Ultrafast Exciton Dynamics in Colloidal CsPbBr3 Perovskite

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Ultrafast Exciton Dynamics in Colloidal CsPbBr Perovskite Nanocrystals: Bi-Exciton Effect and Auger Recombination Janardhanakurup Aneesh, Abhishek Swarnkar, Vikash Kumar Ravi, Rituraj Sharma, Angshuman Nag, and Kumaran Nair Valsala Devi Adarsh J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b00762 • Publication Date (Web): 10 Feb 2017 Downloaded from http://pubs.acs.org on February 12, 2017

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The Journal of Physical Chemistry

Ultrafast Exciton Dynamics in Colloidal CsPbBr3 Perovskite Nanocrystals: Bi-exciton Effect and Auger Recombination J. Aneesh,1 Abhishek Swarnkar,2 Vikash Kumar Ravi,2 Rituraj Sharma,1 Angshuman Nag,2,* and K. V. Adarsh1,* 1

Department of Physics, Indian Institute of Science Education and Research (IISER), Bhopal 462066, India.

2

Department of Chemistry, Indian Institute of Science Education and Research (IISER), Pune 411008, India.

Abstract: Exciton many body interactions is the fundamental light–matter interaction which determines the optical response of the new class of colloidal perovskite nanocrystals of the general formula CsPbX3 [X = Cl or Br or I]. However, the understanding of exciton many body interactions manifested through the transient bi-excitonic Stark effect at the early time scales and the Auger recombination process in this new class of materials still remain rather incomplete. In this article, we studied the many body exciton interactions under controlled conditions through ultrafast transient absorption spectroscopy. A large bi-excitonic redshift ∼30 meV to the effect of hot excitations on the excitonic resonance is observed at the early timescales. From the fluence dependent studies, it is evident that the samples have only single and bi-exciton lifetimes suggesting that the band edges are two-fold degenerate. This explicit experimental evidence for the exciton many-body interactions in CsPbBr3 nanocrystals provides a powerful tool to explore the development of their prospective applications in light emitting devices, lasers, and solar cells. *Author to whom correspondence should be addressed: [email protected], [email protected]

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Introduction Organic-inorganic lead halide perovskites such as APbX3 [A = CH3NH3, and X = Br or I] exhibit exceptionally low trap density (1010 per cubic centimeter) even when prepared at a temperature as low as room temperature.1,2 This defect-free nature of APbX3 is one of the key reasons for having high diffusion length (~ 10 µm) and long lifetime (~2 µs) of charge carriers, which eventually leads to the high efficiency of solar cells fabricated using a cost-effective solution processed method.1,3 The highest certified solar cell efficiency achieved so far employing such perovskites is 21%.4 Motivated by the success of bulk and thin films, colloidal nanocrystals of APbX3 (A = CH3NH3 and Cs) were prepared recently.5-7 Subsequently, multiple reports appeared in an attempt to understand and control size, shape and composition of APbX3.8-10 Interestingly, in spite of having the large surface to volume ratio, colloidal CsPbBr3 nanocrystals exhibited nearly ideal (90 %) photoluminescence (PL) quantum yield,7 along with reduced PL blinking,11 and high carrier mobility (~4500 cm2V-1s-1) within a nanocrystal (measured using THz spectroscopy),12 suggesting near-absence of non-radiative trap states. This nearly trap-free nature of CsPbBr3 nanocrystals can be explained by their electronic band structure with the unusual anti-bonding character of valence band maximum, and large spin-orbit coupling influencing the conduction band minimum.13,14 In last one year, colloidal CsPbBr3 nanocrystals have been used for energy-efficient light emitting diodes,15 solar cells,16 gain media for laser,17 photodetector18 and single photon emitters19 for quantum information technology. All these experimental and computational results suggest that colloidal CsPbBr3 nanocrystals are intrinsically different than the popular II-VI and III-V quantum dots, and have the potential to outperform these well-studied quantum dots for optoelectronic applications in the visible region.


