Charge-carrier Diffusion and Radiave Efficiencies in Hybrid Metal Halide Perovskites

Prof Laura Herz

Clarendon Laboratory, University of Oxford

VIS ? THz I

UNSW 2016 The race for efficient, cost-effecve photovoltaic cells

Multi-junction, crystalline inorganics

single-junction, crystalline inorganics (GaAs,Si) CIGS

Solution-processed (or low-T evaporated) organics and DSCs http://www.nrel.gov/ncpv/images/efficiency_chart.jpg Hybrid Metal- Halide Perovskites Background: solar cell architectures and materials

“Planar heterojuncon” solar cells “Excitonic” or “nanocomposite” cells • Low exciton binding energy • High exciton binding energy → mostly free charges at 300K → require energy offsets to induce • High charge-carrier mobility and charge separaon diffusion lengths → doping • Low charge-carrier diffusion lengths gradients or electron/hole- → must separate charges into selecve contacts suffice to different material components to collect charges effecvely inhibit recombinaon

Organic Photovoltaics (OPV) 200 nm - + - + - + - +

Typical examples: crystalline silicon Typical examples: Dye-sensized solar or GaAs solar cells cells (DSC), organic photovoltaics (OPV) Features: highly efficient, but Features: lower efficiencies, cheap energy-intensive fabricaon (low-temperature processing) Charge diffusion in hybrid lead trihalide perovskites

light pulse Excite MA-PbI3-x Clx film on which either electron perovskite (PCBM) or hole (spiro- PL quencher OMeTAD) acceptor has been deposited

Model PL quenching as arising from diffusion of Time after excitation (ns) charge carriers to Extract charge-carrier interface, assuming unity diffusion length L=√(Dτ) quenching efficiency of ≈1μm

Stranks, Eperon, Grancini, Menelaou, Alcocer, Leijtens, Herz, Petrozza, Snaith, Science 342, 341 (2013). Hybrid lead trihalide perovskites combine the best of both worlds: low- temperature processing yielding charge carrier diffusion lengths that exceed the opcal absorpon depth! Organic-inorganic trihalide perovskite solar cells:

Hybrid metal halide perovskites have rapidly established themselves as new optoelectronic materials, allowing: • solar cells with high PCE >20% • varied range of processing protocols • low-cost, abundant ingredients • high absorpon in the solar range • long (micron) charge diffusion Metal Cathode Metal Cathode HTM Perovskite HTM lengths allow for planar Perovskite Mesoporous TiO2 heterojuncon designs ETM ETM • light-emission/lasing reported Metal anode Metal anode

What are the mechanisms governing charge- carrier mobility, recombinaon and diffusion? How are optoelectronic properes affected by composion? Outline

Prototypical MA-PbI3 & MA-PbI3-xClx: Other materials/properes? excellent optoelectronic properes! Lead-free? MA-SnI3 • Propensity towards n vacancies gives rise to unintenonal hole doping • Rapid charge recombinaon

Tuneable materials for tandems?

• Shallow, low-density traps A-Pb(BrxI1-x)3 • Non-Langevin Bimolecular recombinaon • Allows for perovskites with Eg~1.7eV • Strong radiave bimolecular transions near the ideal band gap for tandem • Decent charge-carrier mobility and solar cells with silicon long charge diffusion lengths • Problems with (photo-)stability • Mostly homogeneous emission broadening Charge recombinaon mechanisms in hybrid lead trihalide perovskites

Trap-mediated (k1) Bimolecular (k2) Auger (k3) phonon

CB2

CB1 CB1 CB1 CB1 E e- trap k

VB1 VB1 VB1 VB1

* non-radiave* radiave , for a direct non-radiave* semiconductor monomolecular strong dependence on hence to some extent bandstructure, phonons, parcularly detrimental required to achieve impuries (because of energy & in low-charge-density strong absorpon momentum conservaon) regime Herz, Ann. Rev. Phys. Chem. 67 (2016) DOI:10.1146/annurev-physchem-040215-112222 *see e.g. Bolink, Adv. Mater. 27, 1837 (2015); Saba, Nat. Commun. 5, 5049 (2014) Charge recombinaon mechanisms in hybrid lead trihalide perovskites

Trap-mediated (k1) Bimolecular (k2) Auger (k3) phonon

CB2

CB1 CB1 CB1 CB1 E e- trap k

VB1 VB1 VB1 VB1

Rate equaon governing the recombinaon dynamics

Examine temperature-dependence of each rate constant to understand the different underlying mechanisms, and how each rate can be tuned! Probing charge dynamics in hybrid perovskites

read-out pulse pump pulse chopper Woll. Examine transient THz conducvity and sample ZnTe λ/4 prism - photoluminescence (PL) decay dynamics THz following excitaon with VIS light pulse: probe THz read-out through electro-optic sampling delay δ • With increasing pump fluence, the decay

