk as shown in fig. 1 in main text, which can be considered as discontinues film. As shown in fig. S1e, we have such film consisting of discrete crystals with about 12.5% coverage, in order to increase the accuracy of the coverage calculation, we averaged the results from 5 SEM images from different area of the same sample to obtain decent statistics. The OD of a continuous film with the same thickness would be then given as: A
(2)
Here I1conti is the intensity of light after a continuous film, and it can be calculated from the intensity of light after a discontinues film with 12.5% coverage in our case (I1): I 3
. %
(3)
Then we can get Aconti as: A
/.
"
# % $
&
(4)
Taking A=0.015, Aconti can be calculated as 0.14. The absorption coefficient ε= A/l, where l is the path length of the light which equals to the thickness of the film 40 nm. We obtain ε=3.5×104 cm-1. The excitation density n can be calculated as photon flux f in photons/cm2 multiplied by absorption coefficient ε: n= fε, table SI summarizes the corresponding excitation density at different laser photon flux in TRPL measurements: Table S1. Excitation density with different laser photon flux Power density (nJ/cm2)
Photon flux (ph/cm2)
Excitation density (cm-3)
0.51
1×109
3.5×1013
5.1
1×1010
3.5×1014
17
3.3×1010
1.2×1015
51
1×1011
3.5×1015
Figure S2. Absorption spectrum of MAPbBr3 nanocrystal film with mean diameter of 400 nm.
S4. Comparison of fitting PL decays of MAPbBr3 BCs using different models. In order to give further support to the used tri-exponential fitting model for the PL decays of BCs samples, we also fit the decays using stretched exponential decays: It I0 ) exp-.// 0 1, where βis the 4
dispersion factor. Such model is widely used for disordered system where there is a distribution of lifetimes. However, as shown in Fig. S3, the fitting by the stretched exponential is obviously much worse than tri-expoential decays. We also extend such stretched exponential decays to three components: 0
0
9 09
It I1 ) exp 3 4 5 6 I2 ) exp 3 4 5 6 I3 ) exp 3 4 5 . The fitting result
shows very similar lifetimes of the three components which similar to the single component fitting as shown in the figure.
Fig. S3 tri-exponential and stretched exponential fitting (single component and three components) of PL decays for BCs with 6.2 um sizes.
S5. Fitting parameters of TRPL decay. Table S2 summarized all the parameters in multi-exponential fitting of TRPL decays. Table S2. Multi-exponential fitting parameters for PL decays of MAPbBr3 microcrystals (MC) and nanoparticles. Sample
Exc. (ph/cm2)
A1
τ1 (ns)
A2
τ2 (ns)
MC 6.2 µm
1E9
0.97
0.39±0.01
0.03
5.86±0.05
1E10
0.90
0.49±0.01
0.06
3.3E10
0.78
0.63±0.01
1E11
0.59
1E9
MC 4.2 µm
MC 2.1 µm
A3
τ3 (ns)
3.88±0.03
0.04
14.58±0.05
0.10
3.90±0.02
0.12
14.83±0.03
1.27±0.02
0.25
5.39±0.01
0.19
16.79±0.01
0.99
0.30±0.01
0.01
4.11±0.10
1E10
0.94
0.50±0.01
0.05
3.44±0.03
0.01
15.70±0.11
3.3E10
0.87
0.75±0.01
0.10
4.75±0.03
0.03
21.15±0.13
1E11
0.79
1.03±0.01
0.18
4.86±0.03
0.03
15.52±0.11
1E9
0.98
0.58±0.03
0.02
6.99±0.21
5
MC 0.4 µm
NPs
1E10
0.96
0.46±0.01
0.03
3.57±0.06
0.01
18.18±0.19
3.3E10
0.88
0.72±0.01
0.09
5.13±0.04
0.03
24.37±0.15
1E11
0.84
1.09±0.01
0.13
5.12±0.03
0.03
22.35±0.13
1E9
0.94
0.68±0.01
0.06
6.43±0.03
1E10
0.92
0.62±0.01
0.07
5.33±0.08
0.01
77.07±1.40
3.3E10
0.91
0.62±0.05
0.07
4.62±0.04
0.02
35.3±0.26
1E11
0.85
1.04±0.01
0.11
5.15±0.04
0.03
24.87±0.20
1E9
0.67
1.03±0.06
0.14
9.19±0.44
0.19
122.37±2.67
1E10
0.41
1.55±0.06
0.16
11.84±0.49
0.40
119.14±1.33
3.3E10
0.26
1.90±0.06
0.18
14.66±0.44
0.56
96.37±0.70
1E11
0.16
2.81±0.08
0.31
18.67±0.44
0.53
78.69±0.80
S6. Stability and reproducibility of PL kinetics. In order to verify that there is no long-term photochemical reaction which affected the PL dynamics the following test was conducted for the NC sample. The PL kinetics was first measured at flux of 50 nJ/cm2, and then the sample was continuously excited at the same excitation intensity for 1h. A PL kinetics at low flux of 5 nJ/cm2 was measured. After continuous excitation for another 1 h, such cycle was repeated once more. As shown in Fig. S4, the PL decay curves are almost identical at both high and low excitation flux. All the experiments are conducted under ambient atmosphere with constant humidity (RH=30%) This proves that no long-term photochemical reaction related to oxygen and water occurs for our samples and the dynamics we observe is reproducible and transient.
