Embodiments include a synthetic jet device formed within layers of a package substrate, such as to provide a controlled airflow for sensing or cooling applications. The jet device includes an electromagnetically driven vibrating membrane of conductive material between a top and bottom cavity. A top lid with an opening covers the top cavity, and a permanent magnet is below the bottom cavity. An alternating current signal conducted through the membrane causes the membrane to vibrate in the presence of a magnetic field caused by the permanent magnet. By being manufactured with package forming processes, the jet (1) is manufactured more cost-effectively than by using silicon chip or wafer processing; (2) is easily integrated as part of and with the other layers of a package substrate; and (3) can be driven by a chip mounted on the package. Embodiments also include systems having and processes for forming the jet.