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Such optoelectronic applications strongly rely on the Coulomb bound electron–hole pairs known as excitons. These excitonic quasi-particles have a pronounced role in their absorption and emission spectra. Therefore, understanding the impact of exciton many body interactions is of crucial importance since they significantly impact the optoelectronic properties. As for example, the many body exciton interactions manifested as the bi-excitonic Auger recombination,20,21 a non-radiative recombination channel in which the exciton transfers its energy to a third particle that is re-excited to higher energy state, hampers the PL efficiency. The fast relaxation of excitons resulting from Auger recombination instills a major complication for applications in light emitting diodes and solar cells because the exciton energy is lost in the form of heat. Although, CsPbBr3 nanocrystals provide strong light–matter coupling and extremely efﬁcient Coulomb interactions when the average number of excitons per nanocrystal is more than one, however, the exciton dynamics in this regime remain unexplored. From the theoretical point of view, this approach offers a new degree of freedom to probe the many body exciton interactions under controlled conditions. In this article, we studied the many body exciton interactions under controlled conditions through ultrafast transient absorption spectroscopy. Our results primarily reveal two types of many body interactions in CsPbBr3 nanocrystals: (1) Biexciton Stark effect exerted by the excitons produced by the pump and probe beams, and (2) The Auger recombination process for band edge carriers at sufficiently high excitation fluence. The remarkable effects in our nanocrystals occur at room temperature and also at ambient conditions are highly advantageous for potential applications. Experimental Section CsPbBr3 nanocrystals were prepared following ref.7 after minor modifications. Details of synthesis methodology is given in the supporting information (SI). Powder x-ray diffraction


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(PXRD) patterns were recorded using a Bruker D8 Advance x-ray diffractometer using Cu Kα radiation (1.54 Å). Transmission electron microscopy (TEM) studies were carried out using a JEOL JEM 2100 F field emission transmission electron microscope at 200 kV. Photoluminescence (PL) and time correlated single photon counting (TCSPC) PL decay measurements were carried out using FLS 980 (Edinburgh Instruments). Nanocrystal dispersion in toluene is used for all spectroscopic investigations reported here. Sub-picosecond exciton dynamics in CsPbBr3 nanocrystals were investigated by the spectrally resolved ultrafast transient absorption (TA) spectroscopy. 120 fs pulses with a central wavelength of 800 nm from a Spectra physics Spitfire amplifier is used for these studies. The pulses with a repetition rate of 1 kHz is sent to a second harmonic crystal for the generation of the 400 nm pump beam which is separated from the 800 nm fundamental beam with the help of a dichroic beam splitter. After sending through a computer-controlled delay stage, the 800 nm beam is passed through a CaF2 plate for the generation of the white light continuum probe beam, which is constantly rotated throughout the experiment to avoid any photo damage. The pump and probe beams were spatially overlapped on the sample, and the change in absorbance of the probe beam, ∆A = - (log[Iex/I0]) , was determined, where Iex and I0 were the transmitted intensities of sequential probe pulses after a delay time ∆t following excitation by the pump beam, and in the ground (in dark) state, respectively. The sample holder is rotated throughout the experiment for minimizing any optical damage to the sample. The pump intensity is varied so as to get different number of excitons per nanocrystal. Details of data analysis, including Chirp Correction (Figure S1 of SI) are given in SI.


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Results and Discussion Structural and Optical Characterization. PXRD pattern in Figure S2 of SI shows CsPbBr3 nanocrystals exhibit orthorhombic structure similar to earlier reports.11,22 TEM image in Figure 1a shows that CsPbBr3 nanocrystals have cubic morphology with an average edge length of 11 nm. To investigate the optical properties, we used UV-visible absorption and PL spectroscopy. Optical absorption of the CsPbBr3 nanocrystals dispersed in toluene shown in Figure 1b displays a sharp excitonic step like absorption with a direct bandgap at 2.45 eV. We observe a strong and narrow (full width at half maximum ~ 110 meV) excitonic PL peak at 2.4 eV (Figure 1b), which exhibit a Stokes shift of ∼50 meV from the corresponding excitonic absorption, in agreement with the previous results.15,17 To quantitatively analyze the exciton dynamics, we need to know the area and width of the exciton transition, which can be calculated from the absorption spectrum. To elucidate detailed information on the exciton absorption, we have deconvoluted the absorption spectrum.23 The resultant of the deconvoluted spectrum shown in Figure S3 of SI, matches with the experimental spectrum. Sub-Picosecond Exciton Dynamics in CsPbBr3 Nanocrystals. In our experiments, the sample was excited with 120 fs pulses centered at 400 nm corresponding to the energy higher than the bandgap of the sample. The pump beam induced change in the absorbance of the probe beam in the wavelength range 440– 600 nm was recorded. We have recorded the TA spectrum at a low pump fluence that corresponds to the average number of excitons per nanocrystal =0.04, which is calculated from the following equation = φ0σ0

