Modeling Permittivity Measurements of Thin Film Materials Versus Film Thickness

Measured permittivity values of thin film polymeric samples were substantially less for thin samples, but asymptotically approached bulk values above <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sim 500\mu \mathrm{m}$</tex>. For <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sim 25 \mu \mathbf{m}$</tex> samples the observed permittivity values were as much as 50% less than for bulk measurements. This behavior has been studied for four common homogeneous polymeric materials for sample thickness in the range of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sim 10\mu \mathrm{m}$</tex> to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$&gt; 3000\mu \mathrm{m}$</tex>. To quantify these observations, an empirical single-parameter model was developed to correct measured permittivity of thin samples based on an effective stray capacitance in series with the samples to compensate for effects attributed to instrumentation.