ultrafast spectroscopy of hybrid lead-halide perovskites · able band gap and low costs of...

Universita degli Studi di Cagliari

Facolta di ScienzeCorso di Laurea Magistrale in Fisica

Ultrafast spectroscopy of hybridlead-halide perovskites

Relatore:Prof. Michele Saba

Candidato:Matteo Lodde

Anno Accademico: 2018-2019

Nissunaumanainvestigazionesipuòdimandareverascienza;s’essanonpassaperlemattematichedimostrazioni;esetudiraichelescienze,cheprincipianoefiniscononellamente,abbianoverità,questononsiconcede,masiniegapermolteragioni.Eprimacheintalidiscorsimentalinonaccadeesperienza,senzalaqualenulladàdisécertezza.

LeonardoDaVinci

Introduction

Oursociety needs access to cheap and abundant sources of energy tomeetthe demand of a steadily increasing population. As a matter of fact,

global energy consumption increases year by year. Since more than 80% ofthe world’s energy requirement is being supplied by the combustion of oil,coal and natural gas, CO2 emissions rose 1.7% last year and hit a new record.1

These emissions cause global warming due to the strengthening of the green-house effect and have deleterious effects on our environment. Due to indus-trialisation this trend is expected to increase. The global population is ex-pected to reach 9.6 billion by 2050 and the total energy consumption to beabout 28 TW. Although these numbers are subject to large fluctuations, theypoint out a solid truth: energy demand will keep growing.

Another well-founded evidence is that fossil fuels (which represent the mainenergy source) are doomed to end, although there are different studies withconflicting results about the year in which all the available reserves are ex-pected be used. The question of alternatives to fossil fuels is thus a hot onefor this century. Among the many possible solutions, the large scale conver-sion of solar energy plays a big role.

The average power provided by Sun is four order of magnitude larger thanthe global energy consumption. For this reason, solar light represents by farthe most abundant renewable energy source in our planet. It is well knownthat solar power is a clean energy sourcewith very low environmental impact.Nevertheless, nowadays less than 4% of the global energy mix is produced byphotovoltaics. This is due to the high cost of solar panels, their low efficiencyand the issues of the energy storage. In order to overcome these problems andmake photovoltaics a valid and reliable alternative to fossil fuels, fundamentalresearch is of paramount importance.

i

Introduction

In the last few years, materials known as perovskites have come to the atten-tion of the scientific community for their unique properties, including highabsorption coefficient, broad absorption spectrum, high charge-carrier mo-bilities which leads to efficient charge transport, long diffusion lengths, tun-able band gap and low costs of fabrication.2 Thanks to this, perovskites canefficiently be used to create a lot of different optoelectronic devices, such assolar cells, light-emitting diodes, lasers, photodetectors and so on.

Nowadays scientist of all around the world are investing a great deal of effortto stabilize thesematerials and improve evenmore their efficiency in order toincrease their competitiveness against traditional inorganic semiconductor- based devices. Despite all the results that have been achieved lately, somephotophysical mechanisms in perovskites are still unknown.

This work focuses on the behaviour of charge-carriers in organic-inorganiclead halide perovskites. The optoelectronic properties of such materials havebeen investigated using ultrafast spectroscopy techniques. Particularly, withtime-resolvedphotoluminescence the diffusion length of the carriers has beenestimated to bemuch larger thanother organicmaterials used in photovoltaics.Using a pump-probe setup, the transient absorption was measured. Fromthese results it has been discovered that, despite perovskites being an intrin-sic semiconductor with comparable effective mass for electrons and holes,there is a different behaviour of the two carriers affecting the absorption ofthematerial. This could be due to selective traps for holes inside the bandgap,or even other more complicated phenomena, that have yet to be investigated.

Contents

1 Perovskites 11.1 The perovskite structure . . . . . . . . . . . . . . . . . . . 11.2 Hybrid lead-halide perovskites . . . . . . . . . . . . . . . . 31.3 Optoelectronic properties . . . . . . . . . . . . . . . . . . . 41.4 Samples preparation . . . . . . . . . . . . . . . . . . . . . . 7

2 Experimental setup 132.1 Ultrafast spectroscopy . . . . . . . . . . . . . . . . . . . . . 132.2 Pump-probe spectroscopy . . . . . . . . . . . . . . . . . . . 162.3 Time-resolved photoluminescence . . . . . . . . . . . . . . 192.4 X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Experimental data 233.1 Photoluminescence . . . . . . . . . . . . . . . . . . . . . . 243.2 Time-resolved photoluminescence . . . . . . . . . . . . . . 253.3 Transient absorption spectroscopy . . . . . . . . . . . . . . 313.4 XRD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 Conclusions 37

iii

1Perovskites

This chapter is meant to describe some properties of metal-halide per-ovskites. Particular emphasis will be placed on the optoelectronic prop-

erties which are the core of this work.

1.1 The perovskite structureThe word perovskitewas first used to describe the crystal structure of mineralcalcium titanate (CaTiO3), discovered by Gustav Rose in the Ural Mountainsin 1839 and named in honour of Russian Count Lev A. Perovski.3 Nowa-days, the term perovskite refers to hundreds of differentmaterials which havea multitude of properties including insulating, antiferromagnetic, piezoelec-tric, thermoelectric, semiconducting, conducting, and even superconducting.They all have in common just the crystal structure, which is the same of cal-cium titanate.4

All perovskites have the general chemical formula close to or derived fromthe composition ABX3, in which A and B are cations with different sizes andX is an anion. Typically, the B cation is a metal and with the anion forms acorner-sharing BX6 octahedra, with the A cation occupying a 12-fold coor-dination site formed in the middle of the cube of eight such octahedra.5 The

1

2 CHAPTER 1. PEROVSKITES

ideal crystal structure is cubic withPm3m space group, shown in Figure 1.1.Nevertheless ideal cubic perovskite structure is not very common and alsothe mineral perovskite itself is slightly distorted. These materials may adopta structure with lower symmetry such as tetragonal or orthorhombic becauseof geometry constraints, pressure or temperature.6

Figure 1.1. Crystal structure of cubic perovskite.

In order to evaluate the structure of perovskites, two factors are widely used,known as Goldschmidt tolerance factor and octahedral factor.

