Driving force and nonequilibrium vibronic dynamics in charge separation of strongly bound electron–hole pairs

Non-perturbative simulations of donor-acceptor interfaces in organic photovoltaics (OPV) reveal the existence of two distinct mechanisms for ultrafast long-range charge separation.
Driving force and nonequilibrium vibronic dynamics in charge separation of strongly bound electron–hole pairs
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When a solar cell made out of an inorganic semiconductor like silicon is exposed to light, electrons can be readily extracted from the valence band to the conduction band and then captured at the electrodes.  In contrast, when light is absorbed by carbon-based materials, photons produce strongly bound electron-hole pairs called excitons, which are collective optical excitations that may be delocalized across several molecular units [1]. The dissociation of excitons is required in order to produce a current [2]. In organic photovoltaics (OPV), blends of materials with different electron affinities are used to provide an energetic landscape that is favourable to charge separation at the interface [3].  Some of these electron-hole pairs however thermalize towards the lowest-energy charge-transfer (CT) state localized at the interface, which is for this reason considered an energetic trap that leads to non-radiative electron-hole recombination [4], as schematically shown in red in Figure 1.

In our most recent publication in Communications Physics, we demonstrate that this charge localization towards the interface can be delayed by the underdamped nature of the high-frequency vibrational modes, maintaining long-range electronhole separation on a picosecond time scale. The non-perturbative simulation method DAMPF  [5-6] has been extended to provide access to charge separation dynamics of a strongly bound electron-hole pair in one-, two- and three-dimensional donor-acceptor networks where a donor is coupled to acceptor aggregates. 

Schematic representation of a one-dimensional chain consisting of a donor and $(N-1)$ acceptors. The Coulomb-binding energy of electron and hole is modelled by $\Omega_k=-V/k$ with $V=0.3\,$eV for $k\ge 1$. The energy-gap between exciton and interfacial CT states is defined as driving force $\Delta=\Omega_0-\Omega_1$.
Figure 1: (Left) Schematic representation of a one-dimensional chain consisting of a donor and (N-1) acceptors. (Right) Eectronic eigenstates of the electronically coupled donor–acceptor system where the driving force is taken to be Δ = 0.15 eV (electronic mechanism) or Δ= 0.3 eV (vibronic mechanism). The probability distributions for finding an electron at the k-th acceptor are vertically shifted depending on electronic energy levels Eα.

By controlling the driving force and the structure of vibrational environments, we identified two distinct mechanisms for long-range charge separation. The first mechanism, activated at low driving forces, is characterized by hybrid exciton-CT states where long-range exciton dissociation takes place on a sub-10 fs time scale, which is not assisted by underdamped high-frequency vibrational modes. In the second mechanism, dominating charge separation at high driving forces, the exciton-CT hybridization occurs and it is mediated by vibronic interaction with underdamped high-frequency vibrational modes, leading to efficient charge separation for a broad range of driving forces. The net result of this mechanism can be understood as the abrupt interruption of thermalization of the exciton during the lifetime of nonequilibrium vibrational structures. This effectively decouples the electronic excitation from the surrounding environment, and the probability of dissociating excitons is increased beyond what one would expect from the rates obtained at thermal equilibrium. These results suggest that non-equilibrium vibrational motion can promote long-range charge separation in ordered donor-acceptor aggregates.

The resulting comprehensive picture of ultrafast charge separation differentiates electronic or vibronic couplings mechanisms for a wide range of driving forces and identifies the role of entropic effects in extended systems. This provides a toolbox for the design of efficient charge separation pathways in artificial nanostructures.

  1. Scholes, G. D. & Rumbles, G. Excitons in nanoscale systems. Nat. Mater. 5,920–920 (2006).
  2. Hedley, G. J., Ruseckas, A. & Samuel, I. D. W. Light harvesting for organic photovoltaics. Chem. Rev. 117, 796–837 (2017)
  3. Brédas, J.-L., Norton, J. E., Cornil, J. & Coropceanu, V. Molecular understanding of organic solar cells: the challenges. Acc. Chem. Res. 42, 1691–1699 (2009)
  4. Coropceanu, V., Chen, X.-K., Wang, T., Zheng, Z. & Brédas, J.-L. Charge-transfer electronic states in organic solar cells. Nat. Rev. Mater. 4, 689–707 (2019).
  5. Somoza, A. D., Marty, O., Lim, J., Huelga, S. F. & Plenio, M. B. Dissipation-assisted matrix product factorization. Phys. Rev. Lett. 123, 100502 (2019)
  6. F. Mascherpa, A. Smirne, A. D. Somoza, P. F. Acebal, S. Donadi, D. Tamascelli, S. F. Huelga and M. B. Plenio, Optimized auxiliary oscillators for the simulation of general open quantum systems. Phys. Rev. A 101, 052108 (2020)

(The cover image was generated by DALL-E 2 from OpenAI using the prompt: "An exciton splitting into a positive hole particle and an electron.  The image depicts a physical process taking place at the microscopic scale, at the interface of a donor-acceptor blend in solar cells. Photorealistic depiction of the particles involved using computer generated graphics. It could appear in the cover of Nature magazine.")

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