Final answer:
In direct band gap semiconductors, the statement 'The electrons in the minimum of the conduction band and the holes in the maximum of the valence band need to have the same momentum' is correct for band-to-band recombination.
Step-by-step explanation:
In a direct band gap semiconductor, the process of band-to-band recombination, also known as radiative recombination, involves an electron from the conduction band recombining with a hole in the valence band. A key characteristic of direct band gap materials like gallium arsenide (GaAs) is that the momentum of electrons and holes participating in this recombination does not need to change, because the minimum of the conduction band and the maximum of the valence band are aligned in momentum space. Therefore, the correct statement is that 'The electrons in the minimum of conduction band and the holes in the maximum of valence band need to have the same momentum' for the recombination process to occur efficiently without the assistance of phonons (vibrations of the lattice structure).