Goldschmidt’s tolerance factor In 1927 Goldschmidt proposed a toler-ance factor, defined as:

t =rA + rXp2(rB + rX)

(1.1)

where rA, rB and rX stand for the ionic radii of the A, B and X ions, respec-tively which allow us to estimate the degree of distortion.7 Since it is basedon ionic radii, it can formally be applied only for purely ionic bondings. Inspite of that, it is often used even for not purely ionic compounds. Moreover,this factor does not provide a comprehensive information about the struc-ture, because it does not take into account the phases transitions which occurwhen pressure and temperature vary. Almost all known stable perovskiteshave tolerance factors between 0.76 and 1.13.8

Octahedral factor Goldschmidt’s tolerance factor t by itself is not sufficientto predict the formation, or not, of the perovskite structure. For this reason,

3

the octahedral factor, defined as

µ =rBrX

(1.2)

(the notation is the same as the previous equation) was introduced.8 This fac-tor ranges between 0.4 and 0.9 for stable perovskites.

1.2 Hybrid lead-halide perovskitesThis work deals with the study of hybrid lead halide perovskites, which appearvery promising for their application in photovoltaic and optoelectronic de-vices such as LEDs. The general chemical formula of these materials is ABX3,in which A is an organic compound or a mix of two organic compounds, B islead and X is a halide atom, typically bromine, iodine, chlorine or a mix.

Originally, the most common organic cation was methylammonium (fromnow on noted asMA) with chemical formula CH3NH+

3 . Several studies havebeen conducted with MAPbI3 perovskites pointing out that, in spite of greatefficiency, these materials suffer from high instability if exposed to UV lightor high temperature. Lately, in order to overcome this instability, formami-dinium (FA) – whose chemical formula is CH(NH2)+2 – has been used eitherpure or mixed with MA.9

Figure 1.2. Ball-and-stickmolecularmodel ofmethylammoniumand formamidinium.

One of the most important features of hybrid halide perovskites is the possi-bility of tuning the band gap of thematerial over a very broad spectrum (from400 nm to over 1100 nm inwavelength), by changing the cationic and anioniccomponents in the structure. The organic cation does not play a major rolein determining the band structure in perovskites, therefore the bandgap ismainly given by the halide atom.


1.3 Optoelectronic propertiesIn the last years, perovskites, have come to the attention of the scientific com-munity for their unique properties, includinghigh absorption coefficient, broadabsorption spectrum, high charge-carrier mobilities which leads to efficientcharge transport, long diffusion lengths, tunable band gap and low costs offabrication.

Light absorptionThe light absorption of a material can be evaluated by its absorption coef-ficient ↵. The absorption coefficient of hybrid lead halide perovskites thinfilm is in the order of 105 cm�1 in the visible region10, as shown in the plot inFigure 1.3.

400 500 600 700 800Wavelength (nm)

0

0.5

1

1.5

2

2.5

(cm

-1)

105

Figure 1.3. Absorption coefficient as a function of the wavelength. Data refers to athin film layers of MAPbI3 with a thickness of 67nm. For larger thicknesses themeasure saturates under 500 nm due to the complete absorption of light.

Due to Lambert-Beer’s law, the intensity of light through a material is givenby:

I = I0 exp(�↵x) (1.3)

in which I0 is the intensity of the incident light and x is the thickness of thematerial. According to this law, it’s easy to conclude that ⇠ 100% of visiblelight is absorbed within 300 nm of penetration.

5

The high absorption coefficient (which is at least one or two order of magni-tude larger than the silicon one in the visible range) allows to build very thinabsorption layers for solar cells, resulting in better carriers collection and -obviously - lower prices for the final device.

Photoexcitation dynamicsThe exciton binding energies for metal halide perovskites are much largerthan thermal energy. (⇠ 2 � 3kBT ). In spite of that, it has been proved thatfree carriers represent the largemajority of photoexcitations.11 As amatter offact, simply comparing the binding and thermal energies is not the right ap-proach for two-particle states (free charges) coupled to single-particle boundstates (excitons), and leads to order-of-magnitudewrong estimates of the ratiobetween the density of free carriers (ncar) and the density of excitons (nexc).A correct evaluation can be obtained using the Saha’s equation:

n2car

nexc=

✓µexckBT

2⇡~2

◆3/2

exp

✓� Eb

kBT

◆(1.4)

in which µexc and Eb are the exciton effective mass and binding energy, re-spectively. The Saha’s statistics takes into account that the probability of anelectron and hole to be uncorrelated scales as the joint density of the two par-ticles (which is the square of the density of either electron density of holedensity for an undoped material, as perovskites are) whereas the probabil-ity to find an exciton (i.e. an bounded state of electron and hole) scales lin-early as nex. At room temperature, for a exciton binding energy lower than100 meV and a maximum carrier density of 1016 cm�3 (which is a reasonableupper bound carrier density achievable under solar light illumination), theSaha’s equation gives n2

car � nexc which means that perovskites behave as“free-carriers” semiconductors, with unbound electrons and holes being thedominant photoexcitations.

What has just been discussed can be proved determining how the intensity ofthe photoluminescence of the samples scales with the laser pulse fluence. Theplot shown in figure 1.4 shows a quadratic dependence between the PL0 (i.e.the photoluminescence emitted in a short temporal window of a few tens ofpicoseconds following a femtosecond laser excitation), and the optically in-jected carriers. This is what we expect to see for a bimolecular recombinationof free electrons and holes.


Figure 1.4. Photoluminescence emission intensity estimated at time t = 0 after excita-tion (PL0) as a function of laser pulse fluence. The quadratic dependence is shownby the dotted lines as a guide for eyes. Relative values for the two materials arearbitrary.11

Charge-carrier recombinationThe charge-carrier recombination dynamics is of paramount importance foroptoelectronic devices. In general, three different recombination processesmay occur, so the recombination rate is given by:

dndt

= �k1n� k2n2 � k3n

3 (1.5)

inwhich k1, k2 and k3 are themonomolecular, bimolecular andAuger recom-bination rate, respectively.12

The decay process can be investigated using an impulsive optical excitationwhich instantaneously creates a density n0 of carriers, that then decay ac-cording to Equation 1.5. At low laser pulse fluence, the linear term in Equa-tion 1.5 is dominant, therefore the decay rate is exponential. This is due tothe monomolecular recombination (also known as Shockley-Reed recombi-nation), which can occur when either electrons or holes recombine singularlydue to the presence of traps. For this reason the monomolecular coefficientis given by:

k1 = ptntrap (1.6)

in which pt is the probability for an electron (or hole) to be trapped, and ntrap

7

is the density of traps.

