Supplementary Information: Free Charge Photogeneration in ...

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1 Supplementary Information: Free Charge 1 Photogeneration in a Single Component High Photovoltaic 2 Efficiency Organic Semiconductor 3 Michael B. Price a,b,1, *, Paul A. Hume a,b,1, *, Aleksandra Ilina a,b , Isabella Wagner a,b , Ronnie R. 4 Tamming a,b , Karen E. Thorn a,b , Wanting Jiao c , Alison Campbell d , Patrick J. Conaghan d , Girish 5 Lakhwani d , Nathaniel J.L.K. Davis a,b , Yifan Wang e,f , Peiyao Xue e , Heng Lu e , Kai Chen a,b , 6 Xiaowei Zhan e , Justin M. Hodgkiss a,b, * 7 8 a School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington, New 9 Zealand 10 b MacDiarmid Institute for Advanced Materials and Nanotechnology, New Zealand. 11 c Ferrier Research Institute, Victoria University of Wellington, Wellington, New Zealand 12 d ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Sydney, NSW 13 2006, Australia 14 e School of Materials Science and Engineering, Peking University, Beijing 100871, China. 15 f College of Materials Science and Engineering, Qingdao University, Qingdao 266071, China 16 17 * Correspondence should be sent to J.M.H. ([email protected]), P.A.H. 18 ([email protected]), and M.B.P. ([email protected]) 19 1 Authors contributed equally to this work 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Transcript of Supplementary Information: Free Charge Photogeneration in ...

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Supplementary Information: Free Charge 1

Photogeneration in a Single Component High Photovoltaic 2

Efficiency Organic Semiconductor 3

Michael B. Pricea,b,1,*, Paul A. Humea,b,1,*, Aleksandra Ilinaa,b, Isabella Wagnera,b, Ronnie R. 4 Tamminga,b, Karen E. Thorna,b, Wanting Jiaoc, Alison Campbelld, Patrick J. Conaghand, Girish 5 Lakhwanid, Nathaniel J.L.K. Davisa,b, Yifan Wange,f, Peiyao Xuee, Heng Lue, Kai Chena,b, 6 Xiaowei Zhane, Justin M. Hodgkissa,b,* 7

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a School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington, New 9 Zealand 10

b MacDiarmid Institute for Advanced Materials and Nanotechnology, New Zealand. 11

c Ferrier Research Institute, Victoria University of Wellington, Wellington, New Zealand 12

dARC Centre of Excellence in Exciton Science, School of Chemistry, University of Sydney, NSW 13 2006, Australia 14

e School of Materials Science and Engineering, Peking University, Beijing 100871, China. 15

f College of Materials Science and Engineering, Qingdao University, Qingdao 266071, China 16

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* Correspondence should be sent to J.M.H. ([email protected]), P.A.H. 18 ([email protected]), and M.B.P. ([email protected]) 19

1 Authors contributed equally to this work 20

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Table of contents 34

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Figure S1. Chemical structures, names, and abbreviations for all materials discussed in the 36

main manuscript. ........................................................................................................................ 3 37

Figure S2. Intensity-dependent photoluminescence quantum efficiency on multiple Y6 thin 38

films (normalised). ..................................................................................................................... 4 39

Figure S3. TA spectra and kinetics of Y6 in solid solution of polystyrene versus neat film. ... 5 40

Figure S4. Fluence dependent exciton kinetics from transient absorption. ............................... 5 41

Figure S5. Excitation energy-dependent exciton kinetics from transient absorption. ............... 6 42

Figure S6. Evidence of long-lived triplets in Y6 neat thin film transient absorption. ............... 6 43

Figure S7. Optically-pumped time-resolved terahertz absorption kinetic of neat Y6, compared 44

to transient absorption kinetic decays of excitons and charges. ................................................ 7 45

Kinetic models of Singlet, CT-state, and Free Charge interconversion .................................... 8 46

