Cation-Dependent Hot Carrier Cooling in Halide Perovskite Nanocrystals

Article abstract of DOI:10.1021/jacs.8b11867

Lead halide perovskites (LHPs) nanocrystals (NCs), owing to their outstanding photophysical properties, have recently emerged as a promising material not only for solar cells but also for lighting and display applications. The photophysical properties of these materials can be further improved by chemical engineering such as cation exchange. Hot carrier (HC) cooling, as one of the key photophysical processes in LHPs, can strongly influence performance of LHPs NCs based devices. Here, we study HC relaxation dynamics in LHP NCs with cesium (Cs), methylammonium (MA, CH₃NH₃⁺), and formamidinium (FA, CH(NH₂)₂⁺) cations by using femtosecond transient absorption spectroscopy. The LHP NCs show excitation intensity and excitation energy-dependent HC cooling. We investigate the details of HC cooling in CsPbBr₃, MAPbBr₃, and FAPbBr₃ at three different excitation energies with low excitation intensity. It takes longer time for the HCs at high energy to relax (cool) to the band edge, compared to the HCs generated by low excitation energy. At the same excitation energy (350 nm, 3.54 eV), all the three LHP NCs show fast HC relaxation (<0.4 ps) with the cooling time and rate in the following order: CsPbBr₃ (0.39 ps, 2.9 meV/fs) > MAPbBr₃ (0.27 ps, 4.6 meV/fs) > FAPbBr₃ (0.21 ps, 5.8 meV/fs). The cation dependence can be explained by stronger interaction between the organic cations with the Pb-Br frameworks compared to the Cs. The revealed cation-dependent HC relaxation process is important for providing cation engineering strategies for developing high performance LHP devices.

Full text of DOI:10.1021/jacs.8b11867

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Article
Cation Dependent Hot Carrier Cooling in Halide Perovskite Nanocrystals
Junsheng Chen, Maria E Messing, Kaibo Zheng, and Tõnu Pullerits
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b11867 • Publication Date (Web): 28 Jan 2019
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Cation Dependent Hot Carrier Cooling in Halide Perovskite Nanocrystals
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Junsheng Chen1, 2, Maria E. Messing,3 Kaibo Zheng1,4, Tonu Pullerits1*
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1 Chemical Physics and NanoLund, Lund University, Box 124, 22100 Lund, Sweden
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2 Nano-Science Center & Department of Chemistry, University of Copenhagen,
Universitetsparken 5, 2100 Copenhagen, Denmark
3 Solid State Physics and NanoLund, Lund University, Box 118, 22100 Lund, Sweden
4 Department of Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby,
Denmark
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Abstract
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Lead halide perovskites (LHPs) nanocrystals (NCs), owning to their outstanding photophysical
properties, have recently emerged as a promising material not only for solar cells but also for
lighting and display applications. The photophysical properties of these materials can be further
improved by chemical engineering such as cation exchange. Hot carrier (HC) cooling, as one
of the key photophysical processes in LHPs, can strongly influence performance of LHPs NCs
based devices. Here we study HC relaxation dynamics in LHP NCs with cesium (Cs),
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methylammonium (MA, CH3NH3 ) and formamidinium (FA, CH(NH2)2 ) cations by using
femtosecond transient absorption spectroscopy. The LHP NCs show excitation intensity and
excitation energy dependent HC cooling. We investigate the details of HC cooling in CsPbBr3,
MAPbBr3 and FAPbBr3 at three different excitation energies with low excitation intensity. It
takes longer time for the HCs at high energy to relax (cool) to the band edge, compared to the
HCs generated by low excitation energy. At the same excitation energy (350 nm, 3.54 eV) all
the three LHP NCs show fast HC relaxation (<0.4 ps) with the cooling time and rate in
following order: CsPbBr3 (0.39 ps, 2.9 meV/fs) > MAPbBr3 (0.27 ps, 4.6 meV/fs) > FAPbBr3
(0.21 ps, 5.8 meV/fs). The cation dependence can be explained by stronger interaction between
the organic cations with the Pb-Br frameworks compared to the Cs. The revealed cation
dependent HC relaxation process is important for providing cation engineering strategies for
developing high performance LHP devices.