Increasing the injected carriers in the material, the decay rate become faster,due to the increasing of free electrons-holes recombination. Solving the dif-ferential equation taking into account just the first two terms (which is knownas Bernoulli’s equation), it follows that the carrier density is given by:

n(t) =n0k1

(k1 + n0k2) ek1t � n0k2(1.7)

using the boundary condition n(t = 0) = n0.

For a very high laser pulse fluence the decay time is steeper due to the Augerrecombination, which is a three particle recombination process, thereforescales as the cube of the carrier density. In the case of lead-halide perovskites,this recombination can be neglected for carriers injection density lower than1018 cm�3.13

BandgapAn interesting property which has already been mentioned in this chapter isthe tunability of perovskites’ bandgap, which can vary in a very broad rangefrom 400 nm to 1100 nm in wavelength, by changing the combination of thecationic and anionic components in the structure.14,15 Particularly, it has beenproved that replacing the halide anion leads to great shifts in the bandgap,while small changes can be achieved replacing the organic cation.

The bandgap of organic lead halide perovskites is shown in Figure 1.5.

1.4 Samples preparationAs mentioned before, this work deals with the analysis of hybrid lead-halideperovskites, withmethylammoniumand/or formamidiniumas organic cation.These perovskites are described by the chemical formulaMA1�yFAyPbIxBr3�x,in which x can vary in the range 0-3 and y between 0 and 1.

All the samples were synthesised as thin film layers with a thickness lowerthan 500nm, on a glass substrate. Since perovskites react very quickly withmoisture and oxygen, all the synthesis has to be done inside an inert atmo-sphere glove-box. After the synthesis the samples were coated in such a wayto protect them from the air and to avoid changing their optical properties.


350 450 550 650 750 850Wavelength (nm)

MAPbI3-xBrx

MAPbCl3 MAPbI3

FAPbI3MAPbBr3-xClx

MAPbBr3

Figure 1.5. Bandgap of organic lead halide perovskites.

In order to study the behaviour of electron and holes and decouple their dy-namics, three different coating layers have been used for each kind of per-ovskite. The first one is poly(methyl 2-methylpropenoate), known as PMMA orplexiglass, which is an inertmaterial, used just to protect perovskites from theair. The other coating layer is Phenyl-C61-butyric acid methyl ester, known asPCBM,which is widely used as electron transport layer (ETL) in organic solarcells. The last coating layer is 2,2’,7,7’-Tetrakis-(N,N-di-4-methoxyphenylamino)-9,9’-spirobifluorene (also known as spiro-OMeTAD), commonly used as holetransport layer (HTL). Therefore for each type of perovskite three differentsamples were prepared, whose structure shown in Figure 1.6.

Perovskite

Glass

PMMA

Perovskite

Glass

PMCB

Perovskite

Glass

SPIRO OMeTAD

Figure 1.6. Schematic drawings representing the structure of the samples synthesisedusing the spin-coating technique. The thickness of the perovskite layer is around300 nm.

Spin coatingAll the samples were synthesised using a technique called spin coating, thatallows to produce very thin and uniform layers. This technique is extremelysimple and reliable, since it just consists in the deposition of few drops of a

9

solution (precursor) on the substrate and then make it spin for few tens ofseconds at a very high speed. Thanks to the centrifuge force, the precur-sor is uniformly spread all over the substrate. Since the solvents are usuallyvery volatile, they evaporate very quickly, during the spinning. The processis shown in Figure 1.7.

Figure 1.7. Schematic drawing of the main steps in spin coating.

The final thickness of the substrate depends on several parameters, e.g. thespeed of the spinning, the time it takes to the solvent to dry and the concen-tration of the solution.

Substrate preparationAll the samples are made using a glass substrate, which are subjected to apreparation process that cleans the surface in order to make the depositionmore efficient.

Firstly the glass is cut in such a way to create a rectangle of around 1 cm2.Then it is put in a beaker with soap and water and washed using an ultrasoniccleaner for 20 minutes at 40�C. After this rough cleaning, it has to be rinsedand cleaned using acetone and IPA. These solvents can be let evaporated usingpure air.

The final step is made using an oxygen plasma asher. This instrument usesa low pressure oxygen plasma to break apart high molecular weight surfacecontaminants (due to the UV light that is produced). Moreover the oxygenspecies created in the plasma (O+

2 , O�2 , O3, O,O+, O�, ionised ozone,metastable

excited oxygen, and free electrons) react with organic contaminants to formwater, carbon monoxide, carbon dioxide, and lower molecular weight hy-drocarbons. These compounds have relatively high vapour pressures and areevacuated from the chamber during processing16.


The result of all these processes is a glass substrate with a clean surface.

MA1�yFAyPbIxBr3�x: two solutions methodMA1�yFAyPbIxBr3�x was firstly synthesised using a two solutions method.A solution (S1) was made using 0.136 mmol of PbBr2 and 0.75 mmol of PbI2in 1 mL of DMF. This solution was heated to 60�C for 30 minutes in order tolet the solutes dissolve. Another solution (S2) of 75 mg of FABr and 190 mgin 6 mL of IPA was made heating to 40�C.

Three drops of S1 solution were deposited in the glass substrate which wasspun at 6000 rpm for 30 seconds. Then it was heated to 80�C for 10 minutes.

A boat was filled with the S2 solution and the hot sample was dipped in it for5 minutes. Then the sample was spun at 6000 rmp for 30 seconds. In orderto let all the solvents dry, the sample was heated to 100�C for one hour.

After this process the perovskite should be ready. So itwas cooled and cleanedpouring IPA while making it spin. Finally it was heated to 100�C for 30 min-utes to let the IPA dry.

MA1�yFAyPbI3: one-pot methodAnother method used to synthesise metal lead-halide perovskites is to put allthe precursor in the same solution. MA1�yFAyPbI3 was synthesised using0.075 mmol of FAI, 0.375 mmol of MAI and 0.15 mmol of PbI2 in 0.5 mL ofDMF. The quantities of solutes are chosen in such a way that the molar ratiobetweenMAI and FAI is 5 and that the molar ratio of FAI+MAI and PbI2 is 3.

The solution can be heated up to 40-50�C to increase the dissolution of PbI2,then few drops are put on the substrate and sample is spun for 30 seconds at6000 rpm. In order to let the solvent dry, the sample was heated to 100�C forone hour.

