Numerical and experimental study on silicon microresonators based on phononic crystal slabs with reduced central-hole radii

摘要

In this paper, we report the numerical and experimental study on micromechanical resonators which are made by introducing defects on an otherwise perfect two-dimensional (2D) silicon phononic crystal (PnC) slab. The 2D PnC slab is made by etching a square array of cylindrical air holes in a free-standing silicon plate with a thickness of 10 μm, while the defects are created by reducing the radii of three rows of air holes at the centre of the 2D PnC slab. Three resonators with different values of reduced radii, i.e., 2 μm, 4 μm and 6 μm, are included in this study. The finite-element-modelling method is used to calculate the band structure of the perfect 2D PnC slab and to analyse the different mode shapes of the structure. The design, numerical modelling, fabrication process, as well as characterization results and discussions of the three PnC resonators are also included. Due to its CMOS-compatibility, aluminium nitride is chosen to be the piezoelectric material of the inter-digital transducers, which are used to generate and detect acoustic waves. Testing is done to characterize the resonant frequency (f), quality factor (Q), as well as insertion loss of each of the three microfabricated PnC resonators and the results are discussed by analysing the simulated transmission spectra, the defected band structures, and the steady-state displacement profiles of the structures at their respective resonant frequencies. The experimental results show that the designed PnC resonators with reduced central-hole radii have higher resonant frequency and higher quality factors as compared to their normal Fabry-Perot counterpart, thanks to the higher-frequency modes supported within the cavity and slow sound effect in the lateral direction introduced by the central holes with reduced radii, respectively. As a result, the achieved (f-Q) product can be as high as 2.96 × 10~(11), which is among the highest for silicon resonators operating in air.