band edge shifts observed in the present study are in a perfectly reasonable range. The combinations SQ2+D149 and SQ2+D149/D131 again exhibit a slightly smaller relative downward shift of Ec by about 160 mV and about 110 mV, reflecting the combined ef-fect of the presence of SQ2 and indoline dyes on the band edge position. In the presence of coadsorbates the downward shift of Ec observed for the three dye combinations is strongly reduced to 70 mV (SQ2/CA), 28 mV (SQ2/CA+D149/CA), and 16 mV (SQ2/CA+D149/D131/OA). However, the band edge shifts found for the three cells with SQ2 and indoline dyes in the absence of coadsorbates are notably higher than the ΔEc/q of ~60 – 110 mV reported for the electrodeposited cells (cf. Table 13), while in the presence of coadsorbates they are smaller than the ΔEc/q of ~40 – 90 mV of the edep-ZnO samples. Furthermore, in contrast to the downward shifts of Ec observed for the electrodeposited samples with indoline dyes upon addition of the coadsorbates CA and/or OA in the previous chapter, no shift (D149/CA) or a slight upward shift (D149/D131/OA) are found for the present np-ZnO cells. These different impacts of SQ2 and the coadsorbates on the conduction band edge in np-ZnO and edep-ZnO could have partially been caused by changes in the relative amounts of SQ2 (as well as other dyes) and CA/OA on the inner surface of the films and partially by different initial sur-face terminations (e.g., -OH groups) of the bare materials without dyes and coadsorb-ates.
Figure 70: Recombination resistance of np-ZnO-based DSCs with different dyes and dye combinations as a function of the Fermi-level voltage (Vf or Voc) from voltage-dependent EIS under illumination with AM1.5G white light (a) or EIS under varied il-lumination with a red LED at open circuit (b). The lines represent linear fits. Legend as in Figure 67.
A similar dye-dependence of the recombination resistance (uncorrected for band edge shifts) is observed for the two different EIS methods, and the trends are roughly in line with the results attained on electrodeposited ZnO (cf. Figure 58). The indoline dyes and indoline dye combinations, both with or without coadsorbates, yielded the highest Rrec, with D131/OA markedly showing the best results. The cells containing SQ2 without CA/OA showed the overall lowest recombination resistances and among them Rrec de-creased with increasing amount of SQ2 in the films (cf. Figure 63). The distinction in Rrec between the np-ZnO-based cells with SQ2 and those containing only indoline dyes is even more pronounced than among the edep-ZnO cells as a result of the larger con-duction band edge shifts. While the presence of coadsorbates in the electrodeposited samples led to higher recombination resistances for all dyes or dye combinations, on nanoparticulate ZnO this improvement was only observed SQ2 or mixtures of SQ2 and indolines. For the edep-ZnO cells with SQ2, SQ2+D149, or SQ2+D149/D131, Rrec
(Figure 58) exhibited a pronounced local minimum at ca -0.3 V as a result of recombi-nation via additional deep traps related to aggregated SQ2 cations. The Rrec curves of the present samples show only very faint indications of a locally increased rate of re-combination at lower voltages: an onset of a flattening at Vf ≈ -0.4 V in the correspond-ing curves from EISAM1.5G (best visible in Figure 72 below) and a flattened slope
to-wards smaller voltages with a potential dip around Voc ≈ -0.35 V (single data point) for SQ2+D149 and SQ2+D149/D131 in the EISoc,red measurements. The presence of some additional deep trap states in the cells with SQ2 without CA/OA was, indeed, indicated by their capacitance curves (cf. Figure 53) showing what appears to be an onset of a local increase below Fermi-level voltages of about -0.3 V. Further supporting this, the current-voltage characteristics of the cells with SQ2, SQ2+D149, and SQ2+D149/D131 (re-plotted with extended current density scale in Figure 71), exhibit an S-shape similar to that of the corresponding J-V characteristics in chapter 6 (best seen in the representa-tion in Figure 59). Nonetheless, in the case of nanoparticulate ZnO the increase of low-er-voltage recombination by (oxidized) SQ2 aggregates appears to be less severe than for the samples based on electrodeposited ZnO.
Figure 71: Current-voltage curves of the np-ZnO-based solar cells (cf. Figure 64) with extended current density range to reveal the characteristic shape of some of the curves, as indicated by arrows.
When plotted against the voltage corrected for conduction band edge shifts Vf-ΔEc/q or Voc-ΔEc/q (see Figure 72), most of the recombination resistance curves are moved clos-er togethclos-er, suggesting that the diffclos-erences in their voltage-dependent rate constants of recombination kr are relatively small.
