Bipolar polaron pair recombination in polymer/fullerene solar cells

We present a study of the rate-limiting spin-dependent charge-transfer processes in different polymer/fullerene bulk-heterojunction solar cells at $10\mathrm{K}$. Observing central spin-locking signals in pulsed electrically detected magnetic resonance and an inversion of Rabi oscillations in multifrequency electron-double-resonance spectroscopy, we find that the spin response of both spin-coated and printed P3HT/PCBM and spin-coated PCDTBT/PCBM solar cells at low temperatures is governed by bipolar polaron pair recombination and quantitatively determine the polaron-polaron coupling strength with double electron-electron resonance experiments. Furthermore spin Hahn echo decay and inversion recovery measurements are performed to measure spin coherence and recombination times of the polaron pairs, respectively.

Figure 1

Schematic diagram of charge transport in bulk heterojunction devices. After absorption of photons [denoted by (1)], the excitons generated diffuse to the interface, where the charges are separated, eventually forming polarons ${\mathrm{P}}^{+}$ and ${\mathrm{P}}^{-}$ [denoted by (2)]. Spin-dependent processes involving these polarons can be either unipolar, where polarons of the same charge form a bipolaron [denoted by (3)], or bipolar, where two polarons of different charge annihilate [denoted by (4)]. The Pauli principle demands that both hopping and recombination are possible only if the spins of the two polarons are antiparallel; polarons with parallel spin orientation will not be allowed to undergo the hopping or recombination process. As sketched exemplarily for the recombination, the respective process can be enhanced by magnetic resonance, when the spin of either polaron is flipped and the parallel spin configuration is changed to an antiparallel one [denoted by (5)].

Figure 2

Light-induced electron paramagnetic resonance (LEPR), cw electrically detected magnetic resonance (cwEDMR), and pulsed EDMR (pEDMR) spectra of P3HT/PCBM. All spectra exhibit the characteristic resonances at the $g$ values of the positive and the negative polarons in P3HT and PCBM, respectively (depicted by vertical dashed lines).

Figure 3

(a) Pulse sequence for the electrical detection of the coherent driving of spin nutations (Rabi oscillations). The current transients following the resonant manipulation of the spin system are integrated, yielding a charge $\mathrm{\Delta }Q$ as the EDMR signal. (b) Electrically detected Rabi oscillations in P3HT/PCBM as a function of the microwave pulse length $t_p$ used to drive the magnetic resonance of the negative or positive polaron.

Figure 4

(a) Fast Fourier transforms of Rabi oscillation measured in P3HT/PCBM by pEDMR for different magnetic fields $B_0$ at a low microwave power. Two strong signals attributed to ${\mathrm{P}}^{+}$ and ${\mathrm{P}}^{-}$ are observed at the fundamental Rabi frequency $\mathrm{\Omega }=\gamma B_1$. Already a weak spin-locking signal with $\mathrm{\Omega }=2\gamma B_1$ is visible at a central magnetic field. (b) At higher microwave power, the spin-locking signal becomes more prominent. In addition, a nuclear magnetic resonance signal with a frequency of $\sim 14.8\mathrm{MHz}$ emerges, caused by hyperfine interaction with ${}^1\mathrm{H}$ protons in the organic material [see (d)]. (c) Simulation of the Rabi map in (b), using a superoperator Liouville space formalism and assuming an exchange coupling between the positive and negative polarons of $J/2\pi =2\mathrm{MHz}$. (d) The frequency of the horizontal features in (b) depends linearly on the magnetic field $B_0$, with a proportionality characteristic for the nuclear magnetic resonance of protons.

Figure 5

(a) Pulse sequence for electron double resonance (ELDOR) using two microwave frequencies to address the positive and negative polarons for a certain magnetic field $B_0$ separately. (b) Without a leading pulse on ${\mathrm{P}}^{-}$, a Rabi oscillation experiment on ${\mathrm{P}}^{+}$ leads to the same oscillation already observed in Fig. 3. With a leading $\pi$ pulse inverting the ${\mathrm{P}}^{-}$ spin, the oscillation in P3HT/PCBM is inverted, as expected for bipolar polaron pair recombination.

Figure 6

(a) Modification of the ELDOR pulse sequence for frequency mapping. A pulse of length $t_{\mathrm{pump}}$ and frequency $f_{\mathrm{pump}}$ is followed by an echo sequence on the ${\mathrm{P}}^{+}$ resonance to measure the influence of the first pulse on the positive polaron. (b) Corresponding ELDOR Rabi map for P3HT/PCBM. A clear and spectrally well resolved Rabi oscillation driving the ${\mathrm{P}}^{-}$ resonance is observed on ${\mathrm{P}}^{+}$.

Figure 7

(a) Pulse sequence for the determination of the spin coupling strength via double electron-electron resonance (DEER). (b) Echo intensity as a function of the delay between the initial $\pi /2$ pulse on ${\mathrm{P}}^{+}$ and the $\pi$ inversion pulse on ${\mathrm{P}}^{-}$ in P3HT/PCBM. The time dependence allows us to estimate the coupling strength to $\sim 2\mathrm{MHz}$.

Figure 8

(a) Pulse sequence used to determine the antiparallel and the parallel recombination times ${\tau }_{\mathrm{ap}}$ and ${\tau }_{\mathrm{p}}$, respectively, of ${\mathrm{P}}^{+}{\mathrm{P}}^{-}$ polaron pairs based on an inversion recovery experiment. (b) Typical time constants of $74\mu \mathrm{s}$ for ${\tau }_{\mathrm{ap}}$ and $3\mathrm{ms}$ for ${\tau }_{\mathrm{p}}$ are found experimentally in P3HT/PCBM at $10\mathrm{K}$. (c) Standard echo sequence including a final $\pi /2$ projection pulse for the measurement of the coherence time $T_2$. (d) Both polarons exhibit similar decoherence properties in P3HT/PCBM with $T_2\approx 1.7\mu \mathrm{s}$.

Figure 9

Fast Fourier transform of Rabi oscillation measurements by pEDMR on printed P3HT/PCBM heterojunctions at $10\mathrm{K}$. Again, the two signals corresponding to ${\mathrm{P}}^{+}$ and ${\mathrm{P}}^{-}$ are observed, with the central spin-locking signal appearing at high microwave powers.

Figure 10

(a) Fast Fourier transform of Rabi oscillations in a spin-coated PCDTBT/PCBM solar cell at $10\mathrm{K}$. Analogous to the P3HT/PCBM cells, signals corresponding to ${\mathrm{P}}^{+}$ and ${\mathrm{P}}^{-}$ and a central spin-locking signal are observed. The feature at $\sim 15\mathrm{MHz}$ is again attributed to hyperfine interaction with hydrogen nuclei. (b) Rabi oscillations on ${\mathrm{P}}^{+}$ and the ELDOR experiment with a leading $\pi$ pulse on ${\mathrm{P}}^{-}$ in the PCDTBT/PCBM solar cell. As with P3HT/PCBM, the Rabi oscillations are inverted in the ELDOR experiment on PCDTBT/PCBM, as expected for bipolar polaron pair recombination.