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Introduction
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In recent years, lead halide perovskites (LHPs) with the general formula APbX3 (X = Cl, Br
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and I), where A is a cation such as cesium (Cs), methylammonium (MA, CH3NH3 ), or
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formamidinium (FA, CH(NH2)2 ), have emerged as promising active material for
optoelectronic applications. For example, the LHPs-based solar cells have reached more than
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23% light-to-electricity conversion efficiency.
Their nanomaterial counterparts show
potential for fabricating various other devices for our daily life such as lighting (e.g. light
emitting diodes, LEDs), displays (e.g. TVs), photo-detectors and lasers. The high performance
of LHPs is related to their broadband absorption, easily tunable optical band gap, efficient
charge generation and transportation, as well as their luminescence properties. These properties
can be further refined by chemical engineering, such as halogen atoms X mixing and cations
A exchange.2
All above applications are based on light absorption or emission and involve a complex
sequence of different photophysical processes. A comprehensive understanding of these
processes in LHPs is a key for further improving the design and utilization of these materials.3
Consequently, photophysics of LHPs have been extensively studied through various theoretical
and experimental approaches.4 Hot carrier (HC) cooling is one of such photophysical processes.
HCs are created by absorption of photons with excess energy above the bandgap. The
mechanisms and dynamics of HC cooling in LHPs and other semiconductor materials are of
fundamental importance for the performance of many types of devices.5 For example, the
potentially highly efficient hot carrier solar cells depend on the details of carrier cooling
dynamics and the lattice energy recycling capability.6-8 In light emitting devices, fast HC
relaxation is preferred because of the competition between intraband HC cooling and charge
trapping from higher energy hot levels.7, 9 Recent experimental results have revealed that bulk
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LHPs have slower HC dynamics at the excess energy of 1.4 eV (~0.4 ps)
compared to
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most organic semiconductors (~0.1 ps).12-13 Moreover, it is possible to slow down the HC
relaxation by more than one order of magnitude via increasing the excitation intensity.3, 11, 14-15
Slow HC relaxation has been also observed in Sn-based perovskites.16 The slow HC relaxation
in bulk LHPs has been related to various mechanisms such as hot-phonon bottleneck,3 large
polaron screening,15 or Auger heating effect.5 Also in LHP nanocrystals (NC), Li et al.
demonstrated NC size dependent slow-down of the HC relaxation and efficient HC extraction
in a device.17 This exemplifies the potential of LHP NCs for HC solar cells.6, 17 HC relaxation
in LHP NCs can be further tuned by chemical engineering. Chung and Mondal et al.
demonstrated that the HC relaxation time is sensitive to the type of halogen atoms in CsPbX3
NCs.7, 18 Also cation mixing can play an important role for HC relaxation in LHPs as
demonstrated in bulk LHPs both experimentally and theoretically.4, 15, 19-20 Cation mixing, as
one of the most practical and successful strategies for chemical engineering, can enhance the
performance of LHP bulk and NC materials.2, 21-22 The influence of the cations on HC
relaxation dynamics in LHP NCs has not been explored so far. A comprehensive understanding
of the cation-dependent HC relaxation dynamics in LHP NCs is not only essential for
understanding the fundamental photophysics but also for improving the performance of the
LHP NC-based optoelectronic devices.
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Figure1. (a). Absorption spectrum (black solid line) and photoluminescence spectrum (red
solid line, λex=400 nm) of CsPbBr3 NCs, the purple, blue and green arrow represents three
different excitation wavelengths/energies (350 nm: 3.54 eV, 400 nm: 3.10 eV and 490 nm:
2.53 eV), respectively. (b). Crystal structures of lead bromide perovskite NCs with three
different cations: cesium (CsPbBr3), methylammonium (MAPbBr3) and formamidinium
(FAPbBr3). (c). Pseudocolour representation TA spectra of colloidal CsPbBr3 NCs for 350 nm
excitation at high excitation intensity with <N>≈34 (corresponding to
I = 2.4×1014 photon/cm2/pulse, n~4.3×1019 cm-3), black dashed line arrow indicates the initial
negative GSB signal increases and reaches the maximum. (d). Normalized GSB dynamics
probed at the band-edge for CsPbBr3 NCs with 350 nm excitation at seven different excitation
intensities (I1=1.0×1012 , I2=4.9×1012 , I3=7.2×1012 , I4=2.4×1013 , I5=5.9×1013 ,
I6=1.4×1014 and I7=2.4×1014 photon/cm2/pulse, corresponding to <N>~ 0.1, 0.7, 1.0, 3.4, 8.4,
20, and 34; n~1.8×1017, 8.8×1017, 1.3×1018, 4.3×1018, 1.0×1019, 2.5×1019 and 4.3×1019 cm-3,
respectively).