Figure 72: Rrec from EISoc,red (a) and from EISAM1.5G (b) as a function of the band edge-corrected voltage. Lines are a guide to the eye only. Assignment of colors and line/
symbol styles as in Figure 67.
However, SQ2, SQ2+D149, and (based on EISoc,red) SQ2+D149/D131 show conduction band edge-corrected recombination resistances that, at a given corrected voltage, would significantly exceed those of all other samples if the curves were extrapolated to extend over the whole voltage range displayed. This must be caused by the very low total den-sity of trap states in the corresponding samples (Table 20). In spite of this, the cells showed the highest rate of recombination at a given (uncorrected) voltage because of the strongly downward shifted conduction band edge. Similar trends were also observed for the electrodeposited counterparts (cf. Figure 58), although they were less pro-nounced due to a smaller conduction band edge shift and a less significant reduction of the total trap density by SQ2.
The recombination parameters β (see Table 21) derived from EISAM1.5G (cf. linear fits to eq. (54) in Figure 70 (a)) are all relatively similar and the average value of 0.44 (maxi-mum deviation of 0.1) is comparable to the average β value of 0.42 determined for the cells based on electrodeposited ZnO with SQ2, D149, and/or D131 (and identical to the average β of 0.44 for edep-ZnO cells when a single outlier was excluded). The co-sensitized cells with SQ2+D149 or SQ2+D149/D131 (both with or without coadsorb-ates) show a tendency towards slightly smaller recombination parameters than the re-maining cells (0.34 – 0.41 compared to 0.4 – 0.5), possibly because the corresponding
Rrec curves showed only a narrow linear range that could be fitted, making the fits rather inexact.
Table 21: Recombination parameters β of the DSCs based on dye-sensitized np-ZnO.
sample code β (EISAM1.5G) β (EISoc,red)
NP_D149 0.49 0.82
NP_D149/D131 0.47 0.82
NP_SQ2 0.47 0.93
NP_SQ2+D149 0.41 0.88
NP_SQ2+D149/D131 0.40 0.85
NP_D149/CA 0.50 0.84
NP_D131/OA 0.44 n.a.
NP_D149/D131/OA 0.47 0.84
NP_SQ2/CA 0.49 0.90
NP_SQ2/CA+D149/CA 0.34 0.90
NP_SQ2/CA+
D149/D131/OA 0.35 0.83
NP_SQ2/CA+
D131/OA+D149/D131/OA 0.40 0.83
The recombination parameters determined from EISoc,red (Table 21, cf. linear fits in Figure 70 (b)) confirm that there is no significant trend dependent on the different dyes or coadsorbates. However, with an average value of 0.86 (maximum deviation of 0.07) they are considerably higher than the values derived from EISAM1.5G. This difference is expected based on the different dependence of the conduction band electron density on the voltage under open-circuit conditions vs. when a current flows through the semicon-ductor. If the applied Vf under AM1.5G illumination takes on the open-circuit value, e.g.
Vf = -0.59 V for D149 (cf. Table 19), the electron density is identical to the electron
density that would be achieved under illumination with red light at Voc = -0.59 V (reached by a sufficient increase of the light intensity). On the other hand, at a Vf value under AM1.5G illumination that is further away from open-circuit conditions, say -0.3 V for D149, the quasi-Fermi level will be 0.3 eV above Eredox at the back contact (x = 0 µm), but will be significantly higher than that at the semiconductor/electrolyte interface (cf. 1.2.1),115 i.e., the electron density would be increased with respect to an open-circuit voltage of Voc = -0.3 V under red illumination (corresponding to a constant quasi-Fermi level of 0.3 eV above Eredox at any location in the semiconductor). Based on these dif-ferences in the density of conduction band electrons available for recombination reac-tions, the recombination resistances measured by EISAM1.5G and EISoc,red should be equal at the voltage where Vf in EISAM1.5G corresponds to the AM1.5G open-circuit value, but should be lower for the EISAM1.5G measurements at any voltage less negative than that.
As a result, the recombination resistance from EISAM1.5G will increase less with decreas-ing Vf (smaller β value) than the Rrec from EISoc,red will do with decreasing Voc (larger β value). Since β is a phenomenological quantity rather than a fundamental microscopic parameter, neither the β value from EISAM1.5G nor that from EISoc,red is “more correct”
than the other; in comparisons with other studies it should simply be ensured that the recombination parameters are compared for the same measurement condition.
