Time resolved photo-induced optical spectroscopy

C H A P T E R

6 Time resolved photo-induced optical spectroscopy Meysam Pazoki and Tomas Edvinsson

˚ ngstro¨m laboratory, Department of Engineering Sciences, Solid State Physics, A Uppsala University, Uppsala, Sweden

6.1 Introduction The emergence of high efficiency perovskite solar cell materials in solid state devices in 2012 [1,2] inspired a great amount of research by which the efficiency was increased from about 10% in 2012 [1] to more than 23% certified solar-to-electricity power conversion efficiency (PCE) in 2018, increased to 25.2% in 2019 [3]. Behind this fast development are previous experience within dye sensitized- organic-, and thin film solar cells and the unique physical and optical properties in the perovskite solar cell materials with the ability to synthesize high quality polycrystalline materials with varying chemical compositions using a multitude of methods. Addressing the key-role processes of the photon absorption, carrier thermalization, exciton dissociation, charge carrier transport and recombination together with other relevant phenomena such as Stark effect, defect migration and electron-phonon interactions are essential to inspect the underlying physics processes for a certain material and their importance for the photovoltaic performance. Time resolved optical spectroscopy techniques provide analysis of the optical fingerprints of the above-mentioned phenomena and the corresponding time evolutions within the times scales of femtoseconds up to seconds. The principle of photo-induced time resolved optical spectroscopy [4] is to trigger the desired process, i.e. by light excitation of the sample and subsequently investigate the consequences on the absorption or emission spectra of the material. For example in the case of contact free perovskite film, radiative recombination rate of electron and holes can be estimated from time resolved photoluminescence (PL) spectrum by recording the emission of the material—at wavelengths near the band edge—after the photoexcitation.

Characterization Techniques for Perovskite Solar Cell Materials DOI: https://doi.org/10.1016/B978-0-12-814727-6.00006-2

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6. Time resolved photo-induced optical spectroscopy

In a perovskite film on a contact material, however, the same measurement will also be dependent on the PL quenching by transport of carriers out of the film and back contact recombination. The time resolved behavior of optical fingerprints of such phenomena can be estimated and analyzed in the terms of charge carrier dynamics as well as on the choice of heterojunction contact material. The fastest processes here cannot be examined by other techniques than electromagnetic (light, X-rays) pump-probe due to the limitations of the electronics speed, while the slowest process have their best evaluation from a combination of photo-induced optical spectroscopy techniques and modulated photo-voltage/photocurrent transient techniques mentioned in Chapter 7. A proper understanding of the photovoltaic processes is achievable through a careful design of the setup, i.e. utilize intensities of the perturbing light that are relevant for solar cell operation, to be in the relevant time scale, and also consider and rationalize the possible interfering phenomena. These techniques are well established for investigation and characterization of solar cell devices especially for the characterization of the dye sensitized solar cells [5], from which the emergence of perovskite solar cell family came to reality [6]. Here, a summary of relevant processes that can be studied by time resolved optical spectroscopy techniques together with an up-to-date presentation of some recent achievements are succinctly reviewed in this chapter with special attention to the prospects and limitations of the techniques for perovskite solar cells. Some case studies for situations corresponding to real device applications are shown with focus on understanding of local field effects and properties important for high performance and stable perovskite solar cells devices. The same methodology applies to the other devices based on organic
inorganic perovskites such as light emitting diodes (LEDs) and sensors, but we will in this chapter mainly focus on the solar cell applications.

6.2 Fundamental processes within the perovskite film Fundamental processes within the perovskite film that influence the performance during the solar cell photovoltaic action as well as a general overview of some commonly used methods are schematically presented in Fig. 6.1. The main processes consist of absorption of the incoming photons (process 1), thermalization of charge carriers, generation of free charge carriers and charge separation (process 2), transport of charges towards the contacts (process 3) and selective collection of the electrons and holes at charge selective contacts (process 4). The overall efficiency of these processes can be formulated into an external quantum efficiency (EQE) expressed in Eq. (6.1).







EQEðλÞ 5 LHEðλÞ Φsep ðλÞ Φtrans ðλÞ Φcoll

(6.1)

where LHE is the light harvesting efficiency, λ is the wavelength, Φsep and Φtrans are the quantum efficiency of the charge separation and charge transport, respectively, and Φcoll is the charge collection efficiency. In the most general case, the charge separation and transport are wavelength dependent but also depend on the time scales of the processes as well as the specific band structure and transport processes active in the material.

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FIGURE 6.1 Schematic illustration of commonly used techniques, typical time scales and processes influencing the performance of the perovskite device, including light absorption, carrier thermalization, electron-hole recombination, charge transport and extraction.