MA-PbI3-x Clx dynamics become increasingly rapid. on quartz • At low fluence, transients become mono- exponenal with ~100ns lifeme

• Can extract k1, k2, k3 from such transients THz photoconductivityTHz through global fits

• Can obtain effecve charge-carrier mobility from THz photoconducvity

Wehrenfennig, Liu, Johnston, Snaith, Herz, Energy Env. Sci. 7, 2269 (2014) J. Phys. Chem. Le. 5, 1300 (2014) Trap-mediated charge recombinaon in MAPbI3

CB1 Analysis of temperature-dependent PL from soluon-processed MAPbI3 films, excited with low fluence so that monomolecular decay dominates:

trap PL transients: PL peak Ÿ orthorhombic tetragonal cubic and absorpon onset Ÿ

VB1 energies as a funcon of T:

orthorhombic tetragonal cubic

MAPbI3

! ! ! • Mono-molecular charge recombinaon at low fluences in the photoluminescence transient tail • Trap-related charge-carrier recombinaon becomes faster at higher temperatures Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Trap-mediated charge recombinaon in MAPbI3

+ CB1 Increased trap-mediated recombinaon rate with increasing temperature:

trap + MAPbI3 ~20meV Ea At high T, ionized, charged VB1 impuries may have larger cross-secon for charge capture. Acvaon energy crystal-phase specific, but mostly shallow traps at room-temperature

14 -3 Relevance to PV operaon: n<10 cm • leads to decline in charge-carrier diffusion lengths Ld (also because charge mobility declines with increasing T) MAPbI3 • But: sll high Ld~1μm at 70°C.

Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Bi-molecular recombinaon (k2) in hybrid lead trihalide perovskites

CB1 What are the mechanisms governing bimolecular recombinaon in lead-halide perovskites?

VB1 One possible model: Langevin theory • Electron moves in electric field generated by hole E J=neμE(r) _ • Capture and recombinaon occurs at distance r + c r where interacon energy is comparable to kbT. c r 0 2 • Current into capture radius: I=ne μ/ε0εr must be kbT equal to rate of change of charge density through capture at: recombinaon: dQ/dt=nek2

Material Mobility Measured k2/μ k2/μ : e/ε0εr Rao defies

evaporated 2 -1 -1 -12 -6 Langevin Φμ=33cm V s k2/μ=3.3×10 cm V 3×10 εr : 1 MA-PbI3-xClx limit by ≈5

2 -1 -1 -6 orders of Anthracene μ=2cm V s k2/μ=6×10 cm V 3.3 : 1 magnitude! Wehrenfennig, Liu, Johnston, Snaith, Herz, Energy Env. Sci. 7, 2269 (2014) Bimolecular charge-recombinaon in MAPbI3: dependence on temperature T

CB1 Photoconducvity dynamics in thin films of MAPbI3 as a funcon of temperature: • Higher-order recombinaon becomes more prominent at lower temperature VB1 • Extract bimolecular recombinaon rate

constant k2 as a funcon of T:

MAPbI3

• Expected from Langevin Theory: charge- carrier mobility increases with decreasing T • From band-structure picture: enhancements in band-edge transions as thermal ! occupaon of electron-hole states narrows Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Auger charge-recombinaon in MAPbI3: dependence on temperature phonon CB2 Auger rate constants (k3) in MAPbI3:

• k3 shows expected strong dependence on temperature CB1 CB1 • shows different temperature-dependences in different crystal structures VB1 VB1 • Confirms strong dependence on bandstructure & phonons • Allows tuning through structure/compositon modificaon

Relevance for devices:

-28 MAPbI3 • at room temperature: k3~10 cm6s-1 • ~25×higher than that for GaAs (4×10-30cm6s-1) • Auger recombinaon contributes significantly for n>>1018cm-3, so not parcularly relevant for PV, but highly important for lasers. Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Charge-carrier mobilies in MAPbI3

Are charge Drude conducvity: mobilies in high-quality lead iodide perovskite films near the intrinsic limit?

