Modeling and optimization of Si crystal
            growth by Siemens, DS, and Cz




                         Vladimir Ka...
What is computer modeling?
Computer modeling is a comprehensive reconstruction or reproduction of
crystal growth process b...
PolySim:   Software for simulation of polysilicon deposition
                                       by Siemens process
Siemens process:
                  established technology for polysilicon production


                                 • ...
Siemens process modeling


                                        Detailed model of Siemens process:
                    ...
Chemical balance of Siemens process


               SiHCl3 (TCS), SiH2Cl2 (DCS), H2


          SiHCl3, SiCl4, SiH2Cl2, H...
How to increase silicon productivity ?
Ugr,     12
         11
µm/min             Cl/Si=3                Т = 1400К
       ...
How to minimize energy consumption ?
 Energy          200
 consumption,
 kwh/kg
                 150




                 ...
High purity silicon production without popcorn like structure




A special criterion analyzes the possibility of cavity f...
Conclusions
1. Model of Siemens process was developed based
   on experience of Si epitaxy and polycrystalline
   growth
2...
PolySim: dependence of integral
characteristics of a Siemens reactor
      on operating conditions
PolySim software concept:
    Detailed modeling of boundary layer near the rod
•
    surface where temperature is much hig...
Simulator of Siemens process

                                                                     Growth rate
Number of t...
PolySim results : reactor characteristics in dependence on
                                                    the TCS flo...
PolySim results : reactor characteristics in dependence on
                                                       temperat...
CGSim:   Software for simulation of Czochralski, LEC, DS,
             and Bridgman crystal growth from the melt
Computer modeling of DS mc Si growth
        2D Global Heat Transfer


                                                   ...
Unsteady modeling of DS of mc Si

2D                                        3D




                                       ...
Unsteady modeling of DS of mc Si




                                     Animation of crystallization front
             ...
3D Ar gas flow above the melt
Complex gas flow structure   Up and down gas flow in the furnace




Ar gas

Si Melt

Si Cry...
Meltdown stage and beginning of crystallization

         Crucible Moving                  Side Insulation Moving




151 ...
Model of oxygen transport in DS Si growth
I. Transport of oxygen in turbulent melt flow
                                µµ...
3D SiO and oxygen concentration distributions
Melt turbulence results in 3D oxygen         SiO distribution in the gas bec...
Unsteady modeling for model DS furnaces
Three DS furnaces with similar design, the same crucible size, but with different ...
Unsteady modeling for the Design A

Temperature




                                             Advantages
              ...
Unsteady modeling for the Design B

Temperature




                                             Advantages
              ...
Unsteady modeling for the Design C

Temperature




                                             Advantages
              ...
Comparison of different types of DS furnace


                           100
                                             ...
Conclusions
We have presented a combined 2D-3D model of DS of mc-Si, which considers melt
and gas convection, heat transfe...
Computer modeling of Cz Si growth
 2D global HT model produces thermal boundary conditions for 3D/2D flow computations
   ...
Study of crystal growth using 2D models
            Temperature analysis coupled
               with melt and gas flow
   ...
Study of melt flow structure and crystallization using
                                                           2D model...
Analysis of unsteady features of crystal cooling
                             Crystal cooling at 450 mm Cz Si growth
     ...
Model of oxygen transport in Cz Si growth
I. Transport of oxygen in turbulent melt flow
                                µµ...
Verification of the oxygen transport model

                                                                              ...
2D calculation of defect incorporation and recombination
                                                 (crystal diamete...
Radial distribution of point defect density and average size
                                             6
              ...
Verification of the model
                                                                                            10 0...
3D Unsteady Calculations of the Crystallization Front
                                                                    ...
Increasing the crystallization (pulling) rate

- by modifications of the heat shields and other elements surrounding
the c...
Reducing the probability of macrodislocation
                      generation

- control of temperature fluctuations in th...
Optimization of turbulent melt flow

                                        Suppressed Turbulence

Intensive Turbulence

...
Published examples of optimization of Cz Si growth

Usually there are no complete descriptions for a crystal growth furnac...
Conclusions
We have presented a combined 2D-3D model of Cz Si growth. The model considers
melt and gas convection, heat tr...
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PolySim and CGSim at PVEXPO 2009

