Temperature-Dependent Charge-Transfer-State Absorption and Emission Reveal the Dominant Role of Dynamic Disorder in Organic Solar Cells

The energetic landscape of charge-transfer (CT) states at the interface of electron donating and electron accepting domains in organic optoelectronic devices is crucial for their performance. Central questions—such as the role of static energetic disorder and vibrational effects—are under ongoing dispute. This study provides an in-depth analysis of temperature-dependent broadening of the spectroscopic absorption and emission features of CT states in devices with small molecule-fullerene blends. We confirm the validity of the electro-optical reciprocity relation between the photovoltaic external quantum efficiency and electroluminescence, enabling us to validate the device temperature during the experiment. The validated temperature allows us to fit our experimental data with several models, and compare extracted CT state energies with the corresponding open-circuit voltage limit at 0 K. Our findings reveal that the absorption and emission characteristics are usually not symmetric, and dominated by temperature-activated broadening (vibrational) effects instead of static disorder.

Figure 1

Measured relative ${\eta }_{\mathrm{PV}}$ and ${\eta }_{\mathrm{EL}}$ spectra for (a) TAPC:${\mathrm{C}}_{60}$ bulk heterojunction solar cells with 5-wt % and (b) 10-wt % donor content, and (c) TCTA:${\mathrm{C}}_{60}$ bulk heterojunction solar cell with 10-wt% donor content. All measured curves are shifted by a constant offset respective to $T_{\mathrm{set}}$. An alternate view on the normalized spectra is given in Fig. S9 of the Supplemental Material [42].

Figure 2

Device temperature $T_{\mathrm{valid}}$ obtained from the electro-optical reciprocity relation between ${\eta }_{\mathrm{PV}}$ and ${\eta }_{\mathrm{EL}}$ [Eq. (2)] with respect to the experimentally expected temperature $T_{\mathrm{set}}$. For the cell with 10-wt% donor content, both temperatures are almost identical, whereas we see significant deviations from the ideal case for the other two cells at lower $T_{\mathrm{set}}$.

Figure 3

Temperature dependency of the squared CT linewidth ${\sigma }^2$ in ${\eta }_{\mathrm{EL}}$ (against validated EL temperature $T_{\mathrm{valid}}$) and ${\eta }_{\mathrm{PV}}$ (against expected device temperature $T_{\mathrm{set}}$) spectra for TAPC:${\mathrm{C}}_{60}$ solar cells. We find smaller emission linewidths for all devices. In the case of ${\mathrm{TAPC}}_{5\mathrm{\%}}$:${\mathrm{C}}_{60}$, where we find $T_{\mathrm{valid}}$ significantly increased for lower $T_{\mathrm{set}}$, the linewidth narrowing appears less steep if $T_{\mathrm{set}}$ is used as reference (black crosses).

Figure 4

Exemplary model fits for (a) $T_{\mathrm{set}}=150\mathrm{K}$ and (b) $300\mathrm{K}$ for the solar cell with 10-wt % TAPC content. We find the best combined agreement for ${\eta }_{\mathrm{PV}}$ and ${\eta }_{\mathrm{EL}}$ at all temperatures with the multiple vibrations model. The extended Marcus model would require a defined substructure of additional absorption lines, separated by the characteristic vibrations energy ${\mathrm{\Lambda }}_{\mathrm{vibr}}$. Respective peaks are not found at low temperatures, which could be explained by the extended disordered Marcus model; however, it would require the ${\eta }_{\mathrm{EL}}$ peak shifting at low temperatures, which is not observed experimentally.

Figure 5

Fitted energies $E_{\mathrm{ct},\mathrm{model}}$ of the CT state according to the simple (SM), extended (EM), disordered (DM), and extended disordered Marcus model (EDM), and the multiple vibrations model (MV), compared to the extrapolated open circuit voltage limit $V_{\mathrm{OC}}(T\to 0\mathrm{K})$. The black line represents identity, which is best approximated by the multiple vibrations model for TAPC:${\mathrm{C}}_{60}$ blends. Models which include static energetic disorder (DM, EDM) overestimate $E_{\mathrm{CT}}$.