Table S1. Rate constants based on Singlet-CT state-free charge model from transient 47

absorption and PLQE measurements. ........................................................................................ 9 48

Figure S8. Variance of Model 1 kinetics compared to measured TA kinetics for simulated 49

PLQE’s that include a rise in value with fluence. .................................................................... 10 50

Table S2. Rate constants based on singlet-free charge model from transient absorption and 51

PLQE measurements. ............................................................................................................... 11 52

Figure S9. Model 2, with no CT states, fitted to experimental TA, PLQE, and compared to 53

the Saha equation. .................................................................................................................... 12 54

Figure S10. Variance of Model 2 kinetics compared to measured TA kinetics for simulated 55

PLQE’s that include a rise in value with fluence. .................................................................... 13 56

Photon Reabsorption in thin films ........................................................................................... 14 57

Figure S11. Simulated PLQE of Y6 with and without the effect of photon recycling. ........... 14 58

Figure S12. Current density-voltage (J-V) curves for single component Y6 devices with 59

different hole extraction layers. ............................................................................................... 15 60

Figure S13. Intensity dependence of short-circuit current density in a low range – from 0.024 61

to 0.1 suns. ............................................................................................................................... 15 62

Figure S14. J-V curves for Y6 devices with very low donor content of PTB7-Th. ................ 16 63

Figure S15. Exciton, electron, and hole dynamics in a 1:1.2 PTB7-Th:Y6 blend measured by 64

transient absorption. ................................................................................................................. 16 65

Figure S16. Exciton and charge kinetics for neat Y6 compared to Y6 blended with 0.2 weight 66

fraction PCBM. ........................................................................................................................ 17 67

Figure S17. Energy levels and electronic couplings for localized exciton and CT states. ...... 18 68

Figure S18. Ionization energy (IE) and electron affinity (EA) calculated using long-range 69

polarizable embedding of charges in a model thin film. .......................................................... 18 70

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Figure S1. Chemical structures, names, and abbreviations for all materials discussed in 73 the main manuscript. a) 2,20-((2Z,20Z)-((12,13-bis(2-ethylhexyl)-3,9-diundecyl-12,13-74 dihydro-[1,2,5]thiadiazolo[3,4-e]thieno[2,"30':4',50]thieno[20,30:4,5]pyrrolo[3,2-75 g]thieno[20,30:4,5]thieno-[3,2-b]indole-2,10-diyl)bis(me-thanylylidene))bis(5,6-difluoro-3-76

oxo-2,3-dihydro-1H-indene-2,1-diylidene))dimalononitrile (Y6)1, b) Poly[(2,6-(4,8-bis(5-(2-77 ethylhexyl-3-fluoro)thiophen-2-yl)-benzo[1,2-b:4,5-b’]dithiophene))-alt-(5,5-(1’,3’-di-2-78 thienyl-5’,7’-bis(2-ethylhexyl)benzo[1’,2’-c:4’,5’-c’]dithiophene-4,8-dione)] (PM6)2, 79 c) 2,2’-[(4,4,9,9-Tetrahexyl-4,9-dihydro-s-indaceno[1,2-b:5,6-b’]-dithiophene-2,7-80

diyl)bis[methylidyne(3-oxo-1H-indene-2,1(3H)-diylidene)]]bis-propanedinitrile (IDIC)3, 81 d) Poly(4-butyltriphenylamine) (Poly-TPD), e) Phenyl-C61-butyric acid methyl ester 82 (PC61BM), f) Poly[4,8-bis(5-(2-ethylhexyl)thiophen-2-yl)benzo[1,2-b;4,5-b']dithiophene-2,6-83 diyl-alt-(4-(2-ethylhexyl)-3-fluorothieno[3,4-b]thiophene-)-2-carboxylate-2-6-diyl)] 84

