Photovoltaics - IPHT Jena

Institute of Photonic Technology 

Albert-Einstein-Straße 9 

07745 Jena 

PD Dr. rer. nat. habil. F. Falk 

Tel. 03641 206438 

e-mail: fritz.falk@ipht-jena.de 

Photovoltaics 

Physics and Technology of Solar Cells 

Figures and Tables 

Fritz Falk 

Institute of Photonic Technology 

Elective Course Master Photonics 

WS 2010/11 

HS3, Helmholtzweg 3 

Tuesday 14:00 - 16:00

Contents 

Manuscript in German: www. ipht-jena.de 6Institut 6 Lehre 

1 Energy Consumption and its Consequences 

1.1 Energy Consumption Yesterday, Today and Tomorrow 

1.2 Supply of Energy Sources 

1.3 The Green House Effect 

1.4 Energy Scenarios 

1.5 Requirements on Solar Cells for Different Applications 

2 Insolation 

3 Basics of Photovoltaics 

3.1 History of Photovoltaics 

3.2 Basic Principles of Solar Cells 

3.3 The Influence of the Band Gap 

3.4 Absorption Coefficient 

3.5 I-V-Diagram of a Solar Cell 

3.6 Overview on Solar Cell Types 

4 Semiconductors I: Equilibrium 

4.1 Crystal Structure 

4.2 Band Diagram 

4.3 Dynamics of Electrons 

4.4 Electrons and Holes 

4.5 Fermi Distribution and Carrier Densities in Undoped Semiconductors 

4.6 Doped Semiconductors 

4.7 Conductivity and Hall Effect 

4.8 Space Charges, Fields, Currents 

4.9 Inhomogeneities in Equilibrium 

5 Semiconductors II: Non-Equilibrium 

5.1 Optical Absorption 

5.2 Carriers in Non-Equilibrium: Quasi-Fermi Levels 

5.3 Generation and Recombination 

5.4 Balance of Charges in Non-Equilibrium 

5.5 p-n-Junction with External Voltage 

5.6 p-n-Junction under Illumination: Solar Cell 

5.7 Thermodynamics of Solar Cells and Efficiency Thresholds 

6 Solar Cell Types I: Wafer Cells 

6.1 Single Crystalline Silicon Solar Cells 

6.2 Multicrystalline Silicon Solar Cells 

7 Solar Cell Types II: Thin-Film Cells 

7.1 General Scheme of Thin-Film Cells 

7.2 Amorphous Silicon Thin-Film Cells 

7.3 Crystalline Silicon Thin-Film Cells 

7.4 Gallium Arsenide Cells 

7.5 CdTe Cells 

7.6 CIGS Cells 

7.7 Polymer Cells 

7.8 Grätzel Cell 

Contents F. Falk, Photovoltaics WS 2010/11

- 3 - 

1 Energy Consumption and ist Consequences 

Fig. 1.1: Worldwide energy consuption 

Table 1.1: Share of primary energy sources used for generation of electricity 2008) 

pit coal brown coal oil gas nuclear water 

Germany 21% 24% 1% 13% 24% 4% 

world 41% 6% 21% 14% 16% 

Fig. 1.2: Predicted energy consumption worldwide by energy sources( Shell Study 1999) 

1 Energy Consumption and ist Consequences F. Falk, Photovoltaics WS 2010/11

- 4 - 

Table 1.2: Reserves (today economically useful) and resources (today not economivally useful) 

of energy sources, and time until they are expected to be used up (as of 2004, data from: J.P. 

Gerling, F.-W. Wellmer, Chemie in unserer Zeit 39 (2005), 236) 

energy source today’s 

share 

reserves 

10 21 J 

ressources 

10 21 J 

reserves to 

last (years) 

coal 0,232 20 117 65 125 

oil 0,342 9 14 34 58 

natural gas 0,196 6 7 38 57 

gas and 

methane hydrate 

0,196 6 55 38 104 

nuclear* 0,062 1 10 25 86 

nuclear fusion 0 

* without breeder technology 

Fig. 1.3: Change of CO 2 concentration in the atmosphere 

(from Physics today, Aug. 2002) 

ressources to 

last (years) 


- 5 - 

Fig. 1.4: Increase of mean temperature of the atmosphere near ground 

(IPCC-Report 2007) 