(1)

where, φ0 and σ0 are the pump fluence represented by the number of photons/cm2 and the absorption cross section of the nanocrystal at the pump wavelength (400 nm) respectively. The


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value of σ0 was found to be ~2.1 × 10-14 cm2 at 400 nm (3.1 eV) following the method discussed in ref. 24 and agrees with σ0 values reported in ref. 25-26 TA of CsPbBr3 nanocrystals immediately following the pump beam excitation is shown in Figure 1c. The most prominent features of the TA spectrum are the following. (1) After pump beam excitation, we ﬁnd that the absorption feature corresponds to the exciton resonance completely disappears and is replaced by a pronounced bleaching. (2) The shape of the early time ((∆t) ≤ 1 ps) TA spectrum looks like an asymmetric derivative feature centered near the exciton peak. (3) A redshift in the exciton transition at the early times, which is consistent with the attractive interaction between the excitons generated by the pump and probe beams known as the Stark effect due to bi-exciton Coulomb interactions.23,27 After ∆t > 1 ps, the derivative feature in the TA spectrum disappears completely and shows a very strong bleach signal at the exciton transition. Further a small induced absorption can also be seen in the higher energy side of the bleach region which can be attributed to the shift produced in the higher transition levels of the nanocrystal. 28, 29 To understand the origin of the asymmetric derivative feature present only for ∆t ≤ 1 ps shown in Figure 1c, we turn to the predictions of the well developed and extensively applied many body theory for exciton interactions in nanocrystals. At these early times, TA spectra are similar to the second derivative of the absorption spectrum (Figure S4 in SI), which is consistent with the bi-excitonic Stark effect.20,30 In this regime, the Coulomb interaction between the excitons, redshift the exciton resonance and is manifested in the TA spectrum as the bleaching signal at the positions of the first resonant exciton absorption and an induced absorption in the longer wavelength regions. At this stage, we assume that the contribution from the state filling to the band edge signals are insignificant, since the low energy states remain unoccupied until this time. With the increase in ∆t, excited carriers relax into low energy states of the band edges and


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lead to the state filling,31,32 (inversion of the carrier population near the band edge compared to ∆t = 0). This contributes to the bleaching via Pauli blocking33 and, more importantly, induced absorption is replaced by strong band edge bleach. A schematic representation of the processes involved in early time TA is presented in the Figure 2a. To obtain the magnitude of the redshift induced by the bi-excitonic Stark effect at the early times, we carried out the global fitting of TA, by using the Gaussian parameters of the exciton transition calculated from the optical absorption. To model the derivative feature of the TA, we assumed that in the presence of hot excitons by the pump beam, the transition energies of the probe excitons is reduced by δxx, where δxx is the redshift in energy due to the exciton - exciton interactions. Then, the TA at each pump-probe delay can be written as the difference between the exciton centered at x1-δxx (probe exciton) and the exciton centered at x1 (pump exciton) in the following way

TA( x, dt ) = A1e e −  

x − x1 − δ xx

2

 − A e −  x − x1   1g w1  w1  

2

(2)

where TA (x, dt) and A are the TA at the delay time dt and amplitude of the resonant exciton transition respectively. The subscripts e and g refers excited and ground states respectively. The solid lines in Figure 2b show the representative fits at selected ∆t using Eq. 2. To verify the δxx values obtained (30 ±5 meV) by the spectral shift is indeed correct, we have calculated the δxx from the amplitudes of the TA.34 The following equations can describe the early time derivative feature of the TA and the later time bleaching signal due to the state filling when the excited carriers relax into low energy states of the band edges

∆A(∆t < 1 ps) = A

δ xx (2 X − δ xx w) [(2 X − δ xx w) 2 + 1]( X 2 + 1)

(3)


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X 2 − 1 − 2( X − δ xx w) 2 A ∆A(∆t > 1 ps ) = ( ) 2 [(2 X − δ w) 2 + 1]( X 2 + 1)

