Correlating Electrical to Mechanical Properties

Figure 3.7 illustrates the importance of high spatial resolution when measuring electrical and mechanical properties of polymer thin films. The untreated P3HT measured at 30°C shows heterogeneity in both mobility and Young’s modulus across a 1 µm2 _{area. As the histograms show (Figure 3.7c-d)), broad distributions are}

found for both, with mobility varying by around an order of magnitude and Young’s modulus by around a factor of 3. There are clear spatial correlations, i.e. patches of high or low mobility or stiffness, which indicate that the variation is real and due to local changes in material properties.

Figure 3.6: Flow diagram of the analysis procedure for FVBS data, showing the separate and linked stages for analysis of the electrical and mechanical data.

Figure 3.7: High resolution FVBS electrical and mechanical map of untreated P3HT at 30°C, showing spatially resolved a) mobility and b) sample Young’s modulus values. c) and d) show the dis- tribution of mobility and modulus values respectively. The values for zero field mobility, µ0, are plotted against the simultaneously

derived field dependence of mobility, γ, in e) and sample Young’s modulus,Es, in f): the blue points are from pixels within the blue boxes shown in a) and b), and the red points from the remaining upper portions of those images.

The mechanical and electrical measurements are taken simultaneously at each point, allowing investigation of correlations between them. Figures 3.7e) and f) show the zero field mobility plotted againstγ and against sample Young’s modulus respectively, with each point on the graphs corresponding to a distinct spatial loca- tion on the sample (pixels in the images Figure 3.7a-b). The comparison between mobility and γ shows that the data lay on two distinct trend lines, emphasized by some of the points being shown in red and some in blue: for both sets, γ increases as mobility decreases, consistent with increased trapping resulting in lower mobility. The blue data points come from the region marked by the blue boxes in Figures 3.7a and b, with the red points from the upper portion of the images. Note that the scan direction is from the bottom to the top of the image. Comparison between the mobility and sample Young’s modulus maps, and consideration of the correlation betweenγ and mobility, suggest that the tip condition changed at around the top of the blue box. This shows how acquiring large datasets and checking the cor- relations between them can give more information and hence enable more reliable determination of material properties.

Considering only the measurements within the blue box, for the untreated P3HT measured at 30°C we find an average value of mobility of 5.1±0.1×10−4 cm2 / V s and of sample Young’s modulus 0.86±0.02 GPa. (Note that incorporating the systematic uncertainty due to calibration of the spring constant of the AFM cantilever, 5%, leads to an additional uncertainty of ∼ 5 % on these values when comparing against other measurements, but does not effect comparisons within the dataset).

From the graph of sample Young’s modulus plotted against mobility, (Figure 3.7f) no clear correlation between stiffness and mobility is apparent. The electri- cal measurements rely on conduction through the thin film, whilst the mechanical measurements probe the surface and near sub-surface. Hence the lack of correlation suggests that the structural variations are occurring over length scales shorter than the thickness of the film. This is supported by the observation that the derived mobility values appear to change over length scales less than 100 nm, i.e. less than the film thickness.

For comparison, Figure 3.8 displays the corresponding results for an annealed P3HT sample measured at 130°C. Again there is a broad distribution of mobility and sample Young’s modulus values, with clear spatial correlations demonstrating that they reflect real variations in material properties. However, the spatial variations are more smoothly varying (i.e. longer range), suggesting that the length scales of the structural variations are longer at this higher temperature after annealing.

Figure 3.8: High resolution map of annealed P3HT at 130°C, show- ing spatially resolved a) mobility and b) sample Young’s modulus values. c) and d) show the distribution of mobility and modulus values respectively. The values for zero field mobility,µ0, are plot-

ted against the simultaneously derived field dependence of mobility, γ, in e) and sample Young’s modulus,Es, in f).

