Dielectric microwave properties of Si-integrated pulsed laser deposited (Ba, Sr)TiO₃ thin films up to 110 GHz

Ba_0.6Sr_0.4TiO₃ thin films with a thickness of 339 nm are deposited directly on the high resistivity silicon through pulsed laser deposition. Coplanar waveguides with a slot width of 4.5 μm are designed to extract the complex permittivity of ferroelectric thin film in the frequency range from 1 GHz to 110 GHz. A fast three-dimensional (3D) finite element method (FEM) model is proposed to implement the permittivity extraction based on the propagation-constant matching, i.e., narrowing the difference between measured and simulated propagation-constants by adjusting the changeable permittivity in the fast 3D FEM model. In order to reduce the calculation overhead, the quasi transverse electromagnetic mode and conformal mapping analysis are introduced to realize the adjusting. The relative difference between measured and simulated propagation-constants is defined to describe the precision of the result. Experimental results show that the relative difference is less than 1.1%. The relative dielectric permittivity of BST films equals 332.6 at 1 GHz and reduces to 240.1 at 110 GHz. The loss tangent is about 17.5% at 110 GHz.