energy and charge transfer cascade in methylammonium lead ... · b. link the time constant(s) for...

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SupportingInformation

Energy and Charge Transfer Cascade in Methylammonium Lead Bromide Perovskite Nanoparticle Aggregates

Marine E. F. Bouduban, Andrés Burgos-Caminal, Rachele Ossola, Joël Teuscher, and Jacques-E. Moser*

Photochemical Dynamics Group, Institute of Chemical Sciences & Engineering, and Lausanne Centre for Ultrafast Science (LACUS), École polytechnique fédérale de Lausanne, CH-1015 Lausanne, Switzerland *E-mail : je.moser@epfl.ch S1. ComplementtoFigure2:Transientabsorptionspectrum

Fig. S1 displays the transient absorption spectra obtained upon laser pulsed excitation of the colloid at lex = 480 nm. Data for lex = 390 nm excitation are provided by Fig. 2 in the main text. The oscillatory feature observed in Fig. 2 for lobs < 500 nm is much weaker here and overlaps with a stronger positive absorbance change peaking at lobs = 438 nm.

Fig.S1 Transient absorbance spectra for lex= 480 nm and time delays rangingfromt=2psto1820ps.Red:t=2ps,purple:20ps,blue:50ps,green:500ps,andyellow:1820ps.

Electronic Supplementary Material (ESI) for Chemical Science.This journal is © The Royal Society of Chemistry 2017

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S2. ComplementtoFigure3:Spectraldataanddynamics

Fig. 3 appearing in the main text aims at supporting the hypothesis of interactions between perovskite nanostructures. In this respect, we present two global fits arising from multi-exponential fitting of datasets obtained with lex = 390 nm and lex = 480 nm, respectively. Fig. S2 features the corresponding spectral data and biexponential kinetic fits to support the accuracy of the global fits.

Fig.S2 Examples of global fit results. A) lex = 480 nm (markers) fitted with abiexponential kinetic equation (bold lines). Red : lobs= 430 nm, pink: 450 nm,purple:460nm,blue:500nm,turquoise:520nm,green:530nm,yellow:540nm,andorange:560nm.B)lex=390nm(markers)fittedwithatriexponentialfunction(boldlines).Red:lobs=420nm,pink:430nm,purple:450nm,blue:470nm,green:490nm,turquoise:480nm,yellow:520nm,darkred:540nm,orange:530nm,anddarkpink:580nm.

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S2. Fittingofkineticequations

Dynamic traces were fitted with multi-exponential functions, convoluted with a Gaussian instrument response function (IRF) when needed. Datasets reported in Figs 3A and 3B span a time window between t = 1 ps and 1880 ps. As a consequence, no convolution with the IRF was needed (Gaussian IRF with FWHM = 90 fs for lex=480 nm, FWHM =200 fs for lex=390 nm).

a) Bi-exponentialfunction:

(S1)

b) Tri-exponentialfunction:

(S2)

Ultrafast photoemission data (Fig. 4B) were fitted with a tri-exponential functionconvolutedwithaGaussianIRFwithFWHM=200fs(lex=390nm:1

(S3)

where µ representsthetime-originoftheIRFandsitswidth,with .

TCSPCdynamicsdidnotneedtobedeconvolutedforinstrumentresponsefunctionandwerefittedwithaasimpletri-exponentialfunction:

(S4)

