Supporting Information Spectral and dynamical properties of single ...
Supporting Information Spectral and dynamical properties of single excitons, biexcitons, and trions in cesium-lead-halide perovskite quantum dots Nikolay S. Makarov, Shaojun Guo, Oleksandr Isaienko, Wenyong Liu, István Robel, Victor I. Klimov* Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
1
1. Derivation of radiative lifetimes from measured photoluminescence dynamics In the analysis of single-exciton photoluminescence (PL) dynamics, we assume that all quantum dots (QDs) in the measured ensemble are characterized by the same radiative time constant (τr,X), while the nonradiative lifetime (τnr,X) may differ from dot to dot due, e.g., to the difference in the number and/or identity of centers for nonradiative recombination; subscript ‘X’ in the notations for the lifetimes indicates that they apply to the single-exciton state. In the case of the n QD subi ensembles with distinct values of the nonradiative lifetime ( τ nr,X ; i = 1, 2…, n), the PL decay can
be described by I PL (t) = ∑ i=1 ki exp ( −t / τ Xi ) , where τ Xi is the effective single-exciton lifetime n
i i given by τ Xi = τ r,Xτ nr,X (τ r,X + τ nr,X ) , and ki is the relative fraction of the QDs in the i-th sub-
ensemble; the ki coefficients are normalized such as
∑
n
k = 1 . The PL quantum yield (QY) of
i=1 i
the individual sub-ensemble is given by qi = τ Xi τ r,X , and the total PL QY of the entire QD −1 sample (Q) can be expressed as Q = ∑ i=1 ki qi = τ r,X ∑ i=1 kiτ Xi . This leads to the following n
n
expression for the radiative lifetime: τ r,X = Q −1 ∑ i=1 kiτ Xi = Q −1 τ X , where τ X n
is the average
exciton lifetime in the QD ensemble expressed as τ X = ∑ i=1 kiτ Xi . n
2. Carrier dynamics for excitation with high-energy photons in relation to carrier multiplication. Carrier multiplication (CM), known also as multiexciton generation (MEG), is a process whereby multiple electron-hole pairs are generated by single photons.1,2 In addition to being fundamentally interesting, CM is also of practical significance as by boosting the photocurrent it could lead to increased photovoltaic efficiencies.3 So far, CM has not been studied for either bulk 2
or QD forms of perovskites. A typical approach for detecting and quantifying CM efficiencies in QDs involves the use of transient spectroscopic techniques for resolving the Auger decay signature of multiexcitons.1 Here we apply this approach for investigating CM in perovskite QDs. In these measurements, we focus on the smallest band gap I-QD sample (PL at 1.816 eV) and use the shortest practical excitation wavelength available to us (258 nm or hv = 4.81 eV), which corresponds to hv/Eg = 2.65. The fundamental energy-conservation-defined threshold for CM is 2Eg, therefore, CM is in principle possible under excitation conditions used in this experiment. In addition to measurements with high energy pump photons, we also use excitation at a sub-CM-threshold energy (hv/Eg = 1.99) as a reference. Figure S3 compares PL traces of the I-QD sample obtained with a superconducting nanowire single-photon detector (SNSPD) using hv = 1.99Eg (black line) and 2.65Eg (colors other than black). The low-pump-intensity trace ( = 0.06) recorded with hv = 1.99Eg, shows slow decay typical of single-exciton recombination. The hv = 2.65Eg trace taken for the same QD occupancy (red line in Figure S3a) does not exhibit signatures of fast Auger recombination either. In fact, both traces perfectly overlap with each other. This result suggests the absence of CM. This assessment is further confirmed by the analysis of the pump-fluence dependence of the A/B ratio (Figure S6b; symbols); A and B are, respectively, the amplitudes of the early time PL signal and the late-time background (see the main text for more detailed definitions of these two quantities). The low-pump-intensity limit of this ratio can be used to evaluate the quantum efficiency of photon-to-exciton conversion.1 As shown in Figure S3b, for both pump photon energies A/B approaches unity, as expected for the no-CM regime. Further, in both cases the A/B ratio follows the expectations based on the Poisson statistics of photon absorption events (line) indicating that one absorbed photon produces just one exciton.
