An structure for electrically isolating a semiconductor device is formed by implanting dopant into a semiconductor substrate that does not include an epitaxial layer. Following the implant the structure is exposed to a very limited thermal budget so that dopant does not diffuse significantly. As a result, the dimensions of the isolation structure are limited and defined, thereby allowing a higher packing density than obtainable using conventional processes which include the growth of an epitaxial layer and diffusion of the dopants. In one group of embodiments, the isolation structure includes a deep layer and a sidewall which together form a cup-shaped structure surrounding an enclosed region in which the isolated semiconductor device may be formed. The sidewalls may be formed by a series of pulsed implants at different energies, thereby creating a stack of overlapping implanted regions.