(PTB7-Th)4. 85

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Figure S2. Intensity-dependent photoluminescence quantum efficiency on multiple Y6 89 thin films (normalised). Measurements were performed on separate days, on 4 different spots 90

on two different spin-coated films. Films were exposed to air for between 2-6 hours during the 91

measurements. Primary sources of error arise from slightly different film thicknesses of 92

different films and different excitation spots, and fluctuations of laser power. A rise in PLQE 93 with intensity is still clearly observed in the ensemble data. 94

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Figure S3. TA spectra and kinetics of Y6 in solid solution of polystyrene versus neat film. 101

a) Time-slices of Y6 in a solid solution of polystyrene (1:50 weight ratio), at low excitation 102 fluence of ~0.5 Β΅Jcm-2. The spectra is markedly different to the thin-film spectra shown in main 103 text Figure 2a, where there is no longer-lasting red-shifted negative peak, indicating only 104 excitons are present. b) Kinetics of the excitonic peak of the Y6 in polystyrene, in blue, versus 105

the extracted charge/CT kinetics from a neat thin film of Y6 showing a much longer decay. 106

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109

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Figure S4. Fluence dependent exciton kinetics from transient absorption. A fast fluence 111 independent decay is present in the first picosecond of the exciton kinetics, extracted by genetic 112 algorithm from transient absorption measurements at specified excitation intensities, pumped 113

with 700 nm pulses. 114

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Figure S5. Excitation energy-dependent exciton kinetics from transient absorption. 118

Pumped with intensities giving approximately 2.5 Γ— 1014 carriers/cm3, the exciton kinetics are 119 the same for the different excitation wavelengths. 120

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Figure S6. Evidence of long-lived triplets in Y6 neat thin film transient absorption. a) 122

Time-slices of un-normalised spectra at later times (beyond 100 ps) of neat Y6 excited at 123 5 Γ— 1014 carriers/cm3, with 700 nm, 150 fs pulses. A rise in the broad negative signal, consistent 124

with the triplet signature identified by Gillet et al.5 around 1200 nm, can be seen after ~800 ps. 125 b) Exciton, charge and triplet kinetics extracted from use of a genetic algorithm to the spectra 126

in Fig S5a. The triplet kinetic is dominant after ~500 ps, though the signal is noisy. c) Exciton, 127 charge and triplet kinetics taken from the peak positions of the respective species (915 nm, 128 980 nm, and 1200 nm), normalised, showing the growth of the triplet species after 600 ps while 129 the charge species decays. 130

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Figure S7. Optically-pumped time-resolved terahertz absorption kinetic of neat Y6, 142

compared to transient absorption kinetic decays of excitons and charges. The Terahertz 143 measurement is pumped by 800 nm, 150 fs pulses. The roughly matching Thz, and transient 144 absorption kinetics indicate that the two measurements are at roughly the same excitation 145

density, calculated as 5Γ—1015 cm-3 for the Thz measurement, and 6Γ—1015 cm-3 for the transient 146 absorption measurement. 147

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Kinetic models of Singlet, CT-state, and Free Charge interconversion 155

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Model 1: Explicit treatment of CT state population: 157

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Equation S1 shows the coupled rate equations and rate constants employed to represent 159

this model. 160

. 161

𝑑𝑆

𝑑𝑑= βˆ’(π‘Žπ‘ ,𝑁𝑅 + π‘Žπ‘ ,𝑅 + π‘Žπ‘ ,𝑠𝑝𝑙𝑖𝑑)𝑆 βˆ’ 𝑏𝑠,𝑁𝑅𝑆2 βˆ’ 𝑏𝑠,𝑐𝑑,𝑓𝑐(𝐢𝑇1 + 𝐢𝑇3 + 𝐹𝐢)𝑆 + π‘Žπ‘π‘‘,𝑓𝑒𝑠𝑒𝐢𝑇1 162

