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Modeling the real efficiency of polymer solar cell basing on kinetics

Modeling the real efficiency of polymer solar cell basing on kinetics . A.Sosorev 1 , D.Godovsky 2 , D.Paraschuk 1 1 Physic Dept, Moscow State University 2 Institute of Elementoorganic Chemistry Russian Academy of Science , also at LG TCM, LG Electronics.

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Modeling the real efficiency of polymer solar cell basing on kinetics

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  1. Modeling the real efficiency of polymer solar cell basing on kinetics A.Sosorev1, D.Godovsky2, D.Paraschuk1 1 Physic Dept, Moscow State University 2Institute of Elementoorganic Chemistry Russian Academy of Science, also at LG TCM, LG Electronics

  2. Theory of the solar cells efficiency (Schockleyand Queissier) Radiative recombination limits the efficiency William Schockley, Hans Queissier, “Detailed Balance Limit of Efficiency of p‐n; Junction Solar Cells”, Journal of Applied Physics, Volume 32 (3) Mar 1, 1961

  3. Models of efficiency of Plastic Solar Cells THERMODYNAMIC COMBINATION AND SEMI-EMPIRICAL KINETIC S.-S. Sun D.Godovsky J.Nelson K.Vandevaal et O.Inganaes C.Brabec P.Blom K.Hummelen • Schockley model is upper limiting case • Not determined: Fermi Energy • Equilibrium • Splitting of Quasi- Fermi levels • What is left : kinetic rates • Elumo, Ehomo • Electrode workfunctions • Number of charges thermodynamics kinetics • Radiation luminescence balances the equilibrium between photons and electrons • Splitting of quasi-Fermi levels occurs • Schockley model works

  4. Marcus Model based results – Godovsky, 2010 0.4  = 0.1eV 0.2 0.3 0.3 0.4 0.5 0.6 0.7 Efficiency of polymer solar cell 0.2 0.8 0.9 1.0 0.1 0 0 1 2 4 3 Eg, band gap of polymer, eV

  5. Model Basics Excited StateC2 kM k-M=0 HotCT-C3 kOB CS state CT-state thermalizedC3’ kOB k1 k-1 Current I krec A Ground StateC1 We do not treat charge transport

  6. Model Basics h e h e e We use to model two main processes: • Exciton-> CT: Marcus theory • CT-state -> separated charges: Onsager-Braun formalism In Onsager-Braun formalism we change diffusion coefficients corresponding to excess energy – thus describing “hot” states Exciton Charge-transfer state Separated charges

  7. Main processes diagram P1. Assume that we have a number of СТ-states. Excitation of donor СТ CS P2. Assume that vibrational relaxation is much faster, than charge separation Donor Ground State

  8. Excited state C2 kM1 k-M1=0 kM2 k-M2=0 CT2Hot C3 k1 k-1=0 CS state C4 Ktr, k-tr knon2 Free C5 CT1 bottom C5 Current I krec Current I A Ground state C1 Model: Equations Kgem Thermalization krec

  9. Model: Peculiarities • Proposed Model • Existence of several electron levels of CT state is assumed • Excess energy of “hot” CT-state is counted directly through Diffusion Coefficient in Onsager-Braun formalism • Marcus process is so fast, that it does not limit whole kinetics of the system Traditional Models Excessive energy of Hot CT state -either is not included -or included indirectly through CT-exciton size -or modified Marcus model for excited vibrational states is applied e Escape probability(modified Onsager-Braun) e R h

  10. Results 1: Isc and efficiency vs excess energy Eg=2.5 eV (not optimal) The model describes significant dependence of Iscvs excess energy observed in some blends • “bad” blend: high recombination kfand/or low mobility • strong r0 dependence “good” blend: low recombination kfor/and high mobility => weak r0 dependence

  11. Results 2 ultimateefficiency vsEg(CS thermalization not considered) Kf =1e7, mu = 1e-8 Kf =1e9, mu = 1e-8 Kf =1 e10, mu = 1e-8 Increase of recombination rate kf Kf =1 e10, mu = 3e-7 • “bad” blend: high recombination kf • strong r0 dependence • We can increase efficiency by utilizing thedonor-acceptor polymers with large D-A separation “good” blend: low recombination kf(a) or high mobility (b) => weak r0 dependence

  12. 0.4  = 0.1eV 0.2 0.3 0.3 0.4 0.5 0.6 0.7 Efficiency of polymer solar cell 0.2 0.8 0.9 1.0 0.1 0 0 1 2 4 3 Eg, band gap of polymer, eV Results 3 λ dependence (CS thermalization not considered) Old model (2010) New model Larger bandgaps are needed as compared to simple Marcus (Godovsky 2010)

  13. Results 4 accounting for thermalization • The lower the thermalization rate, the lower driving force is needed to obtain maximal performance

  14. Conclusions • We treated the polymer solar cells operation using only kinetics and applying Marcus theory and Onsager-Braun formalism • We found, that the slowest process , determining the whole kinetics and hence EQE is CT splitting into free charges vsthermalization • The LUMO level of acceptor in model assuming Hot CT is even lower than in simple Marcus model since maximized Marcus transfer should be to Hot CT stateto have enough excess energy for charge separation – we win in EQE but loose Voc • The mechanism behind the decrease of efficiency for polymer solar cells, if kinetic model can be applied is heat dissipated during molecular reorganization – Marcus, and that we need excess energy to separate charges (Onsager-Braun).

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