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STR presentation at PV EXPO 2009
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PolySim and CGSim at PVEXPO 2009

  1. 1. Modeling and optimization of Si crystal growth by Siemens, DS, and Cz Vladimir Kalaev1, Yoshiki Tsukada2 1STR Group Ltd. St. Petersburg, Russia 2SimSciD Corp. Yokohama, Japan
  2. 2. What is computer modeling? Computer modeling is a comprehensive reconstruction or reproduction of crystal growth process by a computer. Numerical model is used for technology optimization for lower operation costs. Advantages of computer modeling in comparison to experimental work: - fast and low cost (from few minutes to several days; only special software and computer are required) - provide information in all points of a furnace, including data which are impossible to measure quantitatively (temperature gradients, thermal stresses, crystallization behavior, fluid dynamics, species transport) -practically, no extra cost for changes of furnace design and growth parameters (several minutes of the work of the user): fast and efficient technology development
  3. 3. PolySim: Software for simulation of polysilicon deposition by Siemens process
  4. 4. Siemens process: established technology for polysilicon production • Experimental research is very expensive and time-consuming • Very limited capabilities for measurements Computational modeling can help: • increase the reactor productivity • reduce energy consumption • increase trichlorosilane-to-silicon conversion Polysilicon deposition reactor efficiency • optimize the material quality • get the better understanding of the process
  5. 5. Siemens process modeling Detailed model of Siemens process: - turbulent gas flow, - resistive rod heating - current stabilization effect - thermal radiation - gas-phase and surface chemistry - a special criterion for prediction of porous structure formation: “popcorn” - gas-phase particle formation (in work) 3D computational model of a polysilicon deposition reactor
  6. 6. Chemical balance of Siemens process SiHCl3 (TCS), SiH2Cl2 (DCS), H2 SiHCl3, SiCl4, SiH2Cl2, H2, HCl, SiCl2, SiCl3, SiHCl + SiCl4, SiHCl3, SiH2Cl2, H2, HCl Silicon Process model includes most important gas-phase species
  7. 7. How to increase silicon productivity ? Ugr, 12 11 µm/min Cl/Si=3 Т = 1400К 10 Silicon growth rate 9 dependence on Cl/H and 8 Cl/Si=3.3 7 Cl/Si ratios in the gas-phase 6 5 4 3 Cl/Si=3.5 2 1 Cl/Si=4 0 -1 Cl/Si=3.7 -2 0 0.25 0.5 0.75 1 Cl/H Productivity depends on gas mixture composition and temperature
  8. 8. How to minimize energy consumption ? Energy 200 consumption, kwh/kg 150 100 50 Rod diameter, mm 0 0 50 100 150 Energy consumption depends on rod size, optical properties of reactor walls, gas- phase mixture composition, temperature, flow velocity, number of the rods.
  9. 9. High purity silicon production without popcorn like structure A special criterion analyzes the possibility of cavity formation between neighboring grains in dependence on local heat- and mass–transport conditions
  10. 10. Conclusions 1. Model of Siemens process was developed based on experience of Si epitaxy and polycrystalline growth 2. 3D computations determine all the reactor characteristics. 3. But 3D computations are very long and and require a lot of simulation expertise, this makes parametric optimization not effective. 4. Engineering tool “PolySim” has been developed, it utilizes the knowledge gained from 3D computations, but makes computations much faster and efficient keeping the good accuracy.
  11. 11. PolySim: dependence of integral characteristics of a Siemens reactor on operating conditions
  12. 12. PolySim software concept: Detailed modeling of boundary layer near the rod • surface where temperature is much higher than in the reactor volume. Averaged characteristics of the gas in the • reactor volume are calculated using special relationships derived from 3D computations. Coupling of the gas volume and boundary layer. • Fast and efficient computational model makes • possible parametric computations of averaged reactor characteristics.