An obvious additional feature is that the mobility and sample Young’s mod- ulus both increase over time for this dataset (note that the slow scan direction, and hence time, goes from bottom to top). It is not clear whether this is a feature of this region of the sample, or of changes in the film due to prolonged annealing at this temperature, but it does show a clear correlation between mobility and stiffness which is also apparent in the scatter plot in (Figure 3.8f). While it is not possible to directly determine the morphology of the sample directly with the AFM, a more crystalline structure would feasibly have a higher stiffness. As such a correlation be- tween the mobility and the stiffness could be expected as a more crystalline material should have a higher mobility.

Interestingly, at this higher temperature on an annealed sample the correla- tion between zero field mobility andγ is less pronounced, (Figure 3.8e), suggesting

3.0 2.5 2.0 1.5 C u rr e n t a t 5 V ( n A ) 25 20 15 10 5 0 Time (hours) a) _b) 5 4 3 2 C u rr e n t a t 5 V ( n A ) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Time (hours)

With N₂ flow Without N

2 flow

Figure 3.9: Measured current at 5 V bias as a function of time with nitrogen flow a) and a sample without b).

that under these conditions transport is less trap dominated. The increase in mo- bility is surprising and significant because with air sensitive materials such as P3HT degradation over time tends to decrease the mobility. The rate of degradation is reduced here by measuring in a nitrogen environment.

Figure 3.9 shows the decrease in current measured at 5 V over time due to sample degradation. The reduced effect of degradation when a constant flow of nitrogen is maintained, (a) relative to measurements in air, (b), is clear. The characteristic degradation time, the time over which the current decreases by a factor of e, in air is around 0.5 hours, compared to nearly 12 hours in N2 flow.

Nitrogen flow therefore allows longer measurements to be viable.

From the results shown in Figures 3.7 and 3.8, direct comparison can be made between the room temperature and high temperature behaviour of P3HT. At 130°C the average mobility has increased by almost an order of magnitude to 32.5±0.4×10−4 cm2 / V s whilst the sample Young’s modulus has decreased by more than 20 % to 0.69±0.02 GPa. The field dependence of the mobility has also dropped between the low temperature and the high temperature. This is in agreement with work by Blom et al., further suggesting that the charges in P3HT are transported by thermally assisted intermolecular hopping [225]. Note that these measurements were taken with different tips and on different samples, but due to the large datasets these changes are statistically significant.

Figures 3.10 and 3.11 show all the data that can be gathered simultaneously from an FVBS measurement. Data from the force curves are: the dwell force a), the adhesion force b), the contact area c), the Young’s modulus f) and the height, which has been flattened for clarity in g). The data from the JV curves are: the mobility d), gamma e) and the current at a 3 V bias in h). The current can be mapped at any value of the bias from the JV curves. White pixels with black bars signify points at which the JKR model did not fit satisfactorily. The current-voltage

Figure 3.10: High resolution FVBS electrical and mechanical map of untreated P3HT at 30°C, showing spatially resolved a) measured dwell force, b) adhesion, c) contact area, d) zero field mobility, e) field dependence of the mobility, f) sample’s Young’s Modulus, g) flattened height and h) current at -3 V. Pixels with vertical black lines show points that have no data due to poor fits. Taken with a Rocky Mountain solid platinum cantilever

Figure 3.11: High resolution FVBS electrical and mechanical map of annealed P3HT at 130°C, showing spatially resolved a) measured dwell force, b) adhesion, c) contact area, d) zero field mobility, e) field dependence of the mobility, f) sample’s Young’s Modulus, g) flattened height and h) current at -3 V. Pixels with vertical black lines show points that have no data due to poor fits.

Figure 3.12: Recording of the temperature measured by the poly- heater for the extent a temperature dependent FVBS measurement.

and force-distance curves for each pixel are stored and can be separately inspected. Analysis of correlations between the multiple material properties measured by this technique can give further insight into the material’s behaviour, and the experimental conditions during measurement. For example, the contact area in Figure 3.10 c) is strongly correlated to the adhesion b), however this is not correlated to the current in h). The current should be related to contact area, as in Figure 3.4, this suggests a change in conditions during the experiment that did not affect the contact area directly, most likely the contamination of the tip with polymer.