Undesired processes, however, such as bonded charge carriers or excitons and recombination of charges (process 5) as well as other processes such as trapping of the charges, defect migration, and band filling effects play important roles in the device photovoltaic behavior. An interplay of all these effects determines the working condition of the device i.e. the competition between the charge generation and recombination and their energy levels determines the charge density profile at certain temperature which is directly related to the quasi Fermi levels and thus the open circuit voltage of the device. The photo-voltage in the solar cell is the difference between the quasi Fermi levels for the electrons and holes under illumination at different electrodes and is lower than the difference in energy between the band edges within the photo-absorber. This loss in energy between the band gap and the resulting photo-voltage (ηloss) can be seen as the energy penalty for withholding the electric field separating the electrons from the holes as well as energy loss coming from un-ideal material properties. A formulation of this loss,

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(ηsep), was derived by Shockley and Queisser in the 1960s and can by neglecting higher order terms be written as Eq. (6.2) " # 8πðkB TÞ2 n2 Eg Voc 5 Eg 2 ηsep 5 Eg 2 kB T ln αLΦrec (6.2) c 2 h3 jgen where φrec is the ratio between the non-radiative and radiative recombination rates Voc is the open circuit voltage, Eg is the band gap, kB is the Boltzmann’s constant, T is the temperature, c is the speed of light in vacuum, h Planck’s constant, n is the refractive index, jgen is the rate of photon absorption in the AM1.5 spectra, α is the absorption coefficient, Φrec is the ratio between the non-radiative and radiative recombination rates, and L is the minority carrier diffusion length; and should be replaced with the material thickness, d, if d , L. Several of these parameters are material dependent and the loss is then naturally dependent on the choice of photo-absorber and the purity of the material. Typical experimental values of voltage loss for state-of-the-art materials in solar cells are: 0.3 eV in GaAs, 0.36 eV in silicon, 0.4 eV in hybrid perovskites, 0.4 eV in InP, 0.4 eV in CIGS, 0.6 eV in CdTe, 0.61 eV in amorphous silicon, and . 0.6 eV in organic solar cells. The hybrid perovskites show a quite remarkable defect tolerance and display low voltage loss and will be one of the topics addressed in Section 6.2.1.

6.2.1 Processes at open circuit condition At open circuit condition, the electron generation rate (G) is equal to the recombination rate (R) G5R

(6.3)

Therefore, with lower recombination rate at each fixed light intensity, the steady state density of electron and holes at valence band (VB) and conduction band (CB) would be higher leading to a higher photo-voltage. Interface recombination [7], ionic movement dependent recombination [8], effect of polarizability domains [9,10] as well as the density of the sub band gap traps [11] within the film are determining and impactful parameters influencing the average charge density dependent recombination rate in the device. The generation rate depends on the steady state absorption spectrum of the light absorber layer and on atomistic level the its relation to the density of empty states at perovskite CB, the number of available states at top VB and the transition probability and the dipole strength for optical transition. Depending on the wavelength dependency of absorption spectrum, a steady state charge profile (electrons and holes with densities n and p) builds up within the film at open circuit conditions. The relation between the device open circuit voltage and charge carrier densities can be described by Eq. 6.4 [11]:   Nc Nv e:Voc 5 Eg 2 kB TLn (6.4) np where e is the elementary charge, and Nc/v are the total available density of charge carriers. Eq. 6.4 can be seen as a phenomenological version of Eq. 6.2, where the effective

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number of charge carriers can be estimated without factorizing the contributing factors from the material properties. The loss of the effective number of charge carriers via recombination could be classified to the interface recombination, bulk recombination and trap assisted recombination, all of which can be classified into radiative and non-radiative recombination with their accumulated ratios expressed as Φrec in Eq. 6.2. The number density, energy states and location of traps within the film are of crucial importance for recombination kinetics for perovskite solar cells. The response by photo-excitation is often dependent on the intensity and history of the film under illumination and should be considered when performing photoinduced absorption spectroscopy as will be discussed later in this chapter. The radiative recombination can be recycled [12] and re-implemented for charge carrier generation, while the non-radiative recombination through the sub band gap states lower the device efficiency from the expected theoretical limit. The latter has been considered as the main bottle neck for further increase of the efficiency at the time for world record 23% perovskite solar cell devices [11] and triggered more research on the modification of crystal growth techniques for obtaining higher quality films. The time evolution of photogenerated carriers n’ can be described by an average recombination rate (k) which is inversely proportional with carrier life time (τ). dn0 1 5 kn0 and kðn0 Þ 5 kradiative 1 k1 1 k2 1 . . . 5 τ ðn0 Þ dt

(6.5)

The recombination rate has contribution from band-to-band radiative recombination (krad) and different non-radiative recombination rates i.e. trap assisted, ionic movement assisted or interface recombination.

6.2.2 Processes at short circuit condition The short circuit current density (Jsc) at each specific wavelength λ is directly proportional to light harvesting efficiency (LHE) and charge collection efficiency (Φcol) expressed in Eq. 6.1 by considering the charge transport within the layers and charge transfer kinetics at interfaces within the scope of charge collection: JscðλÞ ~ LHEðλÞ:Φcol ðλÞ

(6.6)

LHE ðλÞ 5 1 2 102AðλÞ

(6.7)

Φcol ðλÞ 5 1 2 τtrans =τrec

(6.8)

LHE depends on the absorption spectrum of the light absorber (A(λ)) (Eq. 6.7). τtrans and τrec are the corresponding recombination lifetime and transport time of charge carriers. The transport time depends on the carrier mobility that in single crystal MAPbI3 perovskite correlates strongly with electron-phonon interactions [13,14]. The response of the device at short circuit can be affected by history of the film under illumination [15] and can be discussed within framework of trap formation/annihilation, interaction with polarizability domains and photo-induced trap migration that are shortly discussed in Section 6.6. Due to the strong light absorption and charge conduction abilities, the

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short circuit current densities in world record mixed perovskite solar cells are already close to the maximum theoretical limit [16] with close to 100% internal quantum efficiencies [17].