MAPbI3The solution used to synthesiseMAPbI3 was composed by 0.45mmol ofMAIand 0.15 mmol of PbI2 in 0.5 mL of DMF. In order to increase the dissolutionof solutes, the solution can be heated up to 60�C and unlike theMAPbBr3, thedeposition can be done using the hot solution.

11

Three drops of the solution were placed on the glass substrate and then it wasspun for 60 seconds at 6000 rpm. Finally the sample was heated up to 100�Cfor 60 minutes.

2Experimental setup

This chapter focuses on the description of the experimental techniquesthat have been used in this work. Particularly, we will concentrate more

on pump-probe spectroscopy and time-resolved photoluminescence whichare the main techniques used in this study.

2.1 Ultrafast spectroscopyThe core of the experimental setup is represented by the light source, an ul-trafast laser which is used to excite the system and also to measure its opticalproperties. The laser characteristics are described in the following sections,as well as the background theory that explains themain phenomena exploitedin the setup.

LaserThe laser sourcewhichwas used is the Libra systemmanufactured byCoherent.It is an all-in-one ultrafast oscillator and regenerative amplifier that producespulses of less than 100 fs duration, a wavelength of 790 nm and with energieslarger than 1 mJ at a 1 kHz repetition rate.17

13

14 CHAPTER 2. EXPERIMENTAL SETUP

This system is a multi-pass amplifier that uses a single Ti:sapphire laser rod.The principle of regenerative amplification is to confine, by polarization, asingle pulse (selected from a mode-locked train) in a cavity, amplify it usingchirpedpulse amplification to an appropriate energy level (the gain is typicallygreater than 106), then cavity dump the output.

In order to achieve the inversion of population in the Ti:sapphire rod, it hasto be optically excited by a pulse from pump laser. In this setup a Evolution-15laser is used, which is a diode-pumped second harmonic Q-switchedNd:YLFlaser. Operating at 527 nm and a 1 kHz repetition rate, it delivers approxi-mately 10 W of pump power to the amplifier module.

TheCoherent Vitesse serves as the seed laser for the Libra system. This moduleincludes a continuous wave diode-pumped green laser (Coherent Verdi) alongwith amode-lockedTi:Sapphire oscillator. TheVitesse output is characterizedby a fixed centrewavelength of 800 nm, pulsewidths below 100 fs, and outputpower in excess of 200 mW at a repetition rate of 80 MHz.

Chirped Pulse AmplificationChirped pulse amplification is a technique for amplifying an ultrashort laserpulse up to the PW, overcoming the problem of self-focusing that could dam-age the gain medium when using intensities of GW/cm2.18

This technique consists of temporally stretch a laser pulsewith a pulse stretcherto increase its pulsewidth by asmuch as 104 times - thus significantly reducingits fluence. Then, this low fluence seed pulse can be injected into the regenera-tive amplifier and the pulse energy increases by up to a factor of 106. Follow-ing amplification, the pulse is ejected and recompressed to near its originalduration. These steps are shown in Figure 2.1.

The core of this system is represented by the pulse stretcher and the pulsecompressor, whosemechanisms is quite simple to describe. Theyuse a diffrac-tion grating in order to disperse all the frequencies in the laser beam, then theoptical path is designed in such a way to let the redder components travel alonger path with respect to the bluer components (or vice versa). Obviously,the pulse compressor is essentially the reverse of the stretcher.

A stretched signal is called positively chirped since the stretcher device intro-duces a positive group velocity dispersion, whereas a compressed signal is

15

Figure 2.1. Schematic drawing representing the main steps used in chirped pulse am-plification. Image adapted from19.

negatively chirped.

Optical Parametric AmplifierAs described in the beginning of this section, the laser source creates veryshort pulses with a wavelength of 800nm. The energy of these photons isnot enough to pump our samples with a single photon process, therefore it isnecessary to tune the beam’s wavelength so that the photon energy would belarger than the band gap of the samples. In order to do that an optical para-metric amplifier (OPA) was used.

In the first stage of an OPA, the laser beam (called pump) with frequency !p

is downshifted into two beams with frequency !s and !i which are knownrespectively as signal and idler. A constraints to the energy of signal and idleris given by the conservation of energy !p = !i + !s.

This effect is achieved using a non-linear crystal. The wavelengths of thesignal and idler are determined by the phase matching condition, which ischanged by the angle between the incident pump laser ray and the optical axesof the crystal. This means that signal’s wavelength can be tuned just turningthe crystal using a stepper motor. In the special case when !s = !i we havethe exact reverse of the second-harmonic generation, which is called degener-ate parametric amplification.

After the signal has been produced, the OPA will amplify it, using again non-linear processes in crystals. A pump photon excites the system to a virtualenergy level, whose decay is stimulated by a signal photon. Therefore anotherphoton is emittedwith the same direction, energy and phase of the signal one.

Since we are interested in a monochromatic beam, the idler is filtered and


only the signal can escape the OPA. Due to the conservation of energy, it fol-lows that it is impossible to obtain a signal with a wavelength lower than thepump. This can be outcome doubling the signal using second-harmonic gen-eration.

The OPA which was used to carry on the experiments described in this workis the TOPAS-800 made by Light conversion which can work from 240 nm to2600 nm.

2.2 Pump-probe spectroscopyThe term pump-probe refers to an ultrafast spectroscopy technique, very use-ful to study excited states and their dynamics in a semiconductor. In this kindof experiments an ultrashort laser pulse is split into two portions: a strongerbeam (known as pump) used to excite the sample and a weaker beam (knownas probe) used to monitor the pump-induced changes in the optical constants,such as reflectivity or transmission.

The pump-probe setup used in this work aims to measure the differentialtransmission of the samples, defined as:

�T

Tdef=

Tex � T0

T0(2.1)

in which Tex stands for the transmittance of the sample after optical excita-tion and T0 is the transmittance of the sample before the optical excitation.According to Lambert-Beer’s law (see equation 1.3) the differential transmis-sion can be written as:

�T

T=

�I

I(2.2)

which ensures that the differential transmission can be computed just usingthe intensities of the probe.

Light-matter interactionLight-matter interaction leads to three main phenomena that can be mea-sured with a pump-probe setup, which are represented in Figure 2.2.