THz photoconducvity spectra are MAPbI3 Re(σ) compable with a Drude-response, i.e. only limited by Im(σ) momentum scaering conductivityσ

0 ω The mobility increases with decreasing T according to T-1.5 in accordance with charge scaering off phonons

MAPbI3 è scaering off impuries and/or crystal boundaries can only play a minor role. è At T=300K, μ~30 cm2/(Vs) è Unlikely to see increases by many En. Environ. Sci. 7, 2269 (2014) Adv. Func. Mater. 25, 6218 (2015) orders of magnitude

Charge-carrier diffusion in MAPbI3 films

Can predict what will happen with charge diffusion if trap density is reduced! Evaluate charge-carrier diffusion length LD in MAPbI3 using:

where , and we 2 -10 3 -1 assume μ=30cm /(Vs), k2=10 cm s , -28 6 -1 k3=10 cm s

In the limit of ultra-low k1, LD depends strongly on charge density n, approaching: nAM1.5

Meaningful values of LD can only be obtained with reference to the charge- Johnston & Herz, Acc. Chem. Res. 49, 146 (2016) carrier density present! Calculang charge-carrier density present in MAPbI3 under solar irradiance

Obtain spaally averaged value of the charge-carrier density nAM1.5 present under solar illuminaon, non-charge extracng condions (flat band, near VOC) Step 1: obtain charge-carrier generaon rate under AM1.5 condions: Charge Generation Rate in300nm thick MAPbI under CW AM1.5 illumination 3 1.5

Max Gen Rate = 1.32e+22cm−3s−1 ) 1 − s 3 −

cm 1 22 +

0.5 Ave Gen Rate = 3.96e+21cm−3s−1 Generation Rate (10

0 0 50 100 150 200 250 300 depth (nm)

Step 2: solve cubic equaon (dn/dt=0): 2 3 =nk1+n k2+n k3 to obtain steady-state value of the charge-carrier density nAM1.5 as a -10 3 -1 funcon of k1 (assuming k2=10 cm s -28 6 -1 and k3=10 cm s )

Johnston & Herz, Acc. Chem. Res. 49, 146 (2016) Charge-carrier diffusion in MAPbI3 films

Can predict what will happen with charge diffusion if trap density is reduced! Evaluate charge-carrier diffusion length LD in MAPbI3 using:

where , and we 2 -10 3 -1 assume μ=30cm /(Vs), k2=10 cm s , -28 6 -1 k3=10 cm s

At AM1.5 (arrows): values around 10μm cannot be exceeded for μ=30cm2/(Vs) because bi-molecular recombinaon nAM1.5 sets a limit.

0.5 LD (y-axis) scales with μ therefore would need e.g. 2 Johnston & Herz, Acc. Chem. Res. 49, 146 (2016) μ=9200cm /(Vs) for LD=175μm

Radiave efficiencies of lead halide perovskite films

Radiave efficiency Φ in MA-PbI3 as a funcon of charge-carrier density n: • Calculate Φ using

for different non-radiave trap-related recombinaon rates k1, assuming -10 3 -1 radiave k2=10 cm s , non-radiave -28 6 -1 k3=10 cm s -1 • Onset of high Φ for τ=k1 =10-100ns occurs at 1-10×1018cm-3 • corresponds to excitaon fluences 7-70μJcm-2 typically reported for ASE or lasing • Onsets of ASE and efficient light emission at lower charge-carrier densies <1015cm-3 will require trap- Johnston & Herz, Acc. Chem. Res. 49, 146 (2016) related lifemes in excess of μs. Lead-free? Charge recombinaon and diffusion in MASnI3

For MASnI3, monomolecular recombinaon MA-SnI3 on compact TiO2 layer is 3 orders of magnitude faster that in

typical MAPbI3. Caused by sizeable p-doping through Sn4+ which governs the charge dynamics: THz photoconductivityTHz

photogenerated + doping Energy Environ. Sci. 7, 3061 (2014) hole densies • From fits: k =8×109 s-1 (τ=110ps) yielding 1 -1 18 -3 hole doping density: doping density: φ p0=5.8×10 cm 15 -3 17 -3 p0=10 cm [see e.g. J. Solid State Chem. 205, 39 (2013): p0= 9×10 cm ] 16 -3 • But: decent effecve charge-carrier 10 cm mobility: φμ=1.6 cm2V-1s-1 1017 cm-3 1018 cm-3 If unintenonal doping and trapping in actual: 5.8×1018 cm-3 MA-SnI3 can be controlled, long charge- carrier diffusion lengths are feasible MASnI3: temperature-dependent PL spectra

• Phase transion at ~110K from tetragonal to orthorhombic structure • Full-width at half maximum of the PL emission suddenly narrows at the phase transion! • Observe higher-lying emission peaks possibly originang from transions involving higher-lying bands:

• Can this excess energy be harvested?