𝑑𝐢𝑇1

𝑑𝑑= βˆ’(π‘Žπ‘π‘‘,𝑁𝑅 + π‘Žπ‘π‘‘,𝑠𝑝𝑙𝑖𝑑 + π‘Žπ‘π‘‘,𝑓𝑒𝑠𝑒 + π‘Žπ‘π‘‘,𝑖𝑠𝑐)𝐢𝑇1 βˆ’ 𝑏𝑐𝑑,𝑁𝑅𝐢𝑇1

2 βˆ’ 𝑏𝑠,𝑐𝑑,𝑓𝑐𝑆 βˆ™ 𝐢𝑇1 + π‘Žπ‘ ,𝑠𝑝𝑙𝑖𝑑𝑆163

+ π‘Žπ‘π‘‘,𝑓𝑒𝑠𝑒𝐢𝑇3 + 1

4𝑏𝑓𝑐,𝑓𝑒𝑠𝑒𝐹𝐢 164

𝑑𝐢𝑇3

𝑑𝑑= βˆ’(π‘Žπ‘π‘‘,𝑁𝑅 + π‘Žπ‘π‘‘,𝑠𝑝𝑙𝑖𝑑 + π‘Žπ‘π‘‘,𝑖𝑠𝑐)𝐢𝑇3 βˆ’ 𝑏𝑐𝑑,𝑁𝑅𝐢𝑇3

2 βˆ’ 𝑏𝑠,𝑐𝑑,𝑓𝑐𝑆 βˆ™ 𝐢𝑇3 + π‘Žπ‘ ,𝑠𝑝𝑙𝑖𝑑𝑆 +3

4𝑏𝑓𝑐,𝑓𝑒𝑠𝑒𝐹𝐢165

+ π‘Žπ‘π‘‘,𝑓𝑒𝑠𝑒𝐢𝑇1 166

𝑑𝐹𝐢

𝑑𝑑= βˆ’π‘Žπ‘“π‘,𝑁𝑅𝐹𝐢 βˆ’ 𝑏𝑓𝑐,𝑓𝑒𝑠𝑒𝐹𝐢2 + 2π‘Žπ‘π‘‘,𝑠𝑝𝑙𝑖𝑑(𝐢𝑇1 + 𝐢𝑇3) 167

Where, S, CT1, CT3, and FC are the singlet, charge-transfer (singlet-like), charge-transfer 168

(triplet-like), and free charge (polaron) state concentrations, and the a and b rate constants are 169

given in Table S1. Key simplifying assumptions are that: the charge splitting rate from CT1 to 170

FC, and from CT3 to FC are the same, as are the S-CT, and S-FC bimolecular annihilation rates. 171

The bimolecular and monomolecular rates of CT1 and CT3 decay are also the same, (a higher 172

CT1 to CT3 intersystem crossing rate6 will make this assumption more accurate) 173

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Table S1. Rate constants based on Singlet-CT state-free charge model from transient 182

absorption and PLQE measurements. 183

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Species Prompt

fraction

Monomolecular rates (s-1) Bimolecular rates (cm3s-1)

Singlet 0.7** Geminate

non-radiative

π‘Žπ‘ ,𝑁𝑅 βˆ— 3.5 Γ— 109 S-S

annihilation

𝑏𝑠,𝑁𝑅 2.0 Γ— 10βˆ’8

Geminate

radiative

π‘Žπ‘ ,𝑅 βˆ— 0.4 Γ— 109

S-CT, S-FC

annihilation

𝑏𝑠,𝑐𝑑,𝑓𝑐 2.6 Γ— 10βˆ’8

Singlet→

CT1

π‘Žπ‘ ,𝑠𝑝𝑙𝑖𝑑 0.6 Γ— 109

Charge-

Transfer

0.1 CT1β†’

Singlet

π‘Žπ‘π‘‘,𝑓𝑒𝑠𝑒 2.0 Γ— 109 CT-CT

annihilation

𝑏𝑐𝑑,𝑁𝑅 2.2 Γ— 10βˆ’8

CT1β†’

