Ultrafast transient absorption spectroscopy analysis of CsPbBr3 perovskite superlattices

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Ultrafast transient absorption

spectroscopy analysis of CsPbBr3

perovskite superlattices

by Zeger Ackerman

Student nr. 11061138

Report Bachelor Project Physics and Astronomy, 15 EC

Conducted between 1-4-2020 and 30-6-2020

Submitted on 9-7-2020

Institute of Physics, University of Amsterdam

Van der Waals- Zeeman Institute

Supervisor:

prof. dr. Peter Schall

Daily Supervisor:

dr. Yingying Tang

Examiner:

dr. Katerina Newell

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Abstract

CsPbBr3 perovskite nanocrystals (NCs) have shown promising properties for applications in

lasers, light-emitting diodes (LEDs), photodetectors and photovoltaic cells. However, a limit to their applicability has been a lack of highly ordered superlattices (SLs) of NCs obtained from colloidal solution. An oil-in-oil emulsion method has led to the self-assembly of NCs into SLs with a spherical morphology called superballs (SBs). For this research, an analysis was performed on ultrafast transient absorption (TA) data of these SBs. The SBs show both exciton, biexciton and hot carrier dynamics in two distinct positions of the spectra. This phenomenon is akin to superfluorescence (SF), leading to the hypothesis that a SB consists of different SL ensembles, one in which the NCs are coupled, and one in which they are not coupled to each other. Together they produce the bimodal spectrum with the coupled ensembles producing a redshift compared to the non coupled ensemble. Future experiments could compare the TA spectrum of colloidal NCs with SBs to provide conclusive evidence for this hypothesis.

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Popular summary (Dutch)

De perovskietstructuur is de kristalstructuur van bepaalde materialen met bijzondere eigenschap-pen. Het perovskiet nanokristal met de chemische formule CsPbBr3 is slechts enkele nanomaters

groot. Mede daarom vertonen CsPbBr3 nanokristallen eigenschappen die veelbelovend zijn voor

gebruik in lasers, leds (light-emitting diodes), sensitieve lichtdetectoren en photovoltaische cellen, beter bekend als zonnecellen. Een limiet op de toepassing hierin was het gebrek aan zeer geordende superkristallen. Deze structuren van tientallen tot honderden nanometers groot zijn opgebouwd uit CsPbBr3 nanokristallen. CsPbBr3 superkrstallen zijn nu vervaardigd door een emulsie van

twee oliën, waarvan de verspreide druppels van één olie de nanokristallen bevatten, te laten ver-dampen. De nanokristallen binnen een drogende en krimpende druppel vormen door hun onderlinge aantrekkingskract uit zichzelf een superkristal met een ronde vorm. In dit onderzoek is een spec-trum geanalyseerd dat is verkregen met vergankelijke absorptie-metingen aan zulke superkristallen. De motivatie voor dit onderzoek was om meer informatie te krijgen over de eigenschappen van superkristallen.

In nanokristallen zijn de gebonden toestanden genaamd excitonen, biexcitonen en hete excitonen gevonden, en in vergankelijke absorptie-meting veroorzaken deze samen een karakteristieke piek, op ´

e´en golflengte. Echter zijn op twee verschillende golflengtes zulke pieken geobserveerd in het spec-trum van de vergankelijke absorptie-meting aan superkristallen. Een mogelijke verklaring wordt hier gegeven. Erin wordt gesteld dat de twee pieken op verschillende golflengtes worden veroorzaakt doordat een superkristal bestaat uit twee verschillende soorten groepen van nanokristallen. In de ene groep zijn de nanokristallen niet gekoppeld met elkaar en in de andere zijn ze wel gekoppeld. De tweede groep zorgt met zijn onderlinge koppelingen voor energieverlies, wat leidt tot een rood-verschuiving van zijn karakteristieke piek, waardoor deze een lagere golflengte heeft dan de piek van de ongekoppelde groep. Om deze hypotheses te testen zou een toekomstig experiment verganke-lijke absorptie-meting kunnen uitvoeren op CsPbBr3 nanokristallen en vervolgens op de door die

nanokristallen gevormde superkristallen. Het verschil tussen de twee spectra zou uitsluitsel kunnen geven over het effect van de superkristalstructuur op de eigenschappen van CsPbBr3.

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Acknowledgements

I would like to thank dr. Yingying Tang and prof. dr Peter Schall for their guidance and help during the entire time of this project. I would also like to thank dr. Dolf Timmerman for his help in the discussion and MSc student Dido van der Gon for her help in the data fitting.

