The stabilities of GaAs(001) As-rich surfaces have been determined for the first time by state-of-the-art total-energy calculations. The As-rich surface is found to be inherently rough
it cannot exist thermodynamically in a complete As monolayer structure, but in a missing-As-dimer or a two-As-layered structure. The steepening relaxation of the As-dimer block is essential to the stability of the As-rich surface. The peculiar interaction between As dimers as obtained, which may play an important role in the growth mechanism. The validity of the electron counting model is discussed. © 1993 The American Physical Society.