3
The fact that we have not observed CM with the 2.65Eg photon is not surprising as leadhalide perovskites are characterized by nearly identical electron and hole effective masses.12 In this case, due to optical selection rules, the photon energy in excess of the band-gap is partitioned equally between a hot electron and a hot hole. For the CM effect to be observed, the excess energy of at least one of the carriers must be equal to the band gap, which increases the CM threshold to 3Eg.4 Indeed, in PbSe QDs, where me ≈ mh, the measured CM threshold (~2.8Eg) is close to this value. Given these considerations, the CM threshold in the studied I-QDs is around 5.4 eV, which is considerably higher than the photon energy used in our measurements (4.81 eV).
3. Degeneracy factors of band-edge states in CdSe and PbSe quantum dots Here we review the information on band-edge state degeneracies for extensively studied CdSe and PbSe QDs. While both CdSe and PbSe are direct-gap semiconductors, they are characterized by different locations of their band minima/maxima in the Brillouin zone, which has a significant effect on the total degeneracies of the QD states. In CdSe, the extrema of the conduction and valence bands are located at the Γ-point of the Brillouin zone. Since there is only one such point in the first Brillouin zone, the degeneracies of the band-edge states are defined solely by the angular momenta (spins) of the electron and hole Bloch wave functions. The electron band-edge state has spin se = 1/2, which results in ge = 2 (based on ge = 2se + 1). The band edge hole state can be characterized by the effective spin sh =3/2,5,6 and hence, corresponding degeneracy gh = 4. The resulting band-edge exciton degeneracy (gX = gegh) is 8. In CdSe QDs, this degeneracy is lifted by effects of crystal field in a hexagonal lattice, shape asymmetry and an electron-hole
4
exchange interaction leading to the fine-structure splitting of the band-edge exciton studied extensively both theoretically7 and experimentally.8,9 While high degeneracy of the band-edge exciton states of CdSe QDs is clearly manifested in high-spectral resolution PL and PL excitation (PLE) studies,8,9 it is hidden in transient absorption (TA) measurements that are mostly sensitive to the electron population of the QDs.10 This selectivity arises from a significant difference between the effective masses of an electron (me) and a hole (mh). Specifically, in CdSe mh >> me, and therefore, electron levels are much more sparse in the energy space than the hole levels. As a result, a single-state occupation factor of a given hole level is much lower than that of a corresponding electron level which it is optically coupled to. Hence, TA is dominated by state-filling signals arising from the populated electron states, and therefore, probes only the degeneracy factors of conduction-band levels. In PbSe QDs, the situation is different as the band extrema in this material are located at 4 equivalent L-points of the Brillouin zone.11 Further, conduction and valence bands in this semiconductor are mirror-symmetric and both are characterized by spin ½. In this case, the total degeneracies of the band-edge states can be calculated from ge = gh = 4(2se + 1) = 8, which leads to the exciton degeneracy gX = 64. As in the case of CdSe QDs, in QDs of PbSe the effects of shape asymmetry12 and an electron-hole exchange interaction11,13-15 lead to a complex structure of the band-edge exciton, which comprises several split-off levels. However, again as in the case of CdSe QDs, the state-filling-induced band-edge bleach in PbSe QDs is only sensitive to one type of carriers, and therefore, displays signatures of the 8-fold degeneracy.16
5
b
a
0.62 nm
5 nm c
d
e
f
Figure S1. Transmission electron microscopy images (TEM) of fabricated perovskite quantum dots (QDs). (a) TEM image of CsPbI3 QDs with the side length L = 11.2±0.7 nm. (b) High-resolution TEM image of CsPbI3 QDs, showing lattice spacing of 0.62 nm. (c) TEM image of CsPbI1.5Br1.5 QDs with L = 10.7±1.1 nm. (d) TEM image of CsPbBr3 QDs with L = 9.3±0.9 nm. (e) TEM image of CsPbBr3 QDs with L = 8.1±1.1 nm. (f) TEM image of CsPbBr3 QDs with L = 6.3±0.5 nm.
6
a PL intensity, a.u.