  13. 13. Simulator of Siemens process Growth rate Number of the rods Instantaneous productivity Rod diameter Energy consumption Rod height Silicon conversion Diameter and height of the chamber Popcorn appearance Gas flow rates Scale of surface non-uniformity Electrical current Average rod surface temperature Total voltage Average gas velocity Total power Pressure Radiation losses POLYSIM Side wall emissivity Convection losses The mean cooling liquid temperature Heat losses with output gases Output gas flow rates Thickness of stainless steel walls Volume gas temperature Re, Gr·Pr Thickness of viscous sublayer Inner wall temperature Cl/Si in output gas mixture Ror center temperature Characteristics of the whole process Characteristics in a local point
  14. 14. PolySim results : reactor characteristics in dependence on the TCS flow rate and pressure 36 rods, 70 mm, T = 1350 K, εwall = 0.7 40 200 1 atm 35 3 atm 6 atm 30 150 10 atm Energy cost, kWt*h/kg Silicon output, kg/h 25 20 100 15 1 atm 3 atm 10 50 6 atm 10 atm 5 0 0 0 5 10 15 20 25 0 5 10 15 20 25 TCS flow rate, kmol/h TCS flow rate, kmol/h Energy consumptions demonstrate complicated dependence on pressure
  15. 15. PolySim results : reactor characteristics in dependence on temperature and pressure 36 rods, 70 mm, TCS = 10 kmol/h , εwall = 0.7, V = 1.5 m/sec 200 70 180 60 1 atm 3 atm 6 atm 160 Energy cost, kWt*h/kg 50 10 atm Silicon output, kg/h 140 40 120 30 100 20 1 atm 80 3 atm 10 6 atm 10 atm 60 0 1300 1400 1500 1600 1200 1300 1400 1500 1600 Temperature, K Temperature, K • Energy consumptions demonstrate complicated dependence on pressure and temperature • Optimal pressure depends on temperature
  16. 16. CGSim: Software for simulation of Czochralski, LEC, DS, and Bridgman crystal growth from the melt
  17. 17. Computer modeling of DS mc Si growth 2D Global Heat Transfer Ar Melt Crystal Insulation Quartz crucible Graphite crucible Support 3D Crystallization Zone ⎛ ∂T ⎞ and ⎜ λ T [K] ⎟ in Q ⎝ ∂n ⎠ gas rad Quasi Steady & The reactor design is based on the data from the paper Bei Wu, Nathan Stoddard, Rondhui Fully Unsteady Ma, Roger Clark, Bulk multicrystalline silicon growth for photovoltanic (PV) application, J. Crystal Growth (2008), doi:10.1016/j.jcrysgro.2007.11.194
  18. 18. Unsteady modeling of DS of mc Si 2D 3D Unsteady asymmetrical flow structure is described by fully 3D modeling of melt flow Process time: 25 h P = 50000 Pa Vcryst ≈ 15 mm/h;
  19. 19. Unsteady modeling of DS of mc Si Animation of crystallization front dynamics and temperature gradient distribution Process time: 25 h Unsteady dynamics of crystallization front Vcryst ≈ 15 mm/h;
  20. 20. 3D Ar gas flow above the melt Complex gas flow structure Up and down gas flow in the furnace Ar gas Si Melt Si Crystal Quartz crucible Graphite crucible Support
  21. 21. Meltdown stage and beginning of crystallization Crucible Moving Side Insulation Moving 151 mm 187 mm
  22. 22. Model of oxygen transport in DS Si growth I. Transport of oxygen in turbulent melt flow µµ → ∇2C , De f f = ( + t ) / ρ , Sc = 10, Sc t = 0.9 V m⋅ ∇C = D o ef f o Sc Sc t Oxygen transport is extremely sensitive to 3 4 specific features of turbulent flow. SiOg ( II ) 2 II. Transport of SiO in Argon flow Ol → 1 ∇ ⋅ ( ρ Vg cSiO − ρ DSiO ∇cSiO ) = 0 (I) Chemical reactions along interfaces: ( 1 ) Quartz dissolution: SiO(g) ↔ Si(l) + O(l) 3SiO2(s) + Si3N4(s) ↔ 6SiO(g) + 2N2(l) ( 2 ) SiO evaporation: Si(l)+O(l) ↔ SiO(g) ( 3 ) SiO deposition SiO(g) ↔ SiO(s) Scheme of oxygen transport ( 4 ) SiO2 resolution SiO2(s)+Si(vap) ↔ 2SiO(g)
  23. 23. 3D SiO and oxygen concentration distributions Melt turbulence results in 3D oxygen SiO distribution in the gas becomes transport to the melt free surface asymmetric Ar gas Si Melt Si Crystal Quartz crucible Graphite crucible Support
