S-shaped current-voltage characteristics of organic solar devices

Measuring the current-voltage characteristic of organic bulk heterojunction solar devices sometimes reveals an S-shaped deformation. We qualitatively produce this behavior by a numerical device simulation assuming a reduced surface recombination. Furthermore we show how to experimentally create these double diodes by applying an oxygen plasma etch on the indium-tin-oxide anode. Restricted charge transport over material interfaces accumulates space charges and therefore creates S-shaped deformations. Finally we discuss the consequences of our findings for the open-circuit voltage $V_{oc}$.

Figure 1

(Color online) Measured current-voltage characteristics of a bulk heterojunction solar cells without PEDOT:PSS layer under illumination. The cell with an additional 10 s oxygen plasma treatment of the ITO substrate shows a regular solar-cell behavior whereas an extension leads to a distinct S-shaped behavior reducing the solar-cell efficiency.

Figure 2

(Color online) Simulated S-shaped current-voltage characteristics due to a reduced majority surface recombination velocity $S_p^a$ for holes at the hole conducting anode. With decreasing velocity, the S-shape gets more distinctive limiting the power-conversion efficiency by diminishing open-circuit voltage, fill factor, and short-circuit current. At the lower right corner a magnification of the $V_{oc}$ dependence on decreasing surface recombination velocity is shown.

Figure 3

(Color online) Space-charge accumulation in semiconductor devices. [Upper row, (a)] At a semiconductor heterojunction the two LUMO energy levels possess a work-function difference of ${\Phi }_n$ at the interface. (b) Additional electrons above the intrinsic concentration, injected by an external electric field cross this interface from an electric unfavorable state to the more favorable one without restrictions. (c) If electrons are forced to overcome this energetic barrier in the opposite direction, a local potential well is established creating a pile up of electrons at the heterojunction. [Lower row, (a)] At a metal-organic interface the work-function difference between the metal Fermi level and the semiconductor LUMO level ${\Phi }_n$ defines the intrinsic electron concentration at the interface. Due to the constant metal work function no potential well or space charge can be created. (b) By a finite surface recombination velocity $S_n$ electron transport through the interface is limited. Electrons which are transported faster toward the interface than they are removed create a space charge. (c) The amount of injected charge carriers is reduced by finite surface recombination velocities creating a local charge-carrier depletion zone at the interface.

Figure 4

(Color online) Energy structure of a solar cell with the energetic levels of HOMO and LUMO (solid and dotted lines) as well as their corresponding quasi-Fermi levels $E_{Fn}$ and $E_{Fp}$ [dashed red (upper) and blue (lower) lines] under illumination. The thick lines indicate the structure under a surface recombination velocity of $S_p^a={10}^{-9}\text{m}/\text{s}$. Thin lines correspond to perfectly conducing contacts $\left(S_p^a\to \infty \right)$. In the case of hole injection by the anode, compare to Fig. 3 [II (b)], at an applied voltage of 300 mV the quasi-Fermi level of holes split up at the anode. Describing the charge-carrier density this generates a space charge combined with a higher electric field $\left(\propto \partial E_{\text{LUMO}}/\partial x\right)$. At a voltage of 900 mV holes are injected into the bulk by the anode, compare to Fig. 3 [II (c)]. Created by the surface recombination, less majority charges are present at the interface creating an electron depletion zone which decreases the local electric field. The cathode energy level (right side) was set to a fixed value of $-4.25\text{eV}$.

Figure 5

(Color online) Device band diagram at the open-circuit voltage for surface recombination rates of (a) infinity and (b) $S_p^a={10}^{-9}\text{m}/\text{s}$. Due to the condition of zero net current $\left(\vec{J}=\overrightarrow{j_n}+\overrightarrow{j_p}=0\right)$ holes pile up at the anode creating a space charge which directly reduces $V_{oc}$. Whereas the quasi-Fermi distribution changes only slightly due to bulk recombination effects, but splits up directly at the contact the band bending and hence the electric field at the anode increases.

Figure 6

(Color online) Open-circuit potential plotted versus the hole surface recombination velocity at the anode. Assuming balanced charge-carrier mobilities $\left({\mu }_n={\mu }_p\right)$ (a) shows a variation of the anode injection barrier from 0.0 to 0.4 eV in steps of 0.1 eV whereas (b) presents the same solar cell under constant injection barriers and charge-carrier mobilities of ${10}^{-10}$, ${10}^{-8}$, and ${10}^{-6}{\text{m}}^2/\text{V}\text{s}$. At high surface recombination velocities no dependence of $V_{oc}$ from the surface recombination velocity can be observed in both cases. A reduction below a critical point results in a linear decreasing of $V_{oc}$ on the semilogarithmic scale which can be attributed to a logarithmic dependence of the local electric field at the contact on the majority charge-carrier density.

Figure 7

(Color online) Calculated current-voltage characteristics with $V_{oc}$ set to voltage axis origin. The anode majority surface recombination velocity is reduced from infinity to ${10}^{-6}\text{m}/\text{s}$. At voltages near $V_{oc}$ an Ohmic transport regime (slope 1) can be found, which changes to a space-charge-limited current at higher voltages (slope 2). The transition between both transport regimes is indicated by an S-shaped deformation of the calculated characteristics.