Excitons versus free charges in organo-lead tri-halide perovskites

Abstract

Excitonic solar cells, within which bound electron-hole pairs have a central role in energy harvesting, have represented a hot field of research over the last two decades due to the compelling prospect of low-cost solar energy. However, in such cells, exciton dissociation and charge collection occur with significant losses in energy, essentially due to poor charge screening. Organic-inorganic perovskites show promise for overcoming such limitations. Here, we use optical spectroscopy to estimate the exciton binding energy in the mixed-halide crystal to be in the range of 50 meV. We show that such a value is consistent with almost full ionization of the exciton population under photovoltaic cell operating conditions. However, increasing the total photoexcitation density, excitonic species become dominant, widening the perspective of this material for a host of optoelectronic applications.

ARTICLE

Received 22 Jan 2014 | Accepted 7 Mar 2014 | Published 8 Apr 2014

Valerio DInnocenzo1,2,*, Giulia Grancini1,*, Marcelo J.P. Alcocer1,2, Ajay Ram Srimath Kandada1, Samuel D. Stranks3, Michael M. Lee3, Guglielmo Lanzani1,2, Henry J. Snaith3 & Annamaria Petrozza1

Excitonic solar cells, within which bound electron-hole pairs have a central role in energy harvesting, have represented a hot eld of research over the last two decades due to the compelling prospect of low-cost solar energy. However, in such cells, exciton dissociation and charge collection occur with signicant losses in energy, essentially due to poor charge screening. Organicinorganic perovskites show promise for overcoming such limitations. Here, we use optical spectroscopy to estimate the exciton binding energy in the mixed-halide crystal to be in the range of 50 meV. We show that such a value is consistent with almost full ionization of the exciton population under photovoltaic cell operating conditions. However, increasing the total photoexcitation density, excitonic species become dominant, widening the perspective of this material for a host of optoelectronic applications.

DOI: 10.1038/ncomms4586

Excitons versus free charges in organo-lead tri-halide perovskites

1 Center for Nano Science and Technology@PoliMi, Istituto Italiano di Tecnologia, via Giovanni Pascoli 70/3, Milan 20133, Italy. 2 Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci, 32, Milano 20133, Italy. 3 University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK. *These authors contributed equally to this work. Correspondence and requests for materials should be addressed to H.J.S. (email: mailto:[email protected])

Web End [email protected]) or to A.P. (email: mailto:[email protected]

Web End [email protected] ).

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Perovskite solar cells were rst introduced in a dye-sensitized conguration, where the dye was replaced by organo-lead halide perovskite crystals (e.g. CH3NH3PbI3 or

CH3NH3PbI3 xClx) sensitizing the surface of mesoporous TiO2

(refs 15). In the perovskite-sensitized conguration, developed within the excitonic solar cell concept, there is no requirement for long-range exciton or charge diffusion, as the perovskite crystals are sandwiched within a nanoscale heterojunction between an electron-accepting metal oxide (TiO2) and a hole-accepting organic hole-transporter (or redox active electrolyte) and long-range transport occurs in those phases. Although the rapid advancement of this sensitized approach has occurred, there has been in parallel a striking divergence in technology, where the mesoporous TiO2 has been proven non-essential5, and simply a solid absorber layer sandwiched within a planar heterojunction has been demonstrated to operate extremely well, with power-conversion efciencies of over 15% already reported6,7. The perovskite absorbers thus appear capable of operating in a similar manner to excitonic absorbers, but also in a comparable conguration and with comparable performance to the best inorganic thin-lm semiconductors6,8. The fundamental question that arises from these studies concerns the nature of the elementary photoexcitations that are involved in the photovoltaic (PV) mechanisms; in particular whether bound excitons are created and transport energy to the heterojunction, thus requiring further ionization at the heterojunction, or whether free charges are spontaneously generated within the bulk of the perovskite912. In order to answer this question, we explicitly need to know the exciton binding energy in the room temperature (RT) crystal phase of the perovskite absorber, and to understand the branching ratio between free carriers and excitons under operating solar cell conditions.

In this work, we use the temperature dependence of the absorption band edge to estimate the exciton binding energy in CH3NH3PbI3 xClx perovskite crystals. Subsequently, we use this

value in the Saha equation, which governs ionization processes13,14, to estimate the equilibrium branching ratio between free charges and bound excitons as a function of temperature and charge density. We nd that at equilibrium, following photoexcitation, there is a predominant fraction, near unity, of free charges in the PV operating regime.