  24. 24. Unsteady modeling for model DS furnaces Three DS furnaces with similar design, the same crucible size, but with different heater arrangement are considered. Unsteady computer modeling is provided to estimate effect of heater arrangement on heat transfer and crystallization process. Heater power history in each design is adjusted to keep crystallization rate of 10 mm/h Design A Design B Design C Only side heater Side, top and bottom Only top and bottom heaters heaters
  25. 25. Unsteady modeling for the Design A Temperature Advantages •Reasonable control of interface shape •Low power consumption Drawbacks Low thermal gradients in the melt Crucible size 840 mm, growth rate 10 mm/h
  26. 26. Unsteady modeling for the Design B Temperature Advantages •Better control of interface shape •Reasonable control of thermal gradients in the melt Drawbacks Reasonable power consumption Crucible size 840 mm, growth rate 10 mm/h
  27. 27. Unsteady modeling for the Design C Temperature Advantages •Reasonable control of thermal gradients in the melt Drawbacks Higher power consumption, than in Design A and B Crucible size 840 mm, growth rate 10 mm/h Low possibilities of interface shape control
  28. 28. Comparison of different types of DS furnace 100 Design A – with side heater gives a Design A Design B capability to control the interface shape Design C Total power concumption, [kW] together with low power consumption. 90 Design B – with top, bottom and side 80 heaters provides optimal conditions for crystal growth, but has about 10% higher power consumption than the 70 furnace with design A. 60 Design C – with top and bottom heaters gives a capability to control thermal gradient inside the melt, but 50 0 5 10 15 20 25 30 with higher power consumption. Time, [h]
  29. 29. Conclusions We have presented a combined 2D-3D model of DS of mc-Si, which considers melt and gas convection, heat transfer by radiation and conduction, crystallization front dynamics, oxygen and carbon transport in the melt and SiO transport in gas. The computer model supports quasi-steady and fully unsteady calculations, considering movement of blocks during meltdown, crystallization, and cooling stages Unsteady numerical modeling of the growth process in three similar DS furnaces with different types of heating has shown the effect of heater position. Heater power history in each case was adjusted to keep the constant growth rate of 10 mm/h and flat or slightly convex crystallization front shape. Using CGSim software it is possible to make comprehensive optimization of DS process: make hot zone modification, adjust heater power histories to obtain high growth rate and desired crystallization front shape.
  30. 30. Computer modeling of Cz Si growth 2D global HT model produces thermal boundary conditions for 3D/2D flow computations T melt / crystal = Tmelting ⎛ ∂T ⎞ Qrad and ⎜ λ ⎟ in ⎝ ∂n ⎠ gas 2D model of global heat transport T [K] 1600 1400 1200 1000 40 0 800 500 600 600 400 argon 1300 crystal 1500 1700 melt λeff melt crucible 3D unsteady model heater ⎛ ∂T ⎞ ⎛ ∂T ⎞ graphite 1700 λ + Qrad = ⎜ λ ⎟ + σεTwall 4 ⎜ ⎟ in 1600 ⎝ ∂n ⎠3 D ⎝ ∂n ⎠ gas insulation CZ growth of 400 mm Si crystal: V.V. Kalaev et al., J. Crystal Growth, 250/1-2 (2003) p.203 Y. Shiraishi et al., J. of Crystal V.V. Kalaev et al., Mat. Sci. in Semiconductor Processing, 5/4-5 (2003) p.369 Growth 229 (2001) p.17
  31. 31. Study of crystal growth using 2D models Temperature analysis coupled with melt and gas flow 450 mm Cz Si growth Temperature Flow Velocity Crystallization front animation Global heat transfer simulation coupled to melt and gas convection is a powerful tool for day-by-day engineering calculations to improve hot zone design and growth parameters.
  32. 32. Study of melt flow structure and crystallization using 2D models 450 mm Cz Si growth Temperature Flow Velocity In large scale crystal growth, the effect of melt convection on crystallization front formation is significant. Melt convection features often govern defects dynamics and macro-dislocation generation in the crystal.
