Photocurrent in bulk heterojunction solar cells

We investigated the photocurrent in poly(3-hexylthiophene-2,5-diyl)(P3HT):[6,6]-phenyl-${\text{C}}_{61}$ butyric acid methyl ester solar cells by applying a pulsed measurement technique. For annealed samples, a point of optimal symmetry with a corresponding voltage $V_{\text{POS}}$ of 0.52–0.64 V could be determined. Based on macroscopic simulations and results from capacitance-voltage measurements, we identify this voltage with flat band conditions in the bulk of the cell but not the built-in voltage as proposed by Ooi et al., J. Mater. Chem. 18, 1644 (2008). We calculated the field-dependent polaron pair dissociation after Onsager-Braun and the voltage-dependent extraction of charge carriers after Sokel and Hughes with respect to this point of symmetry. Our analysis allows to explain the experimental photocurrent in both forward and reverse directions. Also, we observed a voltage-independent offset of the photocurrent. As this offset is crucial for the device performance, we investigated its dependence on cathode material and thermal treatment. From our considerations we gain insight into the photocurrent’s voltage dependence and the limitations of device efficiency.

Figure 1

(Color online) Photocurrent density $J_{\text{Ph}}$ vs applied voltage of a typical P3HT:PCBM solar cells with Ca/Al cathode under 1 sun. The POS is indicated by the blue circle. The voltage-dependent symmetric shape of $J_{\text{Ph}}$ is shifted by a constant offset to more negative values. Note that the density of recorded data points is higher between 0 and 1 V applied voltage. The inset shows the current flowing under pulsed illumination, with an increase in the applied voltage every millisecond.

Figure 2

(Color online) Energy structures of a simulated organic solar cell in the dark (left) and under illumination of 1 sun (right). The simulated HOMO and LUMO levels (solid lines) and quasi-Fermi levels for electrons and holes (dashed lines) of a 100-nm-thick cell are shown, with the ITO contact on the left and the metal contact on the right side. (a) At $V_{\text{POS}}$ (QFB) the bands are flat in the bulk, while the electric field is finite in the contact regions. (b) At an applied voltage equal to the built-in potential $V_{\text{BI}}$ the vacuum levels at the position of the electrodes match, but the internal electric field is nonzero over the whole device.

Figure 3

(Color online) Typical result for a capacitance-voltage measurement of an annealed P3HT:PCBM solar cell with Ca/Al cathode in the dark. Normalized capacitance $C/A$ (left axis) and Mott-Schottky plot (right axis). A linear fit to the Mott-Schottky plot results in a value of 0.59 V for the quasi-flat-band voltage.

Figure 4

(Color online) Photocurrent density vs applied voltage. (a) Influence of thermal treatment for solar cells with Ca/Al cathode. (b) Cells with Ca/Al and Ag cathode, in each case for two different active layer thicknesses. The magnitude of the voltage-independent offset can be influenced by thermal treatment and choice of cathode material.

Figure 5

(Color online) Plot of the photocurrent in reverse direction (with the origin shifted to POS) against (a) effective voltage and (b) calculated field for cells with different active layer thicknesses. While the characteristic points, indicated by the red dashed lines, lie on top of each other in the left graph, they disperse in the right graph.

Figure 6

(Color online) Comparison of experimental photocurrent (cell with Ca/Al cathode under 1 sun) and a model based on Braun-Onsager theory and extraction. Field-dependent part of $J_{\text{Ph}}$ in forward and reverse direction (left axis) and PP dissociation probability (right axis) vs effective voltage. The black lines show the PP dissociation after Braun (dotted), extraction after Sokel and Hughes (dashed) and their combined product (solid).

Figure 7

(Color online) Effective photocurrent $J_{\text{Ph}}-J_{\text{Ph}}\left(V_{\text{POS}}\right)$ vs applied voltage for two solar cells with Ca/Al and Ag cathode (symbols). For both cells, the experimental data (symbols) agrees well with the model, Eq. (5) (solid lines).