105 104 103 102
CsPbBr3 (VQD = 804 nm3): Streak1 Streak2 total PL CsPbBr1.5I1.5 (VQD = 1225 nm3): Streak1 Streak2 CsPbI3 (VQD = 1405 nm3):
1
10
Streak1
1012
1013
1014
Streak2
total PL
uPL
total PL
uPL
1015
1016
Fluence, photons/cm2
PL intensity, a.u.
b 107
106 σ = 3.5x10−15 cm2 CsPbBr3: VQD = 250 nm3 105 12 10
CdSe: VQD = 47.7 nm3 1013
1014
1015
1016
Fluence, photons/cm2 Figure S2. Absorption cross-section measurements for perovskite QDs using different photoluminescence(PL) based techniques. (a) In one method, absorption cross-sections (σ) were derived from streak-camera measurements of PL saturation at long delay after excitation (after completion of Auger recombination); two independent sets of measurements for each QD sample are denoted in the legend as “streak1” and “streak2”. Two
7
other approaches were the measurements of saturation of time-integrated PL intensity (labeled “total PL”) and saturation of a late-time PL signal measured by PL upconversion (labeled uPL). The absorption cross-sections obtained from these measurements are shown in Figure 3c of the main paper. (b) PL saturation of a late-time signal (measured with a streak camera) for perovskite Br-QDs (black solid squares) and CdSe QDs (red solid triangles). Despite a large difference in QD volumes (250 versus 47.7 nm3 for the perovskite and CdSe QDs, respectively) the absorption cross-sections of these two samples are virtually identical (σ = 3.5×10-15 cm3).
8
PL intensity, a.u.
a
CsPbI3 = 0.07 0.03
0.1 0.014 0.006
0
b
hν = 2.65 Eg
hν = 1.99 Eg
0.01
1
Time, ns
4
2
3
1.99 Eg 2.65 Eg
A/B
3
2
1
0
0.01
0.1
1
Figure S3. Pump-fluence dependence of PL dynamics in perovskite QDs in the case of excitation with highenergy photons. (a) Fluence-dependent PL dynamics measured with SNSPD for I-QDs (Eg = 1.816; based on the PL peak position) using excitation at 4.81 eV (hv = 2.65Eg; traces shown by colors other than black) in comparison to the low-fluence ( = 0.006) PL decay obtained with the 1.99Eg excitation (black line). The lowest-intensity 2.65Eg trace is virtually identical to that measured with hv = 1.99Eg, indicating the absence of CM. (b) The A/B ratio (i.e., the ratio of the total PL amplitude to its single-excitonic component) as a function of pump fluence for hv = 2.65Eg (red circle) and 1.99Eg (black squares) along with the dependence calculated for the Poisson statistics of photon absorption events without CM (line).
9
Wavelength, nm 700
600
500
Normalized PL intensity
1.0
CsPbBr1.5I1.5 :
0.8
0.01 0.09 0.76 6.11 47.7 382
0.6 0.4 0.2 0.0 1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
Energy, eV Figure S4. Fluence-dependent PL spectra recorded with a streak camera at 0 ps. At low excitation fluences the PL peak of the I-QDs at zero time agrees well with the spectral position of the steady-state PL (see Figure 1b-c). As the excitation fluence increases (above = 1), a shorter-wavelength shoulder starts to develop, and thus the PL peak gets broader. At the same time, the decay probed at the shoulder gets faster than the biexciton, indicating contribution from higher-order multiexciton recombination.
10
10-1
-Δα, a.u.
:
0.73 2.92 11.7 46.7
1.46 5.84 23.4
CsPbBr1.5I1.5 10
-2
10-3
0
50
100
150
200
Time, ps Figure S5. Biexciton decay in mixed Br1.5I1.5-QDs probed by transient absorption (TA). Pump-fluence dependent multiexciton decay of the band-edge bleach obtained using TA (the single-exciton contribution is subtracted from the higher-fluence traces) shows no other lifetimes than that of a biexciton. This suggests that the band-edge states are two-fold degenerate.
