Positron decay curves in various semiconducting elements and in the semimetals As, Sb, and Bi have been measured with a delayed coincidence system with 0.35 nsec full width at half-maximum prompt time resolution. The annihilation in ideal, pure semiconductors is found to be characterized by a simple exponential decay: The second low-intensity decay component may be entirely due to spurious effects. In nonintrinsic Si and Ge powders, however, a second decay component with considerable abundance is observed whose presence is assigned to unclear extrinsic processes. The intrinsic decay component in diamond, Ge, and Si can be interpreted as due to annihilation with the valence electrons, taking into account the screening effect through an evaluation of the dielectric constant. In S, Se, and Te the effect of the electron charge distribution is dominant over the effect of electron polarizability.