6.2.3 Devices under working conditions The current voltage (I
V) relation for solar cell devices has the general form of diode equation (Eq. 6.9) in which the total resistance of the device (R) including all the series, ionic movement, transport and shunt resistances, determining the shape of the current voltage curve and therefore affect the fill factor (FF) and consequently also the power conversion efficiency of the device.     eV I 5 I0 exp 21 (6.9) nkB T   1 eV ~ exp (6.10) R nkB T Eqs. (6.9) and (6.10) describe the diode equation and the resistivity where e, kB and n are elementary charge, Boltzmann constant and the diode ideality factor, respectively. The transport resistance within the perovskite film is directly proportional to the mobility, while the shunt resistance depends on electron lifetime and different recombination processes. There are different processes such as trapping of electrons in defects, defect migration, and band filling effects that play roles for the above-mentioned processes under working conditions. Table 6.1 presents the related time scales of important phenomena for perovskite solar cell devices. A proper evaluation of the effects, the relevant time scale and possible interfering phenomena which are necessary to be considered for obtaining TABLE 6.1 Typical time scales for photovoltaic processes in the MAPbI3 based perovskite solar cells. Process

Time scale

Reference

Excitation

Instantaneous

[74]

Exciton dissociation

A few ps

[74]

Band filling

ps-ns

[22]

recombination

ns- a few μs

[36,46,75]

transport

ns-μs

[76]

Charge transfer

tens of ps

[46]

Stark effect

ns-s

[20]

Thermalization

fs-low ps

[77]

Electron-phonon scattering time

fs

[70]

See also Ref. [14] for a detailed discussion.

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the relevant information as well as identifying when the time scales of the different processes overlap. A detailed summary about the charge carrier dynamics in perovskite solar cell materials can be found in Ref. [14]. All these processes are intimately interconnected and by changing one part of the device or composition/thickness of the perovskite light absorber, many of these parameters can change. The latter stress the importance of characterization of these phenomena under relevant and well-defined conditions for finding suitable criteria for materials and device optimization. Our focus in this chapter would be to describe the concepts based on the MAPbI3 hybrid perovskite, which also is one of the most thoroughly investigated materials within the perovskite family. The approach would be the same for high efficiency mixed cation and mixed halide perovskite materials.

6.3 Light absorption and charge separation kinetics Incoming photons with energies higher than the band gap are able to excite electrons from the energy states in the valence band (VB) to states in the conduction band (CB), leaving a hole in the valence band. Excited electrons (holes) thermalize and cool down to the lowest unoccupied states in the CB (VB) and liberate the additional energy as phonons to the lattice. For indirect band gaps, which is not the case for the common lead halide perovskite materials, a conservation of energy and momentum, should be fulfilled i.e. a transfer of additional momentum is essential for the electron to be excited and thus implies that the light absorption occurs at a lower rate compared to direct band gap material. For metal halogen based perovskite solar cell materials, a wide range of band gaps from less than 1.2 eV (for CH3NH3Sn0.5Pb0.5I3) [18] to more than 4 eV (for CH3NH3BaI3) [19] have been reported and tuning of the gap by metal, monovalent cation and anion exchange as well as mixed approach is under ongoing investigations (see Chapters 1 and 3 for a detailed description). The band gap and the absorption coefficient are of fundamental importance for device efficiency in the stand-alone or tandem applications, and relates to the device color, transparency, efficiency per mass and the material cost (as stressed in Chapter 11), while the band gap tuning also can be detrimental for other processes resulting in lower power conversion efficiency. In MAPbI3, a halide-to-metal charge transfer is the main process for the VB to CB transition, while a charge transfer from iodide localized electrons to the organic cation is also possible in blue and UV light according to density functional theory calculations [20]. In the latter case, a negatively charged inorganic network and positively charged organic molecule can approach a state of lower charges; in which the material behavior under illumination can change significantly. In particular, this can trigger formation of CH3NH2 and a free H1 which subsequently can couple to I2 and by that diffuse more easily as HI in the material. Different excitation wavelengths (i.e. for MAPbI3, near band edge 760 nm and blue light 420 nm) also result in different thermalization degrees. Recently, excitation wavelength dependence of ionic movement in the perovskite devices by which the degree of thermalization was investigated and revealed that the amount of released phonons using near bandgap light (red light) and light absorbing deeper in the band structure (blue light)