Free Charge

π‘Žπ‘π‘‘,𝑠𝑝𝑙𝑖𝑑 1.7 Γ— 109

Geminate

non-radiative

π‘Žπ‘π‘‘,𝑁𝑅 2.2 Γ— 109

CT1 ↔ CT3 π‘Žπ‘π‘‘,𝑖𝑠𝑐† 1.0 Γ— 109

Free

Charge

0.2 Geminate

non-radiative

π‘Žπ‘“π‘,𝑁𝑅 1.2 Γ— 109 Non-

geminate

radiative

𝑏𝑓𝑐,𝑓𝑒𝑠𝑒 2 Γ— 10βˆ’6

*Rate constants estimated from TA and PLQE of Y6: polystyrene blends. 185

** Prompt singlet fraction is fixed by experiment. Free charge fraction here represents number of free charge 186 pairs, which is converted into absolute number of free charges as an initial condition of solving the differential 187 equations. 188

†Estimated from [Hou et al.6] 189

190

The fitted values here are illustrative of a fit that has low (relative) variance to the transient 191

absorption data, and also reproduces the rise and decay in PLQE, as seen in figures 3b and 3c 192

of the main text. With nine free parameters, the interdependency, and hence uncertainty of each 193

individual parameter is substantial, though each fitted value falls within a range that appears 194

physically plausible – for instance, the S-S annihilation rate, 𝑏𝑠,𝑁𝑅 =2.0 Γ— 10βˆ’8 cm3s-1 is lower 195

than previous literature determinations of this value7, as would be expected from our new 196

interpretation, but is still only 10 times lower than previous measurements. 197

We can use the model above to put conservative bounds on the minimum steady-state free 198

charge fraction, at a given excitation density. For a wide range of the above recombination 199

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constants, we calculate the theoretical PLQE. If the PLQE at an excitation density of 1016 cm-3 200

is greater than the PLQE at 1013 - 1015 cm-3, we calculate the error associated with the global fit 201

of the kinetic model to the fluence-dependent transient absorption kinetics of singlets and free 202

charges+CT states, and also the steady-state free charge fraction. If the calculated PLQE shows 203

no rise with increasing excitation density, it is not consistent with the rise shown in our 204

experimental PLQE data (of ~10% of max PLQE), and therefore is not included for error 205

analysis. Figure S7 shows the results of this analysis. There exist 3 local minima in the variance 206

to the TA kinetics, however we see that even with our conservative exclusion criteria (only 207

requiring a rise in PLQE with fluence of any magnitude), the model cannot admit solutions 208

where the steady state free charge fraction is lower than ~0.25 (or higher than 0.8). 209

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Figure S8. Variance of Model 1 kinetics compared to measured TA kinetics for simulated 213

PLQE’s that include a rise in value with fluence. Kinetics were normalised before 214

calculating the error. 215

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Model 2: Only Singlet and Free Charge, no explicit CT states: 225

Equation S2 shows the coupled rate equations and rate constants employed to represent 226

this model. 227

𝑑𝑆

𝑑𝑑= βˆ’(π‘Žπ‘ ,𝑁𝑅 + π‘Žπ‘ ,𝑅 + π‘Žπ‘ ,𝑠𝑝𝑙𝑖𝑑)𝑆 βˆ’ 𝑏𝑠,𝑁𝑅𝑆2 βˆ’ 𝑏𝑠,𝑓𝑐𝐹𝐢 βˆ™ 𝑆 +

1

2𝑏𝑓𝑒𝑠𝑒 βˆ™ 𝐹𝐢 228

𝑑𝐹𝐢

𝑑𝑑= βˆ’π‘Žπ‘“π‘,𝑁𝑅𝐹𝐢 βˆ’ (𝑏𝑓𝑐,𝑁𝑅 + 𝑏𝑓𝑒𝑠𝑒)𝐹𝐢2 + 2π‘Žπ‘ ,𝑠𝑝𝑙𝑖𝑑 βˆ™ 𝑆 229

Where, S, and FC are the singlet, and free charge (polaron) state concentrations, and the a and 230

b rate constants are given in Table S2. 231

Table S2. Rate constants based on singlet-free charge model from transient absorption 232

and PLQE measurements. 233

234

Species Prompt

fraction

Monomolecular rates (s-1) Bimolecular rates (cm3s-1)