Here we have investigated HC relaxation dynamics in lead bromide perovskite NCs with three
different cations (Figs. 1 and S1): cesium (CsPbBr3), methylammonium (MAPbBr3) and
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formamidinium (FAPbBr3) using transient absorption (TA) spectroscopy. The method has been
widely used for studies of HC relaxation dynamics in LHPs.3, 5, 7, 11, 14, 17, 23 Consistent with
earlier studies, we see strong excitation intensity dependence of HC relaxation dynamics. With
increasing excitation intensity, HC dynamics slows down due to the hot-phonon bottleneck and
Auger heating effects. At low excitation intensity limit we reveal clear cation dependence of
HC dynamics. Perovskite NCs based on inorganic cation (Cs) have the slowest, while the
FAPbBr3 NCs have the fastest HC relaxation. This can be explained by the increased carrier-
phonon coupling due to the interaction between organic cation with Pb-Br framework.
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Results and Discussion
Figure 1c shows a pseudocolour TA spectrogram of CsPbBr3 NCs excited at 3.54 eV (350 nm)
with an intensity of 2.4×1014 photons/cm2/pulse corresponding to the initial average generated
electron-hole pairs per NC <N>~34 and average carrier density n~4.3×1019 cm-3 (<N>=I·σ,
evaluated from the excitation intensity I and absorption cross section σ of the NCs, see
supplementary information S2). The average carrier density per NC volume is determine as
n=<N>/VNC, where VNC is the NC volume estimated by the average size of the cubic shape NCs
(see supplementary information S1). Two obvious features appear: i) a negative ground state
bleach (GSB) signal located around the bandgap (2.45 eV), which is induced by the band filling
effect; ii) a positive photoinduced absorption (PIA) signal below the bandgap (less than
2.41 eV). The shift of the PIA signal in respect to the GSB is a typical signature of exciton-
exciton interaction and can be used to evaluate the so called bi-exciton binding energy.7, 24
While HCs relax to the lowest-energy states, the positive PIA signal decays and is replaced by
a strong GSB signal. At the same time, the initial negative GSB signal increases and reaches
the maximum (see the arrow in Figure 1c). All three types of NCs with different cations show
analogous GSB and PIA features while the time-constants of kinetics vary. (see Figs. 1c, S3
and S4) The PIA decay and GSB buildup are the result of the carriers arriving at the band edge
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during the initial thermalization and relaxation.7, 18 Here we determine the time-constant of the
process via global fitting of the TA kinetics by a sum of exponentials with global time constants
(lifetimes) as variables (see supplementary information S4). We point out that polaron
formation can be involved in the early time excited state dynamics, as one of the consequences
of the carrier-phonon coupling. 25-26 Since here we focus on the hot carrier cooling process, no
further discussion of the polaron formation will be carried out in the current work.
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Table1. Excitation energy dependence of the time constant of the rising signal (τc) at the band-
edge for colloidal NCs with three different cations with low excitation intensity conditions.a,b
NCs
CsPbBr3
MAPbBr3
270±20
235±20
<100
FAPbBr3
210±20
180±20
<100
τc (fs, λex=350 nm) 390±20
τc (fs, λex=400 nm) 310±20
τc (fs, λex=490 nm) <100
a The low excitation intensities are listed in Table S3. CsPbBr3 NCs: <N>~0.1, 0.1 and 0.3 for
λex=350 nm, 400 nm and 490 nm, respectively. MAPbBr3 NCs: <N>~0.2, 0.1 and 0.3 for
λex=350 nm, 400 nm and 490 nm, respectively. FAPbBr3 NCs: <N>~0.1, 0.1 and 0.3 for
λex=350 nm, 400 nm and 490 nm, respectively.
b The error is obtained from fitting.
