Transport Effects on Capacitance-Frequency Analysis for Defect Characterization in Organic Photovoltaic Devices

Using capacitance-frequency ($C\text{−}f$) analysis to characterize the density-of-states (DOS) distribution of defects has been well established for inorganic thin-film photovoltaic devices. While $C\text{−}f$ analysis has also been applied to bulk-heterojunction (BHJ) organic photovoltaic (OPV) devices, we show that the low carrier mobility in the BHJ material can severely alter the $C\text{−}f$ behaviors and lead to misinterpretations. Because of the complicated nature of disorders in organic materials, artifacts from an erroneous $C\text{−}f$ analysis are difficult to identify. Here we compare drift-diffusion simulations with experiments to reveal situations when the validity of $C\text{−}f$ analysis for defect characterization breaks down. When a flat-band region is present in the low-mobility active layer, the capacitive response cannot follow the electrical modulation and behaves as if the active layer is a dielectric at frequencies higher than the characteristic frequency determined by carrier mobility and thickness. The transition produces a fictitious shallow defect when defect analysis is applied. Even in fully depleted devices, the defect distributions derived from $C\text{−}f$ analysis can appear at spuriously deeper energies if the mobility is too low. Through simulations, we determine the ranges of mobility and thickness for which the $C\text{−}f$ analysis can effectively yield credible defect DOS information. Insight from this study also sheds light on transport limitation when using capacitance spectroscopy for defect characterization in general.

Figure 1

(a) Schematic band diagram of a $p$-doped device in the dark at zero bias voltage. The crossing point between the Fermi level $E_f$ and the defect energy $E_0$, $M$, within the depletion zone marks the position of the occupancy change. (b) $C$ vs $f$ in the dark at zero bias (black solid line) of the device shown in (a) and the corresponding defect DOS distribution (red dashed line) derived from the $C\text{−}f$ spectrum using Eq. (3), which has a Gaussian distribution with a peak energy at $E_0$ and a disorder width ${\sigma }_t$.

Figure 2

(a) $C$ vs $f$ in the dark at zero bias for inverted $\mathrm{P}3\mathrm{HT}:{\mathrm{PC}}_{61}\mathrm{BM}$ devices with different active-layer thicknesses: 55 nm (red), 120 nm (dark yellow), 225 nm (blue), 325 nm (green), and 500 nm (gray). Defect DOS derived from $C\text{−}f$ analysis for 55- and 120-nm devices The solid line in (b) shows the Gaussian fit of the defect DOS according to Eq. (4); the corresponding fitting parameters are shown as the inset. (c) $C$ vs $f$ for a 500-nm-thick $\mathrm{P}3\mathrm{HT}:{\mathrm{PC}}_{61}\mathrm{BM}$ device under different biases: 0.2 V (gray), 0 V (black), $-1\mathrm{V}$ (red), $-2\mathrm{V}$ (blue), $-3\mathrm{V}$ (dark yellow), and $-4\mathrm{V}$ (green). (d) Defect DOS derived from $C\text{−}f$ analysis for 225-, 325-, and 500-nm devices. All color schemes used in (b) and (d) are the same as in (a). The inset of (d) depicts the spurious shallow-defect peak position $E_t*$ vs $f/t$ for the three thicker devices with a fit according to Eq. (9).

Figure 3

The simulated fictitious shallow-defect position $E_t*$ for a 225-nm device with $p=5.8\times {10}^{15}{\mathrm{cm}}^{-3}$ and hole mobility varying from ${10}^{-6}{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ to ${10}^{-3}{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$. Inset: $C$ vs $f$ for different mobilities: black (${10}^{-6}{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$), red (${10}^{-5}{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$), blue (${10}^{-4}{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$), and green (${10}^{-3}{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$).

Figure 4

(a) $C$ vs $f$ of the fullerene-based OPV devices with different P3HT concentration: 1 wt % (black), 2 wt % (green), 5 wt % (red), 10 wt % (dark yellow), and 20 wt % (blue). All results are normalized to the value at 1 MHz. The arrow indicates the shift of $C\text{−}f$ with decreasing ${\mu }_h$ (P3HT concentration). (b) Defect DOS distributions extracted from (a). All results are normalized to their peak value to emphasize the energy position change. The arrow indicates the shift to deeper position in the device with decreasing ${\mu }_h$ (P3HT concentration). (c) Normalized $C\text{−}f$ simulated for the fullerene-based OPV devices with different ${\mu }_h$ values that correspond to P3HT concentrations. (d) Corresponding simulated defect DOS distributions (normalized). All color schemes used in (b), (c), and (d) are the same as in (a).

Figure 5

Simulation results of devices with varying hole mobility ($y$ axis) in logarithmic scale and active-layer thickness ($x$ axis). The color indicates the energy position shift of the defect DOS distributions between the output and input of the simulations. The white line demonstrates a boundary below which there is no artifact.