The recombination resistance (Figure 72) and chemical capacitance (Figure 69) from EISoc,red were used to determine the effective electron lifetime τn via eq. (47). In addi-tion, τn was obtained independently by intensity-modulated photovoltage spectroscopy at open circuit under red illumination of varied intensity. Based on the identical meas-urement conditions (open-circuit condition, same light source and light intensities) and the theoretical equivalency of the time constants derived from these two methods (cf.
sections 1.4.4 and 1.4.5), it is expected that identical voltage-dependent (cf. eq. (19)) τn
curves are obtained for a given sample. Figure 73 shows that this is roughly the case for most of the samples, but the τn values for SQ2 and, to a smaller degree, for combinations of SQ2 and indolines without coadsorbates show quite pronounced differences. This is most likely the result of an overestimation of Rrec and/or Cµ from EIS, because the spec-tra of these specific cells in part showed Rrec||Cµ-related semicircles that were not clear-ly distinguishable from the other spectral features, see example in Figure 105 in Ap-pendix D. The cells with indoline dyes (with or without coadsorbates) as well as the co-sensitized cells SQ2/CA+D149/D131/OA and SQ2/CA+D131/OA+D149/D131/OA
showed the longest lifetimes, followed by the co-sensitized sample SQ2/CA+D149/CA, then the cell SQ2/CA and lastly the three cells containing SQ2 without coadsorbates with the shortest lifetimes.
Figure 73: Effective electron lifetimes of the np-ZnO solar cells as obtained by IMVS measurements (triangles) and derived from EIS (squares) (see legend in Figure 67 for the meaning of the different colors).
The electron transport times τtr in the np-ZnO-based solar cells were analyzed in com-parison with the τtr in the cells based on edep-ZnO using intensity-modulated photocur-rent spectroscopy (IMPS) at short circuit under red illumination of varied intensity, see Figure 74. At lower short-circuit currents, the nanoparticulate and electrodeposited ZnO films yielded similar electron transport times, but with increasing Jsc, the τtr difference between the two different types of ZnO structures increased because of the steeper slope observed for the electrodeposited samples. The latter was the result of the flatter trap distribution of these cells (as reflected in their higher α values, cf. Figure 55 and Table 20), which should increase the slope of the electron transport time as a function of the Fermi-level voltage (cf. eq. (15) and eq. (69)) and, in consequence, the slope of τtr vs.
Jsc. For both groups of cells, the electron transport time was smallest (i.e., best) for the samples with SQ2, SQ2+D149, or SQ2+D149/D131. To determine to what extent the different transport times observed for different dyes or dye combinations are related to the samples’ different total trap densities (eq. (15) and eq. (69)), the τtr were normalized by Nt/Nt,ref (cf. Table 20), see Figure 75.
Figure 74: Electron transport times from IMPS measurements of DSCs with varied dyes and dye combinations (cf. plot legends in previous sections) based on nanoparticu-late ZnO films (a) or based on electrodeposited ZnO films (b) as a function of the con-stant background value of the short-circuit photocurrent density.
Figure 75: IMPS-derived electron transport times of DSCs based on nanoparticulate ZnO films (a) or electrodeposited ZnO films (b) after normalization by the relative total trap density Nt/Nt,ref (common reference sample: NP_D149).
Both in the case of np-ZnO and edep-ZnO, the normalized transport times were virtually identical for the different dyes and dye combinations, indicating that the differences in τtr were caused by variations in the total trap density. However, SQ2, SQ2+D149, and SQ2+D149/D131 showed clearly lower transport times than the remaining cells even after normalization, suggesting that these samples, which contained strongly aggregated SQ2 (cf. Figure 63), exhibited an increased apparent electron diffusion coefficient D0
(cf. eq. (15)). It has been previously reported that excited electrons in DSCs can move between oxidized dye molecules via hopping,290, 302 thus allowing them to move along the film thickness (perpendicular to the substrate) without having to be injected into the semiconductor. Consequently, it is conceivable that in the present case larger amounts of (oxidized) SQ2 aggregates on the ZnO surface allowed for relatively fast hopping of excited electrons, possibly enabling them to reach the substrate on additional pathways.
When comparing the normalized electron transport times of the np-ZnO samples and the electrodeposited samples (neglecting the SQ2-containing samples without coadsorbates discussed above), the curves of the latter now generally are below those of the nanopar-ticulate cells. This could be the result of the smaller film thicknesses compared to np-ZnO and would then indicate a relatively similar diffusion coefficient D0 for the two different types of structures. However, due to the different slopes (trap distribution pa-rameters) found for np-ZnO cells and cells based on electrodeposited ZnO, no final con-clusions about the diffusion coefficient can be made on the basis of the present results.