Monte Carlo simulation results are presented for the growth by molecular‐beam epitaxy (MBE) of diamond‐structure semiconductors on both specular (001) surfaces and surfaces misoriented by up to 2° from (001) toward (110). The simulation includes calculation of the topography and reconstruction of the surface. Based on the resulting surface structures the streak profile and peak intensity of specularly reflected electron beams are calculated using a kinematic scattering approximation. The results confirm models proposed to explain oscillations observed in the intensity of beams of electrons specularly reflected from terraced surfaces parallel to the terrace edges during MBE. Small clusters of atoms are shown to nucleate on the surface of the terraces and gradually become incorporated into the terrace edges as growth proceeds. On specular surfaces, nucleation occurs randomly followed by growth and coalescence of islands. Stable, statistically random, surface structures are shown to develop leading to an increase in the root‐mean‐squared roughness of the surface with increasing time. These structures result in a gradual damping of oscillations in the specularly reflected electron beam intensities. The damping rate decreases with increasing surface diffusion and decreasing surface roughness. The strongly bound atomic dimers present on (2×1)‐reconstructed diamond‐lattice (001) surfaces are shown to influence surface diffusion and hence the critical size for nucleation of new surface layers.