MASnI3: temperature-dependent PL spectra

• Large (~200meV) Stokes shi between PL peak emission energy and

absorpon edge (for MAPbI3 this is only at most a few tens of meV!) • Sign of significant energec disorder introduces by defects • At T>110K temperature-dependence of emission FWHM is typical for charge- carrier scaering with ionized impuries • Sharp drop in FWHM below 110K suggests that unintenonal dopant carrier concentraon drops significantly at the phase transion!

Parro, Milot, Stergiopoulos, Snaith, Johnston, Herz, JPC Leers 7, 1321 (2016) MASnI3: temperature-dependent PL transients

• Significant increase in PL lifemes below 110K again suggests that unintenonal dopant carrier concentraon drops at the phase transion! • Small changes in crystal structure seem sufficient to reduce background doping concentraon! CBM

defect level _ kT

• Can we replicate this effect e.g. through A-caon replacement?

Parro, Milot, Stergiopoulos, Snaith, Johnston, Herz, JPC Leers 7, 1321 (2016) Tunable mixed halide system: FAPb(BryI1-y)3:

• FAPb(BryI1-y)3 is a highly band-gap tunable material

system that may allow applicaons in tandem cell FAPbBr3 c • But: instability near the central region (0.3

y=1 (bromide)

FAPbI3

cubic trigonal

y=0 (iodide)

Rehman, Milot, Eperon, Wehrenfennig, Boland, Snaith, Johnston, Herz, Eperon, Stranks, Menelaou, Johnston, Herz, Snaith Adv. Mater. 27, 7938 (2015) Energy Environ. Sci. 7, 982 (2014) Tunable mixed halide system: FAPb(BryI1-y)3:

But: FAPb(BryI1-y)3 is unstable under illuminaon, in parcular for 0.3

Invesgate optoelectronic properes of as-cast materials, Rehman, Milot, Eperon, Wehrenfennig, at low excitaon intensity and Boland, Snaith, Johnston, Herz, before light-induced changes Adv. Mater. 27, 7938 (2015) have occurred. Effect of disorder in FAPb(BryI1-y)3:

FAPb(BryI1-y)3 shows increase in disorder, trap density and decrease in charge-carrier mobility near the central region (0.3

• Trap-related recombinaon rates (k1) are highest for mixed-halide material • Increased FWHM of PL in central region indicave of higher energec disorder 2 • Mobility values dive between FAPbI3 (27cm /Vs) and 2 2 FAPbBr3 (14cm /Vs) to values <1cm /Vs for y=0.4 • Charge-carrier diffusion lengths under ~AM1.5:

Rehman, Milot, Eperon, Wehrenfennig, Boland, Snaith, Johnston, Herz, Adv. Mater. 27, 7938 (2015) Bimolecular charge-recombinaon in FAPb(BryI1-y)3: dependence on bromide content y

CB1 Photoconducvity dynamics in thin films of following VIS excitaon: • Higher-order recombinaon becomes VB1 more prominent for higher y • Extract bimolecular recombinaon rate

constant k2 as a funcon of y:

• k2 increases with bromide fracon y • link with electronic bandstructure? • affected by exciton binding energy?

Rehman, Milot, Eperon, Wehrenfennig, Boland, Snaith, Johnston, Herz, Adv. Mater. Adv. Mater. 27, 7938 (2015) Auger charge-recombinaon in hybrid perovskites: dependence on bandstructure phonon CB2 Auger rate constants (k3) in FAPb(BryI1-y)3:

• k3 increases with increasing bromide y in FAPb(BryI1-y)3 CB1 CB1 • Confirms strong dependence on bandstructure • Allows tuning through structure modificaon VB1 VB1

FAPb(BryI1-y)3

Relevance for devices: -28 • at room temperature: k3~10 cm6s-1 • ~25×higher than that for GaAs (4×10-30cm6s-1) • Auger recombinaon contributes significantly for n>>1018cm-3, bromide fraction y so not parcularly relevant for PV, Rehman, Milot, Eperon, Wehrenfennig, but highly important for lasers. Boland, Snaith, Johnston, Herz, Adv. Mater. 27, 7938 (2015) Solving the instability problem in mixed-halide perovskites

Choose system A-Pb(BryI1-y)3 that has the same structure for A-PbI3 and A-PbBr3:

FA-Pb(BrxI1-x)3 FA0.83Cs0.17-Pb(BrxI1-x)3 FA Cs -PbI FA-PbI3 cubic cubic 0.83 0.17 3 instability region region instability stable stable XRDcounts