Figure S4. TRPL kinetics of NCs at excitation flux of 50 nJ/cm2 and 5 nJ/cm2 measured at different times within a continuous laser excitation (50 nJ/cm2) in between. 6
S7. Dependence of relative PL quantum yield of BCs and NPs on the excitation intensities. The relative PL quantum yield of BCs and NPs was evaluated by calculating the integrated-PL intensity of the PL decays, which is proportional to the number of emitting photons after each excitation pulse. The QY is then proportional to the integrated PL decays divided by the excitation concentration (Nc), which represents the number of incident photon per volume. (QY ∝ I =>?.@A /C ) As optical configuration
(i.e sample position, optical alignment) is the same for measurement with different excitation intensity, the spatial collection efficiency of the emission light should also keep the same. Therefore we can normalize the QY data with the value under lowest excitation intensity to plot the intensity dependence QY as shown in Fig. S5. For both BCs and NPs, the QY increase with the increasing excitation intensity. The QY of BCs can be increased several times while in NPs the enhancement is much less indicated less trapping filling would occur, which is consistent with the discussion in section 3.4 in the main text.
Fig. S5 Evolution of the relative PL quantum yield of BCs and NPs under different excitation intensity.
S8. Detailed model of trap filling and fitting process: The detailed calculation procedures of the model have been described in the reference. 2 In brief, the equilibrium between free carriers and excitons can be described using the Saha equation.
2
When
photodoping (i.e accumulated trap filling) is present, the Saha equation can be generalized as the following equation expressing the concentrations of electrons (ne), holes (nh) and excitons (nx) corresponding to the overall untrapped photogenerated species density N: DE
FG
6 HI 6 CJ 6 4IC, 7
(5)
LM PQRSTU /VW XY N LO
where I L
D= DE D J ,
(6)
and νi = λi3, λi is the thermal wavelength of the species i. nT is
concentration of filled traps and NT is the concentration of total traps. Here we assume that nT varies little and is only dependent on average concentration of electrons
D= .
Z D= .
during the PL recording time t0 among the repetition pulses. Then we can get the
following rate equations: [G [
\]] CJ D J D= . \[=] CJ 6 D J D= . 0,
(7)
where Rpop and Rdep are the recombination rates of trap population and depopulation, respectively. Taking equations (5)&(6) we can obtain the average concentration of electrons as: Z D= .
D= .
≈ _I 6 D J , _ a
ln d1 6 e
Fe
G ∙FgeG
h,
(8)
Here N(0) can be simplified as initial excitation density Nc. γ0 is the total rate of electronic decay not involving traps. Substitution of equation (8) into (7) gives:
D J i 6 Hi 6 4jCJ , i j
(9)
SFgkFeG Y l
g gk kF l
g gk
_a
,
(10)
,
(11)
ln d1 6 e
Fe
G FgeG
h , \ \]] /\[=] ,
(12)
which are the equations 2~5 in the main text. During the fitting of the trapping model, we first assume that both traps exhibit filling but due to different trap population and depopulation rates, the ratio of unoccupied trap densities between two type of traps varies with different excitation intensity. Therefore we can plot A1/(A1+A2)~Nc data and fit with the expression combination equation 1,7&8 in the main text: F F gFm
nG nG gnGm
eG g o Hom gp0eG m m eG g o Hom gp0eG geGm g o Ho m gp0 eGm m m m m
,
(13)
Here nuncT1 and nuncT2 are the concentration of filled traps 1 and 2, respectively. NT1 and NT2 are the concentrations of original concentration of trap 1 and trap 2, respectively. In the fitting, A was calculated as 7×1015 cm-3, PL recording time t0 was 2.5×10-7 s, and γ0 was taken as the rate of the charge 8
recombination not contributing to the trap filling process (i.e. the slow component in PL kinetics). We first set all the four fitting parameters (NT1, NT2, R1, and R2) while analyzing the largest 6.2 µm BCs. The best fitting results give the R2 to be 35.8 as shown in table SIII. Considering R is the ratio between trap population and depopulation rates, we can then roughly estimate the depopulation time of trap 2 using the trap population time obtained in PL kinetics (lifetime of the second component ~4 ns) to be 143 ns. This depopulation time is significantly shorter than the interval between the pulses in our measurement (250 ns). Therefore we conclude that no considerable trap filling should occur in trap 2 since the depopulation rate is too fast. The model is then modified for the case that trap filling occurs only in trap 1 as follows: F F gFm
nG nG geGm
m
m
eG g o Hom gp0eG m
m
eG g o Ho m gp0eG geGm
.