HC relaxation time is governed by not only the intrinsic properties of different materials but
also by the initial HC density and excitation energy. Multiple-exciton states can be populated
by an intense laser pulse leading to high initial HC density in NCs. An important decay channel
for multiple-exciton states is Auger-recombination process, which can “re-heat” the HCs and
effectively slow down the HC cooling.5 This is called Auger heating effect, which has been
observed in both LHP bulk and NC materials.5, 17 Moreover, Coulomb screening and hot-
phonon bottleneck effects can also be present and decrease the HC cooling rate at high initial
HC density conditions.3, 11, 15 Our TA measurements show clear dependence of HC relaxation
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dynamics on excitation intensity for all three NCs which were studied. For example, as shown
in Fig. 1d the normalized GSB dynamics probed at the band-edge for CsPbBr3 NCs with
350 nm excitation at seven different excitation intensities (I1=1.0×1012 , I2=4.9×1012 ,
I3=7.2×1012 , I4=2.4×1013 , I5=5.9×1013 , I6=1.4×1014 and I7=2.4×1014 photon/cm2/pulse,
corresponding to <N>~ 0.1, 0.7, 1.0, 3.4, 8.4, 20, and 34; n~1.8×1017, 8.8×1017, 1.3×1018,
4.3×1018, 1.0×1019, 2.5×1019 and 4.3×1019 cm-3, respectively). Though, below a certain
intensity limit, the intensity dependence of the relaxation disappears (Fig. 1d and
Supplementary information Fig. S6) revealing intrinsic HC relaxation of LHP NCs. The
excitation energy can also affect the HC relaxation time by changing the excess energy of the
carriers. We study the HC relaxation after excitation at three different wavelengths/energies
(350 nm: 3.54 eV, 400 nm: 3.10 eV and 490 nm: 2.53 eV, Fig. 2 and Table 1). In all three
materials we found that the time it takes for HCs to reach the band edge is clearly increased
with increasing the excitation energy. The lowest excitation energy (2.53 eV) is very close to
the bandgap with negligible excess excitation energy and therefore the GSB signal appears
within the time resolution of the setup (100 fs). At higher excitation energies (3.54 eV and 3.10
eV), well above the bandgap, pronounced rising component appears corresponding to the HC
relaxation to the band edge.
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Figure 2. Normalized GSB dynamics probed at the band-edge for colloidal NCs with three
different cations with low excitation intensity condition. (a). CsPbBr3 NCs with 490 nm,
400 nm and 350 nm excitations corresponding <N>~0.3, 0.1 and 0.1; n~3.7×1017, 1.4×1017 and
1.8×1017 cm-3, respectively. (b). MAPbBr3 NCs with 490 nm, 400 nm and 350 nm excitations
corresponding <N>~0.3, 0.1 and 0.2; n~8.4×1017, 2.1×1017 and 4.3×1017 cm-3, respectively. (c).
FAPbBr3 NCs with 490 nm, 400 nm and 350 nm excitations corresponding <N>~0.3, 0.1 and
0.1; n~5.5×1017, 1.9×1017 and 2.3×1017 cm-3, respectively. (d). GSB dynamics of CsPbBr3,
MAPbBr3 and FAPbBr3 NCs with 350 nm excitations corresponding <N>~0.1, 0.2 and 0.1;
n~1.8×1017, 4.3×1017 and 2.3×1017 cm-3, respectively.
Based on the discussion above we conclude that the intrinsic HC relaxation in LHP NCs with
different cations should be studied by exciting the NCs with the same excitation energy at low
excitation intensity limit. We will concentrate at the two higher excitation energies (350 nm
(3.54 eV) and 400 nm (3.10 eV)), which reveal that the HC relaxation time of NCs is in sub ps
timescale, <0.4 ps and that the time decreases as the cation changes from Cs, to organic cations
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MA and FA (Fig. 2 and Table 1). The observed timescales of HC relaxation to the band edge
in our LHP NCs are within the same order of magnitude as what has been previously reported
for other LHP NCs7, 17-18 and large size CdSe and PbSe NCs.27-28 The cation-dependent trend
in HC relaxation times is consistent with recent reports in LHP bulk materials.26, 29 This shows
that the cations play a critical role for HC relaxation in LHP materials.
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Now we take a closer look at the TA dynamics at low excitation intensity limit (<N> is between
0.1 and 0.3) where the HC relaxation in NCs is not influenced by hot-phonon bottleneck and
Auger heating effect which would slow down HC relaxation at high carrier density.3, 5, 30
A
possible origin for the observed fast HC relaxation could be the coupling to surface related
defect/trap sates.7, 17, 31-32 However, it is not the case here because the photoluminescence (PL)
excitation (PLE) spectra closely match the absorption spectra (Supplementary information Fig.