Singlet 0.7** Geminate

non-radiative

π‘Žπ‘ ,𝑁𝑅 βˆ— 3.5 Γ— 109 S-S

annihilation

𝑏𝑠,𝑁𝑅 2.6 Γ— 10βˆ’8

Geminate

radiative

π‘Žπ‘ ,𝑅 βˆ— 0.4 Γ— 109

S-FC

annihilation

𝑏𝑠,𝑓𝑐 3.2 Γ— 10βˆ’8

Singletβ†’ FC π‘Žπ‘ ,𝑠𝑝𝑙𝑖𝑑 0.6 Γ— 109

Free

Charge

0.3** Geminate

non-radiative

π‘Žπ‘“π‘,𝑁𝑅 0.9 Γ— 109 Non-

geminate

radiative

𝑏𝑓𝑐,𝑓𝑒𝑠𝑒 6 Γ— 10βˆ’8

Non-

geminate,

non-

radiative

𝑏𝑓𝑐,𝑁𝑅 1 Γ— 10βˆ’8

*Rate constants estimated from TA and PLQE of Y6: polystyrene blends. 235

** Prompt singlet and charge fraction is fixed by experiment. Free charge fraction here represents number of free 236 charge pairs, which is converted into absolute number of free charges as an initial condition of solving the 237 differential equations. 238

239

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Figure S9. Model 2, with no CT states, fitted to experimental TA, PLQE, and compared 241 to the Saha equation. a) Model 2, above, fitted to fluence dependent exciton and charge 242

kinetics from transient absorption. b) the same model overlaid on fluence-dependent PLQE 243 data c) Comparison of the free charge fraction calculated from the kinetics model, red line, to 244

a model from the Saha equation, blue line, with an effective mass of 1.7 me and exciton binding 245 energy, EB = 175 meV. 246

247

248

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250

Figure S10. Variance of Model 2 kinetics compared to measured TA kinetics for 251

simulated PLQE’s that include a rise in value with fluence. Kinetics were normalised before 252

calculating the error. The error is calculated as described above for Model 1, specifying the 253

criteria as needing a rise in PLQE. The variance for this model is smaller than that found for 254

the more complex Model 1, and the smallest free charge fraction at steady state is ~0.74. In this 255

model, the variance minima occurs for a steady-state free charge fraction of between 0.74 and 256

0.83. 257

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Photon Reabsorption in thin films 275

Photon reabsorption effects in photoluminescence quantum efficiency (PLQE) measurements 276

were quantified as per Richter et al.8 We estimated the escape probability with the same 277

method8, based on the optical ellipsometric constants measured by Kerremans et al.9, giving a 278

conservative estimate of escape cone loss of πœ‚π‘’π‘ π‘ = 15%. The externally measured PLQE, 279

including effects of reabsorption and photon recycling, is given by, 280

πœ‚π‘’π‘₯𝑑 = πœ‚ βˆ™ πœ‚π‘’π‘ π‘

1 βˆ’ πœ‚ + πœ‚ βˆ™ πœ‚π‘’π‘ π‘ 281

Where πœ‚ is the internal PLQE. With no photon recycling, πœ‚π‘’π‘₯𝑑 = πœ‚ βˆ™ πœ‚π‘’π‘ π‘ 282

283

284

Figure S11. Simulated PLQE of Y6 with and without the effect of photon recycling. The 285 simulated, fluence dependent PLQE based on model 2 above, illustrating the small, but non-286 zero enhacement in externally measured PLQE expected due to photon-recycling in thin films 287

of Y6. 288

289

290

291

292

293

294

295

296

297

298

299

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0.0 0.2 0.4 0.6 0.8 1.0 1.2-6