Photobleaching The first one is known as photobleaching. Pump absorptionexcites electrons to the conduction band, decreasing the population of elec-

17

A

Ground state

Excited state

ProbeX

B

Ground state

Excited state

Probe S. E.

C

Ground state

Excited state 1

Probe

Excited state 2

Figure 2.2. Schematic drawing representing photobleaching (A), stimulated emission(B) and photoinduced absorption (C).

trons in the valence band, and filling states in the conduction band. Thereforethe sample absorption decreases, and the differential transmission increases.For this phenomenon, a peak can be observed in the differential transmissionplot just after the pump strikes the sample.

Stimulated emission The probe can create a stimulated emission in the sam-ple which leads to an increasing of photons with the same direction, wave-length and phases with respect to those which create the probe beam, and are- thus - indistinguishable. For this reason, stimulated emission increases thedifferential transmission.

Photoinduced absorption The last phenomenon is photoinduced absorption.It consists of absorption of the probe pulse, resulting in excitation of electronsfrom an excited state to another excited state. Since this transition was notavailable before the excitation, the differential transmission is negative.

Practical implementationBoth the pump and probe are usually obtained from the same laser beam,which is splitted into two path. The two trains of pulses, for the pump andthe probe, are shifted in time, one with respect to the other, using a delay line,i.e. increasing the optical path of the probe beam. The path can be changedusing a set of sliding mirrors whose position is controlled by a brushless mo-tor, in such a way to scan a range of time from 0.1 to 8000 ps, which should besmaller than the time separation between two pulses. The pump probe delayis fixed during each data point acquisition.


The detector time-integrates the signal transmitted, on a very slow time scale,many orders of magnitude longer than the pulse width. Therefore, the timeresolution does not depend on the time-resolved detection but just on thetime correlation between pulses. Being r the repetition rate of the laser, thelongest delay one can investigate is given by the time separation between twopulses, which is 1/r.20

The transmittance of the sample in the ground stateT0 canbemeasured block-ing one out of two pump pulses with a chopper. This halves the effective rep-etition rate to r/2.

Both the pump and probe beams should be focused on the same spot, in orderto achieve space overlap. It is advisable to use a pump spot larger then theprobe one, to assure overlap evenwhen the pumppulseswander a bit in space,for instance, because of imperfect delay stage.

The probe pulse should in principle be a small and negligible perturbation, toavoid changing the optoelectronic properties of the sample, hence it shouldhave a much smaller intensity than the pump. As a probe, it is very useful touse a supercontinuum white, in order to obtain the differential transmissionalong all the visible spectrum. This can be obtained exploiting the non-linearproperties of sapphire crystal.

A 3D representation of the experimental setup is shown in Figure 2.3.

Figure 2.3. Representation of the experimental setup used for the pump-probe mea-surements.

19

2.3 Time-resolved photoluminescenceThe term time-resolved photoluminescence (TRPL) refers to the study of ra-diative recombinationprocesses that occur inmaterials on time scales as shortas pico to nano seconds.

In order to achieve such timescales a very short laser pulse is needed to excitethe sample. Since the techniques used to obtain a very short laser pulse havealready been discussed, this section focuses on the description of the streakcamera (which is the core of a TRPL setup), and the description of the setup.

Streak cameraThe streak camera is an ultra high-speed detector which captures light emis-sion phenomena occurring in extremely short time periods. The operatingprinciple is shown in Figure 2.4.

Figure 2.4. Operating principle of a streak camera. Image from the booklet “Guide tostreak cameras”21.

In a streak camera the light beingmeasured passes through a slit and strikes toa photocathode, inwhich photons are “converted” into electrons. The numberof electrons is proportional to the number of photons. The electrons are thenaccelerated passing through a pair of accelerating electrodes and bombardedagainst a phosphor screen.

A set of deflection plates (sweep plates) apply a linearly increasing voltagewhile the electrons travel between them. In this way electrons path is changedaccording to the time onwhich they are created by the photocathode. Finally,electrons strikes to a phosphor screen. The light emitted by this screen is cap-tured by a CCD camera.


Practical implementationA 3D representation of the experimental setup is shown in Figure 2.5. The

Figure 2.5. Representation of the experimental setup used for the time-resolved pho-toluminescence.

laser source and the optical parametric amplifier are the same used for thepump-probe measurement. In this setup the light beam strikes to the sampleforming an angle of 20� with respect to the normal of the surface.

In order to collect only the photoluminescence light, a high-pass filter is usedto select the photoluminescence and absorb the scattered laser light.

2.4 X-ray diffractionX-ray diffraction (XRD) is a technique used for determining the atomic andmolecular structure of a single crystal, powder or thin film layer, in which thecrystalline structure causes a beam of incident X-rays to diffract into manyspecific directions22.

21

Bragg’s lawTheworkingprinciple ofXRD is basedon theBragg’s law22. When amonochro-matic beam of X-rays (this phenomenon works with whatever electromag-netic wave or particle, like neutrons, whose wavelength has the same order ofmagnitude of the lattice parameter) impacts on a crystal, a diffraction patternis formed.

This scattering process can be explained using either a classic or a quantumtreatment.

In the first case, we can explain the diffraction patter of the X-ray beam justconsidering the reflection in the surface of the crystal and on the other planesthat form the crystal, as shown in Figure 2.6.

Figure 2.6. Diagram that represent the reflection of theX-ray in the surface of the crys-tal and in the following plane.

The constructive interference condition can be achieved when

2d sin(✓) = n� (2.3)

in which d is the distance between two crystals planes, ✓ is the angle betweenthe incident beam and the crystal plane and � is the electromagnetic wave-length.

Using quantummechanics, this phenomenon can be seen from another pointof view. Each family of planes of the direct lattice is linkedwith a vector in thereciprocal lattice (i.e. a vector in the k-space). In a crystal there are only a finitenumber of planes, therefore even the vectors in the k-space are finite. Thismeans that in each elastic collision between a photon and a crystal ion, onlysome momenta can be transferred. It follows that the scattering process is


possible only when the difference between the scattered photon momentumand the incident photon momentum matches an allowed k-space vector.

Instrument descriptionASiemensD5000diffractometerwas used. It adopts theBragg-Bentanoparafo-cussing geometry (defined byW. H. Bragg and J. C.M. Brentano) in ✓/2✓ con-figuration. In this configuration, the X-ray tube is fixed, whereas the sampleholder and the detector move in such a way to form an angle ✓ and 2✓ withthe x-ray beam, respectively.

