Influence of Disorder and State Filling on Charge-Transfer-State Absorption and Emission Spectra

This paper is a contribution to the Physical Review Applied collection titled Photovoltaic Energy Conversion.

We conduct comprehensive temperature-dependent measurements of the charge-transfer- (CT) state photocurrent and emission spectra for two organic small molecule donor:fullerene (${\mathrm{C}}_{60}$) acceptor bulk heterojunction solar cells. We reveal that the CT spectral width and position are affected by static energetic disorder in the blend, especially evident at low temperatures. The relative contributions of the static and dynamic disorder broadening in the CT spectra are effectively extracted through consideration of a Gaussian CT energetic distribution. However, electroluminescence (EL) spectra can only be interpreted when injected carriers reach thermal equilibrium sites within the disordered density of states and emission occurs from the lowest possible CT energy. For the blend with the smaller energetic disorder, this is the case near room temperature; for the other blend with larger static disorder, carriers fail to reach thermal equilibrium sites even at room temperature and EL spectra need to be interpreted with care. For example, in the latter case, the effect of energetic disorder might not be apparent from EL spectra because the lowest energy sites are not participating. Nonetheless, these states contribute to the photocurrent generation-recombination and energy-loss processes and thus demand accurate characterization, which we show is feasible through temperature-dependent external quantum-efficiency measurements.

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Figure 1

(a) EQE spectra of TAPC:C₆₀ for substrate temperatures ranging from 80–296 K. The CT EQE spectral tails, normalized at 1.57 eV, are shown in the inset. (b) Percent change in EQE with respect to room temperature (296 K). (c) Extracted values of E_CT(expt.) (blue circles) and λ_(expt.) (red diamonds) as a function of temperature. (d) CT absorption peak (blue circles) and FWHM (red diamonds) as a function of temperature. The error bars are obtained by varying the data window in the low-energy EQE tail used to fit Eq. (3).

Figure 2

(a) EQE spectra of NPB:C₆₀ for substrate temperatures ranging from 80–296 K. The CT EQE spectral tails, normalized at 1.7 eV, are shown in the inset. (b) Percent change in EQE with respect to room temperature (296 K). (c) Extracted values of E_CT(expt.) (blue circles) and λ_(expt.) (red diamonds) as a function of temperature. (d) CT absorption peak (blue circles) and FWHM (red diamonds) as a function of temperature. The error bars are obtained by varying the data window in the low-energy EQE tail used to fit Eq. (3).

Figure 3

Extraction of the CT energetic distribution standard deviation $({\sigma }_{\mathrm{CT}})$, for TAPC:C₆₀ (blue circles) and NPB:C₆₀ (red diamonds) solar cells. Dashed lines show the linear fitting through the experimental data points. The y intercepts yield E_CT values of 1.50 and 1.51 eV, respectively, for the TAPC and NPB devices. The slopes of the fitted lines are equal to ${\sigma }_{\mathrm{CT}}^2/2k_B,$ yielding ${\sigma }_{\mathrm{CT}}=52\pm 5\mathrm{meV}$ for TAPC:C₆₀ and ${\sigma }_{\mathrm{CT}}=76\pm 3\mathrm{meV}$ for NPB:C₆₀. The uncertainties in ${\sigma }_{\mathrm{CT}}$ are estimated considering the error bars in E_CT values from Figs. 1 and 2.

Figure 4

Reduced EL spectra for injection current densities ranging from 10–350 mA/cm² for (a) TAPC:C₆₀ and (b) NPB:C₆₀ solar cells. The top and bottom spectra are for 80 and 296 K substrate temperatures, respectively. Spectral linewidth narrows as the temperature reduces from 296 to 80 K for both devices. The TAPC:C₆₀ spectral peak redshifts by approximately 30 meV in this temperature range, whereas the NPB:C₆₀ peak remains nearly fixed.

Figure 5

Approximation of the CT emission peak from the absorption peak, assuming absorption, and emission spectra maintain reciprocity. The solid line with blue circles is the experimental CT absorption peak (E_CT(expt.)+ λ_(expt.)). The solid line with purple crosses is the experimental emission (EL) peak from Fig. S12 within the Supplemental Material [45], at 150 mA/cm² injection current density. The red dashed line is the expected emission peak, E_CT(expt.)− λ_(expt.), estimated from the absorption peak. The E_CT(expt.) and λ_(expt.) values used are shown by the blue circles and red diamonds in Figs. 1 and 2, that correspond to ${\sigma }_{\mathrm{CT}}=52\pm 5\mathrm{meV}$ for TAPC:C₆₀ and ${\sigma }_{\mathrm{CT}}=76\pm 3\mathrm{meV}$ for NPB:C₆₀. The top figure is for TAPC:C₆₀, whereas the bottom one is for NPB:C₆₀.

Figure 6

Relative contribution of the static disorder broadening $(D_{\mathrm{stat}})$ in the total CT absorption spectral linewidth for TAPC:C₆₀ (blue circles) and NPB:C₆₀ (red diamonds). The linewidth is static disorder dominated below approximately 165 and approximately 300 K, respectively, for TAPC and NPB devices.