Contact openings are produced in a semiconductor body by forming a plurality of self-aligned structures on a main surface of a semiconductor body, each self-aligned structure filling a trench formed in the semiconductor body and extending above and onto the main surface. Adjacent ones of the self-aligned structures have spaced apart sidewalls which face each other. A spacer layer is formed on the sidewalls of the self-aligned structures. Openings are formed in the semiconductor body between adjacent ones of the self-aligned structures while the spacer layer is on the sidewalls of the self-aligned structures. Each opening has a width and a distance to the sidewall of an adjacent trench which corresponds to a thickness of the spacer layer. Self-aligned contact structures can also be produced on a semiconductor body, with or without using the spacer layer.