ResultsTemperature dependence of optical absorption. In Fig. 1, we show the optical absorption spectra taken in a broad temperature (T) range from RT 290 K to 4.2 K, on a poly-

crystalline lm of CH3NH3PbI3 and of its mixed-halide analogue CH3NH3PbI3 xClx. We study both at lms deposited on glass,

which are polycrystalline with crystal sizes larger than 500 nm in diameter7 (Fig. 1a,b), and perovskite lms inltrated into a mesoporous oxide scaffold, where the perovskite crystals are on the order of 60 to 100 nm in size7 (Fig. 1c,d). Figure 1a shows the spectra of the CH3NH3PbI3 in a spectral range between 690 nm and 825 nm. A sharp peak at B765 nm emerges at lower temperatures, which we attribute to an excitonic transition. At 170K, a second excitonic peak emerges at 740 nm. Upon further reduction of temperature, the latter peak gains strength in intensity and monotonically shifts to longer wavelengths, whereas the rst peak disappears. We assign this behaviour to a phase transition of the perovskite crystal, notably from a tetragonal to an orthorhombic structure15,16, which commences at 170 K, inducing a blue shift in the absorption edge of about 60 meV, and completes at 150 K. Within this temperature range, the two phases coexist, possibly due to the polycrystalline nature of the sample. At 4.2 K a single excitonic feature peaks atB760 nm,

similar to what has been observed in single crystals of CH3NH3PbI3 (refs 17,18).

At RT, however, we cannot observe a clear gap between the excitonic peak and the conduction band continuum. We also note that as the temperature increases, especially in the low-temperature stable crystalline phase, the absorption band edge blue shifts. This Varshni trend is often observed in lead composite semiconductors with a positive thermal expansion coefcient of the band gap, dEg/dT19,20.

The CH3NH3PbI3 xClx perovskite absorption spectra are

presented in Fig. 1b. They show a similar trend in temperature, with evident positive dEg/dT in the low-temperature phase;

however, some important differences exist. First of all, the phase transition is activated at a lower temperature (B140 K), and is completed by 120 K, probably due to different chemical/structural environments in the two compounds. Secondly, the excitonic peak emerges with a stronger intensity with respect to the broad continuum (see spectrum at 4.2 K).

A different scenario appears when looking at the absorption spectra of the perovskite crystallites formed in the mesoporous Al2O3 scaffold (Fig. 1c,d), which imposes a smaller crystal size of the crystals7. Both materials show a broad band edge with no evident excitonic peak and are blue shifted with respect to the at samples. The structural phase transition can still be observed at the same temperature for the CH3NH3PbI3 xClx (see

Supplementary Fig. 1 in the SI where the complete temperature range is reported). However, upon cooling, the spectra remain featureless. Thus, smaller crystals show virtually no resolvable excitonic transition. We can exclude any connement phenomena as in this case one would expect an opposite trend, that is, appearance of the exciton optical transition as the crystal size is reduced. On the other hand, the reduction in size, the enhancement of the surface area and the presence of a scaffold during the crystallization process is likely to increase the relative contribution of surface effects, which may result in structural strains and/or doping mechanisms, which notably reduce the exciton binding energy21.

Interestingly, when we fabricate a combination of the above sample structures, that is, a thin B80 nm interpenetrated mesostructured composite covered by a B350 nm at perovskite capping layer (see cartoon in Fig. 2a), as is the case for the optimized device presented in ref. 7, the resulting absorption spectrum is a combination of the absorption spectra of the two layers (Fig. 2b). This suggests that the presence of the thin mesoporous interlayer is responsible for tuning the optoelectronic properties of the material by tuning the crystal size. This may have important consequences for device performance, where generally higher photovoltages are obtained for mesostructured devices than for planar structures7.

Exciton binding energy estimation. The optical analysis presented above suggests the presence of an excitonic transition, probably very close to the continuum. Indeed, the presence of a WannierMott exciton with a binding energy of about 45 meV has been predicted in the single crystal of CH3NH3PbI3 at low temperatures17,18. Temperature-dependent, time-resolved photoluminescence (PL) is one approach for estimating the exciton binding energy in a semiconductor. We indeed observed a reduction in PL intensity of CH3NH3PbI3 xClx when increasing

the temperature; however, the PL dynamics did not allow for an unambiguous assignment to the enhancement in thermal dissociation rate of excitons at higher temperatures. As such, here, we estimate an upper limit of the exciton binding energy in CH3NH3PbI3 xClx, by using the temperature-dependent

absorption line width of the observed excitonic transition.