  33. 33. Analysis of unsteady features of crystal cooling Crystal cooling at 450 mm Cz Si growth Temperature Temperature gradient in the crystal Si charge meltdown and crystal cooling are optimized using 2D unsteady modeling. This helps to speed up melting and cooling stages and to prevent beginning of melt crystallization from the gas/melt interface.
  34. 34. Model of oxygen transport in Cz Si growth I. Transport of oxygen in turbulent melt flow µµ → ∇2C , De f f = ( + t ) / ρ , Sc = 10, Sc t = 0.9 V m⋅ ∇C = D o ef f o Sc Sc t Oxygen transport is extremely sensitive to gas flow specific features of turbulent flow. ( II ) II. Transport of SiO in Argon flow 3 4 → ∇ ⋅ ( ρ Vg cSiO − ρ DSiO ∇cSiO ) = 0 SiOg 2 Chemical reactions along interfaces: (I) Ol ( 1 ) Quartz dissolution: SiO2(s)↔ Si(l) + 2O(l) melt flow 1 heat flux ( 2 ) SiO evaporation: Si(l)+O(l) ↔ SiO(g) ( 3 ) SiO deposition SiO(g) ↔ SiO(s) Scheme of oxygen transport ( 4 ) SiO2 resolution SiO2(s)+Si(vap) ↔ 2SiO(g)
  35. 35. Verification of the oxygen transport model Oxygen concentration along S iO ma s s fra ction [units ] crystal and free surface C Oxygen [10 17 a toms /cm 3 ] 10 crystal melt free surface 9 8 7 6 5 4 experiment 3 02 0 .0 1 3 2 0 .0 0. 1 8 0 0 0.05 0.1 0.15 9 radial position [m] (Coxy )max 2.5·1018 atoms/cm3 10 11 There are strong concentration gradients of oxygen concentration along the free surface and crucible. Turbulent mixing makes homogeneous C Oxyge n [ 10 17 a toms /cm 3 ] concentration in the melt core.
  36. 36. 2D calculation of defect incorporation and recombination (crystal diameter is 300 mm) Interface computed Interface computed with a 2D using a 3D approximation approximation The effect of melt turbulent flow on Cv - Ci [cm-3] the formation of the crystallization 2.1E+14 1.8E+14 front is much 1.4E+14 more significant 1.1E+14 7.8E+13 for 300 mm 4.5E+13 crystal growth. 1.2E+13 -2.1E+13 -5.4E+13 -8.7E+13 2D 3D Technological parameters. Crystal height is 300 mm, pulling rate is 0.7 mm/min, cruciblecrystal rotation are 6-12 rpm, Ar flowratepressure are 1000 slh 15 mbar.
  37. 37. Radial distribution of point defect density and average size 6 4.0x10 9 4x10 2D interface 2D interface 3D interface 3D interface -3 -3 Void density, cm Particle density, cm 9 3x10 6 3.5x10 9 2x10 6 3.0x10 9 1x10 6 2.5x10 0 0 1 2 3 4 5 0 1 2 3 4 5 7 Radial position, cm Radial position, cm 60 Oxygen precipitate average size, nm 55 Void average size, nm 6 50 5 45 2D interface 40 2D interface 3D interface 4 3D interface 35 3 30 0 1 2 3 4 5 0 1 2 3 4 5 Radial position, cm Radial position, cm Technological parameters: Crystal diameter is 100 mm. Crystal height is 300 mm, pulling rate is 2 mm/min, cruciblecrystal rotation are 5-20 rpm, Ar flowratepressure are 675 slh 25 mbar. This values correlate well with data presented in [1] T. Sinno et al., Mat. Sci. Eng. 28 p.149 (2000)
  38. 38. Verification of the model 10 0 power s pectral dens ity T [K] experiment 1700 calculations 10 -1 1695 -2 10 1690 experiment s imulations 10 -3 -3 1685 10 -2 10 -1 10 0 10 0 20 40 60 80 frequency [ Hz ] Time [s ] Power spectral density of temperature Temperature fluctuations in the melt, 1 fluctuations. cm lower the free surface. Growth parameters: The crystal diameter is 100 mm. The crucible/crystal rotations are 5/(-20) rpm. Argon flow rate and pressure are 750 slh and 30 mbar. The average crystallization rate is 2 mm/min. The experimental data are taken from the following paper: Mat. Sci. and Eng. B73 (2000) p.130. CGSim predicted the average amplitude and spectral characteristics of the temperature fluctuations in the melt near the triple point.
