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Evaluation
To evaluate the quality of our data with respect to the model, the intensity and angle coordinates of the minimum in the SPR band were measured and compared to the model, for each thickness, as can be seen in the scatterplots below.
The error in the intensity data was ±0.004 relative to the absolute scale on the absolute scale of 0 to 1, and was determined by the 8-bit resolution of the camera.
Because of the uncertainty involved with estimating the size of the dark band projected on the screen, the error in the angle measurement was greater than estimated by the resolution of the calipers used to measure the band. Considering the human error involved, we estimated that the angle was measured to within a 1% accuracy of its actual value. This yielded errors in the angle measurement on the order of ±0.4 degrees.
In this experiment we successfully confirmed the literature model for the thickness dependence of SPR in thin silver films. The overall thickness dependence trends were observed in the data collected, with correlations between the intensity, angular shift, and band width of each thickness tested. For the two thinnest samples, the intensity data matched the model to within 1.6 sigma for the 19.9 nm sample and to within 8.4 sigma for the 32.1 nm sample. Additionally, the angular dependence of the intensity minima was observed to have an overall phase shift of 0.3 degrees, with the remaining deviations being in agreement with the aforementioned error in thickness. Finally, of the five samples tested, the optimal thickness for observing an intensity minimum due SPR was confirmed to be 50.6 nm.
Further examining the deviation in the SPR angle from the model, there appeared to be a systematic phase shift of 0.3 degrees, which could be attributed to a mis-calibration of the experimental set-up. Applying this phase shift uniformly to the data set resulted in a significant 0.7 sigma improvement in the correlation between the model and the data observed. The remaining deviation between the model and the data collected could be attributed to the previously discussed error in the thickness of the samples. While the model demonstrates that the thickness of the samples primarily affects the magnitude of the intensity observed, a phase shift in the SPR minimum is observed with thicker samples, which is one plausible explanation for the remaining deviations in the model versus the data collected.
Analyzing the intensity data, we observed that for the two thinnest samples the minimum intensity matches the model well (within 1.6 and 8.4 sigma). However, with the thicker samples the intensity deviates from the model, having higher intensity values. We believe this is a result of inaccuracy in the thickness of the samples. The sample thickness was calculated based on the rate of deposition in the Vacuum Deposition System, and if the deposition rate was greater than measured by the sensor, the actual sample thickness would have deviated linearly from the calculated value. Since this is the behavior being observed in the intensity data, this is a likely cause of the growing deviation from the model. It is probable that either the thickness sensor in the VAC system is mis-calibrated or the measurements used to determine the rate of deposition onto the sample were inaccurate.
Conclusions
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