Refractive index, thickness and wavelength at which they are measured form a continuum answer. Typically, refractive index has to be assumed from literature based on value for bulk of the material and a given wavelength. Unfortunately, for nanolayers, such refractive index (RI) is not sufficiently close to the real value. RI varies for different deposition methods and even between different investigators [1]. Hence, for precise thickness (or true thickness) determination, RI has to be determined as well.
To summarize, traditional optical methods, such as SPR and ellipsometry, require prior knowledge of either refractive index (RI) or thickness (d) from other sources for accurate characterization. The main reasons to measure RI together with thickness are:
Hence, generic RI values from literature are not sufficient to accurately assess true layer thickness [1], [2].
Similarly to traditional ellipsometry and SPR, it is possible to assume thickness correlation and use peak minimum parameter directly. However, this method is less reliable as it requires to assume several parameters and approximations.
MP-SPR acquires full SPR curves, which enable use of modeling method, which works for ultrathin (subnanometer, Ångström thick layers), thin (from nanometer to 150 nm) and also thicker (up to microns thick layers forming waveguides) layers.
MP-SPR Navi™ LayerSolver™ software is a dedicated software for modeling and calculating thickness and refractive index of multilayer optical systems under the SPR measurement conditions. The software uses established Maxwell equation formalism for the calculations (See chapter “Mathematics of Surface Plasmon Resonance).
In addition to calculating single SPR curves, LayerSolver™ allows the use of multiple datasets (for instance form different wavelengths or before and after deposition) in calculations, as well as to link or constrain calculation parameters between different datasets.
Please see Mathematics of SPR to learn the mathemathical principles of the calculations.
[1] H.G. Tompkins, S. Tasic, J. Baker, D. Convey, "Spectroscopic ellipsometry measurements of thin metal films," in Surface and Interface Analysis, vol. 29, pp. 179–187, 2000
[2] N. Granqvist , H. Liang , T. Laurila , J. Sadowski , M. Yliperttula , and T. Viitala, "Characterizing ultrathin and thick organic layers by surface plasmon resonance three-wavelength and waveguide mode analysis," in Langmuir, in press.
[3] H. Liang, H. Miranto, N. Granqvist, J.W. Sadowski, T. Viitala, B. Wang, M. Yliperttula, "Surface plasmon resonance instrument as a refractometer for liquids and ultrathin films," Sensors and Actuators B: Chemical, vol. 149(1), pp. 212-220, 2010
How does the SPR peak respond to change in thickness in water?
Surface measured with two different wavelengths (here 785 nm and 670 nm). The thickness remains the same in both cases. The difference in the curves is due to the change of refractive index in relation to the measured wavelength. See animation
How does the SPR peak respond to layer thickness change in thickness in air?
Measure of thick samples (waveguide effect). Thickness up to few micrometers (with light nonabsorbing samples) can be measured. See animation.
How does the SPR peak respond to change in thickness when the sample absorbs light?
Light absorbing samples, such as porphyrins or gold and silver nanoparticles, cause intensity changes to meaured curves. See animation.
Figure 4. Illustration of the two wavelength analysis principle. Black and orange line are RI – d continuum answers for both of the wavelengths. Dashed line is sifted curve based on the dRI/dλ value, which enables a unique solution for the thickness and RI.
Multi-Parametric Surface Plasmon Resonance (MP-SPR) can be used to determine unique thickness and refractive index (RI) of ultrathin films without prior knowledge of the RI or the thickness of the layer. Polyelectrolyte multilayer was measured using MP-SPR two wavelength method and analysed by LayerSolver™ software module. Thickness of 5 bilayers was found to be 16.8nm and RI 1.48 at 785nm.
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