11
Table S1. Spectroscopic properties of Cs-Pb-halide perovskite QDs
σ400 nm
λPL/hvPL
(nm)
(cm2)
(nm/eV)
6.3
3.5×10-15
487 /
Composition L
CsPbBr3
τr,X
ΔXX
τ2X
CA
(ns)
(ns)
(meV) (ps)
(ps)
(cm6s-1)
0.40
2.70
6.8
26
3.0×10-28
0.44
3.40
7.7
38
9.3×10-28
0.51
3.98
7.8
47
1.7×10-27
0.42
15.4
36.6
11
0.36
47
4.0×10-27
0.41
17.8
43.4
12
0.57
92
2.7×10-27
Q
τcool
2.546 CsPbBr3
8.1
8.0×10-15
507 / 2.446
CsPbBr3
9.3
1.3×10-14
511 / 2.427
CsPbBr1.5I1.5
10.7
1.5×10-14
584 / 2.123
CsPbI3
11.2
1.3×10-14
683 / 1.816
L is the side length of the cubically shaped QD; σ400 nm is the absorption cross-section at 400 nm; λPL (hvPL) is the peak PL wavelength (energy); Q is the PL quantum yield; ΔXX is the excitonexciton interaction energy; is the average single-exciton lifetime; τr,X is the single-exciton radiative lifetime; τcool is the intraband cooling time; τ2X is the biexciton Auger lifetime; CA = (L3)2(8τ2X)–1 is the effective Auger constant.
12
References. 1. Schaller, R. D.; Klimov, V. I. Phys. Rev. Lett. 2004, 92, 186601. 2. Ellingson, R. J.; Beard, M. C.; Johnson, J. C.; Yu, P.; Micic, O. I.; Nozik, A. J.; Shabaev, A.; Efros, A. L. Nano Lett. 2005, 5, 865-871. 3. Hanna, M. C.; Nozik, A. J. J. Appl. Phys. 2006, 100, 074510. 4. Schaller, R. D.; Petruska, M. A.; Klimov, V. I. Appl. Phys. Lett. 2005, 87, 253102. 5. Norris, D. J.; Sacra, A.; Murray, C. B.; Bawendi, M. G. Phys. Rev. Lett. 1994, 72, 26122615. 6. Efros, A. L.; Rosen, M. Annu. Rev. Mater. Sci. 2000, 30, 475-521. 7. Efros, A. L.; Rosen, M. Phys. Rev. B 1998, 58, 7120-7135. 8. Nirmal, M.; Norris, D. J.; Kuno, M.; Bawendi, M. G.; Efros, A. L.; Rosen, M. Phys. Rev. Lett. 1995, 75, 3728-3731. 9. Norris, D. J.; Efros, A. L.; Rosen, M.; Bawendi, M. G. Phys. Rev. B 1996, 53, 16347-16354. 10. Klimov, V. I.; McBranch, D. W.; Leatherdale, C. A.; Bawendi, M. G. Phys. Rev. B 1999, 60, 13740-13749. 11. Kang, I.; Wise, F. W. J. Opt. Soc. Am. B 1997, 14, 1632-1646. 12. Andreev, A. D.; Lipovskii, A. A. Phys. Rev. B 1999, 59, 15402-15404. 13. An, J. M.; Franceschetti, A.; Dudiy, S. V.; Zunger, A. Nano Lett. 2006, 6, 2728-2735. 14. An, J. M.; Franceschetti, A.; Zunger, A. Nano Lett. 2007, 7, 2129-2135. 15. Bartnik, A. C.; Efros, A. L.; Koh, W. K.; Murray, C. B.; Wise, F. W. Phys. Rev. B 2010, 82, 195313. 16. Schaller, R. D.; Petruska, M. A.; Klimov, V. I. J. Phys. Chem. B 2003, 107, 13765-13768.