-4

-2

0

2

4

6

Y6 single component

Cu

rre

nt

den

sit

y (

mA

cm

-2)

Voltage (V)

with PCP-Na

with PEDOT:PSS

300

Figure S12. Current density-voltage (J-V) curves for single component Y6 devices with 301

different hole extraction layers. With PEDOT:PSS, PCE of the best performing device pixel 302

was 0.09%. With PCP-Na,10 the best performing device achieved 0.63% PCE. 303

304

305

Figure S13. Intensity dependence of short-circuit current density in a low range – from 306 0.024 to 0.1 suns. The blue line shows a fit to the current vs intensity with an exponent of 307

0.985, indicating small bimolecular and space-charge recombination losses at these very low 308 fluences. 309

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0.0 0.2 0.4 0.6 0.8 1.0-10

-5

0

5

10

PTB7-Th:Y6

Cu

rre

nt

den

sit

y (

mA

cm

-2)

Voltage (V)

1:50

1:100

310

Figure S14. J-V curves for Y6 devices with very low donor content of PTB7-Th. For the 311

device with a ratio of PTB7-Th:Y6 ratio of 1:100, power conversion efficiency was 1.23%, and 312

for the 1:50 blend, PCE was 2.26%. 313

314

315

316

317

Figure S15. Exciton, electron, and hole dynamics in a 1:1.2 PTB7-Th:Y6 blend measured 318 by transient absorption. a) un-normalised transient absorption measurements of a blend film 319 excited with 800 nm, 150 fs pulses, at 1x1014 carriers/cm3. Exciton, Y6 charge, and PTB7-Th 320 charge kinetics are attained by using the genetic algorithm described in the main text, with 321

mask spectra also described in main text Fig 2. As expected, the PTB7-Th hole lags the Y6 322 charge signature rise. And the Y6 charge rise shows a higher prompt rise than the PTB7-Th 323 charge prompt rise b) Normalised kinetics of those shown in Fig S15a. 324

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325

Figure S16. Exciton and charge kinetics for neat Y6 compared to Y6 blended with 0.2 326

weight fraction PCBM. a) Un-normalised exciton kinetics from transient absorption of neat 327 Y6 and Y6:PCBM measured at the same excitation density, approx. 5x1014 cm-3, excited with 328

800 nm, 150 fs pulses. b) the corresponding charge kinetics. While the exciton decay is 329 accelerated for the Y6 PCBM blend between 1- 800 ps compared to the neat Y6, the charge 330 decay is slowed in the blend film compared to the neat film. This supports the hypothesis that 331

increased quadrupolar fields in the blend film can delay charge recombination, and shift the 332 dynamic exciton-charge equilibrium slightly towards charges. 333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

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18

Pair 1

E (eV) |𝑉| (meV)

Ex1 Ex2 CT1 CT2 GS

Ex1 1.73 - 46 36 5 9

Ex2 2.01 46 - 86 32 5

CT1 1.69 36 86 - 35 76

CT2 2.03 5 32 35 - 36

351

352

353

354

355

356

Figure S17. Energy levels and electronic couplings for localized exciton and CT states. 357

Calculations were performed on Ο€-stacked molecular pairs extracted from the Y6 crystal 358

structures (Figure 5), with alkyl chains truncated to ethyl to reduce computational expense. 359

Localized states were obtained from a separate calculation in which the molecules were 360

separated from one another by 10 Γ…. At this distance, interactions involving orbital overlap are 361

negligible, resulting in the formation of localized CT states. Localized excitonic states were 362

obtained by applying the fragment excitation difference diabatization scheme to the relevant 363

adiabatic states of the reference system.11 The non-orthogonality of the localized states in the 364

crystal geometry is accounted for by application of a LΓΆwdin orthogonalization, however we 365

note that the effect of this procedure on the calculated values is minor in the present example.12 366