ΔA(λ, t) = A0 + A1(λ) ⋅exp –tτ1

⎛⎝⎜

⎞⎠⎟

+ A2 (λ) ⋅exp –tτ 2

⎛⎝⎜

⎞⎠⎟

ΔA(λ, t) = A0 + A1(λ) ⋅exp –tτ1

⎛⎝⎜

⎞⎠⎟

+ A2 (λ) ⋅exp –tτ 2

⎛⎝⎜

⎞⎠⎟

+ A3(λ) ⋅exp –tτ 3

⎛⎝⎜

⎞⎠⎟

ΔA(λ, t) = 12

yi (λ)i=1

3

∑ ⋅exp µ – tτ i

+ 12

στ i

⎛⎝⎜

⎞⎠⎟

2⎡

⎣⎢⎢

⎤

⎦⎥⎥⋅ 1+ erf

t – µ + σ2

τ i

⎛⎝⎜

⎞⎠⎟

2 ⋅ σ

⎧

⎨⎪⎪

⎩⎪⎪

⎫

⎬⎪⎪

⎭⎪⎪

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

FWHM = 2σ ⋅ 2 ⋅ ln2

I(t) = a ⋅exp –tτ1

⎛⎝⎜

⎞⎠⎟

+ b ⋅exp –tτ 2

⎛⎝⎜

⎞⎠⎟

+ c ⋅exp –tτ 3

⎛⎝⎜

⎞⎠⎟

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S3. Globalfittingprocedure

Global fits of transient absorbancedatahavebeenused in thiswork to assess thepresenceof interstructure interactions.Acomprehensivereviewofglobalanalysiscanbefoundelsewhere,1andanillustrationoftheparticularcaseoftransientabsorptionspectracanbefoundinreference2.

To perform a global fit, datamust first be sampled, and an appropriate number ofkinetictracesmustbeextracted.Then,thepointistoapplyakineticmodel,usuallymulti-exponential,whereallthetracesareforcedtoevolvewiththesametimeconstant(s).Thisyieldsthefollowingpointbypointprocedure:

1) Extractionofkinetictracesevery10nm,betweenlobs=420and600nm.2) Individualfittingofafewsampledtracestoobtain(i)anaccuratefittingequation

and(ii)agoodinitialguessfortheglobalfit(fasterconvergence).3) Performingoftheglobalfit:

a. Selectthebestfittingfunction(fromstep2).b. Linkthetimeconstant(s)forallthekinetictracesincluded.c. Fillupfittingcoefficientsforeachtraceaccordingtotheguessesobtained

instep2.d. Performfitwithareasonablenumberofiterations(typically40):

i. Ifconvergenceisreached:assessfitqualitywiththecalculatedresiduals.

ii. Ifconvergenceisnotreached:readjustinitialguessesandrepeat.4) Extractionoftheamplitudecoefficient(s)foreachtraceintonewsetsofdata

(onesetpercoefficient,ie.perexponential).Inourcase:A1andA2forlex=480nmandA1,A2andA3forlex=390nm.

5) Plottingoftheconstitutedamplitudedatasetsversuswavelengths.

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S4. Electroabsorptioncontributiontotransientspectra

The oscillatory feature observed in the transient absorption spectra below 500 nm(Fig. 2) is believed to be due to a photoinduced electroabsorption effect. Separation ofphotogenerated carrier pairs localized in perovskite nanoparticles indeed submits thematerial contained between an electron and a hole to an electric field that affects itsabsorptionspectrum.Theabsorbancechangeataparticularwavelengthcanbeshowntobequadratic in the field intensity, in accordance with the Stark or Franz-Keldysh-Aspnestheories.3

The analysis of the spectral shape of the electroabsorption feature allows to drawimportantconclusionsonthekindofcarrierpairsattheoriginoftheeffect.Intheframeoftheperturbationtheory,thedifferentialelectroabsorption(EA)signalcanbedescribedbytheperturbativeexpansioninthefield:4

(S5)

whereA(l)istheabsorbanceatthewavelengthl,Etheappliedelectricfield,andm0kandp0k respectively the change in the permanent dipole moment and the change in thepolarizabilityuponthetransitionofinterest(0→k).Notethatthefirstterm(linearinthefield)isexpectedtocanceloutforanisotropicmaterial,suchastheperovskitecontainedinourcolloidalsuspensions.

AsitclearlyemergesfromEq.S5,theelectroabsorptionsignalcanbedecomposedinalinearcombinationoffirstandsecondderivativesofthelinearabsorptionspectrumA(l).Thesecondandthirdtermsoftheexpansionarequadraticinthefieldanddonotcanceloutinanisotropicmaterial.Theamplitudeofthesecondderivativecontributionisprovidedbythe change inpermanentdipolemomentm0k of thematerial and is adirectprobeof thepresenceofCTexcitonsamongthephotogeneratedspecies.

Fig. S3A displays the linear absorption spectrum of a suspension of CH3NH3PbBr3nanoparticle aggregates, along with its calculated first and second derivatives. A linearcombinationofbothcontributionsS(l)definedbyEq.S6,whichconstitutesabestfitofthetransientabsorptionspectrumrecordedatatimedelayof2ps(Fig.S3B),isalsoplottedonthesamegraph.