Figure 2.7. Geometry and diagram of the Siemens D5000.

Figure 2.7 shows in detail the working mechanism of the instrument. Thebeam source is a X-ray tube in which electrons are emitted using thermioniceffect in the anode. After being accelerated using a very high voltage (tens ofkV) they strike to a copper cathode and X-ray are emitted.

3Experimental data

Inthis chapter the experimental data ofmetal-halide perovskiteswill be pre-sented and discussed. As already discussed in section 1.4, for each type of

perovskite, three samples with a different coating layer, were prepared. Thiscoating layer, beside protecting the perovskite from oxygen and moisture,can also affect the optoelectronic properties. This latter property has beenexploited in order to study the behaviour of carriers (electrons and holes) inthese materials. For this purpose each perovskite was coated with an ETL(electron transport layer), a HTL (hole transport layer) or an inert material.

For each sample two main measurements were carried out in order to studythe dynamics of the excited state: TRPL and pump-probe. In both of themthe laser light impinged on the samples from the glass substrate, in order forthe light to be absorbed in the firsts nanometres and let the injected carriersreach the coating layer by diffusion. In this way the diffusion length of thecarriers was evaluated using the model represented in Figure 3.1.

23

24 CHAPTER 3. EXPERIMENTAL DATA

Glass

Coating

PV

I / I0

z

Figure 3.1. Schematic drawing representing the absorption of light in the first tens ofnanometres of the perovskite and the diffusion of carriers along the material. Onthe left the qualitative trend of the Beer’s law (see eq. 1.3) versus the depth of theabsorber (z) is shown.

3.1 PhotoluminescenceAs a first check of the samples, we can compare their photoluminescencespectrum (obtained integrating the TRPL in a time-range of ⇠100 ns), asshown in figure 3.2. These data are in accordance to the bandgaps reported in

700 750 800 850Wavelength (nm)

0

0.2

0.4

0.6

0.8

1

PL (n

orm

.)

MAPbI3MA1-yFAyPbI3MA1-yFAyPbI3-xBrx

Figure 3.2. Comparison of the normalised PL of the three types of perovskites (coatedwith PMMA) studied in this work.

Figure 1.5. We can see that adding formamidinium to the perovskite compo-sition the bandgap decreases, whereas adding bromine the bandgap increases.

25

Using the same method we can also compare the photoluminescence of thesame type of perovskite with a different coating 3.3. From these data we can

700 750 800 850Wavelength (nm)

0

0.2

0.4

0.6

0.8

1PL

(nor

m.)

MA1-yFAyPbI3-xBrxPMMAPCBMSPIRO

Figure 3.3. Comparison of the normalised PL of the same perovskite(MA1�yFAyPbIxBr3�x) with different coating layers. The shoulder at800nm is due the second order of the pump which has not been filtered properly.The samplewith perovskite/PMMAhas a high photoluminescence that overcomethis peak.

see that the coating layers don’t affect significantly the emission spectrum ofthe sample.

3.2 Time-resolved photoluminescence

Spectrogram analysisFrom a time-resolved photoluminescence measurement a 3D plot (spectro-gram) is obtained, in which the photoluminescence is resolved in time andwavelength. An example of this kindof spectrogramrelated toMA1�yFAyPbIxBr3�x

coatedwith PMMA is shown in Figure 3.4. From this plot we can extract boththe time profile of the peak and the spectrum for a fixed range of time. In-tegrating the horizontal green slice, we can obtain the photoluminescence asa function of the wavelength. On the other hand, integrating a vertical slicecentred in the peak, the time profile can be extracted.


640 660 680 700 720 740 760 780 800 820 840Wavelength (nm)

120

140

160

180

200

220

240

260

280

300

Tim

e (n

s)

0

1

2

3

4

5

6

7

8

T/T

(nor

m)

0

0.2

0.4

0.6

0.8 1

T/T (norm.)

B

A C

Figure 3.4. A Spectrogram referring to the sample MA1�yFAyPbIxBr3�x coated withPMMA. B Spectrogram integrated along the green box. C Time decay obtainedintegrating the spectrogram along the white slice.

TRPL versus fluenceThe first set of measurements dealt with the analysis of the TRPL with thevariation of the laser pulse fluence. In order to do that the laser spot wasacquired using a calibrated camera.

This analysis was done using the sample with MA1�yFAyPbIxBr3�x coatedwith PMMA. The data are shown in Figure 3.5.

As highlighted by the red arrow, the time decay decreases as the fluence in-creases. This is what we expect to see because at high fluencies high orderrecombination processes can occur in the material, as already discussed inSection 1.3.

From these profiles we can extract the photoluminescence intensity at timezero (PL0) to respect of the laser pulse fluence, as shown in Figure 3.6. Forsmall excitation densities, the PL0 scales as the square of the laser pulse flu-ence, in perfect agreement with what is shown in Figure 1.4.

27

0 2 4 6 8 10Time (ns)

0.01

0.1

1

PL (n

orm

.)

0.200.490.991.984.959.9019.80

Fluence( J/cm2)

Figure 3.5. Normalised time-resolved photoluminescence of the perovskiteMA1�yFAyPbIxBr3�x. As the fluence increases, the time decay decreases.

10-1 100 101 102

Fluence ( J/cm 2)

100

102

104

106

PL0 (a

.u.)

Figure 3.6. The PL0 as a function of the laser pulse fluence. The slope of the linear fitis 1.9(1).

Comparison of different types of perovskitesThe first type of perovskites that was measured is MA1�yFAyPbIxBr3�x. Theplot in Figure 3.7 compares the PL time decay of this perovskite with threedifferent coatings (PMMA, PCBM and spiro-OMeTAD) as described in sec-tion 1.4.

From the data in Figure 3.7 is quite evident that the time decay of the sam-ple with PMMA is much larger compared to that one of the same perovskitecoated with an ETL or HTL. This is due to the fact that these layers trap elec-trons (ETL) or holes (HTL), hence the photoluminescence is quenched. Sincethe photoluminescence is due to the recombination of electrons and holes, it


0 1 2 3 4 5 6 7 8 9Time (ns)

0.01

0.1

1PL

(nor

m.)

MA1-yFAyPbIxBr3-xPMMAPCBMSPIRO

Figure 3.7. Normalised time-resolved photoluminescence decay. The time range hasbeen chosen in such a way that at time zero the laser pulse strikes the sample. Thepump wavelength was 430 nm.

does not make any difference if we trap electrons, holes or both.