Fig. 1.5: Predicted temperature change of the earth’s atmosphere according to different 

models and different assumptions compared to observations (from: IPCC Report 2001) 


- 6 - 

Fig. 1.6: Scenarios for the expected temparture change (from IPCC Report 2007) 

Table 1.3: Share of renewable energy sources for generation of electricity in Germany 2009 

total 16% 

water 3,3% 

wind 6,4% 

photovoltaics 1,0% 

geothermal 0,02% 

biomass 4,4% 

waste 0,9% 


- 7 - 

Table 1.4: Production and market share of solar cells by countries 

country produktion 

share 

2009 

market 

share 

2008 

China 38% 0,2% 

share in totally 

installed 

capacitiy 2008 

Germany 15% 27% 40% 

Japan 12,5% 4% 16% 

Taiwan 12,2 

USA 4,4% 6% 9% 

Spain 3% 48% 25% 

Tab. 1.5: Produktion share of solar cells by companies (2009, Photon International 3/2010) 

Produktionsanteil Firmen 

First Solar (USA, D) 8,9% 

Suntech Power (China) 5,7% 

Q-Cells (D, Thalheim S-A) 4,8% 

Sharp (JP) 4,8% 

Yingli (China) 4,3% 

JA Solar (China) 4,2% 

Trina (China) 3,2% 

Sunpower (Philippinen) 3,2% 

Gintech (Taiwan) 3,0% 

Kyocera (JP) 3,2% 


2 Insolation 

Fig. 2.1: Radiation density 

above atmosphere [Würfel] 

Upper part: 

referred to energy interval 

Lower part: 

Referred to wavelength interval 

Fig. 2.2: Radiation density on 

ground [Hu] 

-8 - 

2 Sonneneinstrahlung F. Falk, Photovoltaik WS 2010/11

-9 - 

Fig. 2.3: Insolation as depending on time of the year and on inclination of solar the 

cell [Hu] 

Fig. 2.4: [Hu] 

2 Sonneneinstrahlung F. Falk, Photovoltaik WS 2010/11

- 10 - 

2 Sonneneinstrahlung F. Falk, Photovoltaik WS 2010/11 

Fig. 2.5: Average yearly global irradiation

- 11 - 

Fig. 2.6: Average yearly global irradiation in Germany 

2 Insolation F. Falk, Photovoltaics WS 2010/11

3 Basics of Photovoltaics 

- 12 - 

1 Absorption of light: cell is not transparent 

Example 

Si wafer cell 

2 Generation of charge carriers 

electrons & holes 

3 Carriers are mobile: diffusion 

6 

4 

5 

Carrier life-time high enough 

Charge separation 

p-n junction 

hetero junction 

p-Si 

3 

4 

1,2 

+ 

3 

4 

6 Carrier leave cell 

Space charge region 5 

contacts 

n-Si 

Fig. 3.1: Basic processes in a solar cell 

conduction band 

band gap 

E g 

valence band 

? ? ? ? ? ? 

hνE g 

3 Basics of Photovoltaics F. Falk, Photovoltaics WS 2010/11 

? ? ? ? ? ? 

fs 

fs 

loss 

µs 

loss 

Fig. 3.2: Photon absorption an carrier excitation in a semiconductor 

6 

electrons 

holes 

- contact 

+ contact

Table 3.1: Band gaps of semiconductors 

- 13 - 

Fig. 3.3: Limits for solar cell efficiency as depending on the band gap. Upper left: Ultimate 

efficiency,upper right: Shockley-Queisser-limit, below: semiempirical efficiency 

[Hu] 

Semiconductor Si a-Si GaAs CdTe CuInSe2 Eg/eV 1,12 1,6...1,7 1,43 1,43 1,05 

3 Basics of Photovoltaics F. Falk, Photovoltaics WS 2010/11

- 14 - 

Fig. 3.4: Efficiency of a two junction tandem solar cell as depending on 

both the band gaps [Lewerenz] 

Fig. 3.5: Theoretical efficiency of a tandem solar cell with n 

junctions and optimized band gaps under AM0 irradiatopn 

[Lewerenz] 


- 15 - 

Fig. 3.6: Absorptions coefficient semiconductors [Hu] 


- 16 - 

Table 3.2: Types of solar cells: maximum efficiency under AM1.5 [(M.A. 