S1), indicating that almost all HCs are effectively funneled to the emitting band-edge states.
The surface defect/trap state related fast HC relaxation is further excluded by the increased
time it takes for the HCs to reach the band edge in case of higher excitation energy (Fig. 2).
Also the excitation wavelength independent high PL quantum yield (PLQY 50~70%,
Supplementary Table S2) and TA decay kinetics (Supplementary information Fig. S8) speak
against the defect-related relaxation scenario. Instead, here we explain the fast HC relaxation
by efficient HC excess energy release to vibrations (longitudinal-optical (LO) phonons)
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through non-adiabatic coupling due to the nuclear motions.
In atomistic description of
semiconductor nanocrystals, the energy levels form a quasi-continuum.33 The small energy
separation between electronic states ensures efficient relaxation of HCs giving energy away to
phonons. The density of states increases at higher energies leading to increased HC energy loss
rates (excess energy loss/relaxation time) in case of higher energy excitation (Tables S4 and
S5). All these arguments support fast HC relaxation in NCs through a sequence of relaxation
steps accompanied by emission of phonons where even multiphonon transitions can occur.34 It
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may happen that the energy separation between electronic states is increased owing to the
quantum confinement. Such effect is usually more pronounced for the lower energy levels.
However, the effect should not play a major role here, as we do not have strong quantum
confinement since the sizes of the NCs (see Fig. S1) are larger than the corresponding Bohr
radii. 35-37
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Figure 3. TA spectra showing hot carrier distributions and cooling. (a). Normalized TA spectra
of colloidal CsPbBr3 NCs for 350 nm excitation at excitation intensity <N>~34 (corresponding
to I = 2.4×1014 photon/cm2/pulse, n~4.3×1019 cm-3). The shortest time delay (red) is 0.1 ps and
the longest (blue) 10 ps. The higher energy tails (between 2.55 and 2.75 eV) are globally fit to
a Boltzmann distribution (gray lines). Carrier temperature is extracted from this fitting. (b).
Time dependent carrier temperature with 350 nm excitation at four different excitation
intensities (I1=1.0×1012, I2=5.9×1013, I3=1.4×1014 and I4=2.4×1014 photon/cm2/pulse,
corresponding to <N>~ 0.1, 8.4, 20, and 34; n~1.8×1017, 1.0×1019, 2.5×1019 and 4.3×1019 cm-
3, respectively).
As the next step, we have evaluated the time dependence of efficient carrier temperature Tc
based on the TA spectra. The high energy tail of GSB signal (e.g., start at ~2.55 eV in Fig. 3a)
reveals energy distribution of state filling by HCs and has been used in earlier studies to extract
Tc of LHP films, NCs and other materials.3, 5, 11, 17, 38 According to the quasi-continuum picture
of the bands,33, 39 the energy level spacing ΔE is much smaller than the room temperature
thermal energy
(
is the Boltzmann constant and T is the absolute temperature). The
푘퐵푇 푘퐵
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initially created non-equilibrium carrier distribution evolves rapidly into a quasi-equilibrium
Fermi-Dirac distribution, on a time scale of ~100 fs.11 This is confirmed by absence of any
non-thermalized carrier distribution signatures, such as narrow spectral features above the
bandgap (Fig. 3a), in timescales accessible with the time resolution of our experiment, ~100
fs.11 Such rapid quasi-equilibrium distribution buildup is usually ascribed to the efficient
carrier-carrier scattering.17, 40
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The quasi-equilibrium carrier Fermi-Dirac distribution can be approximated as Maxwell-
Boltzmann distribution function for HC excess energy ≫ quasi-Fermi energy (Ef).3 Therefore,
once the quasi-equilibrium is reached, Tc can be extracted by fitting the high energy tail of the
TA spectra (e.g., between 2.55 eV and 2.75 eV for CsPbBr3 NCs, for the details about
MAPbBr3 and FAPbBr3 NCs, see Supplementary Information S7) with the Maxwell-
(
)
Boltzmann distribution function
, see Fig. 3a. It has been reported that the
exp 퐸푓 ― 퐸 /푘퐵푇푐
effective mass of electron and hole are roughly equal in LHPs,17, 41-43 and electron temperature
(Te) roughly equals to the hole temperature (Th). Therefore, Tc represents an average
temperature of the electrons and holes.3, 5, 11 The excess electronic energy ~1.2 eV, after
absorbing the high energy photon of 3.54 eV, is equally distributed between an electron and
hole. The temperature which corresponds to the thermal energy
= 0.6 eV would
퐸 = 1.5푘퐵푇
be ~4500 K. The highest effective temperature obtained 100 fs after low intensity excitation
(only one excitation per NC) is about 1000 K, 1500 K and 3000 K for the Cs, FA and MA
based NCs, respectively (see Fig. S11). The trend is correlated with the size of the NCs (see
Fig S1) – larger NCs (Cs is the largest, MA is the smallest) lead to more extensive drop of the
effective temperature within the first 100 fs. The reported temperature drop in bulk LHP
(infinite size) confirms this trend17, 20. In the bulk material the cooling is further accelerated by
the carrier-carrier scattering.
