Optoelectronic oscillators have dominated the scene of microwave oscillators in the last few years thanks to their great performances regarding frequency stability and phase noise. However, miniaturization of such devices is an up-to-date challenge. Recently, devices based on a phonon–photon interaction have gathered a lot of interest thanks to their extreme compactness and working frequency directly in the GHz. In this frame, a still-missing element to obtain long-term frequency stability performances is an on-chip delay within the feedback loop. Here, we experimentally show filtering and slow propagation of 2 GHz acoustic waves on a Gallium Arsenide membrane heterogeneously integrated on a silicon wafer. By engineering the dispersion of an acoustical waveguide, we evidence a group velocity below 1000 m/s for the mode able to propagate. Thus, an integrated delay implementation is at reach for potential improvement of opto-acoustic devices such as optomechanical oscillators or wireless applications.

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