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a b

Energy (eV)

1.55 1.5

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

Energy (eV)

1.55 1.5

1.75 1.7 1.65 1.6

1.75 1.7 1.65 1.6

0.64

290 K 250 K 210 K 170 K 160 K 150 K80 K40 K4.2 K

290 K 250 K 210 K

130 K 120 K

160 K 150 K 140 K

80 K40 K4.2 K

0.62

0.60

0.58

0.56

Optical density Optical density

Optical density Optical density

0.54

0.52

0.50

Flat CH3NH3Pbl3

Flat CH3NH3Pbl3xClx

700 720 740 760

780 800 820

700 720 740 760 780 800 820

Wavelength (nm)

Wavelength (nm)

c d

Energy (eV)

1.55 1.5

Energy (eV)

1.55 1.5

1.75

1.7 1.65 1.6

1.75

1.7 1.65 1.6

0.65

0.60

0.55

0.50

0.45

0.45

0.40

0.35

0.30

0.25

0.20

Meso CH3NH3Pbl3

Meso CH3NH3Pbl3xClx

290 K4.2 K

290 K4.2 K

720 740 760 780 800 820Wavelength (nm)

0.40

0.35

700 720 740 760 780 800 820 Wavelength (nm)

700

Figure 1 | Temperature dependence of the absorption spectra of the mixed-halide perovskites. Absorption spectra of CH3NH3PbI3 and CH3NH3PbI3-xClx as a function of temperature (2904.2 K). (a, b) Thin lms on a glass substrate and (c, d) on a mesoporous Al2O3 substrate.

Flat substrate

a b

Energy (eV)

1.6 1.55 1.5

Flat substrate MesoAl2O3

MesoAl2O3

0.8

0.7

0.6

0.5

0.4

0.3

0.2 700 720 740 760 780 Wavelength (nm)

Optical density (arb.units)

+Capping layer

MesoAl2O3+ capping layer

0.9 1.75 1.7 1.65

MesoAl2O3

800 820

Figure 2 | Absorption spectra of mesostructured thin lms. (a) Schematic presentation of the average crystals dimension for differently prepared samples, that is, deposited on a glass substrate (top), on a thick Al2O3 scaffold without a perovskite capping layer (bottom) and a thin Al2O3 scaffold with a perovskite capping layer (middle). (b) Absorption spectra of CH3NH3PbI3 xClx, thin lms collected at 4.2 K. The lms were deposited on a at glass

substrate (blue line), a thick mesoporous Al2O3 (dark red line) and according to the optimized device structure where part of the perovskite lm is inltrated in the mesoporous Al2O3 and an additional crystalline perovskite capping layer is present7 (red line). For better comparison, spectra are offset.

As inhomogeneous broadening due to disorder is generally temperature independent, here we only take into account the homogeneous broadening mechanism within the two-level system22. The coherence lifetime T2 of the excited state transition can be affected by the natural population decay of the excited

state (T1) and by elastic scattering events (with rate g) that do not change the excited state population but contribute to the broadening of the transition. For most polar inorganic solids at high temperatures (for example, T4100 K), phonon interaction leads predominantly to exciton ionization (through inelastic

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scattering)22,23. This approximation is valid in our case, as the exciton absorption broadening occurs together with a reduction in the intensity of the optical excitonic transition, thus the population decay rate, 1/T1, can be described as the sum of an intrinsic decay rate (k0) and thermal dissociation rate (kT)22,

1T1 k0 kT: 1

We model the rate of exciton thermal dissociation (kT) according to the following equation,

kT nTe EB kBT= 2 where EB is the exciton binding energy, kB is the Boltzmann constant and nT is the attempt frequency. Substituting the relationship between T1 and T2, 1

T2

1

2T1

g (ref. 22), into the

equation for the line width, Dn 1/pT2 we obtain:

Dn Dn0 nTe EB kBT= 3 where Dv0 accounts for the temperature-independent broadening. For a better t of the temperature dependence of the experimental line width hDv, the linear form of equation (3) is considered:ln hDv hDv0 ln hnT

T (K)

1.5 320 280 240 200

2.0

2.5

3.0

3.5

EB kBT

= 4 In Fig. 3, the natural logarithm of the excitonic transition line width of CH3NH3PbI3 xClx is plotted as a function of the inverse

of temperature in the range between 150 K and 290 K. The data are visualized in such a scale to emphasize the match between the experimental trend and the theoretical model. By tting the data with equation (4), (Fig. 3), we estimate an exciton binding energy of 5520 meV. The ts are shown in Fig. 3 along with the experimental data. For statistical relevance, the points reported in the graph are derived from repeated measurements of many different samples. Details of the analysis are presented in section Supplementary Methods of the SI.