  39. 39. 3D Unsteady Calculations of the Crystallization Front Geometry ∂T ⎛ ∂T ⎞ nx ⎜ λcrys crys − λmelt melt ⎟ Vcrys = ρ crys ∆H ⎜ ∂n ⎟ ∂n ⎝ ⎠ Vcrys = Vcrys − Vcrys * relative ∆X = Vcrys * TimeStep relative The experiments provided in Siltronic AG are published in: [1] Mat. Sci. in Semiconductor Processing 5/4-5, 2003, p.369-373; [2] J. Crystal Growth 250/1-2, 2003, p.203-208. [3] J. Crystal Growth, 266/1-3 ,2004, pp. 20 - 27 The crystal diameter is 100 mm The crystal diameter is 300 mm Computation, H=240mm 20 Computation, H=300mm Experiment, H=240mm Experiment, H=300mm 40 Computation, H=300mm Interface deflection, [mm] Computation, H=700mm Experiment, H=300mm 35 15 Experiment, H=700mm Interface deflection, [mm] 30 25 10 20 15 5 10 5 0 0 0 50 100 0 100 200 300 Radial position, [mm] Radial position, [mm]
  40. 40. Increasing the crystallization (pulling) rate - by modifications of the heat shields and other elements surrounding the crystal - changes in the crystal and crucible rotation rate - optimization of the crucible position with respect to the heaters - changes in the crucible design General idea: One needs to increase the heat flux (temperature gradient) in the crystal and to decrease the heat flux in the melt. But it is necessary to avoid (i) crystal twisting, (ii) macrodislocations, and (iii) melt supercooling.
  41. 41. Reducing the probability of macrodislocation generation - control of temperature fluctuations in the melt - control of SiO transfer in the gas to avoid recirculation zones and formation of SiO particles - control of thermal stresses in the crystal near crystallization front - control of silica crucible dissolution (SiO2 particles) by decreasing the temperature along the melt/crucible boundary - control of significant melt supercooling to avoid formation of polycrystalline Si particles
  42. 42. Optimization of turbulent melt flow Suppressed Turbulence Intensive Turbulence There are fluctuations of the crystallization rate. There is Instant melting at the crystal no instant melting. rim and in the center of the crystallization front.
  43. 43. Published examples of optimization of Cz Si growth Usually there are no complete descriptions for a crystal growth furnace, no full details about growth parameters. So, it is very hard to extract from literature or patents an optimal solution for a particular growth configuration. From literature overview, it is possible to estimate the following optimization for a Cz furnace initially designed for the growth of Si for electronics: Decreasing the total heater power from 25% to 50%. Increasing the crystallization rate from 15% to 40%. Decrease of the probability to get polycrystalline growth by 70% [1] B. Fickett, G. Mihalik, Semiconductor Fabtech., 1999, 10th Edition, Henley Publishing, London, p. 191. [2] L.Y. Huang, P.C. Lee, C.K. Hsieh, W.C. Hsu, C.W. Lan, Journal of Crystal Growth 261 (2004) 433–443 [3] O.V. Smirnova, N.V. Durnev, K.E. Shandrakova, E.L. Mizitov, V.D. Soklakov, “Optimization of Furnace Design and Growth Parameters for Si Cz Growth, Using Numerical Simulation”, to be published in Journal of Crystal Growth 2007
  44. 44. Conclusions We have presented a combined 2D-3D model of Cz Si growth. The model considers melt and gas convection, heat transfer by radiation and conduction, calculations of crystallization front shape, oxygen transport in the melt and SiO transport in the gas, including deposition, and defects dynamics. 2D unsteady modeling of melt down and cooling stages provide with information on crucible and melt overheating, thermal gradients in the cooled crystal and freezing of the melt remainders Multiple verification examples show high predictive capability of CGSim software. Good correspondence between results of computations and experimental data is obtained for temperature distributions, thermal fluctuations in the melt, crystallization front shape, oxygen transport Using CGSim software it is possible to make considerable optimization of hot zone design for Cz Si growth and: increase the pulling rate, decrease probability of twisting phenomena, decrease probability of macrodislocation generation, decrease power consumptions, etc.

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