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Abbreviations

0D Zero-dimensional 1D One-dimensional 2D Two-dimensional 3D Three-dimensional AB Absorption bleaching Eg Band gap energy

Epump Pump energy

fs Femtosecond IA Induced absorption LED Light-emitting diode NC Nanocrystal

nm Nanometre

PL Photoluminescence

PLQY Photoluminescence quantum yield ps Picosecond QD Quantum dot SB Superball SF Superfluorescence SL Superlattice TA Transient absorption

t1 Short life-time component of bleaching signal

t2 Long life-time component of bleaching signal

tdecay Life-time of induced absorption signal

tpp Pump-probe delay time

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1 Introduction

CsPbBr3 perovskite nanocrystals (NCs) display a multitude of promising optoelectronic properties,

giving them the potential to be used as new lasers, LEDs, photovoltaic cells and photodetectors. These properties include spectrally narrow and broadly tuneable photoluminescence (PL) [1] and high photoluminescence quantum yield (PLQY).[2] The properties of NCs are in part due to their small size, the smallest of which has a diameter of 2.6 nm.[3] CsPbBr3superlattices (SLs), i.e. crystal

lattices of these NCs [4], are sought after because of their exotic behaviour that the single NCs do not display. Aside from their collective properties like coherent superfluorescence (SF) [5], SLs can provide units for the fabrication of a SL film, ideal for devices.

Perovskite NCs, including zero-dimensional (0D) perovskite quantum dots (QDs), are cubically ordered on a nanometre scale. The NCs show an emission peak within the visible region that is tuneable by their size. The overall cubic shape of these NCs allows for the assembly of cubically ordered SLs, which retain a bright PL with a redshift due to NC-NC coupling. The optical, electronic and hot carrier properties of the NCs have been the subjects of significant research.[4] However, the properties of SLs are relatively unknown. The goal of this research is to investigate the exciton, biexciton and other carrier dynamics in superballs (SBs), which are CsPbBr3 perovskite SLs with a

spherical morphology. Understanding and being able to control these properties will pave the way to novel photoelectronic devices.

A proven way to investigate the carrier dynamics is by using ultrafast transient absorption (TA) spectroscopy.[6] TA spectroscopy can be a method to present the underlying dynamics and optoelectrical effects as a result of the SL structure. For this research, we analysed TA data that was gathered on CsPbBr3SBs in order to increase our understanding of hot carrier dynamics in SBs and

to discover differences in behaviour between NCs and SBs. We determined the physical processes resulting in the time-dependent spectral shape of the difference absorption data by estimating the rise-times and life-times of the decay of the signals. Understanding the underlying dynamics of CsPbBr3 SBs will help in refining the design of the SBs and other SLs into practical materials for

optoelectrical applications like photovoltaics, photon detecting, lasing and LEDs.[1]

Figure 1: Protescu et al. (2015)[1]: (a) The cubic CsPbBr3 perovskite lattice. (b) TEM image of a

CsPbBr3 perovskite NC.

1.1 Perovskite NCs

All-inorganic lead halide perovskites, CsPbX3 (X = Cl, Br, I), are semiconductors with the three-dimensional connected PbX6 structure. Recently they have been researched for their broadly

tune-able band gap and high PLQY. For this research, data on specifically CsPbBr3 was analysed.

CsPbBr3 crystallises in a cubic perovskite lattice, shown in figure 1. The entire crystal with this

lattice is called a perovskite NC for its 100_{to 10}1 _{nm scale size. CsPbBr}

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the cubic symmetry of the perovskite lattice.

QDs are zero-dimensional (0D) because their size is confined in all directions, as shown in figure 2a. This means that the edges of the crystal are of the same order as the Bohr exciton radius, creating quantised energy transition levels. By having a tuneable size which changes the degree of quantum confinement, NCs give tuneable optical range, as is shown in figure 2b. Bulk CsPbBr3

perovskite has a band gap energy Eg ≈ 2.38 eV [7] while for NCs Eg can be higher, following the

relation

∆Eg= ~ 2_π2

2m∗_r2,

where m∗ is the exciton reduced mass and r is the NC radius. Due to quantum confinement, the optical transition of CsPbBr3perovskite NCs can cover the region 450 nm - 522 nm (2.38 eV - 2.76

eV). CsPbBr3 NCs of 12 nm to 14 nm are situated in the weak quantum confinement regime.[7]

(a) (b)

Figure 2: The effects of quantum confinement. (a) Krahne et al. (2012)[8]: Confinement effects in nanomaterials: 0D QDs, one-dimensional (1D) nanorods and two-dimensional (2D) nanoplatelets. The higher (lower) the number of confined (free) dimensions, the more quantised the energy tran-sition levels are. In bulk (3D) perovskite, there is no quantum confinement. (b) Protescu et al. (2015)[1]: The CsPbBr3 band gap energy dependence on NC size.

1.2 SLs and SBs

Since CsPbBr3 NCs are cubic, they can form a cubic lattice of NCs called a SL. NC-NC

attrac-tions allow for the self-assembly of SLs with little NC vacancies and weak delocalisation of those vacancies.[4] The NCs used for assembly have sizes between 12 nm and 14 nm, making the assembly of a single SL with the maximum size possible. SLs could become building units for a SL film, which is a step closer towards a practical size for large-scale application. A SB is a SL with a spherical morphology, as shown in figure 3. This is a result of its assembly method. The data that was analysed for this research was gathered on SBs with radii of 90 ± 25 nm.