Numerical simulation of the fraction of free charges vs excitons. Under thermodynamic equilibrium, there is a coexistence of free charges and excitons, and an interchange between the two species. The fraction of free charges (nFC) vs.

excitons (nexc) is not only determined by the binding energy, which determines how long electron-hole pairs remain bound, but also by the excitation density (n), which inuences how often electrons and holes meet to form excitons13,14.

In the PV working regime, the total excitation density can be estimated from the absorbed solar ux and the excitation lifetime. We can estimate the absorbed solar ux by integrating the absorption of the perovskite lm over the 100 mWcm 2 AM1.5 solar spectrum. The species lifetime can be estimated by measuring the PL decay in neat perovskite lms (equivalent to operation under open-circuit conditions with ideal n- and p-type contacts that introduce no additional non-radiative decay channels) or in perovskite lms contacted by a selective hole-or electron acceptor (similar to the scenario in the operating solar cells), which we have measured to beB270 ns and 5 ns, respectively24. We hence determine the steady state excitation density (where excitations can be free charge or excitons) to be between 1013 and 1015 cm 3. If we assume a dielectric constant of 6.5 (ref. 18) and a binding energy of approximately 50 meV, the exciton radius can be calculated to be B2.3 nm. Considering this

160

In (hvhv 0)

4.0

4.5

5.0

0.003 0.004 0.005

1/T (K1)

0.006 0.007

Figure 3 | Estimation of the exciton binding energy. Plot of the exciton absorption band broadening hDn in CH3NH3PbI3 xClx at layer vs inverse

temperature (150KoTo290K). For each point, the error bar indicates the maximum variation of the experimental value due to the 10 K uncertainty in the determination of the sample temperature. The solid line is the t realized according to equation (4), which gives an estimation for the binding energy of EB (5520) meV and an attempt frequency of (7 fs) 1.

w2 0.92.

1.0

a b

x(n FC/n)

0.8

0.6

0.4

1.0 EB=50 meV

4 K40 K80 K 120 K

160 K 200 K 240 K 290 K

PV regime

x(n FC/n)

0.8

0.6

0.4

0.2

0.0

1013 1014

EB=35 meV EB=55 meV

EB=75meV

1015 1016 1017

n (cm3)

1018 1019 1020 1021 1013 1014 1015 1016 1017 1018 1019 1020 1021

0.2

0.0

n (cm3)

Figure 4 | Modelling of the fraction of free charges over the total photoexcitation. (a) Simulation of the free charge fraction over the total excitation density (x nFC/n) at thermal equilibrium according to equation (5) described in the text. For this simulation, we used an exciton binding

energy of (5520) meV and an exciton reduced mass, m 0.15 me (ref. 18). The shaded area represents PV operating conditions (PV regime).

(b) Simultaion at different temperatures. With an exciton reduced mass m 0.15 me from ref. 18 and the estimated binding energy of 50 meV.

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value (in agreement with ref. 15) we can neglect excitonexciton interaction, which only occurs for n41020 cm 3, because there is essentially no wavefunction overlap. Consequently, we can safely assume that the binding energy is independent of excitation density23,25. Within such an approximation, we can apply the law of mass action for WannierMott excitons, as described by the SahaLangmuir equation13,14. The fraction of free charges over the total density of excitation, x, for a 3D semiconductor can be expressed as13:

x21 x

1 n

2pmkBT

h2

3=2e

EB

kBT

5

where EB is the exciton binding energy, m is the reduced mass of the exciton (approximated to 0.15 me (ref. 18), see Supplementary Fig. 2 for modelling as a function of reduced exciton mass), h is Plancks constant, T is temperature and n is the total density of excitation, n nFC nexc. The form of this equation is quite

intuitive; the higher the temperature, the greater the ratio of free charge to excitons, but the higher the density of excitations, the lower the ratio of free charge due to the greater possibility for free electron-hole capture events. In Fig. 4a, we model the fraction of free charges over a wide range of total photoexcitation densities. Our key nding is that at RT, at excitation densities that may be realistic for operating solar cells (no1015 cm 3), free charges represent the dominant population. The model shows that upon temperature reduction, the exciton population starts to increase, becoming dominant below 120 K (see Fig. 4b)13.