13
1
1. Derivation of radiative lifetimes from measured photoluminescence dynamics In the analysis of single-exciton photoluminescence (PL) dynamics, we assume that all quantum dots (QDs) in the measured ensemble are characterized by the same radiative time constant (τr,X), while the nonradiative lifetime (τnr,X) may differ from dot to dot due, e.g., to the difference in the number and/or identity of centers for nonradiative recombination; subscript ‘X’ in the notations for the lifetimes indicates that they apply to the single-exciton state. In the case of the n QD subi ensembles with distinct values of the nonradiative lifetime ( τ nr,X ; i = 1, 2…, n), the PL decay can
be described by I PL (t) = ∑ i=1 ki exp ( −t / τ Xi ) , where τ Xi is the effective single-exciton lifetime n
i i given by τ Xi = τ r,Xτ nr,X (τ r,X + τ nr,X ) , and ki is the relative fraction of the QDs in the i-th sub-
ensemble; the ki coefficients are normalized such as
∑
n
k = 1 . The PL quantum yield (QY) of
i=1 i
the individual sub-ensemble is given by qi = τ Xi τ r,X , and the total PL QY of the entire QD −1 sample (Q) can be expressed as Q = ∑ i=1 ki qi = τ r,X ∑ i=1 kiτ Xi . This leads to the following n
n
expression for the radiative lifetime: τ r,X = Q −1 ∑ i=1 kiτ Xi = Q −1 τ X , where τ X n
is the average
exciton lifetime in the QD ensemble expressed as τ X = ∑ i=1 kiτ Xi . n
2. Carrier dynamics for excitation with high-energy photons in relation to carrier multiplication. Carrier multiplication (CM), known also as multiexciton generation (MEG), is a process whereby multiple electron-hole pairs are generated by single photons.1,2 In addition to being fundamentally interesting, CM is also of practical significance as by boosting the photocurrent it could lead to increased photovoltaic efficiencies.3 So far, CM has not been studied for either bulk 2
or QD forms of perovskites. A typical approach for detecting and quantifying CM efficiencies in QDs involves the use of transient spectroscopic techniques for resolving the Auger decay signature of multiexcitons.1 Here we apply this approach for investigating CM in perovskite QDs. In these measurements, we focus on the smallest band gap I-QD sample (PL at 1.816 eV) and use the shortest practical excitation wavelength available to us (258 nm or hv = 4.81 eV), which corresponds to hv/Eg = 2.65. The fundamental energy-conservation-defined threshold for CM is 2Eg, therefore, CM is in principle possible under excitation conditions used in this experiment. In addition to measurements with high energy pump photons, we also use excitation at a sub-CM-threshold energy (hv/Eg = 1.99) as a reference. Figure S3 compares PL traces of the I-QD sample obtained with a superconducting nanowire single-photon detector (SNSPD) using hv = 1.99Eg (black line) and 2.65Eg (colors other than black). The low-pump-intensity trace ( = 0.06) recorded with hv = 1.99Eg, shows slow decay typical of single-exciton recombination. The hv = 2.65Eg trace taken for the same QD occupancy (red line in Figure S3a) does not exhibit signatures of fast Auger recombination either. In fact, both traces perfectly overlap with each other. This result suggests the absence of CM. This assessment is further confirmed by the analysis of the pump-fluence dependence of the A/B ratio (Figure S6b; symbols); A and B are, respectively, the amplitudes of the early time PL signal and the late-time background (see the main text for more detailed definitions of these two quantities). The low-pump-intensity limit of this ratio can be used to evaluate the quantum efficiency of photon-to-exciton conversion.1 As shown in Figure S3b, for both pump photon energies A/B approaches unity, as expected for the no-CM regime. Further, in both cases the A/B ratio follows the expectations based on the Poisson statistics of photon absorption events (line) indicating that one absorbed photon produces just one exciton.
3
The fact that we have not observed CM with the 2.65Eg photon is not surprising as leadhalide perovskites are characterized by nearly identical electron and hole effective masses.12 In this case, due to optical selection rules, the photon energy in excess of the band-gap is partitioned equally between a hot electron and a hot hole. For the CM effect to be observed, the excess energy of at least one of the carriers must be equal to the band gap, which increases the CM threshold to 3Eg.4 Indeed, in PbSe QDs, where me ≈ mh, the measured CM threshold (~2.8Eg) is close to this value. Given these considerations, the CM threshold in the studied I-QDs is around 5.4 eV, which is considerably higher than the photon energy used in our measurements (4.81 eV).
