A method of fabricating a sample support membrane used to support an electron microscope sample starts with forming a first layer on a first layer of a substrate (S100). A second surface of the substrate that faces away from the first surface is etched to form an opening that exposes the first layer (S102). A second layer is formed on the first layer (S104). The region of the first layer that overlaps the opening as viewed within a plane is removed to expose the second layer (S106).