opened up by aggregated SQ2) counteracted the successful increase of the light-harvesting efficiency to 85 and 83% with respect to the cells D149 and D149/D131 (ηlh
= 69 and 67%) and rendered their short-circuit current densities and overall photovoltaic performance much lower than those of the indoline dye cells. In the presence of coad-sorbates (cells SQ2/CA+D149/CA and SQ2/CA+D149/D131/OA), the integrated light harvesting efficiencies (72 and 69%) were only slightly improved compared to the cor-responding samples without SQ2 (67% for D149/CA and 66% for D149/D131/OA), and the charge collection efficiency and combined electron injection and/or dye regeneration efficiency were also similar or only slightly better (ηinj·ηreg of 86 and 87% compared to 91 and 85%, ηcc of 85 and 90% compared to 90% for D149/CA and D149/D131/OA).
While the calculations predict a slight increase of IPCE and Jsc (cf. theoretical values in Table 19) at least for SQ2/CA+D149/D131/OA compared to D149/D131/OA, the measured short-circuit current densities of the co-sensitized np-ZnO-based cells with SQ2 and coadsorbates were all lower than those of D149/CA and D149/D131/OA. The incorrect prediction for SQ2/CA+D149/D131/OA may have resulted from temporal variations of the photovoltaic performance (cf. chapter 9). The sample sensitized with SQ2/CA+D131/OA+D149/D131/OA exhibited a smaller Jsc than the cell with SQ2/CA+D149/D131/OA (as predicted by the theoretical Jsc values) because of its re-duced charge collection efficiency (from 90 to 80%) and its slightly rere-duced light har-vesting efficiency (from 69 to 67%), underlining once again the redundancy of the addi-tional step in the sensitization process.
7.7 Analysis of the Variation in the Open-Circuit Voltage and
were determined by a modification of eq. (76) by use of the ratio of the inverse recom-bination resistances Rrec instead of the ratio of recombination currents under illumina-tion, which should be equally valid based on the relationship between Rrec and the re-combination factor J0k in eq. (54).
Table 23 shows the partial contributions to the voltage differences of the various np-ZnO DSCs with respect to the cell with D149 by conduction band edge shifts (ΔVoc(ΔEc/q), cf. Table 20), differences in the short-circuit photocurrent density (ΔVoc(ΔJsc), cf. Table 19), and differences in the rate of recombination as reflected by changes in Rrec at a corrected voltage Vf-ΔEc/q = -0.55 V (ΔVoc(ΔRrec), cf. Figure 72 (b)). The calculated total voltage changes ΔVoc,calc (sum of ΔVoc (ΔEc/q), ΔVoc (ΔJsc) and ΔVoc (ΔRrec)) largely deliver qualitatively correct predictions of the experimental total voltage changes ΔVoc. Quantitatively, the calculations tended to underestimate the volt-age losses observed for the cells containing SQ2 without coadsorbates by 40 – 80 mV, most likely as a result of additional recombination via deep traps (cf. Figure 72 and Figure 71 and discussion) that is not described by the β-recombination model. This is roughly in line with an additional voltage loss of about 60 mV found for the correspond-ing edep-ZnO cells as a consequence of the presence of monoenergetic traps located about 0.3 eV above Eredox (cf. Figure 58 and Table 15). The calculated origins of the voltage changes between the np-ZnO cells with different dyes and coadsorbates mostly corroborate the results discussed for the corresponding electrodeposited cells (cf. Table 15). Among the cells with indoline dyes only, experimentally a beneficial effect of the presence of D131 on Voc was observed, while coadsorption of CA or OA led to only a slight improvement (D149/CA) or even to a decrease (D149/D131/OA) of Voc with re-spect to the counterparts without coadsorbates, in agreement with the trends observed among edep-ZnO cells. The calculations in the present case did not precisely predict these changes of Voc among the indoline dye cells. Nevertheless, the different contribu-tions to ΔVoc determined for D131/OA indicate that an upward shift of the conduction band and a reduction of the rate constant of recombination may have been the reason for the good Voc’s attained in the presence of D131.