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Since we only have one electron and hole in the system, the many-body carrier-carrier
scattering effects are unlikely to explain the large temperature drop. Instead, we follow the
argumentation that since in NCs far above the bandgap the density of electronic states is high
and thereby the laser pulse spectrum covers a broad range of k-vectors. The corresponding
electronic wavepacket can be therefore rather localized and the excitation will be bulk-like.44
Such wavepacket is very strongly coupled to the motion of ionic nuclei and will rapidly loose
energy. The relative localization effect is expected to be stronger for the larger NCs because of
the higher density of states for high energy excitations. This can explain the correlation between
the very fast initial energy loss and the size of the NCs.
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The fastest reported kinetics of HCs in LHP systems is about 20 fs 45 putting an upper limit for
the dephasing times of the corresponding initial electronic wavepacket. After the dephasing the
excitation will be spread over the whole NC and at 100 fs the higher energy tail of the bleach
signal can be well fit by the exponential function corresponding to the Maxwell-Boltzmann
distribution allowing to extract the effective temperature Tc. At low excitation intensity
condition (<N> is between 0.1 and 0.3) Tc decays exponentially to room temperature in time
scale similar to the band-edge signal rise following the same cation dependent trend, FA is the
fastest and Cs the slowest (see Fig. 3b and Fig. S11).
We relate the HC relaxation in LHP NCs to the carrier-phonon interaction – stronger interaction
leads to faster cooling.46 Recent calculations by Kais et al, have suggested that charge carrier-
phonon coupling plays an important role for HC cooling process in CsPbI3, MAPbI3 and
FAPbI3.4 The LHP NCs that we are using here have different halogen atom compared to that
work,4 but the perovskite framework structures are similar and cations are the same. Hence the
results of this theoretical study are applicable here supporting our conclusion that the motion
of organic cations (MA and FA) enhances charge carrier-phonon coupling compared to the
coupling in case of inorganic Cs cations.4 Recent combined molecular dynamics and electronic
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structure calculations have shown that the vibrational modes of the organic cation (MA in this
case) provide important contributions to the density of states broadening.47 We have calculated
the electronic structure of the three perovskite systems (Supporting Information, Fig. S13). As
shown in Fig. S13, contribution of Cs to the electronic density of states (DOS) in the relevant
energy range of valence and conduction band is negligible while the organic cations MA and
FA contribute more. FA contribution to the DOS is particularly pronounced. This result is well
in line with the conclusion that the carrier-phonon coupling in FAPbBr3 is enhanced.4, 7, 48 The
size of FA cation is much larger than MA and Cs cations,49 which increases the interaction
between the FA and the perovskite Pb-X framework. The increased interaction is supported by
the calculations showing significantly stronger excited state charge distribution on FA
compared to what can be seen for Cs and MA (Fig. S13). Furthermore, inelastic neutron
scattering has shown that bulk modulus of FAPbBr3 is smaller (material is softer) than
MAPbBr3.50 All these results agree well with the previous theoretical work.51 The interaction
between organic cations and Pb-X framework can alter the lattice phonons in hybrid LHPs
compared with the inorganic CsPbBr3.20 The phonon modes of CsPbBr3 are mostly distributed
over the Pb-X framework.20, 52 However, in MAPbBr3 and FAPbBr3, organic cation libration
and torsion modes can couple to the Pb-X modes53 which are essential for nonadiabatic
coupling leading to relaxation. Including spin-orbit coupling was recently found essential for
quantitatively correct calculations of the relaxation rates in LHPs.54 The organic cation related
phonon modes show a significant overlap with the Pb-X modes and can therefore participate
in the HC-phonon relaxation.20 Hence the organic cation (MA and FA) based LHP NCs show
faster HC relaxation than the Cs based LHP NCs. The FA cation shows stronger interaction
between the Pb-X framework compared with that of MA cation.55
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The hot carrier relaxation rate has been shown to depend on the NC size in LHPs – in the
smaller NCs the cooling is slower.17 Also here the NC sizes are slightly different. However, as
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discussed above, we do not have strong quantum confinement here as the sizes of the NCs (see
Figure S1) are larger than the corresponding Bohr radii.35-37 Furthermore, here the largest NCs
(Cs, 9.3 nm) show the slowest cooling and the intermediate size (FA, 8.5 nm) is the fastest –
clearly, in our samples the cooling is more influenced by the cations than the small size
variations.