FA-PbBr3 FA Cs -PbBr trigonal cubic 0.83 0.17 3

McMeekin, Sadoughi, Rehman, Eperon, Saliba, Hörantner, Haghighirad, Sakai, Korte, Rech, Johnston, Herz, Snaith, Science 351, 151 (2016) Stable mixed-halide perovskites with mixed Cs-FA caons

Optoelectronic properes of FA0.83Cs0.17Pb(Br0.4I0.6)3

• Band-gap at 1.74eV ideal for tandem with Si FA Cs Pb(Br I ) Charge-carriera 0 .8recombination3 0.17 0.4 0.6 3 2 69 µJ/cm

dynamics 6 -1 48 µJ/cm2 • Good monomolecular lifeme: 157ns 3 k1 = 6 x10 [s ] 2 -10 3 -1 34 µJ/cm

] k = 0.4 x10 [cm s ] 2 2 2 - 24 J/cm -28 6 -1 µ • High stability under intense light illuminaon 0 k3 = 0.3 x10 [cm s ] 2 1 17 µJ/cm [ 2 µ = 21 [cm² V-1 s-1] 2 T 12 µJ/cm 2 / 2 • T 9 µJ/cm High charge-carrier mobility (21cm /Vs) Δ - 1 • Long charge-carrier diffusion length (~3μm) • Low Urbach energy (16meV) 0 0 500 1000 1500 2000 2500 • Pump-Probe Time Delay [ps] 17% PCE in planar-heterojuncon solar cell

FA Cs Pb(Br I ) 1 b 0.83 0.17 0.4 0.6 3 FA0.83Cs0.17Pb(Br0.4I0.6)3 4s ] 8s FA0.83Cs0.17Pb(Br0.4I0.6)3 m

µ 1.0 60s [

120s ] PL d L )

e d

180s z e h i t l z

i 0.8

l spectra a g 1 15 -3 240s L(10 cm ) = 2.9 m a -2 n µ 5 W cm m

Charge-carrier m r r e

under o o L n N

( [

diffusion length (at 0.6 -2 n

y 0.1 y

t 5Wcm t i o i

i 15 -3 s s n

s 10 cm ) ~ 3µm n e t u e t f n 0.4 f I n i I

L D L P PLLife tlifetimeime τ = 157 n157nss 0.1 P 0.2 1015 1016 1017 1018 1019 1020 0.0 0.01 Charge Carrier Concentration [cm-3] 660 680 700 720 740 760 780 800 0 50 100 150 200 250 300 350 400 Wavelength (nm) Time [ns] McMeekin, Sadoughi, Rehman, Eperon, Saliba, Hörantner, Haghighirad, Sakai, Korte, Rech, Johnston, Herz, Snaith, Science 351, 151 (2016) Conclusions & Acknowledgements

• Charge-recombinaon in hybrid metal halide perovskites has contribuons from 1. Trap-related monomolecular rates depending on trap-density & depth 2. Bimolecular electron-hole recombinaon that is strongly non-Langevin 3. Auger recombinaon that depends on bandstructure and temperature • At AM1.5 charge-carrier diffusion lengths in lead iodide perovskites with μ=30cm2/ (Vs) will not exceed ~10μm even if all trap-related recombinaon is eliminated. • Lowering the onset of efficient light emission into the intermediate charge-density regime (<1015cm-3) requires trap-related lifemes well in excess of microseconds

• MA-SnI3: much faster monomolecular recombinaon due to n vacancy (p-doping)

• A-Pb(BryI1-y)3: A=MA, FA exhibit stability gap in central region where the crystal structure changes, which can be overcome by use of mixed caesium/FA caons

Co-workers and collaborators:

Rebecca Milot, Waqaas Rehman, Chrisan Wehrenfennig, David McMeekin, Beth Parro, Ming Zhen Liu, Giles Eperon, Chris Menelaou, Michael Johnston, Henry Snaith Physics, University of Oxford 3-year early stage researcher posion available on new ITN network: "Interfaces in opto-electronic thin film mullayer devices" (INFORM). EC eligibility criteria: • Not resident in the UK for more than 12 months in the past three years • No PhD Thesis submied yet (could come as PhD student or first postdoc) • no more than 4 years full me research experience If interested & eligible, email or talk to me: [email protected] Parcipang group leaders at Oxford: Laura Herz, Michael Johnston, Henry Snaith Parcipang Instuons: Imperial College London, University of Oxford, Technion, University of Bayreuth, Humboldt Universität Berlin, TU Eindhoven, Holst Center, InnovaonLab, Universite de Fribourg, University of Cyprus, Universitat de Valencia