Charge-carrier Diffusion and Radia ve Efficiencies in Hybrid Metal Halide Perovskites
Prof Laura Herz
Clarendon Laboratory, University of Oxford
VIS ? THz I
UNSW 2016 The race for efficient, cost-effec ve 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 heterojunc on” 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 separa on diffusion lengths → doping • Low charge-carrier diffusion lengths gradients or electron/hole- → must separate charges into selec ve contacts suffice to different material components to collect charges effec vely inhibit recombina on
Organic Photovoltaics (OPV) 200 nm - + - + - + - +
Typical examples: crystalline silicon Typical examples: Dye-sensi zed solar or GaAs solar cells cells (DSC), organic photovoltaics (OPV) Features: highly efficient, but Features: lower efficiencies, cheap energy-intensive fabrica on (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 op cal absorp on 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 absorp on in the solar range • long (micron) charge diffusion Metal Cathode Metal Cathode HTM Perovskite HTM lengths allow for planar Perovskite Mesoporous TiO2 heterojunc on designs ETM ETM • light-emission/lasing reported Metal anode Metal anode
What are the mechanisms governing charge- carrier mobility, recombina on and diffusion? How are optoelectronic proper es affected by composi on? Outline
Prototypical MA-PbI3 & MA-PbI3-xClx: Other materials/proper es? excellent optoelectronic proper es! Lead-free? MA-SnI3 • Propensity towards n vacancies gives rise to uninten onal hole doping • Rapid charge recombina on
Tuneable materials for tandems?
• Shallow, low-density traps A-Pb(BrxI1-x)3 • Non-Langevin Bimolecular recombina on • Allows for perovskites with Eg~1.7eV • Strong radia ve bimolecular transi ons 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 recombina on 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-radia ve* radia ve , for a direct non-radia ve* semiconductor monomolecular strong dependence on hence to some extent bandstructure, phonons, par cularly detrimental required to achieve impuri es (because of energy & in low-charge-density strong absorp on momentum conserva on) 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 recombina on 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 equa on governing the recombina on 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 conduc vity and sample ZnTe λ/4 prism - photoluminescence (PL) decay dynamics THz following excita on 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- exponen al with ~100ns life me
• Can extract k1, k2, k3 from such transients THz photoconductivityTHz through global fits
• Can obtain effec ve charge-carrier mobility from THz photoconduc vity
Wehrenfennig, Liu, Johnston, Snaith, Herz, Energy Env. Sci. 7, 2269 (2014) J. Phys. Chem. Le . 5, 1300 (2014) Trap-mediated charge recombina on in MAPbI3
CB1 Analysis of temperature-dependent PL from solu on-processed MAPbI3 films, excited with low fluence so that monomolecular decay dominates:
trap PL transients: PL peak orthorhombic tetragonal cubic and absorp on onset
VB1 energies as a func on of T:
orthorhombic tetragonal cubic
MAPbI3
! ! ! • Mono-molecular charge recombina on at low fluences in the photoluminescence transient tail • Trap-related charge-carrier recombina on becomes faster at higher temperatures Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Trap-mediated charge recombina on in MAPbI3
+ CB1 Increased trap-mediated recombina on rate with increasing temperature:
trap + MAPbI3 ~20meV Ea At high T, ionized, charged VB1 impuri es may have larger cross-sec on for charge capture. Ac va on energy crystal-phase specific, but mostly shallow traps at room-temperature
14 -3 Relevance to PV opera on: n<10 cm • leads to decline in charge-carrier diffusion lengths Ld (also because charge mobility declines with increasing T) MAPbI3 • But: s ll high Ld~1μm at 70°C.
Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Bi-molecular recombina on (k2) in hybrid lead trihalide perovskites
CB1 What are the mechanisms governing bimolecular recombina on in lead-halide perovskites?