Green et al., Solar Cell Efficiency Tables (Version 36), Prog. Photovolt. 18 (2010), 346] and 

production share in 2009 [Photon Int. 2/2009] 

Type Efficiency 

Lab/Module 

% 

Wafer Cells 

Production 

share 

2009 

% 

Further Work 

single crystalline Si 25.0/13-17 341 Processes, 

Cell Configurations 

multi-crystalline Si 20,4/11-15 483 Processes, 

Cell Configurations 

Thin Film Cells 

amorphous Si 10.1/5-8 61 Low cost processes 

CdTe 16.7/9-11 90 Higher efficiency in 

production 

CIS/CIGS 19.4/10-11 17 Higher efficiency in 

production 

nanocrystalline Si 10,1/... - Research 

micro-/polycrystalline Si 10,5/7 - Research 

Grätzel 10,4/... - Research, processes 

Polymers 5,1/... - Research, more stable 


- 17 - 

4 Semiconductors I: Equilibrium 

Diamond lattice: 

fcc with base 

Zink-blende lattice (cubic) Wurtzite lattice (hexagonal) 

Zink-blende lattice Wurtzite lattice 

Fig. 4.1: Semiconductor lattices 

4 Semiconductors I: Equilibrium F. Falk, Photovoltaics WS 2010/11

- 18 - 

Fig. 4.2: First Brillouin zone of diamond lattice 

Table. 4.1: Band gaps of semiconductors (at room temperature) 

Si a-Si GaAs CdTe CuInSe2 

E g/eV 

1,12 1,6...1,7 1,43 1,43 1,05 

Fig. 4.3: Band structure of Si [Enderlein] 


Fig. 4.4: Band structure of GaAs 

Fig. 4.5: Band structure of CdTe 

- 19 - 


- 20 - 

Fig. 4.6: Basic structure of an electron band (left) and electron motion under a constant force 

(right) 

Fig. 4.8: Electrical conductivity of metals 

Fig. 4.7: Density of states in crystalline silicon (left) and in amorphous silicon (right) 


Fig. 4.9: Fermi distribution for 

different temperatures 

- 21 - 

Fig. 4.10: Density of states (left), Fermi distribution (middle) and density of occupied states 

(right) 


- 22 - 

Table 4.2: Band gap,, effective mass and carrier density in intrinsic semiconductors 

semiconductor Si GaAs 

E g/eV 

1,12 1,43 

m /m 1,08 0,067 

nZ 0 

m /m 0,55 0,47 

pZ 0 

-3 n i/cm 

at 300 K 

10 6 

10 10 

Table 4.3: Energy level of donors and acceptors in silicon 

donors E-E c D/meV acceptors EA-E v/meV 

P 45 B 44 

As 53 Al 68 

Sb 42 Ga 72 

Bi 71 In 155 

Fig. 4.11: Fermi level as depending on temperature for different 

doping levels (n doping increasing from 1 to 3) 


- 23 - 

Fig. 4.12: Carrier density in n- doped semiconductors as a function of inverse temperature 

Fig. 4.13: Carrier density as a function of inverse temperature in n-doped semiconductors 

which contain also p-dopands 


- 24 - 

15 -3 

Table 4.4: Carrier mobilities at 300 K (for Si and GaAs dopand density 10 cm ) 

Si GaAs CdTe CuInSe2 a-Si 

2 -1 -1 ì /cm V s 1350 8800 600 320 0,1...1 

n 

2 -1 -1 -3 

ì /cm V s 500 400 10 10 ...0,03 

p 

Fig. 4.14: Mobility of electrons and holes at 300 K as 

depending on doping level[Enderlein] 

Fig. 4.15: Mobilities for different doping levels of silicon as depending on temperature 

[Enderlein] 


- 25 - 

Fig. 4.17: Resistivity of n- or p-doped silicon at 300 K 

[Colinge] 

Fig. 4.18: Measurement arrangement for Hall effect 

Fig. 4.16: Conductivity of pure intrinsic Si and Ge 

as depending on temperature [Enderlein] 


- 26 - 

Table 4.5: Debye length in instrinsic semiconductors at 300 K 

semiconductor Si GaAs 

-3 

l D/cm 

1,15�10 0,116 

Fig. 4.19: Band bending near the surface of an intrinsic semiconductor due to surface charges 