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(4)

xx

where A is the absorption amplitude and X =

(h ω − E e )

w

. Ee and w are the exciton energy and

half width measured from the optical absorption. From the best fit to the early time derivative and late time bleaching features of TA shown in Figure S5 in SI, we have estimated the value of δxx = 35 ±4 meV. The value is comparable with that determined by using equation 2 (30 ±5 meV). In the next step, we have numerically simulated the ratio of the amplitudes of the early time absorption (Am) and later bleaching (Bm) maxima from Eq. 3 and 4 as a function of δxx and is shown in Figure 2c. The details can be found Figure S6 in SI. From Figure 2c, we can see that Am/Bm is a direct function of δxx. Using the experimentally calculated Am/Bm ≈ 0.5 ratio from the TA spectrum shown in Figure 3, we have determined the value of δxx = 31 meV using Figure 2c. The early time band edge absorption of the of the TA spectrum at 2.39 eV is eventually replaced by a strong bleaching at 2.44 eV due to the state filling when the excited carriers relax into low energy states of the band edges. We have utilized this characteristic feature of the early time TA to estimate the intraband cooling time of the excited carriers.32 To determine the intraband cooling time, we have fitted the decay of band edge absorption feature at 2.39 eV using a single exponential function with a decay constant (intraband cooling time) 0.41 ± 0.04 ps. As time grows to 1 ps, this absorption feature at 2.39 eV is faded by the increased bleaching signal resulting from the state filling by the cooling of the excited state carriers. Therefore, the intraband cooling time can also be determined from its decay. Expectedly, the decay time constant (= 0.45 ± 0.02 ps) of the buildup of the band edge bleach (Figure 3), also validate the assignment to intraband cooling time.


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Average number of excitons per nanocrystal, early time absorbance and redshift. To provide a consistent picture of the bi-excitonic spectral redshift and the early time absorbance, we have varied the average number of exciton per nanocrystal () from 0.04 to 28.5 by increasing the pump fluence. The Transient absorption contour plot for different pump fluence (different ) is shown in Figure S7 in SI, and the temporal evolution of the induced absorption and bleach signal for different pump fluence is shown in Figure 4. From these figures and the analysis discussed in the previous section, we can conclude that the magnitude of the redshift is independent of the pump beam fluence. This hallmark observation clearly indicates that the redshift comes from the many body interactions between the excitons generated by the pump and probe beams. To establish an exact relationship between the magnitude of TA and , we have analyzed the pump beam dependence of the exciton bleach using Poisson distribution. In this context, we have defined P(N,t) the probability to have N excitons in a selected nanocrystal at time t as N −< N > P ( N ) = < N > exp

N!

(5)

where is the average number of excitons per nanocrystal. Then we can define the normalized TA bleach at 2.45 eV at a time t0 immediately after the intraband relaxation and before the Auger recombination as

∆A(t0 ) / A = 0.5 P(1, to ) + [1 − P(0, t0 ) − P(1, t0 )]

(6)

Here the fraction 0.5 coming from the fractional bleach of the 2-fold degenerate band edges of the CsPbBr3 nanocrystals.25-26 From Eq. 5 the probabilities corresponding to no exciton and single exciton per nanocrystal is given by P(0,t0)=exp(-) and P(1,t0)= exp(-) respectively. Now from Eq. 6, the early time normalized TA can be modelled as


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∆A(t0 ) / A = 1-(1+0.5)exp(-)

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(7)

Figure 5a shows the plot of ∆A(t0)/A as a function of the at a delay time 3 ps, which very well fit to the Eq. 7. Furthermore, this analysis clearly confirms the 2-fold degeneracy of the CsPbBr3 nanocrystals. By fitting the data, we can accurately determine the initial number of exciton density in the nanocrystals. At long delay time tL=600 ps after Auger recombination is finished and only one exciton remains in the nanocrystal i.e., there will be no nanocrystals with more than one exciton, we can define the amplitude of the transient bleach at 2.45 eV using Poisson distribution as ∆A(t L ) / A = 0.5[1 − P(0, t L )] =0.5(1-exp-)

(8)

Figure 5b shows the plot of ∆A(tL)/A as a function of the at a delay time of 600 ps, which exactly fit to the Eq. 8. Importantly, ∆A(tL)/A is equal to that predicted by the Poisson distribution. Auger recombination in CsPbBr3 nanocrystals. To examine the reversibility of the TA after intraband cooling, we now turn our attention to the many body interactions of the band edge carriers. For nanocrystals, sufficiently high excitation fluences lead to the recombination of the excitons by non-radiative Auger recombination process.34 To make an estimation of the Auger recombination, we have compared TA decay curves of different pump fluence. For this, we first normalized the decay curves so as to match their long term decay values. The normalization procedure is based on the assumption that at sufficiently long ∆t, there is only a single exciton left in each nanocrystal and consequently, the Auger recombination is negligible. After that, we have used the simple subtractive procedure25 to determine the bi- exciton Auger recombination decay constant. Here we have subtracted the TA of > 0.04 from the trace recorded for > 1, and decay traces are given in Figure 6a. It can be seen that a single exponential decay fits