DiscussionWe have identied that the exciton binding energy in the organo-lead mix-halide perovskite is 5520 meV. This indicates that free charges are predominantly generated and are responsible for PV operation following light absorption, akin to a conventional inorganic semiconductor thin-lm solar cell. This indicates that the role of the heterojunction in the perovskite solar cells is simply to enable selective charge collection, and not to facilitate exciton ionization. Notably, while perovskite cells are not excitonic in their operating principles, they still preserve a large absorption oscillator strength at the band edge, reminiscent of the underlying excitonic transition. This is a clear advantage in light harvesting near the band edge, enabling extremely thin-lm solar cells to fully absorb light across the solar spectrum, and is in part responsible for the exceptional performance of the planar heterojunction perovskite solar cells9. Moreover, according to what we have shown, tuning the total density of photoexcitation allows for tuning of the nature of the primary photoexcitation at the thermodynamic equilibrium, that is, from free charges to excitons, thus opening up the way for application of these intriguing materials to a host of optoelectronic devices.

Methods

Sample preparation. Glass substrates were cleaned sequentially in 2% hallmanex detergent, acetone, propan-2-ol and oxygen plasma. The compact TiO2 layer (B50 nm) was deposited by spin coating (at 2,000 r.p.m. for 60 s) a mildly acidic solution of titanium isopropoxide in ethanol, followed by annealing at 500 C for 30 min. The B0.5 mm TiO2 and Al2O3 mesoporous layers were deposited by spin coating from stock solutions followed by sintering at 550 C for 30 min, as described previously3, with appropriate dilutions to give the thin mesoporous Al2O3 layer (B80 nm).

The perovskite precursor solutions were prepared using methods described previously for the mixed halide3. In brief, the CH3NH3PbI3 xClx or CH3NH3PbI3

precursor solutions were formed by dissolving methylammonium iodide and either lead (II) chloride (Sigma-Aldrich) or lead (II) iodide (Sigma-Aldrich) in anhydrous N,N-DimethylformamideDMF at a 3:1 molar ratio of MAI to PbCl2/PbI2, with nal concentrations of 0.88 M lead chloride/iodide and 2.64 M methylammonium iodide. The perovskite layer was then formed by spin coating the precursor solutions directly on the glass substrate, compact layer or the mesoporous layer at 2,000 r.p.m. in air. The at and thin meso samples were spin coated without

dilution but mesoporous samples were spin coated from diluted (three parts in four) precursor solutions. After spin coating, the CH3NH3PbI3 xClx lms were

annealed at 100 C for 45 min, and the CH3NH3PbI3 at 150 C for 15 min. For the at and thin mesoporous samples (that is, those without thick mesoporous layers), the perovskite lms were sealed by spin coating a layer of the insulating polymer poly(methylmethacrylate)(10 mg ml 1, 1,000 r.p.m.; Sigma-Aldrich) on top in order to ensure air- and moisture-insensitivity.

Ultravioletvisible absorption. Absorption measurements were performed using a spectrophotometer (Perkin Elmer Lambda 1050) and a continuous ow static exchange gas cryostat (Oxford Instruments Optistat CF). The cryostat consist of three chambers, one inside the other. The sample is housed inside the internal chamber lled with gaseous He. The cryogenic liquid (He) is uxed inside the second chamber allowing temperature control of the He atmosphere of the sample chamber. Eventually, a third chamber is evacuated (B10 510 6 mbar) in order to assure thermal isolation from the external ambient.

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Acknowledgements

We thank Dr F. Tassone and Prof R Cingolani for useful discussions on the photophysics of Wannier excitons; Dr J. Ball and G. Eperon for help with sample preparation; European Union Seventh Framework Programme [FP7/2007-2013] under grant agreement n 604032 of the MESO project and The Royal Society International Exchanges Scheme 2012/R2 for funding. H.J.S. thanks for funding the Engineering and Physical Sciences Research Council (EPSRC), the European Research Council (ERC-StG 2011 HYPER Project no. 279881), Oxford Photovoltaics Ltd. through a Nanotechnology KTN CASE award, and by a Royal Society Wolfson exchange grant. Dr S. Stranks thanks Worcester College, Oxford, for additional nancial support.

Author contributions

The Ultravioletvisible spectra were taken by V.D. and M.J.P.A. The simulations were run by V.D., G.G. and A.R.S.K. Samples were prepared by V.D., G.G., S.S. and M.L. All authors contributed to the data analysis and the manuscript preparation. A.P. and H.J.S. supervised the whole project.

Additional information

Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications

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How to cite this article: DInnocenzo, V. et al. Excitons versus free charges in organo-lead tri-halide perovskites. Nat. Commun. 5:3586 doi: 10.1038/ncomms4586 (2014).

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