- 27 - 

Fig. 4.20: Band bending near the surface of an 

n-doped semiconductor due to surface charges 


Fig. 4.21: Band diagram of a p-n-junction 

- 28 - 

Table 4.6: Diffusion potential at a p-n-Übergang in silicon at 300 K in case N A=ND -3 

N A=N D/cm 

15 

10 

16 

10 

17 

10 

18 

10 

19 

10 

20 

10 

V /V 0,542 0,654 0,766 0,878 0,991 1,103 

D 

w 1,4 µm 440 nm 140 nm 44 nm 14 nm 4,4 nm 

Fig. 4.22: Band diagram, carrier densities, and space charge density at a p-n-junction 


- 29 - 

4 Semiconductors I: Equilibrium F. Falk, Photovoltaics WS 2010/11 

E 0 or EFig. 0-e�: 

4.23: vacuum Metal/se 

leve

- 30 - 

Fig. 4.24: Band diagram of a semiconductor heterojunction 

without interface charges. Above: before contact, below: 

after contact 


- 31 - 

5 Semiconductors II: Non-Equilibrium 

Fig. 5.2: Quasi Fermi levels under illumination 

Fig. 5.1: Tauc-Plot of amorphous silicon, 

deposited at different temperatures 

[Diss. C. Horbach, KFA Jülich] 

5 Halbleiter II: Nichtgleichgewicht F. Falk, Photovoltaik WS 2010/11

- 32 - 

Fig. 5.3: Carrier life time in silicon as depending on 

excess carrier density [Lewerenz u. Jungblut] 


Reverse bias 

n-type + 

Forward bias 

n-type - 

without external voltage 

In equilibrium 

- 33 - 

5 Halbleiter II: Nichtgleichgewicht F. Falk, Photovoltaik WS 2010/11 

Fig. 5.4: p-n-junction under external bias

- 34 - 

Fig. 5.5: I-V-Curves of diodes (be aware of different 

voltage scales in case of reverse and forward bias) 

Fig. 5.6: I-V-curves of diodes, logarithmic scale for current 


- 35 - 

Fig. 5.7: Width of space charge region of a silicon p-njunction 

as depending on bias 

N A=N D=10 16 cm -3 , g=12 

metal contact 

absorber 

Fig. 5.8: Scheme of a silicon wafer cell 

anti-reflection coating 

back contact (Al) 

emitter 


in the dark 

illuminated but without 

equilibrium between 

p- and n-side 

- 36 - 

illuminated, when equilibrium 

between p- and n-side is reached 

Fig. 5.9: Band diagram of a silicon wafer cell 


Fig. 5.10: I-V-curve of a solar cell in the dark 

and under illumination 

- 37 - 


- 38 - 

Fig. 5.11: Fill factor and efficiency of a silicon wafer cell as depending on the ratio i p/i s if 

illuminated by a wavelength of 500 nm at 300 K 


Fig. 5.12: Circuit diagram of a solar cell 

Fig. 5.13: Influence of series resistance on the 

I-V-curve of a solar cell 

- 39 - 

Fig. 5.14: Influence of a shunt (parallel resistance) 

on the I-V-curve of a solar cell 


- 40 - 

6 Types of Solar Cells I: Wafer Cells 

Fig. 6.1: Scheme of a single crystalline silicon wafer cell 

Fig. 6.2: Czochralski method to grow silicon single crystals 

6 Solarzellentypen I: Waferzellen F. Falk, Photovoltaik WS 2010/11

Fig. 6.3: Wire saw for wafering 

- 41 - 

Fig. 6.4: Phosphorus doping profile generated by annealing at 

950�C for different times [Goetzberger] 


- 42 - 

Fig. 6.5: ReCombination activity of various species in p- und 

n-doped silicon,Shown is the product of resulting carrier life 

time and foreign atom concentration 


- 43 - 

Fig. 6.6: Open circuit voltage as depending on diffusion 

length for different values of surface recombination 

velocity [Goetzberger] 

Fig. 6.7: Short circuit current as depending on 

diffusion length for different values of surface 

recombination velocity [Goetzberger] 


- 44 - 

Fig. 6.8: Solar cell efficiency as depending on absorber doping level for 

different wafer thickness [Goetzberger] 