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are significantly different and thus that thermally assisted ion displacements play an important role for the device current voltage behavior and hysteresis [20,21]. Transient absorption spectrum of the MAPbI3 perovskite show two distinct peaks at 470 nm and near band edge 750 nm. The near band edge peak has been considered as a fingerprint transition to analyze Stark effects [20], Burstein-Mott effects [22], excited state properties [23], excitonic features [24], while the nature of the first band is still less investigated. In some cases the transitions are discussed in terms of two valence band transitions to one CB [22] and the second band as a charge transfer state to higher CB states [25]. Order disorder phases and phase mixtures within the hybrid perovskites have also been analyzed in terms of multiple CB and VB states in Ref. [26]. The generated electron and hole pairs might be attracted by Columbic type forces; into a bounded electron-hole pair, an exciton. Presence of strong excitons can be beneficial for light emitting devices but not favorable for photovoltaic devices in which one desires to separate the excitons into free charge carriers in the bulk or at charge selective contacts. High dielectric constant of the lead perovskite is one of the key properties leading to high dielectric screening of Columbic forces and thus lowers exciton binding energy in 3D perovskites which can be overcame by thermal energy at room temperature (B 25 meV) and is beneficial for high photovoltaic efficiency of the device [27]. The reported values for exciton binding energies for MAPbI3 are in the range of 2
63 meV [28] which is of course dependent on the crystalline phase and thus also dependent on the working temperature of the device. Therefore, the charge separation within the tetragonal and cubic phases of MAPbI3, which are the most relevant phases in the device under working condition, are close to 100%. Typical mixed perovskite films spontaneously form free un-bonded charge carriers in the femtosecond regime (Table 6.1). In polymer and organic solar cells, however the charge separation of the excitons to the free carriers is a challenging task limiting the efficiency of the device. The extended perovskite solar cell family, two-dimensional (2D) and bromine based perovskites [29,30] as well as bismuth perovskites [31] have excitons with higher binding energy which can be beneficial for LED applications but less beneficial for solar cell applications. Beard and co-workers have compared the trap assisted and Auger recombination kinetics in bromine and iodine based lead perovskites through time resolved photoinduced spectroscopy techniques. Different exciton binding energies is responsible for higher recombination rates in bromine based perovskites [32]. A analytical expression for different carrier recombination kinetics in lead perovskite films, Eq. 6.5, has been derived in Ref. [33]. Excitonic fingerprint wavelengths are close to the band edge usually showing up as sharp peaks near the band edge in the absorption spectrum. As an example, in Ref. [34] it has been suggested that Br rich compositions shows strong excitonic peaks in mixed perovskite solar cell family near the band edge which are detectable in the PL spectra. There is no direct and certain method to find excitonic peaks in the UV
vis spectrum at room temperature since many different phenomena have their optical fingerprints near the band edge, while the overall behavior of the peaks in different conditions, temperatures, etc can be studied and fitted within exciton-theories criteria. Exciton binding energy can be evaluated by several approaches i.e. fitting of Elliot’s

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theory to the band edge curvature [35], thermally activated PL quenching [36] or thermal broadening of the absorption onset [37]. Pump probe spectroscopy has also been implemented widely to study exciton formation and dissociation within the perovskite solar cells. The determination of the excitons however is not very straightforward, due to the large variation of dielectric constant depending on frequency, temperature, light intensity and the interpretation of near band edge features [38]. Exciton dynamics became more important in the materials which carry higher binding energy excitons such as 2D perovskites and bromide based lead perovskite that are investigated i.e. in Ref. [29,30].

6.4 Charge recombination, transfer and transport kinetics Photoluminescence spectra and the time evolution of the PL peaks have been extensively used to study the charge recombination kinetics within the perovskite solar cell materials family. Since the electron lifetime and transport time within the film are on the orders of a few microseconds and are complicated by ion displacements in some cases, the approaches taken fromother new generation solar cells with longer electronic life times, such as dye sensitized and polymer solar cell technologies, have to be applied with care (see Chapter 7). In general, three types of electron-hole recombination are commonly considered in which the time derivative of the charge density (dn/dt) is the linear, second and third power of the charge density within the film [14,33] expressed in Eqs. 6.11 and 6.12. dn 5 2 k3 n3 2 k2 n2 2 k1 n dt

(6.11)

R 5 k3 n2 1 k2 n 1 k1

(6.12)

They can be ascribed to trap assisted (linear term), free charge carrier (second order) and Auger (third order) recombination kinetics [14,39] in which just the free charge recombination is radiative and there is no strong signature from radiative trap assisted recombination in perovskites yet. R is total recombination rate. Different charge recombination kinetics via time and spatially resolved micro-photoluminescence spectroscopy of large and small grain MAPbI3 perovskite films have been explored by Mohite et al. in Ref. [6]. The nature of traps within MAPbI3 have been evaluated by density functional theory calculations [39,40] and experimental approaches [41]. The results show the lack of deep traps within the bandgap, where the processes from recombination to deep traps seem to play no dominant role in the photovoltaic performance for high efficiency devices based on MAPbI3 and mixed perovskites. Defect densities of about 109
1014 have been reported for the MAPbI3 perovskite [39]. Although density of traps is quite low within the single crystal lead halide perovskite materials [42], the trap density in polycrystalline materials and perovskites based on other metals can be substantially higher and could

