Energy Loss in Organic Photovoltaics: Nonfullerene Versus Fullerene Acceptors

The energy loss experienced by organic photovoltaics (OPVs) is the difference between the lowest photogenerated exciton energy of a donor or acceptor and the open circuit energy. It sets a fundamental limit to the open-circuit voltage and hence the efficiency of OPVs. This loss can be as large as 0.7 eV for fullerene acceptors, although nonfullerene acceptors (NFAs) reduce this to ≤0.6 eV. Here, we systematically quantify the relationship between charge transfer energy loss $(\mathrm{\Delta }{E}_{\mathrm{CT}})$, nonradiative recombination loss, exciton binding energy, and intra- and intermolecular electron-phonon couplings. Density functional theory and comprehensive quantum mechanical modeling are used to associate molecular volume, effective conjugation length, and the nonbonding character of molecules to these types of energy losses. Nonradiative recombination in donor-NFA heterojunctions is quantified by the charge transfer state emission quantum yield and its Frank-Condon shift. Our analytical results are consistent with measurements where $\mathrm{\Delta }{E}_{\mathrm{CT}}$ is varied between 0 and 0.6 eV using a variety of fullerene derivatives and thiophene-based NFAs paired with donor molecules. Molecular design rules to decrease the energy loss in OPVs derived from our analysis are provided.

Figure 1

Energy diagrams of (a) charge transfer from the acceptor exciton (A*) to the charge transfer (CT) state (A⁻/D⁺), and (b) nonradiative recombination from the CT state (A⁻/D⁺) to the ground state (A/D). The Gibbs free energies are $\mathrm{\Delta }{E}_{\mathrm{CT}}$ in (a) and $E_{\mathrm{CT}}$ in (b). Symmetric parabolic potentials are assumed for the initial and final states. The vibrational levels ($n$, $n^{\mathrm{\prime }}$, and $n^{\mathrm{\prime }\mathrm{\prime }}=\{0,1,2,\dots \}$) are equally spaced. Equilibrium configurations of A*/D, A⁻/D⁺, and A/D manifolds are indicated by $Q_1$, $Q_2$ and $Q_3$, respectively.

Figure 2

Charge transfer rate, $k_{\mathrm{CT}}$, vs the energy loss on CT state formation, $\mathrm{\Delta }{E}_{\mathrm{CT}}$, as functions of (a) the intermolecular reorganization energy, λ₀, and (b) intramolecular coupling strength, S. (c) Nonradiative recombination rate $k_{\mathrm{nr}}$ vs $E_{\mathrm{CT}}$ as functions of ${\lambda }_0$ and (d) S.

Figure 3

(a) The molecular structure of BT-ClC. The red bold line traces the electron-conjugation path comprising alternating $\mathrm{C}$—$\mathrm{C}$ single and double bonds. Blue dashed circles indicate the electron-rich (i.e., oxy-) and deficient (i.e., chloro- and cyano-) moieties that affect the electron distributions in the molecules. (b) The electron and hole density distributions along the molecular length of BT-ClC calculated using density-functional theory (DFT). (c) The molecular structural formulas of IDT-IC and IDTIDT-IC that have different lengths of the electron-donating cores as indicated in the shaded regions.

Figure 4

(a) Exciton binding energy, $E_B$, found via DFT vs effective molecular volume for several acceptor molecules indicated in legend whose molecular formulas are in Supplemental Material [38]. The red solid line is a fit assuming electron confinement within the effective molecular volume for each molecule. The calculation assumes a dielectric parameter, f = 5. 4. The shaded area is the 95% confidence band. The blue dashed line assumes fdepends on molecular polarizability from (b). The confidence limits of the calculations are shown by dotted lines. (b) The calculated molecular polarizability along the molecular longitudinal axis, a_xx, vs the effective molecular length l. The dashed line is the fit using an empirical power law described in text.

Figure 5

Measured $k_{\mathrm{CT}}$ vs ΔE_CT for HJs comprising (a) 1. BT-IC/PBDBT, 2. BT-IC/J61, 3. BT-IC/P3HT, 4. BT-ClC/PCDTBT, 5. BT-ClC/PBDBT, 6. BT-ClC/J61, (b) 1. IT-IC/PCDTBT, 2. IT-IC/PBDBT, 3. IT-IC/J61, 4. IT-IC/P3HT, and (c) 1. PC₇₁BM/F8T2, 2. PC₇₁BM/F8, 3. PC₇₁BM/F8BT, 4. ICBA/F8T2, 5. PC₆₁BM/F8T2, 6. PC₆₁BM/F8, 7. PC₆₁BM/F8BT, 8. C₇₀/CBP, 9. C₇₀/TCTA, 10. C₇₀/NPD, and 11. C₇₀/TPTPA. The dashed lines in (a) and (b) are the fits using semi-classical Marcus theory [Eq. (4) in text]. The blue dashed line in (c) is a guide to the eye. Nonshaded sections are the Marcus normal regions, and shaded sections are the inverted regions. All molecular structural formulas are found in Supplemental Material [38].

Figure 6

Measured $k_{\mathrm{CT}}$ vs temperature, T, for (a) BT-IC/PBDBT and (b) IT-IC/PBDBT HJs. The dashed lines are the fits assuming thermal activation.

Figure 7

Electroluminescence (EL) and external quantum efficiency (EQE) spectra of OPVs based on (a) neat IT-IC, PBDBT, and their blended heterojunction. (b) Neat PC₇₁BM, PBDBT, and their blended heterojunction. The CT state emission at low energy is extracted from the EL spectra by subtracting the spectra from the neat layers. The CT state absorption spectra are extracted by a Gaussian fit of the EQE spectra along the low energy shoulders. The arrows between the short lines indicate the Franck-Condon shift, E_FC, of the CT spectra.