6.2 Principal Component Analysis
6.2.2 Correlation between OSC Properties
During the characterisation, measured data is obtained for both electrical and optical properties of an OSC, from which the OSC properties are derived. All OSCs on one substrate have been subjected to exactly the same production parameters, not even the time intervals between steps varied among them.
Although the variations in the properties of the OSCs on one substrate are
6.2. PRINCIPAL COMPONENT ANALYSIS 145 small (see section6.1.3), the experimental series showed that the assumption of all OSCs on one substrate being the same does not hold.
For example, one subtle dierence, which had not been considered before, is the radial distance of the OSC on a substrate from the centre of the substrate (see gure4.8). This is motivated by the nature of the spin-coating process, during which the lm of absorber solution dries from the centre on outwards, possibly having an eect on both the optical and electrical properties of an OSC. Transmission measurements with polarised light have shown a dierent angle dependence of the transmission at the centre and at the periphery of a substrate [65]. The eect on the corresponding electronic properties has yet to be shown. The question is, what is due to statistical variations per substrate and what can be explained by e.g. the dierence in radial position of the OSCs?
Thus, a PCA taking only the measured properties of OSCs into account was carried out and should reveal such correlations, if any. This analysis applies the observations from all 286 OSCs, trying to nd explanations for the spread per substrate. Table 6.11 shows the rst ten of 16 principal component vectors. The meaning of the OSC properties, which were included in the PCA are described in section 5.3.2. The power conversion eciency is not included in the analysis, because it is a linear combination ofVoc,Jsc andF F. Fitting the simple diode model to the IV-characteristics (see section 5.3.2) generally did not yield sensible parameters for the OSCs with a F F below 0.4. Since all OSCs were included in the PCA, the model parameters are omitted.
PC 1
The rst principal component (46.7% of the variance) is dominated by the electrical properties of the OSCs as shown with bold in the PC 1 column of table6.11. Neither the radial distance to the substrate centre nor the position of the extrema in the absorption spectrum have a signicant contribution.
However, the correlation between the electronic properties is generally as expected. The higher the current density at 1V forward bias (J1V) the lower the resistance there R1V, which holds both for the dark and the illuminated case. Vmpp and Jmpp contribute in the same direction, which is expected from the positive correlation withF F. The higher Rsc, the lower Roc is also expected for the same reason. It is interesting to note that from the set of the
146 CHAPTER 6. EXPERIMENTS AND ANALYSIS
Table6.11:Thistableshowsalongthecolumnstherst10ofatotalof16principalcomponentvectorsobtainedfromthecorrelationmatrixRbetweentheOSCpropertiesonly.Theanalysisincludedbothelectricalandopticalproperties.Themeaningofthevariablesisdescribedinsection5.3.2.Thefulltablecanbefoundonpages192and193.
PC1PC2PC3PC4PC5PC6PC7PC8PC9PC10···RadialDistance-0.040.060.35-0.430.72-0.270.27-0.020.09-0.05Voc0.18-0.320.40-0.29-0.150.10-0.38-0.02-0.06-0.39Jsc0.190.240.390.39-0.12-0.46-0.170.150.16-0.12FF0.350.06-0.170.020.050.100.18-0.220.050.02J1Vdark0.290.09-0.300.050.180.170.150.58-0.13-0.43R1Vdark-0.330.000.230.06-0.100.21-0.020.140.460.15J1Vill0.33-0.070.06-0.020.050.180.000.540.240.34R1Vill-0.320.14-0.040.13-0.100.120.32-0.060.23-0.65···Vmpp0.33-0.160.13-0.16-0.070.13-0.19-0.15-0.09-0.23Jmpp0.310.170.170.25-0.05-0.240.09-0.050.25-0.10Rsc0.30-0.130.09-0.11-0.130.340.35-0.270.460.05Roc-0.33-0.130.17-0.14-0.050.14-0.100.370.14-0.07Absorption1stMin0.020.420.22-0.37-0.420.010.220.14-0.290.10Absorption1stMax0.030.540.13-0.21-0.130.190.04-0.04-0.070.02Absorption2ndMin0.040.30-0.46-0.42-0.02-0.21-0.47-0.040.47-0.08Absorption2 ndMax0.01-0.39-0.17-0.28-0.41-0.540.390.160.07-0.01 Eigenvalueλα7.472.941.461.230.950.560.480.330.250.13Variance/%46.718.49.17.75.93.53.02.11.60.8···Cum.Variance/%46.765.074.181.887.791.394.396.397.998.8
6.2. PRINCIPAL COMPONENT ANALYSIS 147 main OSC parametersVoc,Jsc andF F, onlyF F has a considerable inuence on PC 1, whereas both Voc and Jsc contribute less. This is not surprising, becauseVoc andJsc are not governed to the extent by, e.g. interface barriers, as is F F.