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dominate the recombination kinetics in such cases. On the other hand, trap assisted recombination depends on the light intensity, in higher light intensities, traps are already filled with charge carriers and show less impact on the charge carrier recombination during the perovskite solar cell device operation [43]. Very recently, Abdi-Jalebi et al. showed that the presence of monovalent cation additives can reduce the near band edge trap density and increase the lifetime of the carriers [44]. In the absence of a charge-selective layer, the recombination of free electrons and holes is mainly responsible for the time dependent PL spectra in a thin film. However, in the presence of a charge selective layer, diffusion and collection of the charge carriers towards the contacts compete with electron-hole recombination [6]. The decay time of the Pl peak to 1/e of its initial value is a fair evaluation of the corresponding lifetimes from which one can estimate the diffusion length of carriers within the film (see Chapter 3 for a detailed description and examples). However, other effects have recently been shown to interfere within the observed spectra where special care has to be taken when interpreting PL data (the fingerprint wavelength for the near band edge transition is around 780 nm for MAPbI3 and mixed perovskites with optical bandgap 1.6 eV). A phase segregation within the mixed perovskite solar cells can occur, especially when high amount of halogens with significantly different lead-halogen bond lengths are used, which can affect the time evolution of the PL spectra. This can for example occur when the amount of bromide is not negligible within a mixed halide perovskite material. The time dependent decay of the main perovskite PL spectrum can then not exclusively be assigned to only the electron-hole recombination anymore as the change in the spectra also can be inferred and ascribed to a phase segregation process [34]. Here, the main mixed perovskite film can be segregated into lead bromine perovskite (finger print wavelength 550 nm bandgap 2.1 eV) and lead iodine perovskite (finger print wavelength close to 780 nm) rich regions where another PL peak arise simultaneously at the expense of a decrease of the main phase PL peak [45]. A comprehensive study about temperature dependence of mono-, bi-molecular as well Auger recombination analyzed via transient PL measurements at different excitation fluencies as well as pump-probe spectroscopy and fitting the data with Eq. 6.6, is reported in Ref. [28]. Charge transfer kinetics for the MAPbI3 films with different scaffolds sandwiched by the typical TiO2 and spiroOMeTAD charge selective layers has been investigated by ultrafast transient absorption spectroscopy [46]. Xing et al. have estimated the diffusion lengths of electron and holes within the MAPbI3 perovskite by PL decay measurements at ns time scale. The decay time of PL peak in the presence of charge selective layers has been compared to the case of an absent selective layer and considering the thickness of the film, a diffusion length of about 100 nm was concluded [23]. Moser et al. reported that the charge separation at both electron and hole selective layers occur close to simultaneously within the timescale of femto- to picosecond time scale [46]. An imbalanced charge transfer results in accumulation of charges in contacts and suppressing the photovoltaic performance of the perovskite solar cell in the case of implementation of improper charge selective layers. De-doping of the perovskite absorber can help to achieve a better balance between the electron and hole transport within the film and thus the device PCE [44].

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6.5 Stark effects, defects and defect migration in perovskite solar cells 6.5.1 Stark effects Photo-induced near band edge optical absorption changes contain important information about the local electric field and thus the local material properties and give insights into how different processes occur within the device after excitation. One near band edge effect is the band filling effect (Burstein-Moss) [22] that bleach the photo-induced absorption spectrum where pre-filled states by electrons and holes can widen the observable optical band gap. These effects are dependent on the light intensity and can remain on the femtosecond to nanosecond time scales and thus overlap with Stark effect features on the GHz to THz frequency scales. Charge accumulation and recombination together with band shifts within the perovskite film can be investigated by kinetics of band filling effects [22]. The optical Stark effect can be defined as the spectral change caused by the presence of an electric field and can be photo-induced - or triggered by ab externally applied electric fields. The effect can be analyzed in terms of the small frequency shift Δν of a selected optical transition due to the electric field E, which is related to the change in the dipole moment between ground-state and excited-state Δμ and the change in polarizability Δα [20,47]. 1 h 3 Δν 5 E:Δμ 2 E:Δα:E 2

(6.13)

Here h is Planck’s constant, Δν the frequency shift and Δα the change in polarizability. The resulting experimentally measured absorption change ΔA is a function of electric field E. For the details of the quantum mechanical aspects of the Stark effect see the supporting information of Pazoki et al. [20]. The criteria for observing the optical fingerprints of the Stark effect can be distinguished according to Eq. 6.13: in the case that E is a small electric field and thus be considered a linear perturbation. Based on the symmetries of the system Hamiltonian, the near band edge absorption changes can be expanded in a power series with respect to the electric field i.e. in terms of first order Stark effect (linear in E) and second order Stark effect (second power of the electric field) that can be experimentally measured and analyzed via: ΔA 3 h 5 2

dA 1 dA E:μ 2 E:Δα:E 1 . . . dv 2 dv

(6.14)