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well to all curves with the same time constant, which yields the bi-exciton Auger recombination decay constant of 34 ± 2 ps. This pump fluence independent time constant for very low to high fluence clearly shows that the CsPbBr3 nanocrystals have only bi-exciton lifetime and any other multiple exciton lifetimes are absent. This observation reconfirms our earlier observation that the band edge states are 2-fold degenerate. Dynamics of single exciton bleach. After calculating the bi-exciton Auger recombination decay constant, we have analyzed the recovery kinetics of the single exciton bleach signal. In this context, we have selected the exciton bleach maximum at 2.44 eV for the lowest excitation fluence that corresponds to = 0.04 (Auger recombination is negligible). The experimental data can be fitted with a single exponential function with decay constant 4.4 ± 0.2 ns (Figure 6b). The decay constant value is matching with the PL lifetime (~4.8 ns) obtained from the PL decay dynamics shown in Figure. S8 in SI.

Conclusions The excited state carrier dynamics of the colloidal CsPbBr3 nanocrystals have been studied by the femtosecond TA spectroscopy. A clear signature of exciton-exciton interaction of attractive nature (Bi-exciton formation) is detected in the earlier time (< 1 ps). The hot carrier cooling is estimated to have a time constant of ~ 0.45 ps from the buildup of the band edge bleach and the decay kinetics of the absorption features. We demonstrate that the key changes in the optical response observed by the multi excitons injection at high fluence shows the evidence of Auger recombination process. Importantly, we observe that CsPbBr3 nanocrystals have only two decay constant (single exciton and bi-exciton Auger recombination) even at high fluence


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indicating that the band edges are 2-fold degenerate. Interestingly, the observed changes are transient and reversible in nature, and the material completely recovers to its initial optical response. We provide explicit experimental evidence for the exciton many body interactions in CsPbBr3 nanocrystals and envision that our findings provide a powerful tool to explore the development of their prospective applications in light emitting devices, lasers, and solar cells.

Supporting Information (SI): See SI for details of sample preparation, femtosecond transient absorption data analysis, XRD, deconvoluted optical absorption spectra, derivation of transient absorption, and PL life time data.

Acknowledgments The authors thank Department of Science and Technology (Project no: SR/S2/LOP-003/2010) and Council of Scientific and Industrial Research, India, (grant No. 03(1250)/12/EMR-II) for financial support. A.N. acknowledges Science and Engineering Research Board (SERB) for Ramanujan Fellowship (SR/S2/RJN-61/2012). A.S. and V.K.R. acknowledges to IISER Pune for fellowships.

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Figure 1. (a) TEM image of CsPbBr3 nanocrystals. (b) Optical absorption (violet circles) and PL (solid cyan line) spectra of CsPbBr3 nanocrystals. Red solid line is the theoretical fit (details in SI). (c) TA at selected pump probe delays.


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Figure 2. (a) Schematics showing the exciton dynamics and the origin of the TA at the early time scales. The bottom panel shows the representative absorption profiles, where AGr and AEx are the ground state absorption (without pump) and excited state absorption (with pump) respectively (b) TA spectra at different delay times and the solid lines are the global fit using Eq.


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2. (c) Am/Bm as a function of δxx calculated using the Eq. 3 and 4. The dotted line gives the estimation of δxx= 31 meV from the experimentally determined Am/Bm=0.5.

Figure 3. The kinetic traces showing the correlation between the early time absorption at 2.39 eV and bleach at 2.44 eV. The solid lines represent single exponential fit, which gives the intraband cooling time of 0.45± 0.02 ps.


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Figure 4. Kinetic traces of CsPbBr3 nanocrystals for (a) bleach maxima at 2.44 eV and (b) induced absorption maxima at 2.39 eV for values from 0.04 to 28.5.


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Figure 5. Plot of ∆A(t0)/A as a function of the (a) at early time scale of 3 ps. (b) at longer time scale of 600 ps (after Auger recombination).


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Figure 6. (a) Pump fluence dependent decay kinetics of bleach signal after subtracting the low pump intensity (=0.04) from the higher pump fluence ( >1). (b) Decay of bleach signal for very low pump fluence ( = 0.04). The solid lines indicate the single exponential fit to the data.


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Ultrafast Exciton Dynamics in Colloidal CsPbBr3 Perovskite

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