Measurement of Dielectric Properties of Thin Films in Open Resonators
Sergey Dudorov, Dmitri Lioubtchenko, Juha Mallat, Antti Räisänen
Introduction
In this work we propose a method to determine dielectric properties of thin films, based on the resonant frequency measurements, when the resonator is loaded with three different sample structures:
Requirements of the proposed method are:
- Planar well-polished samples
- Desired substrate thickness is t = lambda/4+ m x lambda/2 ± lambda/8, m = 0, 1, 2...
The advantage of this method is that there is no need to know the geometry of the resonator and precise thickness of the substrate and of the thin film.
Theory in brief
The basic equations are the following:
where n1 and n2 are the refractive indices of lower and upper layers, respectively, k is the resonant wave number, t1 and t2 are the thicknesses of lower and upper layers, respectively, d = D - t1 - t2 , F1,2,3 are phase corrections, parameter ß can be eliminated,
Below is the scheme of the measurement system.
After manipulations the following relation can be derived:
where dff is the resonant frequency shift when a thin film is on the upper side of the substrate, and dfs is the frequency shift when a thin film is on the lower side of the substrate.
Example of the experimental results of thin film dielectric properties measurement
Permittivity of a 6 µm AZ4562 photoresist thin film was measured when placed on a 0.33 mm sapphire substrate. Measurement was performed at 95.1 GHz and 100.3 GHz. Frequency shifts were 5.6±1 MHz & 29±1 MHz and 4.3±0.5 MHz & 18±0.5 MHz, respectively. The calculated n2f =ef were 2.6±0.4 and 3.0±0.3, respectively. The results can be regarded as excellent as the film is extremely thin. This proves the potential of the method.