VB1 One possible model: Langevin theory • Electron moves in electric field generated by hole E J=neμE(r) _ • Capture and recombina on occurs at distance r + c r where interac on 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: recombina on: dQ/dt=nek2
Material Mobility Measured k2/μ k2/μ : e/ε0εr Ra o 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-recombina on in MAPbI3: dependence on temperature T
CB1 Photoconduc vity dynamics in thin films of MAPbI3 as a func on of temperature: • Higher-order recombina on becomes more prominent at lower temperature VB1 • Extract bimolecular recombina on rate
constant k2 as a func on of T:
MAPbI3
• Expected from Langevin Theory: charge- carrier mobility increases with decreasing T • From band-structure picture: enhancements in band-edge transi ons as thermal ! occupa on of electron-hole states narrows Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Auger charge-recombina on 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 modifica on
Relevance for devices:
-28 MAPbI3 • at room temperature: k3~10 cm6s-1 • ~25×higher than that for GaAs (4×10-30cm6s-1) • Auger recombina on contributes significantly for n>>1018cm-3, so not par cularly relevant for PV, but highly important for lasers. Milot, Eperon, Snaith, Johnston, Herz, Adv. Func. Mater. 25, 6218 (2015) Charge-carrier mobili es in MAPbI3
Are charge Drude conduc vity: mobili es in high-quality lead iodide perovskite films near the intrinsic limit?
THz photoconduc vity spectra are MAPbI3 Re(σ) compa ble with a Drude-response, i.e. only limited by Im(σ) momentum sca ering conductivityσ
0 ω The mobility increases with decreasing T according to T-1.5 in accordance with charge sca ering off phonons
MAPbI3 è sca ering off impuri es 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! Calcula ng charge-carrier density present in MAPbI3 under solar irradiance
Obtain spa ally averaged value of the charge-carrier density nAM1.5 present under solar illumina on, non-charge extrac ng condi ons (flat band, near VOC) Step 1: obtain charge-carrier genera on rate under AM1.5 condi ons: 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 equa on (dn/dt=0): 2 3
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 recombina on 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
Radia ve efficiencies of lead halide perovskite films
Radia ve efficiency Φ in MA-PbI3 as a func on of charge-carrier density n: • Calculate Φ using
for different non-radia ve trap-related recombina on rates k1, assuming -10 3 -1 radia ve k2=10 cm s , non-radia ve -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 excita on fluences 7-70μJcm-2 typically reported for ASE or lasing • Onsets of ASE and efficient light emission at lower charge-carrier densi es <1015cm-3 will require trap- Johnston & Herz, Acc. Chem. Res. 49, 146 (2016) related life mes in excess of μs. Lead-free? Charge recombina on and diffusion in MASnI3
For MASnI3, monomolecular recombina on 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 densi es • 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 effec ve charge-carrier 10 cm mobility: φμ=1.6 cm2V-1s-1 1017 cm-3 1018 cm-3 If uninten onal 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 transi on at ~110K from tetragonal to orthorhombic structure • Full-width at half maximum of the PL emission suddenly narrows at the phase transi on! • Observe higher-lying emission peaks possibly origina ng from transi ons 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
absorp on edge (for MAPbI3 this is only at most a few tens of meV!) • Sign of significant energe c disorder introduces by defects • At T>110K temperature-dependence of emission FWHM is typical for charge- carrier sca ering with ionized impuri es • Sharp drop in FWHM below 110K suggests that uninten onal dopant carrier concentra on drops significantly at the phase transi on!
Parro , Milot, Stergiopoulos, Snaith, Johnston, Herz, JPC Le ers 7, 1321 (2016) MASnI3: temperature-dependent PL transients
• Significant increase in PL life mes below 110K again suggests that uninten onal dopant carrier concentra on drops at the phase transi on! • Small changes in crystal structure seem sufficient to reduce background doping concentra on! CBM
defect level _
• Can we replicate this effect e.g. through A-ca on replacement?
Parro , Milot, Stergiopoulos, Snaith, Johnston, Herz, JPC Le ers 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 applica ons 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 illumina on, in par cular for 0.3