1.3 Excitons

In a semiconductor, an electron in the valence band can be excited to the conduction band by absorbing a photon. The vacancy an electron leaves behind in the valence band after being excited is called a hole. An excited electron or hole can be a free carrier transporting charge through the material, displaying the photoelectric effect. However, if the electron is bound to a hole due to attraction of its opposite charge, it is not a free carrier. It forms an electron-hole pair called an exciton. On a longer timescale, ∼ 100 _{ns for CsPbBr}

3 NCs, excitons decay via the emission of

photons.[10-13] Due to the exciton binding energy, the energy of the emitted photon Eγ is less than

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Figure 3: STEM image of perovskite SBs with an average size of 90 nm. The NCs were clearly cubically ordered even though the SB morphology was spherical. (2019) Reprinted with permission from dr. Y. Tang.[9]

1.4 Recombination and cooling

After a certain time, the exciton decays when the electron recombines with the hole. This occurs after a life-time which depends on the type of recombination and the number of other excitons in the NC. The most common type for a single exciton is radiative emission, followed by non-radiative emission through phonons, which are lattice vibration particles. If a particle is excited by a photon with Eγ larger than Eg, it becomes a hot carrier. A hot carrier electron is on a higher energy level

of the conduction band and as a hot exciton, it takes between 0 and 2 ps to relax to the lowest conduction band before it decays.[14] The relaxing occurs via the emission of phonons.

The biexciton decays when one of the two excitons recombines. This recombination can take the form of non-radiative Auger recombination or biexciton radiative emission. With the latter, a photon with Eγ = Eg is emitted. This is the same process as for a single exciton; however its time

scale is 4 times shorter than that of single exciton radiative decay.[13] The life-time of a biexciton, tXX ∼ 2 - 200 ps, is thus shorter than the life-time of an exciton, tX > 500 ps.[15] With Auger

recombination, the energy released by a decayed exciton is transferred to the other exciton of the exciton pair and excites it into a hot exciton. The single hot exciton then decays like an original hot exciton, first relaxing and then recombining. In CsPbBr3 NCs, the Auger recombination was found

to dominate the biexciton decay.[12]

1.5 TA spectroscopy

A way to detect the hot carrier dynamics and measure binding energies of excitons and biexcitons in a material is by using TA spectroscopy.[6] In figure 4, a simplified TA setup is shown. In it, a pump pulse of a laser first excites a fraction of the NCs. A time-period tpp later, a broadband probe

pulse of low intensity, to not cause multistep processes, is shot at the NCs to measure an absorption spectrum. This spectrum minus the absorption spectrum of the NCs without the pump pulse is the difference absorption ∆A(tpp, λ). As a function of tpp and λ it can be analysed to understand the

hot carrier dynamics within the SLs, in which the NCs might behave differently when excited by the pulse. tpp is the pump-probe delay time, i.e. the time between the pump and the probe. When tpp

is negative, the probe arrives before the pump and thus no difference absorption signal is observed, except for noise.

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Figure 4: A simplified TA setup. First a laser pump pulse is shot at the sample, followed by a continuous probe pulse with a variable delay time tpp. The transmission is detected by the

detector. Temps (2016). Retrieved from https://www.temps.phc.uni-kiel.de/en/research/ laboratories-and-instrumentation/fs-transient-absorption on May, 2020.

Biexciton dynamics can be studied using TA spectroscopy provided there is a measurable biex-citon amount, which requires a significantly high pump fluence, that is, the energy of a pump laser pulse per sample area (µJ/cm2_{). In a TA setup a biexciton is produced either completely by the}

pump pulse or one half, an exciton, is produced by the pump pulse and the other half is produced by the probe pulse.

1.6 Induced absorption and bleach

The exciton, hot exciton and biexciton dynamics, after a laser pulse pump produces a hot exciton and a lower energy probe produces an exciton in CsPbBr3NCs, are illustrated in figure 5a. The hot

exciton binds with the band edge exciton via Coulomb interaction between the excitons, becoming a hot biexciton. The biexciton binding energy δXX is negative, which results in a redshift for the

lowest optical transition Eg+ δXX.[10, 11, 14] This unoccupied low energy state gives rise to more

absorption, leading to an increase (induced absorption) of the ∆A signal. Induced absorption (IA) denotes the absorption of probe pulse photons by the sample after being excited by the pump. It is also called excited-state absorption. The occupied state at the band edge gives rise to less absorption, leading to a decline (bleach) of the ∆A signal.