PC 2
The largest contributions to PC 2 (18.4% of the variance) come from the extrema of the absorption spectrum. Voc and Jsc, which had the least in-uence of the electronic parameters on PC 1, are the electronic parameters with the largest inuence on PC 2. Again the radial distance of the OSCs to the substrate centre has only negligible inuence. The extrema of the absorption show an interesting behaviour. Whereas the rst three extrema being observed at small wavelengths exhibit the same trend, the forth ex-tremum (second maximum) shows the opposite trend. The rst minimum is associated with the lm thickness of the absorber layer, as shown by optical simulations [65]. However, the shift of the other extrema has not yet been analysed systematically. If indeed these extrema show the same trend in the optical simulations, more than the rst absorption minimum could be used for determining the layer thickness, increasing the quality of the thickness estimations. Assuming that the rst absorption minimum is a measure of the absorber layer thickness, the correlations with Voc and Jsc indicate that the thicker the OSCs, the lower the Voc, but the higher Jsc. The absorber thickness was in the range of 80nm, a region, where optical simulations show that a further increase of Jsc is possible up to 90nm due to increased light harvesting. This agrees with the discussed PCA. TheVoc however decreases with increasing absorber layer thickness in the range obtained. A reduction of Voc with increasing thickness of the absorber layer is sometimes reported in literature, but has not seen in the OSCs made by our group so far.
PC 3
PC 3 (9.1% of the variance) has four contributions with an absolute value of more than 0.3: the radial distance of the OSC to the substrate centre (0.35),Voc(0.40),Jsc (0.39) and the second absorption minimum (-0.46). PC 3 is the rst PC on which the radial distance has a signicant contribution.
It suggests that an increase of the distance to the centre of the substrate correlates with an increase of the two electronic parameters (Voc and Jsc)
148 CHAPTER 6. EXPERIMENTS AND ANALYSIS and a decrease in the position of the second absorption minimum. The fact that only one of the absorption extrema contributes signicantly to PC 3 is surprising. The position of the second minimum varies between 435 and 459nm. However, the maximum observed dierence in polarised transmission is in between 500 and 600nm [65]. Thus rather a dependence with the second absorption maximum, which lies in this region, would be expected, if the observed dierence in polarised transmission has an eect on the electrical properties. This has to be further investigated with absorption, polarised transmission and IV measurements on a new set of substrates.
Other Observations
PC 5 (5.9% of the variance) has three dominant contributions larger than 0.4: the radial distance (0.72), the position of the rst (-0.42) and second absorption maximum (-0.41). At rst sight, this trend seems contradicted by the corresponding values on PC 4. However, in 0th order approximation the three mentioned parameters dominate PC 5, whereas there are other parameters on PC 4 which need to be taken into account as well, e.g. an lowering of the position of the 2nd absorption minimum. The analysis takes place in a 16-dimensional space and all signicant contributions have to be taken into account. Otherwise, the chosen direction based on only a few dominant contributions to a PCV deviates too much from the actual PCV.
Furthermore it is likely that the PCs from PC 4 and onwards cover the noise in the data, rather than real pattern by virtue of their small eigenvalue.
Conclusions
• TheF F correlates strongly with the electrical properties (all with abso-lute contributions above 0.29) on the rst principal component (46.7%
of the variance). However, there are two notable exceptions: the Voc and the Jsc. This is as expected, because Voc and Jsc are less aected by interface barriers, which have a stronger inuence on the other elec-trical properties.
• Voc andJsc correlate more with the optical properties, which are found on the second PC, containing nearly 20% of the data variance. Since the optical properties can be used as measure of the absorber lm thickness,Vocand Jsc appear to depend on the device thickness, rather
6.2. PRINCIPAL COMPONENT ANALYSIS 149 than the interface barrier, which aects F F. The eect of dierent absorber layer thickness has to be investigated further, but as rst approximation it can be said thatJscraises andVocfalls with increasing absorber layer thickness. This behaviour is claimed by some groups, but has not been observed in our group before.
• The radial distance has its rst signicant contribution to PC 3 (only 9.1% of the variance). The rst two PCs have little contribution of the radial distance of the OSCs on a substrate, indicating that more than 65% of the variance in the data can be explained by statistical variations.
• Considering PC 3, the higher the radial distance, the higher Voc and Jsc, but at the same time the second absorption minimum shifts to shorter wavelength. The origin of this behaviour has not been found yet. The shift of only the second absorption minimum might indicate a changed absorption at 450nm, which in turn can aect Voc and Jsc. This has to be investigated with optical simulations of the absorption spectrum.