Structures including electrical isolation and methods of forming a structure including electrical isolation. A semiconductor layer is formed over a semiconductor substrate and shallow trench isolation regions are formed in the semiconductor layer. The semiconductor layer includes single-crystal semiconductor material having an electrical resistivity that is greater than or equal to 1000 ohm-cm. The shallow trench isolation regions are arranged to surround a portion of the semiconductor layer to define an active device region. A polycrystalline layer is positioned in the semiconductor layer and extends laterally beneath the active device region and the shallow trench isolation regions that surround the active device region.