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Figure 4. (a) Power loss as a function of the inverse carrier temperature of CsPbBr3 NCs with
350 nm
excitation
at
two
different
excitation
intensities
(I1=5.9×1013,
I2=2.4×1014 photon/cm2/pulse, corresponding to <N>~ 8.4 and 34; n~1.0×1019 and
4.3×1019 cm-3, respectively). (b) Time dependent carrier temperature with 350 nm excitation
for CsPbBr3, MAPbBr3 and FAPbBr3 NCs at excitation intensity 1.4×1014, 8.0×1013 1.3×1014
photon/cm2/pulse, corresponding to <N>~ 20, 4.0 and 6.9; n~2.5×1019, 1.1×1019 and
1.1×1019 cm-3, respectively, the solid lines are obtained from exponential fit.
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Table 2. Fit parameters for time dependent carrier temperature for CsPbBr3, MAPbBr3 and
FAPbBr3 NCs temperature with 350 nm excitation at excitation intensity 1.4×1014, 8.0×1013
1.3×1014 photon/cm2/pulse, corresponding to <N>~ 20, 4.0 and 6.9; n~2.5×1019, 1.1×1019 and
1.1×1019 cm-3, respectively.a
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Cations
τ (ps)
A1(K)
τ (ps)
A2(K)
1
2
Cs
0.4
1100
3600
1700
5
3
3
320
350
940
MA
0.2
FA
0.15
( ― (푡 ― 0.1))/휏1
푇푐(푡) = 퐴1푒
+ 퐴2푒( ― (푡 ― 0.1))/휏2 +300
a Fitting function:
At higher excitation intensity due to the hot-phonon bottleneck the cooling process slows down.
The rise of the bleach signal at the band edge becomes longer (Fig. S9) and a slower phase
appears in the cooling process in all three different NCs that we have investigated (Figure 3b,
Fig. S10 and S12). The physics of the cooling timescales is related to the coupling between
thermal pools. Here we follow the temperature of the electronic system which is coupled to the
pool of LO phonons. Owing to the anharmonicity of the vibrations, the LO phonons give energy
further to the acoustic phonon pool. Finally, the energy dissipates to the solvent environment.
Following the theory of hot electron relaxation via optical-phonon emission56 we have
presented electronic energy power loss as a function of reverse electronic temperature in Fig.
4a (see details in supplementary information S9) for CsPbBr3 NCs with 350 nm excitation at
two different excitation intensities (I1=5.8×1013, I2=2.4×1014 photon/cm2/pulse, corresponding
to <N>~ 8.4 and 34; n~1.0×1019 and 4.3×1019 cm-3, respectively). Despite of the noise, one can
clearly identify two stages in the power loss, visualized by red and blue lines in the figure. The
steep red part of the power loss corresponds to the situation where electronic temperature is
higher than the optical phonon temperature. The blue line corresponds to the regime where the
electronic system and the LO-phonons have reached equilibrium and the thermal energy can
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move back and forth between electrons and the LO modes. Sometimes this has been called
phonon energy up-conversion.20 In the Cs-based NCs, shown in Fig 4a, the breakpoint between
the two regimes occurs at about 600 K. From this point the further cooling depends on LO-
phonon relaxation giving energy away to acoustic phonons and takes place in timescale of ~3
ps (MA and FA) to ~5 ps (Cs), see Fig. 4b and Table 2. It has been argued that blocking of the
acoustic phonon propagation in case of low thermal conductivity, would slow down the
process.20 Here we have NCs where the phonon propagation is naturally confined within the
small size of the crystal. However, due to the large number of degrees of freedom even in a
small NC, room temperature is reached relatively quickly in our experiment.