The first observation of a Stark effect in perovskite solar cells was reported by De Angelis and co-workers [48] in 2014. The photo-induced absorption spectroscopy (PIA) [20] spectra of the perovskite solar cell materials have been shown to have Stark effect characteristics. In photo-induced absorption spectroscopy the perturbation of the system under illumination can be done by small or large amplitude pulsed lights and the material absorption changes in presence and absence of perturbation can be measured and finally a delta absorption spectrum can be extracted [20]. Fig. 6.2 shows a schematics of PIA

Characterization Techniques for Perovskite Solar Cell Materials

FIGURE 6.2 (A) A schematic of PIA setup for Stark spectroscopy of perovskite solar cell materials. Blue (light gray in print version) and red (dark gray in print version) perturbation lights implemented to probe the Stark effects and the photo induced optical changes recorded by the Si detector. (B) A typical frequency dependent Stark spectrum measured with different photon energy excitations [blue (light gray in print version) and red (dark gray in print version)] from a mixed lead halide perovskite device indicating the extension of the Stark effect to the time scales of several seconds. Figure adapted from Ref. [20] M. Pazoki, T.J. Jacobsson, J. Kullgren, E.M.J. Johansson, A. Hagfeldt, G. Boschloo, et al., Photoinduced stark effects and mechanism of ion displacement in perovskite solar cell materials, ACS Nano 11 (2017) 2823
2834. https://doi.org/10.1021/acsnano.6b07916. Copyright (2017) American Chemical Society.

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spectroscopy together with typical frequency dependent Stark measurements of the perovskite solar cells. In the PIA setup, the accuracy and sensitivity of the detector are high, making the absorption change measurements of up to 1027 feasible. The latter is a superior characteristic of PIA compared to conventional transient absorption spectroscopy (TAS) spectrum in laser spectroscopy. High sensitivity of PIA Stark spectrum can detect unique near band edge fingerprints of the perovskite material and is thus able to be implemented for the studies of phase segregation processes during light illumination of mixed anion perovskite films. In Fig. 6.3, the Stark effect with blue light (470 nm) and red light (630 nm) excitation is shown for lead halide perovskites with different A-cation dipole strength (Cs 1 -FA 1 -MA 1 ). An A-site cation with a stronger dipole is seen to charge compensate a locally created field better than a cation with lower dipole, and red light excitation show a frequency dependence in contrast to the blue light excitation [20]. The effect is also apparent in delayed Voc decay in high efficient mixed cation hybrid perovskite devices (PCE . 19%) when illuminated with blue light. The picture emerging is that blue light provides sufficient excess energy after thermalization to overcome the iodide displacement activation energy illustrated in Fig. 6.3 (F). On the other hand, the perturbed electric fields can also be applied externally and not through the photo induced electric fields. In this case, the same setup of PIA can be used

FIGURE 6.3 (A) Cation dependent Stark shift, (B) and (C) first (1H), second (2H), and third harmonics (3H) changes in DA at intermediate frequencies (1 kHz) and high frequencies (10kHz) for MAPbI3 and FAPbI3, respectively. (D) The frequency dependent photoinduced Stark effect with red (630 nm) and blue light (470 nm) excitation for MAPbI3, (E) Blue and red excitation dependence on the VOC decay in a 19% efficient mixed cation hybrid perovskite device, and (F) illustration of the maximum available thermalization energy under red and blue light excitation and the LO-phonon activation in the perovskite structure. Figure adapted from Ref. [20] M. Pazoki, T.J. Jacobsson, J. Kullgren, E.M.J. Johansson, A. Hagfeldt, G. Boschloo, et al., Photoinduced stark effects and mechanism of ion displacement in perovskite solar cell materials, ACS Nano 11 (2017) 28232834. https://doi.org/10.1021/ acsnano.6b07916. Copyright (2017) American Chemical Society.

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without perturbing excitations and instead by using applied electric field on the sample, which then transforms the technique into electro-adsorption spectroscopy [20]. Investigated second harmonic electro-reflectance [48] spectra of MAPbI3, and FAPbI3 have been reported by Wu et al. [49].

6.5.2 Dielectric relaxation Perovskite solar cell materials are soft in the terms of possible structural changes during photovoltaic action of the device and include energetically favorable photo-induced structural changes [50], such as ionic movement [51], trap formation [45], annihilation [52], reorientation of dipolar cations, as well as interfacial changes [53]. These photoinduced changes can be both limiting the performance but also beneficial for the photovoltaic operation of a device in a larger perspective i.e. tilting of the metal halogen octahedra in inter-atomistic scales can cause optical absorption changes [54]. Reorientation of the dipolar cations can modify the band gap [55] and charge carrier mobility [55], and ionic movement affect the distribution of the ionic species in the material and thus the local charge recombination [8] and even device stability which is reflected in the current voltage hysteresis of the device. These structural changes often cause changes in local electric fields, which can be studied by Stark spectroscopy during the photovoltaic operation of the device. So far, the Stark effects in MAPbI3 have mainly been used for analysis within the framework of interfacial charges in dye-sensitized solar cells [49] and the local electric fields due to the structural changes such as ionic movement and tilting of the octahedral [20]. These structural changes can be counted as dielectric response of the material. The latter is interestingly depending on the dipole moment of the monovalent cation as recently reported [20]. Higher rotational freedom and dipolar moment of the monovalent cation can screen the local electric fields after the photoexcitation and thus resulting in a lower-intensity Stark effect. The phenomenonis related to the instantaneous dielectric response of the monovalent cation and the local distortions within the PbI6 octahedra in the perovskite films.

