Anchor Losses in AlN Contour Mode Resonators

Abstract

In this paper, we analyze possible sources of dissipation in aluminium nitride (AlN) contour mode resonators for three different resonance frequency devices (fr) (220 MHz, 370 MHz, and 1.05 GHz). For this purpose, anchors of different widths (W <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> ) and lengths (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> ) proportional to the acoustic wavelength (λ) are designed as supports for resonators in which the dimensions of the vibrating body are kept fixed. The Q extracted experimentally confirms that anchor losses are the dominant source of damping for most anchor designs when f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> is equal to 220 and 370 MHz. For specific anchor dimensions (W <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> /λ is in the range of 1/4-1/2) that mitigate energy leakage through the supports, a temperature-dependent dissipation mechanism dominates as seen in higher f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> resonators operating close to 1.05 GHz. To describe the Q due to anchor losses, we use a finite-element method with absorbing boundary conditions. We also propose a simple analytical formulation for describing the dependence of the temperature-dependent damping mechanism on frequency. In this way, we are able to quantitatively predict Q due to anchor losses and qualitatively describe the trends observed experimentally.