Calculating thickness and refractive index from full SPR curves

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:

1. Refractive index (RI) and thickness (d) depend on each other [3],[2]. Measurements of traditional ellipsometry or traditional SPR result in a continuum answer, where RI and d depend on each other [3].
2. Refractive index (RI) of material varies for different deposition techniques and even for different investigators [1]. RI changes for instance with the surface roughness or porosity of the material. Similarly also composites and alloys can have varying RI.
3. Refractive index (RI) of the material varies with different thickness of the material (in relation to concentration of polymer for instance) and/or with different environmental conditions, such as electric field, moisture or pH.

Hence, generic RI values from literature are not sufficient to accurately assess true layer thickness [1], [2].

Multi-Parametric Surface Plasmon Resonance enables determination of thickness and refractive index simultaneously using multiple wavelengths (or "spectroscopic SPR").

Optical modeling of the full SPR curve recorded by MP-SPR

1. Thickness

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.

2. Thickness and refractive index

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.

References:

[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

Click below to see animations of how SPR curves behave with thickness and refractive index change at different wavelengths: