We have calculated the height-height correlation function by means of Monte Carlo simulations of a solid-on-solid model. These simulations reveal that the position and sizes of the islands formed during the first half-monolayer are highly correlated, a feature which has also been noted in recent x-ray studies of growth by OMCVD. This morphology results in the emergence of a characteristic length, ℓ, in the correlation function, which is found to obey the scaling law ℓ = (D)/J)γ, where D is the diffusion length, and J is the deposition flux. The value of the exponent γ varies with coverage and depends on the growth conditions.