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In hot carrier solar cells, the charge carrier injection occurs at the energy significantly above
the bandgap (see Figure S16). The heat that is anyway released by the hot carriers, helps the
low-energy “cool” carriers at the band edge to reach the injection levels.6,8 Another important
factor is the cooling rate of the thermal pool in respect of the rate of absorption. Here we have
three thermal pools – electrons, optical phonons and acoustic phonons. A possible scenario for
the hot carrier solar cell application would be a rapid cooling of the electronic system until
equilibrium with the optical modes is reached. From the systems studied here, the FA based
NCs have the fastest relaxation (least heat lost to the acceptor due to too early injection) and
the quasi-equilibrium temperature is the highest, ~1300 K (see Fig. 4b). The thermal energy of
the optical phonon pool needs to stay at sufficiently high level until the next photon is absorbed.
In our current system the optical phonons lose the energy to the acoustic phonons within 3-5 ps
which is far too fast even in case of solar concentrators (see details in supplementary
information S10). Can one engineer anharmonicity of the optical modes to the extent that would
sufficiently isolate the corresponding thermal pool from the rest of the phonon bath?
Alternatively, one could think of engineering the isolation at the level of acoustic phonons. In
this case the whole crystal lattice would be heated up. It is unlikely that the new perovskite
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solar materials would be suitable for such scenario because they would most likely degrade at
the temperatures needed for substantial gain in hot carrier solar cell efficiency enhancement.6
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In summary, the HC relaxation in CsPbBr3, MAPbBr3 and FAPbBr3 NCs has been studied by
using transient absorption spectroscopy. The HC relaxation to the band-edge is excitation
intensity dependent. With high excitation intensity HCs show slower relaxation compared with
low excitation intensity, due to the Auger heating effect and hot-phonon bottleneck. Apart from
excitation intensity, we find that HC relaxation process is excitation energy dependent, due to
HCs generated by higher excitation energy occupy the higher energy levels, and it takes longer
time for the HCs to relax to band-edge compared to the HCs which are generated by excitation
energy close to the band-edge. To obtain the intrinsic HC relaxation dynamics and compare it
in NCs with different cations, we measured the TA spectra at low excitation intensity with three
different excitation energies and extracted the HC relaxation time. Our experimental results
reveal that HC relaxation dynamics in LHP NCs is cation-dependent. Inorganic cation Cs based
LHP NCs show slower HC relaxation compared with organic cations (MA and FA) based LHP
NCs. This can be ascribed to that the motion of organic cations (MA and FA) enhances charge
carrier-phonon coupling compared to inorganic Cs cations. FA cation based LHP NCs show
fastest HC relaxation among the three types of LHP NCs, this indicates that FA cation interacts
stronger with Pb-X framework compared with MA and Cs cations. The effect can be explained
by the larger size of FA cation. We conclude that the HC relaxation is facilitated by the
interaction between the cations and the Pb-X framework. HC cooling in LHP NCs can be tuned
for device application by cation mixing and engineering.
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Author information
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Corresponding Author
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T.P. (tonu.pullerits@chemphys.lu.se)
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Notes
The authors declare no competing financial interest.
Acknowledgements
This work was funded by the Swedish Research Council, Swedish Energy Agency, KAW
foundation and NanoLund. K. Z thanks the financial supported by the Independent Research
Fund Denmark-Sapere Aude starting grant (No. 7026-00037A) and Swedish Research Council
VR starting grant (No. 2017-05337).
Supporting Information Available:
CsPbBr3, MAPbBr3 and FAPbBr3 NCs preparation and characterization, NC absorption cross-
section determination, TA spectra of CsPbBr3, MAPbBr3 and FAPbBr3 NCs, Extract HC
relaxation time from TA spectra by global fitting, Photoluminescence quantum yield,
Excitation energy dependent HC relaxation, Time dependent carrier temperature of CsPbBr3,
MAPbBr3 and FAPbBr3 NCs, Computational Details, Power loss of the hot carriers, Hot
carrier cooling model and Achieving high excitation intensity with concentrator photovoltaics.
This material is available free of charge via the internet at http://pubs.acs.org.
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