3. Degeneracy factors of band-edge states in CdSe and PbSe quantum dots Here we review the information on band-edge state degeneracies for extensively studied CdSe and PbSe QDs. While both CdSe and PbSe are direct-gap semiconductors, they are characterized by different locations of their band minima/maxima in the Brillouin zone, which has a significant effect on the total degeneracies of the QD states. In CdSe, the extrema of the conduction and valence bands are located at the Γ-point of the Brillouin zone. Since there is only one such point in the first Brillouin zone, the degeneracies of the band-edge states are defined solely by the angular momenta (spins) of the electron and hole Bloch wave functions. The electron band-edge state has spin se = 1/2, which results in ge = 2 (based on ge = 2se + 1). The band edge hole state can be characterized by the effective spin sh =3/2,5,6 and hence, corresponding degeneracy gh = 4. The resulting band-edge exciton degeneracy (gX = gegh) is 8. In CdSe QDs, this degeneracy is lifted by effects of crystal field in a hexagonal lattice, shape asymmetry and an electron-hole
4
exchange interaction leading to the fine-structure splitting of the band-edge exciton studied extensively both theoretically7 and experimentally.8,9 While high degeneracy of the band-edge exciton states of CdSe QDs is clearly manifested in high-spectral resolution PL and PL excitation (PLE) studies,8,9 it is hidden in transient absorption (TA) measurements that are mostly sensitive to the electron population of the QDs.10 This selectivity arises from a significant difference between the effective masses of an electron (me) and a hole (mh). Specifically, in CdSe mh >> me, and therefore, electron levels are much more sparse in the energy space than the hole levels. As a result, a single-state occupation factor of a given hole level is much lower than that of a corresponding electron level which it is optically coupled to. Hence, TA is dominated by state-filling signals arising from the populated electron states, and therefore, probes only the degeneracy factors of conduction-band levels. In PbSe QDs, the situation is different as the band extrema in this material are located at 4 equivalent L-points of the Brillouin zone.11 Further, conduction and valence bands in this semiconductor are mirror-symmetric and both are characterized by spin ½. In this case, the total degeneracies of the band-edge states can be calculated from ge = gh = 4(2se + 1) = 8, which leads to the exciton degeneracy gX = 64. As in the case of CdSe QDs, in QDs of PbSe the effects of shape asymmetry12 and an electron-hole exchange interaction11,13-15 lead to a complex structure of the band-edge exciton, which comprises several split-off levels. However, again as in the case of CdSe QDs, the state-filling-induced band-edge bleach in PbSe QDs is only sensitive to one type of carriers, and therefore, displays signatures of the 8-fold degeneracy.16
5
b
a
0.62 nm
5 nm c
d
e
f
Figure S1. Transmission electron microscopy images (TEM) of fabricated perovskite quantum dots (QDs). (a) TEM image of CsPbI3 QDs with the side length L = 11.2±0.7 nm. (b) High-resolution TEM image of CsPbI3 QDs, showing lattice spacing of 0.62 nm. (c) TEM image of CsPbI1.5Br1.5 QDs with L = 10.7±1.1 nm. (d) TEM image of CsPbBr3 QDs with L = 9.3±0.9 nm. (e) TEM image of CsPbBr3 QDs with L = 8.1±1.1 nm. (f) TEM image of CsPbBr3 QDs with L = 6.3±0.5 nm.
6
a PL intensity, a.u.
105 104 103 102
CsPbBr3 (VQD = 804 nm3): Streak1 Streak2 total PL CsPbBr1.5I1.5 (VQD = 1225 nm3): Streak1 Streak2 CsPbI3 (VQD = 1405 nm3):
1
10
Streak1
1012
1013
1014
Streak2
total PL
uPL
total PL
uPL
1015
1016
Fluence, photons/cm2
PL intensity, a.u.
b 107
106 σ = 3.5x10−15 cm2 CsPbBr3: VQD = 250 nm3 105 12 10
CdSe: VQD = 47.7 nm3 1013
1014
1015
1016
Fluence, photons/cm2 Figure S2. Absorption cross-section measurements for perovskite QDs using different photoluminescence(PL) based techniques. (a) In one method, absorption cross-sections (σ) were derived from streak-camera measurements of PL saturation at long delay after excitation (after completion of Auger recombination); two independent sets of measurements for each QD sample are denoted in the legend as “streak1” and “streak2”. Two
7
other approaches were the measurements of saturation of time-integrated PL intensity (labeled “total PL”) and saturation of a late-time PL signal measured by PL upconversion (labeled uPL). The absorption cross-sections obtained from these measurements are shown in Figure 3c of the main paper. (b) PL saturation of a late-time signal (measured with a streak camera) for perovskite Br-QDs (black solid squares) and CdSe QDs (red solid triangles). Despite a large difference in QD volumes (250 versus 47.7 nm3 for the perovskite and CdSe QDs, respectively) the absorption cross-sections of these two samples are virtually identical (σ = 3.5×10-15 cm3).