6.5.3 Relevance to defects Defect formation, ion migration and photo induced defect migration have been investigated widely and are related to current voltage hysteresis effects, optimization of the photovoltaic efficiency, stability and the fundamental photo-physical processes within the perovskite solar cell materials and devices [21]. Depending on the formation energy and energy state of the trap, they can have optical fingerprints in the PL or absorption spectrum or even indirectly affect other relevant processes such as photo-induced Stark effects outlined above and charge recombination. Light illumination can cause defects [45] and reversibly healed in the dark and thus form a situation with dynamically formed and healed defects; their presence and density were analyzed from PL spectrum in Ref. [45]. On the other hand, De Angelis and coworkers reported the annihilation of defects after illumination which was studied by illumination-time dependent PL kinetics near the band edge [52]. The latter depended

Characterization Techniques for Perovskite Solar Cell Materials

6.6 Electron-phonon interactions and polarons in CH3NH3PbI3 perovskites

153

strongly on the availability of oxygen for the film during the illumination. The defects play important role in the photovoltaic action of the device, as they dictate the maximum voltage and efficiency of the perovskite devices [56], can migrate within the film and cause phenomena such as current-voltage hysteresis and further can accumulate at interfaces and cause degradation processes within the perovskite and at the interfaces [57]. Proper encapsulation of the device [58] or presence of very thin intermediate stable layers such as two-dimensional perovskites [59] turns out to be beneficial for achieving a good device stability. As defects migration play important roles within the device, more investigations, are needed to fully rationalize and understand how the defect migration affects the device operation and stability under working conditions which encourages further characterization of their optical fingerprints by photo-induced absorption spectroscopy studies. Photoinduced absorption changes in the perovskite solar cell materials can give information on local field changes and has recently been used to study thermalization effects, dipolar response, ion-, and defect migration [20,21,60].

6.5.4 Comparison with other solar cell technologies Stark spectroscopy is not limited to perovskite solar cells and have been used for characterization of dye sensitized [49,61], and organic solar cells [62] as well as quantum confined systems [63,64]. The time constants and the origins of the spectral shifts in different material classes, however, are very different making a full comparison in-between fields challenging. In dye sensitized solar cells the processes involved are rather widely explored: photo-injected electrons within the individual nanoparticles together with surrounding counter ions from the electrolyte within the Helmholtz layer are able to produce perpendicular electric fields relative to the dye. This particular configuration makes it possible to study the Helmholtz layer capacitance and dye coverage [61] within time scales of micro to milliseconds. Electron-hole lifetime here is a limit since by the electron hole recombination the photo-induced electric field would disappear. In perovskite solar cells this time-constants are extended from ns to several seconds and is intimately suggested to be related to both octahedral tilting and ion migration [20]. Therefore, together with Stark features, many other interfering phenomena can occur simultaneously and contribute to the photo-induced absorption spectrum. In organic solar cells Stark spectroscopy has been used to characterize the interfacial electric fields resulting from the charge separation at interfaces via ultra-fast time resolved optical spectroscopy in the fs regime [62]. As described in the article Stark realities [47], the Stark spectroscopy is a promising tool not fully explored so far for the perovskite solar cell materials and worth further investigations.

6.6 Electron-phonon interactions and polarons in CH3NH3PbI3 perovskites Thermalization: Immediately after the light absorption, the generated charge carriers (here called hot carriers) cool down to the CB and VB edges by transferring the excess energy to the lattice through electron (hole)-phonon interactions (process 2 in Fig. 6.1). The relevant time scale is sub or a few ps for many material systems. Slow hot-hole cooling in

Characterization Techniques for Perovskite Solar Cell Materials

154

6. Time resolved photo-induced optical spectroscopy

lead iodide perovskite films has been experimentally measured [65] by time resolved techniques and demonstrated by DFT calculations as well [66]. The phrase ‘slow’ for cooling processes here still relates to sub ps scales, but are referred to as slow since carrier cooling in perovskite films are slower than the ones found in silicon and CIGS films, but also come quite naturally from the heavier elements included in the lead-halide perovskites. Photo-induced absorption spectroscopy has been used for determining the carrier cooling time constants for the planar MAPbI3 films [65] which is one order of magnitude slower than carrier cooling in GaAs films. Recording the time resolved transient absorption spectrum or PL spectra under different temperatures (Fig. 6.4) the energy distribution of hot-electronic states can give information about the carrier cooling dynamics. Frost et al. have showed that the thermalization kinetics for above band-gap photoexcitation likely includes an energy transfer to large polaronic states through the electron (hole)-phonon interactions [67]. The thermalization cooling rate has been estimated by fitting the data with Fro¨hlisch model and determined to be 78 meVps21 for MAPbI3 films [67]. These cooling kinetics are importantly relevant for hot-carrier solar cell applications that are theoretically able of passing the Schockley-Queisser limit [68] as expressed in Eq. 6.2 within special photovoltaic regimes. The published data about the carrier cooling, so far, show an advantage of perovskite solar cells in comparison to other thin film solar cell technologies in terms of the carrier cooling, by having an order of magnitude slower cooling time and could be worth exploring further. Impacts on mobility and polarons: The Drude model [69] has been widely used for describing transport phenomena in perovskite solar cells [14]. Based on the Drude model, the static conductivity (σ) of the carriers can be described by σ5

