Localized state distribution and its effect on recombination in organic solar cells

Transient photocurrent (TPC) and transient photovoltage (TPV) measurements are reported in bulk heterojunction organic solar cells. TPC is used to measure the band tail and deep trap density of states within the interface band gap and to identify the carrier species from the relative contribution of drift and diffusion. Steep exponential band tails are observed near the donor valence band edge, changing to a broader distribution of states at larger trap energies. The effect of the localized state distribution on the recombination is analyzed—particularly for geminate recombination, where it is shown that band tails can substantially enhance the probability that geminate pairs ionize to form free carriers. The TPV response is shown to have completely different characteristics from those of TPC, and the explanation is provided.

Figure 1

Schematic density of states distribution N(E) for a disordered semiconductor showing mobile and localized states separated by a transport energy. (a) Narrow polaron band typically used to describe organic materials; (b) Band model typically applied to inorganic materials.

Figure 2

Transient photocurrent in PCDTBT:PCBM measured at times extending well beyond the transit time, and comprising a set of measurements indicated by the different colors. The transit time is the change of slope near 1 μs. Dashed lines are fits two different power law decays with exponent values indicated. (Inset) Detail of the transient near 0.1 ms, showing the result of increasing illumination intensity.

Figure 3

Illumination intensity dependence of the transient photocurrent at 0.1 ms in the same PCDTBT:PCBM device as in Fig. 2, showing saturation of the photocurrent at high illumination intensity.

Figure 4

(Color online) Transient photocurrent in P3HT:PCBM measured at times extending well beyond the transit time, and comprising a set of measurements indicated by different colors. The transit time is the change of slope near 0.3 μs. Dashed lines are fits two different power law decays with exponent values indicated.

Figure 5

Illustration of the initial carrier profile of optically excited electrons and holes within the solar cell, for illumination from the left side. Drift currents for electrons and holes are in opposite directions, while the diffusion currents are in the same direction.

Figure 6

(Color online) Transient photoconductivity of (a) PCDTBT:PCBM and (b) P3HT:PCBM at the bias voltages indicated, showing the change of sign of photocurrent that occurs for the slower carrier at a lower bias than for the faster carrier.

Figure 7

(Color online) Measurement of the transient photovoltage response at different values of the open circuit voltage as indicated, determined by changing the intensity of the white bias illumination. The transient response in the dark is also shown. The measurements use a load resistance of 1 MΩ.

Figure 8

(Color online) Experimental measurement of the density of states distribution for a PCDTBT:PCBM solar cell derived from the data of Fig. 2 using the analysis described in the text. The dashed line is an exponential with the indicated slope parameter $E_0$.

Figure 9

(Color online) Experimental measurement of the density of states distribution for a P3HT:PCBM solar cell derived from the data of Fig. 4 using the analysis described in the text. The dashed lines are exponentials with the indicated slope parameters $E_0$.

Figure 10

Plot of the inverse of the photovoltage response time constant scaled according to Eq. (12) (data points) for (upper) a PCDTBT:PCBM solar cell and (lower) a P3HT:PCBM solar cell, compared to the measured dark current (lines) for the same devices.

Figure 11

(Color online) Schematic illustration of the energy lowering of the CTE when the carriers transfer to band tail localized states. The Coulomb energy, the band tail energy and the combined total energy are shown as function of carrier separation, relative to the energy of distant mobile polarons at the transport energy. The crosses in the band tail energy curve and the total energy reflect that there are a finite number of close band tail states and represent the first, second, third etc nearest neighbor, eventually reaching a continuum.

Figure 12

Illustration of the electron and hole wavefunction comprising the CTE showing their exponential decay into the adjacent material due to the potential well created by the band offset.

Figure 13

Plot of the rate factor that reduces the radiative recombination rate of the CTE due to the reduced electron-hole wavefunction overlap. The two plots are for the uniform and discrete wavefunction approximations as discussed in the text.