As tpp increases, hot carrier relaxation takes place between 0 - 2 ps [14], in which the hot excitons

relax to the lowest energy state due to phonon emission, also called thermalisation. Due to the Pauli exclusion principle, no more than two excitons are allowed in the lowest energy state in these perovskites, which have two-fold degenerate conduction and valence band edges.[10] When the hot exciton relaxes, its electron fills the last free conduction band edge state and its hole fills the last free valence band edge state. This state-filling prevents IA, and the IA signal decays exponentially with a decay time tdecay. At the same time however, it produces an exponential rise in the bleaching signal

at the band gap with a rise-time tr. Therefore tr reflects tdecay.[16] The IA signal, the bleaching

signal and the resulting difference absorption spectra for different tpp are illustrated in figure 5b.

On a longer timescale, tpp < 200 ps, the biexcitons recombine via Auger recombination or

biexciton radiative emission. This decreases the number of occupied states in a sample and therefore also the bleaching signal. For tpp> 500 ps, the decrease of the number of occupied states is caused

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(a) (b)

Figure 5: (a) Exciton, hot exciton and biexciton dynamics in CsPbBr3 NCs. The IA signal is

redshifted by δXX compared to Eg. Figure modified from Aneesh et al. (2017)[14, 15, 17] (b)

The TA signals at different delay times after the pump pulse has excited the sample. The black shaded curve represents bleaching due to state filling, the blue shaded curve represents IA and the red shaded curve is the sum of the two and is therefore the observed negative difference absorption spectra. Figure modified from Yumoto et al. (2018)[14]

2 Methods

2.1 SB assembly

The synthesis of NCs and the subsequent assembly of the SBs with the oil-in-oil emulsion method were performed by dr. Yingying Tang.[9]

The SBs were self-assembled from NCs with the oil-in-oil emulsion method. They had an average size of 90 nm. The NCs composing the SBs had a diameter of 12 - 14 nm. The emulsion consisted of FC-40 oil and NC containing toluene with 008-FS as surfactant, as is illustrated in figure 6. By vortex mixing, oil-in-oil emulsion droplets were formed that provided a template for the spherical SLs (SBs), enforced by the interfacial tension. During the evaporation of the solvent, SLs assembled by crystallisation of the NCs inside the drying emulsion droplets. The SBs were stable for at least two months and exhibit long-range cubic ordering even though the morphology was spherical. Since the emulsion droplets were not monodisperse yet, neither was the SB size. A SB consisting of NCs produces novel properties.

2.2 Ultrafast TA setup

The ultrafast TA measurement was set up and performed by PhD students Deepika Poonia and Marco van der Laan at TU Delft under the supervision of prof. dr. Laurens D.A. Siebbeles.

The sample, a cuvette with a colloidal solution of SBs in FC-40, was placed inside an air-tight holder with two quartz windows on opposite sides to allow light beams to pass through. A fundamental beam was produced as 180 fs pulses with a 1028 nm wavelength at a 5 kHz frequency by a Yb:KGW oscillator (Light Conversion, Pharos SP). A fraction of the fundamental beam was split off and produced a probe spectrum (400 - 1600 nm) by supercontinuum generation in a sapphire crystal. However, most of the fundamental beam was optically amplified by an Optical Parametric Amplifier and underwent non-linear frequency mixing by a second harmonic module (Light Conversion, Or-pheus), transforming into the pump beam with a width of 180 fs and a tuneable wavelength between 310 - 1330 nm. The pump beam and the probe beam reached the same position at the sample with a

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Figure 6: Oil-in-oil emulsion of FC-40 and NC containing toluene with 008-FS as surfactant, before solvent evaporation.

Table 1: Pump energies and pump fluences used in the TA setup. Epump (eV) Pump fluences (µJ/cm2)

2.43 - 637 1095 2.76 127 637 1146 3.10 127 637 1146

relative angle of ∼ 8◦. The relative time difference tpp of the pump and the probe beam arrival was

adjusted by an automated delay-stage, see figure 4. Through a mechanical chopper, one in every two pump pulses arrived at the sample. The transmission of the probe pulse through the sample was detected by a CMOS detector (Ultrafast Systems, Helios). Then the differential absorption is defined as ∆A = ln _I pump Ino pump , (1)

where Ipump is the detected light of the probe pulse for the sample at time tpp after being exposed

to a pump pulse and Ino pump is the detected light of the probe pulse for the sample exposed to no

pump pulse, since it was chopped. The transmission of the pump beam through a pinhole of 1 mm radius was measured by a thermopile sensor (Coherent, PS190Q) which resulted in an estimate for the pump fluence. The gathered dataset contained ∆A(tpp, λ) values for pump-probe delay times

in the range -4 ps < tpp < 2.9 ns and probe wavelengths in the range 439 nm < λ < 914 nm (1.36

eV< E < 2.82 eV). The pump energies Epumpand pump fluences used in the TA setup are given in

table 1. The pump fluence is the total pump energy per pulse per cm2_.