(S6)

ΔA(λ) = – ∂A(λ)∂λ

⋅m0k ⋅E – 12⋅ ∂A(λ)

∂λ⋅ p0k ⋅E

2 + 12⋅ ∂

2A(λ)∂λ 2 ⋅m0k

2 ⋅E2 + ...

S(λ) = 1⋅ ∂A(λ)∂λ

+ 10 ⋅ ∂2A(λ)∂λ 2

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The overwhelming contribution of the second derivative, whose amplitude is tentimelargerthanthatofthefirstderivative(Eq.S6),showsthatapermanentdipolechangem0k caused by the electronic transition is dominant. This provides an evidence for thepresenceofalargenumberofCTexcitons2psafterpulsedphotoexcitationofthesample.

Fig.S3 A)LinearabsorptionspectrumofCH3NH3PbBr3nanoparticles(blackline).Theredlinerepresentsa linearcombination(Eq.S6)ofthecalculatedfirstderivative(darkgrey line)andsecond derivative (light grey line) of the absorption spectrum. B)The transient absorptionspectrummeasuredatatimedelayof2ps(blackline,λex=390nm,energyfluence=9µJcm–2)isbestfittedwiththedifferentialspectrumcalculatedwithEq.S6(redline).

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S5. Photoemissionquenchingbydonorsinsolution–Stern-Volmerplots

Fig.S4 SchematizedmolecularstructuresofthedonormoleculesN,N,N,N-tetrakis-(4-methoxyphenyl)benzidine(MeO-TPD)and1,4-bis(diphenylamino)benzene(BDB).

The intensity of the photoemission of colloidal solutions of perovskite nanoparticles was measured for increasing concentrations of the donor molecules MeO-TPD and BDB. The photoemission is observed to be quenched efficiently for donor concentrations in the solution of the order of 10–4 mol L–1. Figure S5 displays Stern-Volmer plots where the ratio I0 / I of the intensity measured without and with the quencher present is plotted versus the quencher’s concentration in solution.

Fig.S5 Stern-Volmer plots for chlorobenzene solutions of CH3NH3PbBr3nanoparticlesinpresenceoftwodifferentquenchers(lem=520nm):MeO-TPD(A)andBDB(B).

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Stern-Volmer plots obtained for the two redox quenchers display a linear portion at low concentrations. A significant deviation from the linearity and saturation of the quenching efficiency, however, is observed for [MeO-TPD] > 10–4 M and [BDB] > 3×10–4 M.

The slopes of the initial linear parts of the plots (Fig. S4) are estimated from a linear regression over the first points and yield values of the Stern-Volmer constant KSV. This constant is defined as KSV = kq · t0, where kq is the second order rate constant of the quenching process and t0 the photoemission lifetime in the absence of quencher.

Table1 Stern-Volmer constants and quenching rate constants extracted fromStern-Volmerplots(Fig.S5).Avaluet0≃10–6sprovidedbyTCSPCmeasurementsisconsideredforthephotoemissionlifetime.

KSV/L·mol–1 kq/Lmol–1s–1MeO-TPD 6.3×104±3.3·103 6×1010BDB 5.3×104±3.2·103 5×1010

Approximate kq values extracted from the Stern-Volmer plots appear to be larger than the

second order rate constant for diffusion between capped nanoparticle aggregates and donor molecules in solution, which approximate value is estimated in our case at kdiff ≃ 109 L mol–1 s–1. This therefore indicates that the quenching processes involving CH3NH3PbBr3 nanoparticles takes place with donor molecules associated within the organic capping layer of the perovskite. This conclusion is also compatible with the observation of the saturation of the quenching process that, by comparison with the case of large MeO-TPD molecules, intervenes at higher concentrations for smaller BDB molecules.

A pseudo-first order reaction rate constant kq’ for electron transfer from a redox quencher, which concentration [Q] is considered practically constant during the reaction, to the perovskite valence band could be defined by kq’ = kq · [Q]. From the maximum concentration values observed within the linear portions [MeO-TPD] = 10–4 M and [BDB] = 3×10–4 M, one then derives kq = 6×106 s–1 and kq = 1.7×107 s–1, which corresponds to time constants t = 1/ kq of the order of 170 ns and 60 ns for the two donors MeO-TPD and BDB, respectively.

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