Built-in potential and validity of the Mott-Schottky analysis in organic bulk heterojunction solar cells

We investigated poly(3-hexylthiophene-2,5-diyl):[6,6]-phenyl-C${}_{61}$ butyric acid methyl ester bulk heterojunction (BHJ) solar cells by means of pulsed photocurrent, temperature dependent current-voltage, and capacitance-voltage measurements. We show that a direct transfer of Mott-Schottky (MS) analysis from inorganic devices to organic BHJ solar cells is not generally appropriate to determine the built-in potential, since the resulting potential depends on the active layer thickness. Pulsed photocurrent measurements enabled us to directly study the case of quasi-flat bands (QFB) in the bulk of the solar cell. It is well below the built-in potential and differs by diffusion-induced band-bending at the contacts. In contrast to MS analysis, the corresponding potential is independent on the active layer thickness and therefore a better measure for flat band conditions in the bulk of a BHJ solar cell as compared to MS analysis.

Figure 1

Time-resolved current density (black) of a pulsed photocurrent measurement. At each voltage step (red), the current density is measured in the dark and under illumination. The pulse duration was chosen sufficiently long (0.5 ms) for the current density to reach steady-state conditions after switching the LED on or off.

Figure 2

Both graphs show a P3HT:PC${}_{61}$BM BHJ solar cell with an active layer thickness of 250 nm at 300 K. (a) Determination of $V_{\text{CV}}$ via Mott-Schottky analysis based on capacitance-voltage measurements. (b) Determination of the point of optimal symmetry ($V_{\text{POS}}$) via pulsed photocurrent measurements.

Figure 3

Energy band diagram of a simulated organic solar cell with ITO contact (left side), metal contact (right side), and an active layer thickness of 100 nm. At an applied voltage equal to $V_{\text{bi}}$, (dashed lines) the simulated HOMO and LUMO levels match at the contacts, and due to band-bending the local electric field is finite over the whole device. At a lower applied voltage $V_{\text{QFB}}$ (solid lines), flat energy bands in the bulk of the device (II) are achieved, while the electric field is finite in the vicinity of the contacts (I and III).

Figure 4

$V_{\text{bi}}$ (black diamonds, determined as shown in Fig. 5), $V_{\text{OC}}$ (red triangles), $V_{\text{POS}}$ (purple squares), and $V_{\text{CV}}$ (green circles) for P3HT:PC${}_{61}$BM bulk heterojunction solar cells with varying active layer thickness. In contrast to $V_{\text{OC}}$, $V_{\text{POS}}$, and $V_{\text{bi}}$, $V_{\text{CV}}$ shows a clear dependency on the active layer thickness (increases with decreasing thickness) and approaches $V_{\text{POS}}$. The dotted lines are guides to the eyes and mark the mean values of the corresponding potentials respectively an exponential fit to $V_{\text{CV}}$.

Figure 5

P3HT:PC${}_{61}$BM solar cell (active layer thickness: 155 nm). An extrapolation of the low temperature region of $V_{\text{OC}}$ (dotted red line) leads to the built-in potential, while a linear extrapolation of the high temperature region (dashed red line) leads to the effective band gap $E_g$ (at $T=0$ K).[5] $V_{\text{CV}}$ (green dots) increases exponentially with decreasing temperature and shows no connection to the built-in potential.