Nonradiative Energy Losses in Bulk-Heterojunction Organic Photovoltaics

The performance of solar cells based on molecular electronic materials is limited by relatively high nonradiative voltage losses. The primary pathway for nonradiative recombination in organic donor-acceptor heterojunction devices is believed to be the decay of a charge-transfer (CT) excited state to the ground state via energy transfer to vibrational modes. Recently, nonradiative voltage losses have been related to properties of the charge-transfer state such as the Franck-Condon factor describing the overlap of the CT and ground-state vibrational states and, therefore, to the energy of the CT state. However, experimental data do not always follow the trends suggested by the simple model. Here, we extend this recombination model to include other factors that influence the nonradiative decay-rate constant, and therefore the open-circuit voltage, but have not yet been explored in detail. We use the extended model to understand the observed behavior of series of small molecules:fullerene blend devices, where open-circuit voltage appears insensitive to nonradiative loss. The trend could be explained only in terms of a microstructure-dependent CT-state oscillator strength, showing that parameters other than CT-state energy can control nonradiative recombination. We present design rules for improving open-circuit voltage via the control of material parameters and propose a realistic limit to the power-conversion efficiency of organic solar cells.

Popular Summary

The key to efficient performance in optoelectronic devices such as solar cells and light-emitting diodes is to minimize the nonradiative decay of excited states. Such decay occurs when the energy of the excited state is dissipated via the creation of vibrations, i.e., heat in the material. This loss is felt particularly strongly in organic semiconductors and may introduce an intrinsic limitation to the performance of organic light-emitting diodes or solar cells. Here, we combine experiment and theory to study how charge carriers dissipate energy in organic solar cells, a loss which occurs primarily at the interface between the charge donor and acceptor.

The key lies in the transition dipole moment of the interfacial excited state, which is an excited state that occurs at the interface between the donor and acceptor species. By tuning the strength of this moment relative to the static dipole moment of the complex, we can control the relationship between the radiative and nonradiative recombination rates of charge carriers.

We validate the model using experimental results. This yields a strategy to limit the nonradiative losses in organic donor-acceptor solar cells. We also develop guidelines to understand and further reduce losses in open-circuit voltage, possibly achieving a power-conversion efficiency of 20%—up from about 14% for single-junction organic photovoltaic cells.

With these results, we aim to understand how to experimentally control our model’s parameter to achieve better power-conversion efficiencies.

Figure 1

Recombination mechanism in organic photovoltaics. (a) Schematic illustrating an electron and hole occupying an interfacial charge-transfer state in a bulk-heterojunction system. (b) The potential energies of the ground state and charge-transfer state at the donor-acceptor interface as a function of the reaction coordinate. The quantized vibrational modes are shown as the colored waves: red for modes of the electronic ground state and blue for modes of the charge-transfer state. The green overlap between the lowest vibrational state of the charge-transfer state (which defines the energy of the apparent charge-transfer state) and a vibrationally excited ground state indicates the nonradiative recombination pathway. The arrows depict possible radiative decay pathways. While we indicate here some radiative decay from higher-energy vibronic modes, most decay originates from the lowest vibronic state of the charge-transfer state.

Figure 2

Nonradiative voltage loss as a function of the energy of the charge-transfer state with respect to changed (a) high-frequency reorganization energy ${\lambda }_v$, (b) low-frequency reorganization energy ${\lambda }_l$, and (c) oscillator strength $f_{\mathrm{osc}}$. (d) Predicted maximum (red line) and minimum (blue line) nonradiative voltage losses $\mathrm{\Delta }{V}_{\mathrm{oc},\mathrm{nr}}$ as a function of the energy of charge-transfer state $E_{\mathrm{CT}}$ obtained using the proposed model sampling a range of values for each of the six parameters. The key parameters for modeling the “maximum” and “minimum” cases are ${\lambda }_v=0.32\mathrm{eV}$, ${\lambda }_l=0.4\mathrm{eV}$, $f_{\mathrm{osc}}=4\times {10}^{-3}$ and ${\lambda }_v=0.15\mathrm{eV}$, ${\lambda }_l=0.05\mathrm{eV}$, $f_{\mathrm{osc}}=4\times {10}^{-1}$, respectively. For comparison, a variety of reported experimental values from the literature are shown (circular symbols) [5, 12, 21, 42, 43, 44]. The data labeled “this work” is obtained from $\mathrm{BIT}\text{−}4\mathrm{F}:{\mathrm{PC}}_{71}\mathrm{BM}$ devices in the experimental section. A complicated version of (d) specifying the references can be found in Fig. S1 [29].

Figure 3

(a) EL and EQE for BIT-4F:PC71BM blend devices with different SVA processing times. The external quantum efficiencies are composed of the directly measured EQE (red solid lines) and the EQE determined from the EL spectra (blue dashed lines). (b) Reproduced EQE spectra based on the optical model derived above. The different curves are obtained by changing only the oscillator strength of the charge-transfer state, keeping the properties of the excitonic state the same.

Figure 4

(a) Calculated (experimental) nonradiative voltage losses ($\mathrm{\Delta }{V}_{\mathrm{oc},\mathrm{nr}}$) as a function of $V_{\mathrm{oc},\mathrm{rad}}$ with respect to different exposure times in solvent vapor for BIT-4F-, 6F-, 8F-, and 10F-based fullerene solar cells (colored symbols) and simulated (modeled) results considering solely the change of transition oscillator strength (gray dashed line with solid circles). (b) The effect of the different parameters of the model on the variation of $\mathrm{\Delta }{V}_{\mathrm{oc},\mathrm{nr}}$ with $V_{\mathrm{oc},\mathrm{rad}}$. The only parameter leading to a strong positive correlation between the two is the oscillator strength. The arrow represents the direction of increasing the specific variable values. The variable ranges are $f_{\mathrm{osc}}=[{10}^{-2},1]$, ${\lambda }_l=[0.1,0.2]\mathrm{eV}$, $R_{\mathrm{CT}/E}=[{10}^{-2},{10}^{-4}]$, $E_{\mathrm{CT}}=[1.45,1.55]\mathrm{eV}$, ${\lambda }_v=[0.1,0.2]\mathrm{eV}$, and $|\mathrm{\Delta }\overrightarrow{\mu |}=[10,30]\mathrm{D}$.

Figure 5

Predicted power-conversion efficiency compared with the radiative limit. The black line is the SQ limit using the AM1.5G sun spectrum, where only radiative recombination is considered; the blue line is the nonradiative limit considering a perfect charge collection (100% of the EQE calculated from modeled absorption spectra) and the ideal Shockley equation (ideality factor of 1); the red line is the more realistic limit assuming 90% EQE absorption and 80% fill factor.