2.3 Chirp correction

A two-dimensional contour plot displaying typical −∆A data as a function of energy E and time delay is shown in figure 7a. It shows that the arrival time of the pump varies per frequency. The chirp correction is a correction of the TA data for dispersion resulting in time delays between different frequencies. To perform the chirp correction, we chose sample points for which the arrival time

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of the pump tpp was equal to 0 ps on frequencies (energies) with a high peak |∆A(tpp, λ)|. The

signal-to-noise ratio is the highest for frequencies with a high peak ∆Amax:= ∆A(tpp,max, λ), since

∆Amax ∆Anoise

is the highest there. This means that for these frequencies it was the easiest to determine the arrival time of the pump, when tpp= 0 ps. It was possible to draw a line through the sample points which

indicates when tpp = 0 ps for all frequencies. To transform that into a horizontal line, the ∆A

dynamics were shifted per frequency to set the horizontal line exactly at 0 ps, as shown in figure 7b. The ∆A signal was then averaged over neighbouring frequency channels to show the ∆A dependence on time and frequency clearly. This halved the spectral solution, and thereby also the number of data points, but it made the IA signal, which has a relatively lower |∆A| than the bleaching signals, more distinguishable.

(a) (b)

Figure 7: An example of chirp correction on TA data. (a) The application of chirp correction in a two-dimensional contour plot of the −∆A spectra. The black line indicates the new time-zero line after the chirp correction. The four sample points setting the new time-zero line are shown in black crosses. (b) The TA data from (a), now chirp corrected and time corrected.

In order to minimise data loss, the original, non-chirp corrected data was chosen to be analysed after characteristic signals had been identified. The frequencies for these signals were picked from the data to be analysed like separate time series. The chirp correction is a time correction for all frequencies simultaneously and is therefore not necessary when analysing the rise or decay of the signal corresponding to one of the signal frequencies. A time correction was done per signal individually, therefore not losing any data like with a chirp correction. Signal which could be left out of the fit was the background signal. In order to achieve this, the average difference absorption for negative tpp was subtracted from −∆A in the entire time series. The background signal was

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2.4 TA analysis

2.4.1 Difference absorption dynamics

Applying equation 1, it is possible to describe the difference absorption dynamics. If the pump pulse creates unoccupied energy states which give rise to more absorption (IA), the portion of transmitted photons reaching the detector decreases and a negative −∆A signal is produced, since Ino pump is

higher than Ipump. On the contrary, occupied energy states give rise to less absorption (bleach) and

produce a positive −∆A signal. The number of occupied energy states is highest when the number of band edge excitons is highest, so as the number of excitons decreases with time, the bleaching signal diminishes as well. To characterise the time decay of −∆A for the signals, a multiexponential fit was performed per signal. To determine the time components of the exponential decay, −∆A was presented on a logarithmic scale. An exponential decay over a time interval is then given by a straight line in that time interval. In figure 8 this method is illustrated.

The non-radiative biexciton Auger recombination dominates the biexciton decay, which in turn dominates the total decay at the picosecond timescale.[12] Hot carrier relaxation is paired with the emission of phonons, which is also non-radiative. Thus, the fast decay component t1 is associated

with non-radiative decay. The slower component t2is associated with excitonic, and therefore mostly

radiative, decay. The data not covered by either line 1 or 2 at ∼ 400 ps in the example in figure 8 shows the transition between non-radiatively dominated decay and decay dominated by radiative emission. By changing tpp at the peak to tpp = 0 ps, it was possible to compare the amplitudes

of the components. The non-radiative amplitude A1 was expected to be larger than the radiative

amplitude A2 for high enough Epump and pump fluence, since those increase the density of hot

carriers and biexcitons.[13]

Figure 8: An example of -∆A dynamics, presenting the exponential decay as the sum of component line 1 with amplitude A1 and component line 2 with amplitude A2. The data between the lines at

∼ 400 ps is a composite of the two.

2.4.2 Fitting rise and decay

The life-times describing the decay of a bleaching signal, that is dependent on two life-time compo-nents t1and t2, is determined by performing a double exponential decay fit on −∆A for tpp > tpp,max.

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The decay fit is thus of the form −∆A = A1e −tpp−tpp,max t1 + A2e −tpp−tpp,max t2 , (2)

where tpp,maxis the start of the decay and A1and A2 are the amplitudes of the decay components.

To make an educated guess for A2 and t2, first a single exponential decay fit is performed on the

data for tpp> 200 ps. In that time frame, there is almost entirely only exciton decay.

The rise-time trdescribes the rise of the bleaching signal. The rise follows a negative exponential

decay curve from tpp = 0 ps until the peak and is therefore a mirrored life-time exponential decay

curve, which is shifted along the −∆A-axis by its peak value −∆Amax. The rise of the bleaching

signal can therefore be fitted using

−∆A = −∆Amax· (1 − e− tpp

tr _). ₍₃₎

An example of the bleaching signal over time is shown in figure 9, with the -∆A values during the rise displayed as black squares and its fit according to equation 3, displayed as a red line.

