Anisotropic Complex Permittivity Measurement of Vanadium Dioxide Thin Films Across Phase Transition Temperature

In this paper, we present methodologies and devices to characterize the uniaxial complex permittivity of vanadium dioxide (VO<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>) thin films on c-plane sapphire. We report the anisotropic complex permittivity values of VO<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> as a function of temperature. To address the challenge of characterizing an anisotropic film with a thickness of tens to hundreds of nanometers, we propose two planar transmission-line-based devices. A coplanar waveguide line and a microstrip ring resonator are designed to be sensitive to the material under test complex permittivity in-plane (ε<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_r</i>,<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">||</sub>) and out of plane (ε<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_r</i>,⊥), respectively. These devices were fabricated in-house with a VO<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> film contrast ratio of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup>. An automated test setup was designed to measure the scattering parameters of the devices near the phase transition with a fine resolution (ΔT = 0.1 °C), enabling the extraction of temperature-dependent complex permittivity over a wide bandwidth covering 1 GHz to 67 GHz. Analytical quasi-static models are used to estimate the permittivity, and the results are further refined by minimizing the standardized error between simulation and measurement using a Bayesian optimizer. VO<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> exhibits stable permittivity and loss tangent near room temperature with a non-linear increase approaching the phase transition point. The extracted permittivity and loss tangent are modeled using sigmoid and exponential functions, respectively, to capture their nonlinear behavior at the phase transition and enable implementation in simulation tools.