Parameter Extraction of Thin-Film Scandium-Doped Aluminum Nitride in Piezoelectric Over Silicon-On-Nothing Platform

We present a method to extract transverse elastic properties (Young's modulus, shear modulus and Poisson's ratio) and relative permittivity of 15% scandium (Sc) doped aluminum nitride (AIN) film from electrical measurements of resonators and parallel plate capacitors. The resonators comprise a vertical stack of
$\boldsymbol{0.3\mu} \mathbf{m}$
thick
$\mathbf{Sc}_{\boldsymbol{0.15}}\mathbf{Al}_{\boldsymbol{0.85}}\mathbf{N}$
being sandwiched between
$\boldsymbol{0.2\mu} \mathbf{m}$
thick molybdenum (Mo) and
$\boldsymbol{2\mu} \mathbf{m}$
thick degenerately doped pre-released silicon (Si) membrane on cavity as fabricated using our piezoelectric over silicon-on-nothing platform. Parallel plate capacitors followed the same vertical stack except that these were fabricated on unreleased but degenerately doped Si layers. Despite the large thickness ratio between pre-released degenerately doped Si membrane to
$\mathbf{Sc}_{\boldsymbol{0.15}}\mathbf{Al}_{\boldsymbol{0.85}}\mathbf{N}$
film, we have successfully extracted 2 elements (
$\mathbf{S_{11}}$
and
$\mathbf{S_{12}}$
) from the compliance matrix using an iterative gradient descent method and relative permittivity of
$\mathbf{Sc}_{\boldsymbol{0.15}}\mathbf{Al}_{\boldsymbol{0.85}}\mathbf{N}$
film.