The decay-time tdecay describes the decay of the IA signal and reflects tr, as is described in

subsection 1.6. The decay function of the IA signal is therefore ∆A = ∆Amax· e

−tpp−tpp,max

tdecay _. ₍₄₎

Figure 9: An example of -∆A dynamics, showing the negative exponential decay fit of the rising −∆A. The black data points show the rise of the bleaching signal, the red line shows the fit.

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3 Results & Discussion

3.1 Spectral shape

A two-dimensional contour plot displaying the bleach signal, −∆A, as a function of energy E and time delay for a pump energy of 3.10 eV and a pump fluence of 1146 µJ/cm2_{is shown in figure 10a.}

Characteristic bleach (red) signals are observed at E = 2.46 eV and E = 2.39 eV. The former is due to occupation of the band edge energy levels by the pump pulse, leading to less absorption of the probe pulse photons. The latter is also due to occupation of the band edge energy levels, while its 2.46 − 2.39 ≈ 70 meV redshift indicates the possible presence of an ensemble of NCs within the SB which are coupled to each other. The redshift is a result of this NC-NC coupling. A bimodal spectrum, a difference absorption spectrum containing two bleaching signals, has been observed in neither 12 - 14 nm CsPbBr3perovskite NCs [11] nor bulk CsPbBr3perovskite [7]. These show only

a single bleaching signal for the band edge each, respectively near E = 2.46 eV and near E = 2.39 eV.

(a) (b)

Figure 10: (a) Two-dimensional contour plot of the −∆A spectra for a pump energy of 3.10 eV and a pump fluence of 1146 µJ/cm2_{. (b) Differential absorption spectrum for a pump energy of 3.10 eV}

and a pump fluence of 1146 µJ/cm2 _{at different t}

pp. The signal at E = 2.39 eV has an apparent

delay compared to the signal at E = 2.46 eV .

A possible explanation for the bimodal spectrum could be a bimodal distribution of the NCs. Two different ensembles of NCs, one in which the NCs are coupled, and one in which they are not coupled to each other, might have produced one bleaching signal each, respectively at E = 2.39 eV and at E = 2.46 eV. This would suggest the uncoupled ensemble produced more NC -like TA spectra while the coupled ensemble produced more SL-like or bulk-like TA spectra. The observed property is akin to SF, which, as mentioned in section 1, is a collective property of highly ordered SLs, with ensembles of NCs within the SL that are more alike coupling to form a SF signal.[5] While no Burham-Chiao ringing behaviour is observed, SF also creates two bleaching signals with a similar 70 meV energy difference between the two.

An IA signal is observed at E = 2.34 eV. This is due to the Coulomb interaction between the excitons produced by the pump and probe pulse, leading to more absorption of probe pulse photons at the unoccupied lower energy level. This is described in subsection 1.6.

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The −∆A spectra for different delay times for a pump energy of 3.10 eV and a pump fluence of 1146 µJ/cm2_{is shown in figure 10b. The IA and bleaching signals experienced an increasing redshift}

for increasing tpp, which is possibly due to carrier relaxation. The bleaching signal at E = 2.39 eV

appeared to be spectrally narrower than the one at E = 2.46 eV. This is due to NCs in the coupled ensemble being more alike, which resulted in a spectrally narrower bleaching signal, compared to those of the uncoupled ensemble.[18]

The bleaching signal at E = 2.39 eV and the IA signal are 2.39 − 2.34 ≈ 50 meV apart, which is comparable to the 48 meV found for bulk CsPbBr3.[7] Additionally, the IA signal has vanished at

tpp= 2.1 ps, at the same time that the bleaching signal at E = 2.39 eV has reached its peak. This

is because the IA signal also originated from the coupled ensemble.

The bleaching signal at E = 2.39 eV reached its peak at a later time than the bleaching signal at E = 2.46 eV. There are also two bleaching signals observed, and only one IA signal. This is possibly due to an overlap of two different signals, the bleaching signal of the coupled ensemble and an IA signal of the uncoupled ensemble. TA spectra from literature show one bleaching signal, and one IA signal at a 70 meV lower energy, for 8.6 nm CsPbBr3 NCs [7] and for 2D CsPbBr3 nanoplatelets.

[13] This supports the hypothesis that the NCs in the uncoupled ensemble also produce a bleaching signal and an IA signal, which are 2.46 − 2.39 ≈ 70 meV apart. An impression of this hypothesis, a two-dimensional contour plot displaying −∆A as a function of energy E and time delay with the schematically illustrated areas of the IA and bleaching signals of the coupled and uncoupled ensembles, is shown in figure 11. At E = 2.39 eV, the IA signal of the uncoupled ensembles and the bleaching signal of the coupled ensemble overlap, which could have produced the observed delay of the resulting bleaching signal.

