A transistor with a gate electrode structure is produced by providing a semiconductor body with a first surface, and with a first sacrificial layer extending in a vertical direction of the semiconductor body from the first surface. A first trench extending from the first surface into the semiconductor body is formed by removing the sacrificial layer in a section adjacent the first surface. A second trench is formed by isotropically etching the semiconductor body in the first trench. A third trench is formed below the second trench by removing at least a part of the first sacrificial layer below the second trench. A dielectric layer is formed which at least covers sidewalls of the third trench and which only covers sidewalls of the second trench. A gate electrode is formed on the dielectric layer in the second trench. The gate electrode and dielectric layer in the second trench form the gate electrode structure.