Momentum distributions of positron-electron pairs in diamond, Si, and Ge are systematically studied using state-of-the-art techniques in experiment and theory, ie, the positron two-dimensional angular correlation of annihilation radiation (2D-ACAR) technique and two-component density-functional (TCDF) theory. It is experimentally examined that all samples are free from positron trapping. An interesting difference among the elemental semiconductors is then clarified, namely, a flat 2D-ACAR distribution of the [001] projection in the low momentum region is found in diamond, while a deep dip is observed at the origin in Si and Ge. These experimental results are compared with those of first-principles TCDF calculations within the local-density approximation based on the scheme by Puska, Seitsonen, and Nieminen [Phys. Rev. B 52, 10 947 (1995)] and the generalized-gradient approximation by Barbiellini et al.[Phys. Rev. B 53, 16 201 (1996)]. Good agreement between theory and experiment confirms the validity of the TCDF. Analysis of calculational results clarifies that the unique electron momentum distribution in diamond is due to the carbon p orbital sharply localized in real space.