In the two-dimensional contour plot displaying −∆A as a function of energy E and time delay for Epump = 2.43 eV, one bleaching signal is replaced by an additional IA signal over the whole

timescale at E = 2.43 eV. This was an effect of the energy of the pump, and this signal was ignored in the further analysis.

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Figure 11: Two-dimensional contour plot of the −∆A spectra for a pump energy of 3.10 eV and a pump fluence of 1146 µJ/cm2_. _{The schematically illustrated areas of the IA and absorption}

bleaching (AB) signals of the coupled ensemble (white contour lines) and the uncoupled ensemble (black contour lines) show an impression of the hypothesis. The IA signal of the uncoupled ensemble and the AB signal of the coupled ensemble overlap, creating an apparent delay of the bleaching signal at E = 2.39 eV.

3.2 Bleach rise-times and IA decay-times

The rise-time trof the bleaching signals at E = 2.39 eV (tr 2.39 eV) and E = 2.46 eV (tr 2.46 eV) and

the decay-time tdecay of the IA signal at E = 2.34 eV, found with fits using equation 3 and 4, as a

function of pump fluence for different pump energies are shown in figure 12a. tr and tdecay were of

the same order of magnitude, ∼ 102fs, which is the same as the width of the laser, 180 fs, producing the pump beam. The results could therefore only be compared in terms of their order of magnitude. Nevertheless, these values are similar to the values other articles found for CsPbBr3 NCs [10, 11]

and 2D CsPbBr3 nanoplatelets [13], which supports that tr reflects tdecay due to the hot carrier

relaxation, as is explained in subsection 1.6. Hot carrier relaxation in CsPbBr3 NCs occurs at a tpp

between 0 - 2 ps, which includes hot exciton relaxation [11, 14] by multiple channels.[19]

Overall, trand tdecaywere longer for Epump= 3.10 eV than for Epump= 2.43 eV by an average of

about twice the laser width. This is due to the relaxation time increasing with increasing Epump.[16]

However, tr 2.39 eV is smaller for Epump= 2.76 eV than for Epump = 2.43 eV. To explain this, the

−∆A dynamics were plotted. The −∆A dynamics at E = 2.34 eV (solid circles) and E = 2.39 eV (open circles) for different pump energies and a pump fluence of 127 µJ/cm2 _{are shown in figure 12b}

and for a pump fluence of fluence of 637 µJ/cm2 _{are shown in figure 12c. A kink in the curve of}

−∆A over time is observed in both figures for Epump= 2.76 eV. The cause of the kink was possibly

a measurement error, however due to the time scales being the same as the laser width’s, only qualitative estimates could be given on the actual rise-time tr for Epump= 2.76 eV. trat E = 2.39

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eV and at E = 2.46 eV are estimated with a fit for the rise starting at tppright after the kink to the

peak, not from tpp = 0 ps to the peak. Therefore the resulting tr values for Epump= 2.76 eV were

possibly shortened.

(a)

(b) (c)

Figure 12: (a) The rise-time tr of the bleaching signals at E = 2.39 eV and E = 2.46 eV and the

decay-time tdecay of the IA signal at E = 2.34 eV for different pump energies and pump fluences.

(b,c) Difference absorption dynamics for pump fluences of (b) 127 µJ/cm2 _{and (c) 637 µJ/cm}2

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3.3 Bleach life-times

A typical example of the decay of a bleaching signal at E = 2.39 eV, for Epump = 3.10 eV and

a pump fluence of 1146 µJ/cm2, is shown in figure 8. We clearly see the decay requires two time components. Thus, equation 2 is used as the fitting function. Applying this fitting procedure to all bleaching signals, we obtain the time components t1 and t2 as a function of pump fluence as shown

in figure 13.

For the bleaching signal at E = 2.46 eV, shown in figure 13a, t2 is ∼ 103 ps, which is assigned

to excitonic decay due to its match with the band gap of NCs in figure 2b. t1 is of a ∼ 102 ps

magnitude. This is in the biexciton life-time range, which is built up of non-radiative biexciton Auger recombination and radiative biexciton decay. The life-times assigned to these processes are, as mentioned in subsection 1.4, respectively 20 - 100 ps and one fourth of the radiative exciton decay. Comparing t1 to t2, it is concluded that the biexciton recombination is dominated by non-radiative

Auger recombination.

For the bleaching signal at E = 2.39 eV, shown in figure 13b, t2 is ∼ 103 ps, similar to t2 for

the bleaching signal at E = 2.46 eV, and it is also assigned to excitonic decay due to its match with the band gap found in an ultraviolet measurement on the same SBs.[9] The presence of two exciton signals in a TA spectrum of CsPbBr3 perovskite has not been observed before and it supports the

bimodal distribution of the NCs which is explained in subsection 3.1. t2 is longer at E = 2.39

eV than at E = 2.46 eV and seems to shorten for higher pump fluences. This indicates possibly slower exciton decay at E = 2.39 eV and an increase in non-radiative exciton decay for higher pump fluences, which could be assigned to the SB structure.