Fig. 6.9: Band diagram of a cell with back surface field 


- 45 - 

Fig. 6.10: Open circuit volatge as depending on the depth and 

maximum concentration of back surface field doping [Goetzberger] 

Fig. 6.11: Reflection at a silicon surface covered with no, 1, and 2 

antireflection coatings as depending on light wavelength 

[Goetzberger] 


- 46 - 

Fig. 6.12: Internal quantum efficiency as depending on 

dislocation density for two different values of 

recombination strength [Möller] 

Fig. 6.13: EFG method for growing silicon sheets 

Fig. 6.14: RGS method to produce silicon foils 


- 48 - 

7 Types of Solar Cells II: Thin Film Cells 

Fig. 7.1: Integrated series connection in amorphosu silicon thin film solar cells 

Fig. 7.2: pin-type amorphous silicon solar cell 

7 Types of Solar Cells II: Thin Film Cells F. Falk, Photovoltaics WS 2010/11

without contact 

with contact 

- 49 - 

Fig. 7.3: band diagram of a pin-type solar cell. Above: 

before conatct of differently doped regions, below: after 

contact 

p-type 

n-type 

nominally 

undoped 

Fig. 7.4: Influence of doping gas concemtration 

during CVD of amorphous silicon on conductivity 


- 50 - 

Fig. 7.5: Open circuit voltage of crystalline silicon thin film solar 

cells as depending on grain size 

[L. Carnel et al., 4th WCPEC 2006,1449] 

Fig. 7.6: Efficiency of crystalline silicon thin film solar cells as depending on grain size [J. 

Werner, Tech. Digest 13 th Sunshine Workshop Thin Film Solar Cells,Tokyo 2000, 41] 


- 51 - 

Fig. 7.7: Light trapping structures in thin film solar cells 

Fig. 7.8: Cell concept of a multicrystalline silicon thin film 

solar cell developed at IPHT 


- 52 - 


- 53 - 

Fig. 7.10: Transmission electron microskopic image of a 

nanocrystalline silicion layer prepared from amorphous 

silicon by excimer laser irradiation (248 nm wavelength , 25 

ns pulse duration) 

Fig. 7.11: Seed layer consisiting of larges silicon crystals 

prepared by melting amorphous silicon by a cw-laser; 

melting time 1 ms (optical micrograph) 


- 54 - 

Fig. 7.12: LLC process: Layered Laser Crystallization 

absorber 

seed 

Fig. 7.13: TEM cross section of a LLClayer 

demonstrating epitaxy 


concentration/cm -3 

1E20 

1E19 

1E18 

1E17 

emitter 

- 55 - 

Concentration profiles by SIMS 

P 

absorber seed glass 

1E16 

0,0 0,5 1,0 1,5 2,0 

depth/µm 

Fig. 7.14: Doping profiles of B and B in ann LLC cell measured by SIMS 

Fig. 7.15: GaAs solar cell 

7 Types of Solar Cells II: Thin Film Cells F. Falk, Photovoltaics WS 2010/11 

B

Table 7.1: Properties of CdTe and CdS 

n-CdS p-CdTe 

E g/eV 2,4 1,5 

P/eV 4,5 4,3 

- 56 - 

Dotierung N D=2@10 17 cm -3 N A=8@10 15 cm -3 

Fig. 7.17: CdTe solar cell 

sun light 

Fig. 7.16: Band diagram of a CdTe solar cell [Lewerenz] 

back contact 

CdTe layer (5 µm) 

CdS layer (100 nm) 

TCO layer (250 nm) 

glass substrate 


- 57 - 

Fig. 7.18: Phase diagram of CdTe [Landolt-Börnstein N.S. 

III/17d] 

Fig. 7.19: I-V-curve (above) and quantum 

efficiency (below) of a CdTe solar cell [D. 