(13)
Here the A1/(A1+A2) represents the ratio between unoccupied density of trap 1 and original density of trap 2. Again we first set all the three fitting parameters (NT1, NT2, and R) free for the largest 6.2 µm BCs as shown in table S3. The R value obtained was then fixed to fit the other two parameters in the rest of the samples. Table S3. Fitting parameters for trap filling processes using different models. Model
I DqJ I 6 I DqJ 6 DqJ I DqJ I 6 I DqJ 6 CJ
Sample
R1
R2
NT1 (1015 cm-3)
NT2 (1015 cm-3)
BC 6.2 µm
4.2×104
35
10.6
0.2
BC 6.2 µm
1.4×105
/
63.9
1.1
BC 4.2 µm
1.4×105
/
84.7
1.7
BC 2.1 µm
1.4×105
/
133.0
3.3
BC 0.4 µm
1.4×105
/
325.6
20.4
S9. Trap filling via charge accumulation for the limited number of traps During a short time of sample irradiation is formed a steady-state equilibrium between charges being trapped (G, as generating term) and trapped charges recombining into their ground state (R, as recombination term). Analogously to equation (10) in the main text we can express the number of trapped carriers after excitation: t r s1 u 〈C〉. (14) The number of trapped carriers will depend on the mean number of excited carriers in NP 〈C〉, maximum number of available traps M, mean number of already trapped carriers Θ, and finally also on the trapping 9
efficiency s V Jk /V Jk 6 Vkyz . The trapping efficiency takes into account that not every charge will get trapped (with rate V Jk ) as there is a competing recombination channel (Vkyz ). The recombination of trapped carriers over an excitation cycle (.z{zAy ) can be expressed by integrating a single-exponential decay with the lifetime of \ Θ d1 exp
|}|~ h 4
≈Θ∗
|}|~ 4
t
>4.
(15)
≪ 1, which can be used in our case because we observe a huge We employ here the approximation |}|~ 4 accumulation of trapped carriers in our experiments, implying that the trap recovery time must be much longer than the used excitation cycle. In the end, we used the laser repetition rate in expression r. A simplification of G=R, which has to be fulfilled for the steady-state equilibrium, leads to equation (14) in the main text: u (16) g
. .〈〉.
S10. Uncertainty estimation in modelling of PL kinetics in NPs The model used to fit the PL decay of perovskite QDs (equations (1) – (6)) experimental data features three unknown parameters, where two of them (number of traps per QD and trap recovery time) can to some extent compensate each other. This brings an uncertainty to determine these parameters. To illustrate reliability of the fit, we provide two examples in Figure S6, where we found the best fit for two fixed numbers of available traps M (namely we assume that 30% of QDs have no traps and 70% of QDs have 1 or 4 traps, respectively).
PL data
M =1
100 kHz 1E11 3.3E10 1E10 3.3E9 2.5 MHz 1E9
M=4
2.0
2.0
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0 0
20
40
60
80
100
0
delay (ns)
20
40
60
delay (ns) 10
80
100
Figure S6. Best fit of normalized PL decays of perovskite QDs for two fixed values of M. In both cases we assume that 30% of QDs are without traps. For the case of M=1 we obtain a better overall agreement - compare especially the low intensities. Note that a vertical offset (0.2) is applied for each dataset for the sake of clarity.
S11. PL kinetics of BCs detected on different spots of the substrates
Figure S7. PL decays for BCs (6.2 µm) measured at different spots of the same samples on the substrates. The almost overlapped curves indicate the spatial homogenous kinetics of the BCs.
Reference: (1)
Tian, Y.; Merdasa, A.; Unger, E.; Abdellah, M.; Zheng, K.; McKibbin, S.; Mikkelsen, A.; Pullerits, T.; Yartsev, A.; Sundström, V.; Scheblykin, I. G. Enhanced Organo-Metal Halide Perovskite Photoluminescence from Nanosized Defect-Free Crystallites and Emitting Sites. J. Phys. Chem. Lett. 2015, 6, 4171–4177.
(2)
Stranks, S. D.; Burlakov, V. M.; Leijtens, T.; Ball, J. M.; Goriely, A.; Snaith, H. J. Recombination Kinetics in OrganicInorganic Perovskites: Excitons, Free Charge, and Subgap States. Phys. Rev. Appl. 2014, 2, 034007.
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