Table 23: Individual contributions ΔVoc(...) to the total differences of the open-circuit photovoltages (ΔVoc,calc: theoretical total change, ΔVoc: experimental change) among the DSCs based on np-ZnO with different dyes or dye combinations, resulting from shifts in the conduction band edge ΔEc/q (positive: downward shift, negative: upward shift), differences in the short-circuit photocurrent density ΔJsc, and changes ΔRrec of the recombination resistance at a corrected voltage Vf-ΔEc/q of -0.55 V. Calculations were performed using the average β parameter of 0.44.
sample code ΔVoc(ΔEc/q) /mV
ΔVoc (ΔJsc) /mV
ΔVoc (ΔRrec) /mV
ΔVoc,calc
/mV
ΔVoc
/mV NP_D149 +/- 0 (ref.) +/- 0 (ref.) +/- 0 (ref.) +/- 0
(ref.)
+/- 0 (ref.)
NP_D149/D131 +/- 0 +/- 0 + 6 + 6 - 30
NP_SQ2 + 267 + 109 - 208 + 167 + 250
NP_SQ2+D149 + 161 + 50 - 110 + 101 + 100
NP_SQ2+D149/D131 + 112 + 44 - 76 + 80 + 120
NP_D149/CA +/- 0 + 3 +/- 0 + 3 - 10
NP_D131/OA - 20 + 36 - 22 - 5 - 40
NP_D149/D131/OA - 11 + 6 + 15 + 10 +/- 0
NP_SQ2/CA + 70 + 79 - 28 + 121 + 80
NP_SQ2/CA+D149/CA + 28 + 12 - 12 + 27 + 40
NP_SQ2/CA
+D149/D131/OA + 16 + 8 - 16 + 7 + 20
NP_SQ2/CA+D131/OA
+D149/D131/OA + 3 + 11 + 1 + 16 + 20
The coadsorbates CA and OA did not seem to have a significant effect on any of the individual quantities contributing to voltage changes, which presents a difference com-pared to the effects of CA/OA on the conduction band edge and rate constant of recom-bination observed on edep-ZnO. For nanoparticulate ZnO the indoline dye molecules
were more stable against replacement by CA/OA, so that D149/CA and D149/D131/OA likely contained relatively small amounts of coadsorbates, decreasing the influence of CA or OA on microscopic processes in the cells. Most notably, the present results con-firm that sensitization of np-ZnO with the squaraine dye SQ2, as in the case of edep-ZnO, led to a very strong voltage loss with respect to D149 due to a large conduction band edge downward shift and a very limited short-circuit photocurrent. The effects of these factors were not fully compensated by the strong Voc-enhancing effect of the low total trap density indicated for SQ2. When CA was coadsorbed with SQ2, the signifi-cant reduction of the downward conduction band edge shift and the increase of Jsc ena-bled a large gain of Voc with respect to the coadsorbate-free sample, also in line with the results found on edep-ZnO. The co-sensitized cells containing SQ2 together with indo-line dyes again showed improved Voc’s compared to SQ2 and SQ2/CA because both the losses related to Jsc as well as the conduction band edge downward shifts were clearly decreased. However, compared to the cells with indoline dyes only, lower Jsc values and downward shifts of the conduction band edge – albeit reduced compared to SQ2 or SQ2/CA – still caused a lower Voc. In the cell SQ2/CA+D131/OA+D149/D131/OA, the downward shift of the conduction band edge was somewhat reduced compared to the cell SQ2/CA+D149/D131/OA, but the Jsc-related voltage loss was larger and the re-combination-related voltage gain was reduced, so that the net effect was a constant ex-perimental Voc, which contributed to the fact that the 3-step co-sensitization procedure did not bring about any advantages over the 2-step process.
In a second step, the origins of the differences in Voc between the cells based on nano-particulate ZnO and the corresponding electrodeposited samples were investigated. Ap-proximate conduction band edge shifts ΔEc/q were determined between each np-ZnO sample and its edep-ZnO counterpart neglecting their different trap distribution parame-ters (cf. Figure 55 and Figure 69 (a), Table 12 and Table 20), see Table 24. The volt-age differences originating in the differences of Jsc and Rrec (at Vf-ΔEc/q = -0.55 V) be-tween the np-ZnO cells and the edep-ZnO cells (cf. Table 11 and Figure 58 (b)) were calculated via eq. (75) and the modified eq. (76) using the edep-ZnO films as references and a β parameter of 0.44 (average value both among edep-ZnO cells and among np-ZnO cells), see Table 24. The calculated total voltage changes ΔVoc,calc (see Table 24) largely confirm the experimental changes ΔVoc, which in all but one case (SQ2) consti-tuted increases for np-ZnO with respect to edep-ZnO. However, the ΔVoc,calc values
dif-fer from the experimental changes ΔVoc by up to 80 mV, which could be due to inexact values of ΔEc/q as a result of the different trap distributions in np-ZnO and edep-ZnO as well as to different additional losses by recombination via deep-lying monoenergetic trap states. The calculated individual contributions in Table 24 reveal that the higher voltages of np-ZnO cells with respect to edep-ZnO cells were caused by their much lower rate constants of recombination and their mostly higher short-circuit photocurrent densities, which overcompensated the mostly positive (downward) relative shifts of the conduction band edge.