8
PL intensity, a.u.
a
CsPbI3 = 0.07 0.03
0.1 0.014 0.006
0
b
hν = 2.65 Eg
hν = 1.99 Eg
0.01
1
Time, ns
4
2
3
1.99 Eg 2.65 Eg
A/B
3
2
1
0
0.01
0.1
1
Figure S3. Pump-fluence dependence of PL dynamics in perovskite QDs in the case of excitation with highenergy photons. (a) Fluence-dependent PL dynamics measured with SNSPD for I-QDs (Eg = 1.816; based on the PL peak position) using excitation at 4.81 eV (hv = 2.65Eg; traces shown by colors other than black) in comparison to the low-fluence ( = 0.006) PL decay obtained with the 1.99Eg excitation (black line). The lowest-intensity 2.65Eg trace is virtually identical to that measured with hv = 1.99Eg, indicating the absence of CM. (b) The A/B ratio (i.e., the ratio of the total PL amplitude to its single-excitonic component) as a function of pump fluence for hv = 2.65Eg (red circle) and 1.99Eg (black squares) along with the dependence calculated for the Poisson statistics of photon absorption events without CM (line).
9
Wavelength, nm 700
600
500
Normalized PL intensity
1.0
CsPbBr1.5I1.5 :
0.8
0.01 0.09 0.76 6.11 47.7 382
0.6 0.4 0.2 0.0 1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
Energy, eV Figure S4. Fluence-dependent PL spectra recorded with a streak camera at 0 ps. At low excitation fluences the PL peak of the I-QDs at zero time agrees well with the spectral position of the steady-state PL (see Figure 1b-c). As the excitation fluence increases (above = 1), a shorter-wavelength shoulder starts to develop, and thus the PL peak gets broader. At the same time, the decay probed at the shoulder gets faster than the biexciton, indicating contribution from higher-order multiexciton recombination.
10
10-1
-Δα, a.u.
:
0.73 2.92 11.7 46.7
1.46 5.84 23.4
CsPbBr1.5I1.5 10
-2
10-3
0
50
100
150
200
Time, ps Figure S5. Biexciton decay in mixed Br1.5I1.5-QDs probed by transient absorption (TA). Pump-fluence dependent multiexciton decay of the band-edge bleach obtained using TA (the single-exciton contribution is subtracted from the higher-fluence traces) shows no other lifetimes than that of a biexciton. This suggests that the band-edge states are two-fold degenerate.
11
Table S1. Spectroscopic properties of Cs-Pb-halide perovskite QDs
σ400 nm
λPL/hvPL
(nm)
(cm2)
(nm/eV)
6.3
3.5×10-15
487 /
Composition L
CsPbBr3
τr,X
ΔXX
τ2X
CA
(ns)
(ns)
(meV) (ps)
(ps)
(cm6s-1)
0.40
2.70
6.8
26
3.0×10-28
0.44
3.40
7.7
38
9.3×10-28
0.51
3.98
7.8
47
1.7×10-27
0.42
15.4
36.6
11
0.36
47
4.0×10-27
0.41
17.8
43.4
12
0.57
92
2.7×10-27
Q
τcool
2.546 CsPbBr3
8.1
8.0×10-15
507 / 2.446
CsPbBr3
9.3
1.3×10-14
511 / 2.427
CsPbBr1.5I1.5
10.7
1.5×10-14
584 / 2.123
CsPbI3
11.2
1.3×10-14
683 / 1.816
L is the side length of the cubically shaped QD; σ400 nm is the absorption cross-section at 400 nm; λPL (hvPL) is the peak PL wavelength (energy); Q is the PL quantum yield; ΔXX is the excitonexciton interaction energy; is the average single-exciton lifetime; τr,X is the single-exciton radiative lifetime; τcool is the intraband cooling time; τ2X is the biexciton Auger lifetime; CA = (L3)2(8τ2X)–1 is the effective Auger constant.
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