Figure 1. Theory of acoustoelectric amplification in standing waves for PS materials.

(a) Schematic cross-section of a PS-BAW resonator, depicting the fundamental thickness mode of vibration. The schematic indicates the various intrinsic loss mechanisms (phonon-phonon scattering, TED and phonon-electron scattering) in addition to the reflection losses. In the absence of other external losses, such as air damping, the total energy loss per cycle is dominated by these loss mechanisms. For a PS material, under the right conditions, the phonon-electron scattering losses can be inverted to achieve acoustoelectric gain. (b) A representative set of output responses for BAW resonators, denoting damped, undamped, and amplified responses (α > 0, α = 0, and α < 0 respectively). (c) The same responses can be visualized by the strain distribution of BAW resonator cross-sections under ideal, damped and amplified conditions (α > 0, α = 0, and α < 0 respectively). The cross-section images here show higher order standing wave BAW resonance modes, and visually exaggerated damping/amplification envelopes for clarity of concept. The color map shows areas of positive (red) and negative (blue) strain. The damped standing wave is the most commonly encountered situation in practical devices. However, this work demonstrates that it is possible to realize highly frequency-selective amplified BAW resonators using PS materials.