Table 24: Different contributions ΔVoc(...) to the change of the open-circuit photo-voltage for DSCs based on nanoparticulate ZnO (this chapter) with respect to the cor-responding DSCs fabricated from electrodeposited ZnO (previous chapter).
ΔVoc (ΔEc/q) /mV
ΔVoc (ΔJsc) /mV
ΔVoc (ΔRrec) /mV
ΔVoc,calc
/mV
ΔVoc
/mV
D149 40 -17 -134 -111 -30
D149/D131 34 -33 -92 -91 -40
SQ2 199 26 -264 -39 0
SQ2+D149 145 8 -212 -59 -90
SQ2
+D149/D131 88 11 -159 -60 -60
D149/CA -19 -32 -49 -100 -40
D149/D131/OA -36 -20 -6 -62 -10
SQ2/CA 22 -2 -45 -24 -60
SQ2/CA
+D149/D131/OA 14 -4 -23 -13 -30
The np-ZnO cell with SQ2 showed a Voc identical to that of its electrodeposited coun-terpart even though its short-circuit photocurrent was somewhat higher than the Jsc of
dye
ΔVoc (np-ZnO vs.
e- ZnO)
the latter and the conduction band edge position was much lower, because the related losses were offset by a gain associated with a significantly smaller rate constant of re-combination. To take a closer look at the variations of the fill factors between the differ-ent np-ZnO-based solar cells, the internal (i.e., series resistance-corrected) values of FF were determined by plotting the cell current density (of the J-V curves, cf. Figure 64) against the Fermi-level voltage Vf, as derived from EIS under AM1.5G type illumina-tion. The results are plotted together with the external fill factors (cf. Table 19) as a function of the open-circuit voltage in Figure 76. In addition, values of FF that were calculated by inserting the experimental Voc and β values of the individual cells into eq.
(35) as well as a simulated curve based on eq. (35) under the assumption of a constant β parameter of 0.44 are presented. The simulated curve and the individual calculated val-ues are well in line, indicating that the differences in the fill factors were mainly deter-mined (via Voc, cf. eq. (34) and eq. (35)) by the changes of the parameters Jsc, Ec, and J0k
(cf. Table 23) and were not significantly influenced by the small variations of the re-combination parameter β. The internal fill factors determined from the J-Vf curves strongly deviate from the simulated curve and the calculated data, showing a steeper increase with more negative Voc and, as a result, clearly higher values in the range -0.55 V – -0.65 V. The external fill factors, on the other hand, closely follow the trend of the calculated data but are generally somewhat lower. It is likely that the determination of the internal FF from the J-Vf characteristics was flawed because of the fact that the EIS-based Vf in the lower voltage range was generally inexact, since the Rrec data that was used to derive Vf was not reliable anymore in this range. In a few cases (SQ2, SQ2+D149, SQ2+D149/D131, and SQ2/CA), Vf did not even reach the internal maxi-mum power point, so that extrapolations had to be used to determine the internal FF.
Comparison between the external FF values and the calculated internal FF suggests that the series resistance causes a quantitatively similar decrease of the fill factor for all samples and corresponding open-circuit voltages instead of changing the slope of FF with respect to Voc.
Figure 76: External (open symbols) or internal (filled symbols and line) fill factors of the DSCs based on nanoparticulate ZnO as a function of the experimental open-circuit photovoltage Voc. The data represented by filled black symbols was determined from experimental J-Vf curves, the data shown as blue symbols was calculated analytically based on the open-circuit voltages and β values of the samples, and the simulated curve was calculated under the assumption of a constant β.