Monomolecular and bimolecular recombination of electron–hole pairs at the

A further project aimed at the investigation of the recombination processes in organic bilayer solar cells. Recombination is an important loss mechanism at the donor-acceptor interface and can be divided into two main types. Geminate recombination describes the recombination of an electron and a hole that were generated from the same exciton. In contrast, non-geminate recombination means that an electron and a hole originating from different excitons recombine.

In this work, we evaluate the contributions from both geminate and non-geminate recombination in organic bilayer systems. The bilayer geometry is chosen because it enables the differentiation between the different recombination types. The devices have to meet several requirements for the recombination studies. Besides a general good solar cell performance, the extraction of the charge carriers should exhibit no difficulties and the solar cell morphology should be stable. Thus, annealing or the insertion of extraction layers should not affect the device efficiency. These demands are fulfilled when applying the novel low bandgap copolymer PCDHTBT0.7/TPDDHTBT0.3 with triphenyldiamine units and additional hexyl spacers at the thiophene units as the donor material. For convenience, this copolymer is named PCDTBTstat in this work. In comparison to the donor polymer, also the small molecule donor p-DTS(FBTTh2)2

known for its high efficiency was used. As acceptor material, C60 was applied. For the investigation of the contributions of geminate and non-geminate recombination, the fill factor of the bilayer solar cells is observed in dependence on the donor layer thickness and excitation light intensity. The fill factor depicts the ratio of the generated charge carriers that can be extracted by the electrodes. Thus, it is a measure of the fraction of recombining charge carriers.

For the intensity dependent recombination study, bilayer solar cells are fabricated from PCDTBTstat and C60. The polymer donor was applied with layer thicknesses of 14 nm, 36 nm, and 66 nm. The acceptor layer was kept constant at 30 nm. The excitation light intensity was varied between 0.02 mWcm^-2 and 100 mWcm^-2 using optical density filters. From the measured current-voltage characteristics, the fill factor can be calculated. Figure 49 illustrates the fill factor for bilayer solar cells in dependence of the excitation light intensity for different polymer layer thicknesses.

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Figure 49: Chemical structures of the small molecule p-DTS(FBTTh2)2 and the low bandgap copolymer PCDTBTstat. b) Fill factor in dependence of the excitation light intensity for bilayer devices made from either PCDTBTstat and C60

or p-DTS(FBTTh2)2 and C60. Excitation was conducted at a wavelength of 580 nm. Polymer layer thicknesses of 14 nm, 36 nm, and 66 nm were applied. Right of the dashed vertical line, the fill factors for AM1.5 illumination is shown. The right axis displays the difference to an estimated ideal fill factor limit of 80%. The horizontal lines illustrate the asymptotic value for the fill factor at infinitely low illumination as calculated by a fit and extrapolation of the data. Geminate recombination is expected to cause the deviation between the horizontal lines and the assumed fill factor of 80%. The shaded area between the horizontal lines and the data points depicts the deficit due to non-geminate recombination. The losses due to non-geminate recombination at AM1.5 excitation are illustrated by arrows. Reprinted from Chapter 7.

The fill factor of the solar cell with 14 nm donor thickness remains constant at 67% over the whole range of the light intensity. However, the fill factor drops from 61% to 50% at AM1.5 excitation for the cell with the 36 nm thick polymer layer and from 51% to 22% for the device with 66 nm thickness, respectively. In addition, the fill factor for a bilayer cell made from the low molecular weight donor p-DTS(FBTTh2)2 with a thickness of 60 nm in combination with C60 is shown. At AM1.5 excitation, the same fill factor of 67% as for the device with the 14 nm thick donor layer is achieved.

At low light intensities, only few excitons are formed. The charges diffuse within their Coulomb potential and can recombine before dissociating into free charge carriers. This process is called primary geminate recombination. When the charges diffuse out of the Coulomb radius, they either can be extracted by the electrodes or they diffuse back and recombine which is referred to as secondary geminate recombination. Both primary and secondary geminate recombination are monomolecular mechanisms. The increase of the donor layer thickness results in a longer diffusion path and thus the probability for recombination is enhanced, leading to a decrease of the initial fill factor from 67% to 50% with increasing polymer thickness from 14 nm to 66 nm.

For an ideal solar cell, a fill factor of 80% is assumed. The difference between this value and the

10^-2 10^-1 10⁰ 10¹ 10²

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highest fill factors of the cells can be attributed to geminate recombination and is indicated by the horizontal lines. At high light intensities, more excitons are generated. Now the probability for non-geminate bimolecular recombination gets higher. This means that the charge carriers can recombine with charge carriers originating from other excitons. For the 14 nm thick polymer layer, no non-geminate recombination can be observed because the free charge carriers are extracted faster than they can recombine. The contribution from non-geminate recombination that reduces the initial fill factor are illustrated by the shaded areas. The findings were supported by Monte Carlo simulations that confirms the increase of the photocurrent when using thin donor layers.

The competing process to recombination in organic solar cells is charge extraction. With increasing hole mobility, more holes should be collected at the electrode. In consequence, high fill factors should be achievable even with high layer thicknesses. This is confirmed by measurements of a bilayer solar cell consisting of 60 nm p-DTS(FBTTh2)2 and C60. As can be seen in Figure 49, this solar cell exhibits a much higher fill factor than the solar cell from PCDTBTstat

with a similar thickness at low light intensity. The hole mobility of the small molecular donor detected by the metal-insulator-semiconductor charge-extraction-by-linearly-increasing-voltage (MIS-CELIV) method is two orders of magnitude higher than that of PCDTBTstat.

Figure 50 summarizes the competition between geminate and non-geminate recombination at the donor-acceptor interface and charge carrier extraction at the electrodes. At low excitation light intensities, diffusion within the Coulomb radius of the exciton can cause recombination of the hole with the corresponding electron according to the primary geminate recombination process (1). When exceeding the Coulomb radius, the hole can be either extracted at the electrode or it diffuses back and recombines with the electron originating from the same exciton by secondary geminate recombination (2). Both mechanisms are monomolecular as the hole and the electron arise from the same exciton. Non-geminate recombination becomes important at high light intensities. Here, holes and electrons from different excitons recombine in a bimolecular procedure.

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Figure 50: Schematic overview of the competition between monomolecular geminate and bimolecular non-geminate recombination at the donor-acceptor interface as well as charge carrier extraction at the electrodes.

The Coulomb radius is abbreviated by rc. Reprinted from Chapter 7.

In this work, we investigated the dependence of the fill factor on the excitation light intensity and the donor layer thickness. Thus, we were able to evaluate the contribution of both geminate and non-geminate recombination in bilayer solar cells.

4.2.3 A facile method for the investigation of temperature-dependant C60 diffusion in