The dynamics at the interface between the perovskite and the three differentlayers is explained below using the drawings in Figures 3.8, 3.9 and 3.10.

PMMA

GLASS

Perovskite PMMA

GLASS

Perovskite

Valence Band

Conduction Band

PUM

P

Valence Band

Conduction Band

A B

Figure 3.8. This schematic drawing explains the dynamic at the interface between per-ovskite and PMMA.A The laser pumps the sample and excites the electrons fromthe valence band to the conduction band. B When electrons in the conductionband recombine with holes in the valence band photons are emitted (photolumi-nescence).

The laser pumps the system and excites the electrons from the valence bandto the conduction band. In the case of an interface perovskite/PMMAneitherelectrons nor holes can be extracted from the perovskite, because in PMMA

29

PCBM

GLASS

Perovskite PCBM

GLASS

Valence Band

Conduction Band

PUM

P

Valence Band

Conduction Band

A B

Perovskite

Figure 3.9. This schematic drawing explains the dynamic at the interface between per-ovskite and PCBM. A The laser pumps the sample and excites the electrons fromthe valence band to the conduction band. BElectrons are trapped in the ETL layerand cannot recombine with holes.

SPIROGLASS

Perovskite SPIRO

GLASS

Perovskite

Valence Band

Conduction Band

PUM

P

Valence Band

Conduction Band

A B

Figure 3.10. This schematic drawing explains the dynamic at the interface betweenperovskite and spiro-OMeTAD. A The laser pumps the sample and excites theelectrons from the valence band to the conduction band. B Holes are trapped inthe HTL layer and cannot recombine with electrons.

the top of the valence band is lower and the bottom of the conduction bandis higher compared to those of the perovskite. Therefore, since carriers areconfined inside the perovskite they can recombine.

PCBM is an electron transport layer, so by definition the bottom of its con-duction band lower to respect to the perovskite one. This means that elec-trons in the interface can fall in the potential well and cannot move back tothe perovskite. Hence, in this scenario, we can have electron-hole recombina-tion just after the excitation, before electrons move along the perovskite andbe trapped.

For a perovskite/SPIRO interface, the dynamic is quite similar to the per-ovskite/PCBM interface. The only difference is that in this case holes are


trapped in the HTL layer.

From the model just outlined, since the quenching in the PL is observed, itmeans that carriers are moving along all the perovskite and are trapped inthe coating layer. Considering that there is no voltage applied to the samples,the motion of carriers is due just to free diffusion (as described in Figure 3.1).Therefore we can conclude that the diffusion length of carriers is at least ofthe same order of magnitude of the perovskite’s thickness (⇠ 300 nm).

This result is quite interesting, since this diffusion length ismuch greater thansolution-processed organic conjugated materials (typical diffusion lengths ofabout 10nm), thermally deposited organicmolecules (typical diffusion lengthsof 10 to 50 nm), and colloidal quantum dot films (diffusion lengths of 30 to80 nm).23 This ensures that in a perovskite solar cell carriers can be extractedeven if the thickness of the absorber layer is hundreds of nanometres thick(in order to harvest as much photons as possible).

In Figure 3.11 the TRPL of the MA1�yFAyPbI3 is shown.

0 1 2 3 4 5 6 7 8 9Time (ns)

0.05

0.1

1

PL (n

orm

.)

MA1-yFAyPbI3

PMMAPCBMSPIRO

Figure 3.11. Normalised time-resolved photoluminescence decay. The pump wave-length was 600 nm.

The trend of the photoluminescence time decay is the same observed for theMA1�yFAyPbIxBr3�x perovskite. This means that even in this samples thediffusion length of electrons, holes or both is of the same order of magnitudeof the perovskite thickness.

31

The last type of perovskites measured was MAPbI3. In Figure 3.12 the TRPLtime decay is shown. Despite these samples having a shorter decay compared

0 1 2 3 4 5 6 7 8Time (ns)

0.1

1PL

(nor

m.)

MAPbI3PMMAPCBMSPIRO

Figure 3.12. Normalised time-resolved photoluminescence decay. The pump wave-length was 400 nm.

to the previous type of perovskites, the qualitative trend of the decay is com-parable, since it decreases when the sample is coated with an ETL or HTL.

3.3 Transient absorption spectroscopy

Spectrogram analysisEven from pump-probe measurements a spectrogram is obtained, as shownin Figure 3.13. Therefore the analysis is the same described in 3.2: data wereintegrated along a vertical slice in order to obtain the photobleaching time-decay.

Transient absorption versus fluenceEven for the transient absorption measurements, the dependence of the pho-tobleaching time decay as a function of the laser pulse fluence was studied.The comparison of the photobleaching time-decay measured at different flu-encies is shown in Figure 3.14. The red arrow highlights that the time-decaydecreases as the laser pulse fluence increases.


550 600 650 700 750 800Wavelength (nm)

0

1

2

3

4

5

6

7

Tim

e (n

s)

Figure 3.13. Spectrogram referring to pump-probe of the sampleMA1�yFAyPbIxBr3�x coated with PMMA.

0 1 2 3 4 5 6 7 8 9Time (ns)

0.05

0.1

1

T/T

(nor

m.) 1.41

2.825.6311.2722.5445.07180.28360.56

Fluence( J/cm2)

Figure 3.14. Photobleaching time-decay as a function of the laser pulse fluence. Thetime-decay decreases as the laser pulse fluence increases.

The photobleaching at time zero is expected to scale linearly as the laser pulsefluence, as it depends on a linear combination of the density of electrons andholes. Nevertheless, this linear trend is valid only at low fluencies, as shownin Figure 3.15.

Comparison of different types of perovksitesFigure 3.16 shows the photobleaching decay in the pump-probe measure-ment. The time decay of the sample coated with PMMA is the same of the

33

100 101 102 103

Fluence ( J/cm 2)

10-3

10-2

10-1

T/T 0

Figure 3.15. Transient absorption evaluated at time zero versus the laser pulse fluence.The line shows the linear trend at low fluencies.

0 1 2 3 4 5 6 7 8Time (ns)

0.01

0.1

1

T/T

(nor

m.)