367

368

Figure S18. Ionization energy (IE) and electron affinity (EA) calculated using long-range 369 polarizable embedding of charges in a model thin film. Calculations were performed for all 370 molecules (1536 in total) in a 10 nm thick model thin film based on molecular dynamics 371

equilibration of the Y6 crystal structure. Dashed lines indicate the DOS onsets determined by 372 photoelectron spectroscopy in air (-IE), and inverse photoemission spectroscopy (EA).13 373

374

375

376

Pair 2

E (eV) |𝑉| (meV)

Ex1 Ex2 CT1 CT2 GS

Ex1 1.72 - 38 72 23 4

Ex2 2.02 38 - 55 85 8

CT1 1.69 72 55 - 65 59

CT2 1.86 23 85 65 - 30

Pair 3

E (eV) |𝑉| (meV)

Ex1 Ex2 CT1 CT2 GS

Ex1 2.00 - 37 25 35 19

Ex2 2.01 37 - 35 25 4

CT1 2.02 25 35 - 0 5

CT2 2.04 35 25 0 - 3

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19

References 377

1. Zhang, G. et al. Single-Junction Organic Solar Cell with over 15% Efficiency Using 378 Fused-Ring Acceptor with Electron-Deficient Core. Joule 1–12 (2019) 379 doi:10.1016/j.joule.2019.01.004. 380

2. Zhang, M., Guo, X., Ma, W., Ade, H. & Hou, J. A Large-Bandgap Conjugated 381 Polymer for Versatile Photovoltaic Applications with High Performance. Adv. Mater. 382 27, (2015). 383

3. Lin, Y. et al. A Facile Planar Fused-Ring Electron Acceptor for As-Cast Polymer Solar 384 Cells with 8.71% Efficiency. J. Am. Chem. Soc. 138, (2016). 385

4. Liao, S. H., Jhuo, H. J., Cheng, Y. S. & Chen, S. A. Fullerene derivative-doped zinc 386 oxide nanofilm as the cathode of inverted polymer solar cells with low-bandgap 387

polymer (PTB7-Th) for high performance. Adv. Mater. 25, (2013). 388

5. Gillett, A. J. et al. The role of charge recombination to spin-triplet excitons in non-389 fullerene acceptor organic solar cells. ArXiv (2020). 390

6. Hou, Y. et al. Charge separation, charge recombination, long-lived charge transfer 391 state formation and intersystem crossing in organic electron donor/acceptor dyads. J. 392

Mater. Chem. C 7, 12048–12074 (2019). 393

7. Firdaus, Y. et al. Long-range exciton diffusion in molecular non-fullerene acceptors. 394 Nat. Commun. 11, (2020). 395

8. Richter, J. M. et al. Enhancing photoluminescence yields in lead halide perovskites by 396

photon recycling and light out-coupling. Nat. Commun. (2016) 397 doi:10.1038/ncomms13941. 398

9. Kerremans, R. et al. The Optical Constants of Solution-Processed Semiconductorsβ€”399

New Challenges with Perovskites and Non-Fullerene Acceptors. Adv. Opt. Mater. 8, 400 (2020). 401

10. Cui, Y. et al. A Novel pH Neutral Self-Doped Polymer for Anode Interfacial Layer in 402

Efficient Polymer Solar Cells. Macromolecules 49, (2016). 403

11. Hsu, C. P., You, Z. Q. & Chen, H. C. Characterization of the short-range couplings in 404

excitation energy transfer. J. Phys. Chem. C 112, (2008). 405

12. LΓΆwdin, P. O. On the non-orthogonality problem connected with the use of atomic 406 wave functions in the theory of molecules and crystals. J. Chem. Phys. 18, (1950). 407

13. Karuthedath, S. et al. Intrinsic efficiency limits in low-bandgap non-fullerene acceptor 408

organic solar cells. Nat. Mater. (2020) doi:10.1038/s41563-020-00835-x. 409

410