Bonnet in Schmid] 


Fig. 7.20: Phasen diagram of CdTe/CdCl 2 

[M. Burgelmann, Appl. Phys. A 69 (1999), 

1499] 

- 58 - 

Fig. 7.21: I-V-curves of CdTe solar cells with and without 

CdCl 2 treatment 

[R.W. Birkmire, E. Eser, Ann. Rev. Mater. Sci. 27 (1997), 625] 


Fig. 7.23: CIGS solar cell 

Table 7.2: Data of CuInSe 2 und CdS 

n-CdS p-CuInSe2 Eg/eV 2,4 1,05 

P/eV 4,5 4,6 

Dotierung N D=2@10 17 cm -3 

- 59 - 

N A=10 16 cm -3 

Fig. 7.22: Lattice parameters and band gaps in the CIGS system 

[H.W. Schock in Schmid; und wie Abb. 7.21] 


- 60 - 

Fig. 7.24: Band diagram of a CIGS solar cell; above: before 

contact, below:after contact [Lewerenz] 

Fig. 7.25: Structure of PPV 

poly phenylene vinylene 


- 61 - 

Fig. 7.26: Polymer solar cell using TiO x 

[A.C. Arango et al., Adv. Mater. 12 (2000), 1689] 

Fig. 7.27: Absorption and quantum efficiency of a 

polymer cell according to Fig.7.26 


enlargement 

X 1 

X 10 3 

X 10 6 

X 10 8 

- 62 - 

Fig. 7.28: Grätzel solar cell in different enlargements 

glass 

transparent contact 

electrolyte 

TiO 2 nanocrystals 

transparent conatct 

glass 

dye 

electrolyte 

TiO 2 nanocrystals 

(20 nm) 

carbon 

nitrogen 

Oxygen 

sulfur 

hydrogen 

ruthenium 


- 63 - 

Fig. 7.29: I-V-curve of a Grätzel dye solar cell 

[M. Grätzel, A.J. McEnvoy, 14th Europ. PSEC 

1997, 1820] 


References 

A. Goetzberger, V.U. Hoffmann, Photovoltaic Solar Energy Generation, Berlin: Springer 

2005 

Overview on technology and systems, not so much physics 

Solar Cells: Materials, Manufacture and Operation, T. Markvart, L. Castañer eds., Oxford: 

Elsevier 2005 

Practical Handbook of Photovoltaics: Fundamentals and Applications, T. Markvart, 

L. Castañer eds., Oxford: Elsevier 2003 

P. Würfel, Physics of solar cells, Weinheim: Wiley-VCH, 2nd ed. 2009 

Short introduction with emphasis on thermodynamics 

H.J. Möller, New Materials: Semiconductors for Solar Cells, in: Handbook of Semiconductor 

Technology, Vol. I, K.A. Jackson, W. Schröter eds., Weinheim: Wiley-VCH 2000, S. 

715-769 

Clean Electricity from Photovoltaics, M.D. Archer, R. Hill eds., London: Imperial College 

Press 2001 

Handbook of Photovoltaic Science and Engineering, A. Luque, S. Hegedus eds., Chichester: 

Wiley 2003 

Mostly technology 

C. Hu, R.M. White, Solar Cells, New York: McGraw-Hill 1983 

R. Brendel, Thin-Film Crystalline Silicon Solar Cells, Weinheim: Wiley-VCH 2005 

J.P. Collinge, C.A. Collinge, Physics of Semiconductor Devices, Boston: Kluwer Acad. Publ. 

2002 

Thin-Film Solar Cells, Y. Hamakawa ed., Berlin: Springer 2004 

A. Goetzberger, C. Hebling, H.-W. Schock: Photovoltaic Materials, History, Status and 

Outlook, Mater. Sci. Eng. R 40 (2003), 1-46 

M.A. Green, Third Generation Photovoltaics, Berlin: Springer 2006 

Visions for high efficiency solar cells making use of new concepts 

K. Seeger, Semiconductor Physics: An Introduction, Berlin: Springer 9 2004 

References F. Falk, Photovoltaics WS 2010/11

R. Enderlein, N.J.M. Horing: Fundamentals of Semiconductor Physics and Devices 

Singapore: World Scientific 1999 

H.J. Möller, Semiconductors for Solar Cells, Boston: Artech House 1992 

A lot of information on defects (properties and consequences) 

Material Parameters 

Landolt-Börnstein, Numerical data and functional relationships in science and technology, 

New Series, Springer, Berlin, Group III, Vols.17a-i, 22a,b 

Properties of Silicon, EMIS Datarevies Series No. 4, INSPEC 1988 

Properties of Amorphous Silicon, EMIS Datarevies Series No. 1, INSPEC 1989 

References F. Falk, Photovoltaics WS 2010/11

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