MA1-yFAyPbIxBr3-xPMMAPCBMSPIRO

Figure 3.16. Normalised photobleaching decay obtained from pump-probe measure-ment. The samples were pumped at 530 nm.

sample coated with the HTL (spiro-OMeTAD), whereas the sample coatedwith the ETL (PCBM) has a shorter decay. This result suggests a different be-haviour of electrons and holes in the type of perovskite in question. In orderto investigate this property, the same measurements were done to differenttypes of perovskites.

Figure 3.17 shows the photobleaching time decay related to MA1�yFAyPbI3.Despite the presence of a spike for t=0ns, which is probably due to defects in


0 1 2 3 4 5 6 7 8Time (ns)

0.01

0.1

1T/

T (n

orm

)

MA1-yFAyPbI3PMMAPCBMSPIRO

Figure 3.17. Normalised photobleaching decay. The pump wavelength was 600 nm.

thematerial that enhance the recombination, the trend is the sameobserved inthe previous sample. We can therefore suppose that the behaviour of carrierswe saw in this material does not depend on the presence of bromine.

Figure 3.18 shows the photobleaching time decay related to theMAPbI3 sam-ples. From the data shown in this plot, we can conclude that the photobleach-

0 1 2 3 4 5 6Time (ns)

0.01

0.1

1

T/T

(nor

m)

MAPbI3

PMMASPIROPCBM

Figure 3.18. Normalised photobleaching decay. The pump wavelength was 400 nm.

ing of the sample coated with PMMA decays as the one coated with SPIRO,whereas the sample coated with PCBM has a faster photobleaching decay.

35

These results are quite surprising. Since perovskites are intrinsic semicon-ductors with comparable effective mass for electrons and holes, it was ex-pected a comparable contribute of electrons and holes to the optoelectronicproperties. As amatter of fact, the transient absorption data suggest that thereis a different behaviour of the two carriers affecting the absorption of thema-terial.

3.4 XRDThe structure of the samples can be evaluated using XRD. Particularly, in or-der to check if the synthesis was successful the diffraction pattern of the sam-ple can be compared with the expected position for the peaks, as shown inFigure 3.19.

10 20 30 40 50 602 (deg)

Cou

nts

(a.u

.)

PV + PMMAPV + PCBMPVPbI2

Figure 3.19. Diffraction pattern of MA1�yFAyPbIxBr3�x coated with PMMA andPCBM and compares with the expected peaks of a cubic MAPbI3 perovskite(Pm3m)

Even if we are dealing with MA1�yFAyPbIxBr3�x, the phases are evaluatedconsidering a cubic structure of MAPbI3 (Pm3m), since the peaks positionsdo not change adding FA in the siteA or Br in the siteX . From the diffractionpattern we can see that all the expected peaks are present in the experimentaldata. The presence of the amorphous PMMAor PCBM layer on the top of theperovskite leads to a very high background and a low signal-to-noise ratio.There is also another peak at 14� wich is due to the presence of PbI2 usedas a precursor for the synthesis. This means that not all the precursors reactduring the synthesis.


Despite the noisy data and the presence of a small phase of PbI2, this analysisproved the presence of a well defined perovskite crystal structure in the thinfilm layer.

4Conclusions

Thiswork has dealtwith the study of optoelectronic properties of organic-inorganic lead-halide perovskites.

Particularly the interface of perovskite/ETL (electron transport layer) andperovskite/HTL (hole transport layer) have been studied. In order to do that,thin film layers of perovskiteswere coatedwith three different layers: PMMA,an inert material used to protect the perovskite from oxygen and moistureand to study the optical properties of the perovskite itself; PCBM, which isan ETL and spiro-OMeTAD which is a HTL. The synthesis was carried outusing the spin-coating technique.

Three different types of perovskites were under study: MA1�yFAyPbI3�xBrx,MA1�yFAyPbI3 and MAPbI3. First of all, their photoluminescence was mea-sured and both the peak and the FWHMwere comparable to those publishedin literature. This analysis gave us a first check of the quality of the synthesisprocess. The structure of MA1�yFAyPbI3�xBrx was also studied with XRD,showing a good agreement with the simulated peaks positions.

The core of this thesis was to apply ultrafast spectroscopy, namely pump-probe and time-resolved photoluminescence in order to study the dynamicsof the excited state of the samples. The time-resolved photoluminescence ofeach perovskite shows a faster time-decay when the sample is coated with an

37

38 CHAPTER 4. CONCLUSIONS

ETLorHTL rather thanwhen is coatedwith an inertmaterial, suggesting thatcarriers can easily diffuse along the material and therefore have a diffusionlength larger than 300 nm (thickness of the perovskite layer).

With the pump-probe setup, the transient absorption of the sampleswasmea-sured. The data showed a quite interesting result, for all the types of per-ovskites we studied, the photobleaching decay of the perovskite/PMMA andperovskite/HTL is virtually the same, whereas the sample perovskite/ETLhas a shorter decay. This result suggests that, despite perovskites being an in-trinsic semiconductorwith comparable effectivemass for electrons andholes,there is a different behaviour of the two carriers affecting the absorption ofthe material.

A possible interpretation is that the contributionof holes to absorptionbleach-ing in organic-inorganic lead-halide perovskites is negligible. This could bedue to selective traps for holes inside the bandgap, or even other more com-plicated phenomena, that have yet to be investigated.

In conclusion, there still remainmanyopenquestions for the community con-cerning the nature of the lowest-excited states in hybrid organic-inorganicperovskites.

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Ringraziamenti

Giunto alla fine del mio percorso universitario desidero ringraziare tutte lepersone chemi sono state a fianco in questi cinque anni, aiutandomi a cresceree realizzarmi, sia come fisico che come persona.

Vorrei ringraziare in primo luogo la mia famiglia, che ha sempre creduto inme, sostenendomi, supportandomi e sopportandomi durante i momenti piùdifficili.

Un grazie di cuore va anche a tutti gli amici e i colleghi, vicini e lontani, chehanno contribuito alla riuscita di questo lavoro garantendo la salute mentaledell’autore.

Un doveroso ringraziamento anche a Valerio per l’aiuto e i preziosi consigli.

In ultimo, ma non per ordine d’importanza, desidero ringraziare il relatoredi questa tesi, professor Michele Saba, i cui insegnamenti sono stati prezio-sissimi. Non dimenticherò mai la strada che abbiamo percorso: grazie peravermi guidato fino a qui!

ultrafast spectroscopy of hybrid lead-halide perovskites · able band gap and low costs of...

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