For the bleaching signal at E = 2.39 eV, t1ranges from 5.6 ± 0.7 · 102fs to 3.8 ± 0.7 · 102ps, which

is a factor 1000 fluctuation. It shows no decrease for an increasing pump fluence, which means it is not the radiative SF decay time component tSF. Something akin to SF might still have occurred

in the SBs. t1 could still partly be due to non-radiative Auger recombination [15], but the large

fluctuation suggests that multiple decay channels contribute to this time component. Even though no third life-time component t3 was found at E = 2.39 eV, it is concluded that t1 at E = 2.39 eV

represents a more complex signal than t1at E = 2.46eV . This supports the presence of a second IA

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(a) (b)

Figure 13: The short and the long time component, respectively t1 and t2, of the decay of the

bleaching signals at (a) E = 2.46 eV and (b) E = 2.39 eV as a function of pump fluence for different pump energies.

3.4 Discussion

The number of NCs observed outside the SBs was low compared to the number of NCs inside the SBs. Even though there might have been some NCs together outside the SBs, it is assumed that both bleaching signals were produced from within the SB. The coupled and the uncoupled ensemble are therefore thought to be situated in the SB.

In figure 3, it appears that some highly ordered SLs might be misaligned with other SLs in order to form the SB. Typically, high ordering and little defects are observed within SLs.[4] However, its spherical morphology might led to misalignments between SLs in the SBs. This might have resulted in a bimodal distribution of larger structured SL and aggregates of smaller SL. The latter has been observed, in a PL measurement, to produce a ∼ 80 meV redshift relative to isolated SLs with clean surfaces.[18] This redshift is a combination of two effects: ∼ 30 meV for the merging of some NCs into bulk and > 50 meV for self-absorption of emitted photons within the sample. The redshift due to merging of the NCs can be dismissed since that has not been observed inside the SBs.[9] The redshift due to self-absorption is solely dependent on the density.[20] This effect can thus also be dismissed, since inside the SB the densities are similar, due to the cubic SL structure. However, SBs might still produce an observable self-absorption redshift compared to NCs.

The bleaching signal at E = 2.39 eV appeared to be spectrally narrower than the one at E = 2.46 eV. However, given the large overlap of the signals, a double Lorentzian fit to determine the full width at half maximum (FWHM) of both has not been attempted. The size distribution of the NCs

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used, 12 - 14 nm, could have decreased the degree of order in the SBs and which affects the NC density of the SBs and possibly spectrally broadens TA signals. The use of monodisperse NCs in SBs could have increased the ratio of coupled/uncoupled NCs if that created the bimodal TA spectra.

The observed slower exciton decay for the coupled ensemble was possibly a result of increased electron and hole movement, which could be tested in TA measurement on SBs with a higher conductivity. The higher conductivity could be achieved by exchanging the ligands surrounding the NCs for different ligands.

The wide t1 range at E = 2.39 eV, from 0.6 ps to 380 ps, could indicate its more complicated

nature due to the overlap of the bleaching and the possible extra IA signal. TA measurement on CsPbBr3perovskite NCs before their assembly into SBs could provide a way to subtract overlapping

signals from the TA spectrum of the SBs.

The assignment of t1and t2to the different exciton and biexciton decay processes can be verified

by an additional TA measurement for lower pump fluences, on the order of 101_µJ/cm2_{or lower, to}

obtain only the single exciton signal.[21] The pump fluences that could be used have been estimated to be 5 µJ/cm2_{for E}

pump= 3.10 eV, 9 µJ/cm2for Epump= 2.76 eV and 13 µJ/cm2for Epump= 2.43

eV. By subtracting the low pump fluence TA spectra from the high fluence TA spectra, this would make it possible to isolate multiexciton signal at early delay times tpp≤ 100 ps. This could identify

the photoelectric behaviour originating solely from the SB structure. The hot exciton and hot biexciton signal could also be separated by subtracting the different components of the hot carriers, provided the same values for Epumpas the ones in this research are used.

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4 Conclusion

In conclusion, a TA spectroscopy analysis was performed on self-assembled ∼ 90 nm CsPbBr3

perovskite SLs with a spherical morphology (SBs) through which two bleaching signals were observed. It is hypothesised that one signal is produced through uncoupled NCs and the other through coupled NCs in the SBs. The coupled NCs possibly produced a ∼ 70 meV redshift in the band gap energy due to a combination of electronic coupling and bulk-like behaviour.

In order to evaluate this hypothesis a future experiment could include TA measurements on CsPbBr3 perovskite NCs before their assembly into SBs to compare their characteristic signal.

Additionally, TA measurements for lower pump fluences could be performed to subtract multiexciton signals. This could provide more insights into the photoelectronic behaviour of SBs.

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Ultrafast transient absorption spectroscopy analysis of CsPbBr3 perovskite superlattices