ne2 τ m

(6.15)

FIGURE 6.4 (A) Hot carrier cooling measured by time resolved transient absorption spectroscopy from MAPbI3 films. Spectral absorption changes during the time gives information about the energetic distribution of carriers and cooling dynamics. Temperature dependent PL decay of (B) FAPbI3 and (C) MAPbI3 perovskites. The PL line broadening analysis determines the electron-phonon interaction within the films. (A) Reproduced from Ref. [65] Y. Yang, D.P. Ostrowski, R.M. France, K. Zhu, J. van de Lagemaat, J.M. Luther, et al., Observation of a hot-phonon bottleneck in lead-iodide perovskites. Nat. Photonics. 10 (2015) 54
59. https://doi.org/10.1038/nphoton.2015.213, with permission from permission from Springer Nature. (B and C) Reproduced from Ref. [70] A.D. Wright, C. Verdi, R.L. Milot, G.E. Eperon, M.A. Pe´rez-Osorio, H.J. Snaith, et al. Electron
phonon coupling in hybrid lead halide perovskites, Nat. Commun. 7 (2016) 11775. https://doi.org/10.1038/ncomms11755, under the Creative Commons 4.0 license.

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6.7 Summary and outlook

155

where m* is the effective mass, e the elementary charge, and τ the carrier scattering lifetime. Carrier scattering can be categorized into defect scattering, phonon scattering, or carrier-carrier scatterings or other system dependent factors depending on the physical state of the material and perturbation. Scattering of already-cooled-down charge carriers with phonons is considered as a limiting temperature dependent factor which limits the carrier mobility and charge transport within the perovskite films; temperature dependence of the photoluminescence (PL) peak intensity possess deterministic information for the electron-phonon interactions and its effect on the carrier motilities [70]. A few fs scattering time has been measured for the scattering of electrons via lattice phonons by Terahertz conductivity measurement [71]. The estimated charge carrier mobilities for perovskite solar cell materials lie in the range of 10 cm2V21s21, [14] in comparison to CIGS and amorphous Si solar cells that typically have the corresponding values of about 0.5 and 1 cm2V21s21 respectively [72,73]. The interaction of electrons with polaron based lattice distortions can play an important role in photovoltaic action of perovskite solar cells [67,74]. This is partly reflected by the effects on the electronic current, where defects and defect migration have been reported in the framework of device hysteresis i.e. in ionic movement dependent electron hole recombination [8] and current decay kinetics [15].

6.7 Summary and outlook The principles of photo-induced time resolved optical spectroscopy have been briefly reviewed with respect to the characteristic time scales of the processes occurring in hybrid perovskite solar cells. The spectral response during and after the incoming photon energies have been transformed into charge carriers, can give important information on the fundamental processes and thus on identification of the beneficial and detrimental processes for the photovoltaic performance. The time scales of the main fundamental processes within perovskite solar cell were outlined as well as an up-to-date presentation of the present understanding of the processes as characterized with these techniques. The processes varies from femtosecond to several seconds and many are strongly dependent on the chemical composition and crystal quality of the material. Phenomena such as local phase segregation, photo-induced trap formation, ion migration, and illumination history dependent carrier dynamics are more unique for perovskite solar cells and need specific attention for relevant device characterization. Special attention is given to photo-induced absorption spectroscopy used as a Stark spectroscopy where the absorption changes from the change in the local electric fields are analyzed. Studies on carrier cooling dynamics and electron-phonon interactions can further shed lights on the fundamental aspects as well as accessible mobilities and PCEs for practical device applications. Analysis of defect formation and dynamics under illumination and the impact on the device performance and stability are discussed as well which are necessary for future device optimization towards the commercialization of perovskites. The approach as well as more conventional ultra-fast spectroscopies can reveal many relevant

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6. Time resolved photo-induced optical spectroscopy

underlying physical processes occurring in the system, their fingerprints and how they can be detected, and bears promise also for future improved understanding as well as widening of possible applications.

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Further reading J.M. Richter, F. Branchi, F.V. de, A. Camargo, B. Zhao, R.H. Friend, et al., Ultrafast carrier thermalization in lead iodide perovskite probed with two-dimensional electronic spectroscopy, Nat. Commun. 8 (2017) 1
7. https:// doi.org/10.1038/s41467-017-00546-z.