Abstract
Three-dimensional computer simulations are performed to obtain the phase diagrams for heteroepitaxially grown ordered quantum dots and quantum rings by surface prepatterning. Concave patterning in a squared array may lead to the formation of ordered dots, whereas convex patterning in a squared array may initially lead to the formation of ordered quantum rings, then a transition into quantum dots with further growth. The evolution of the surface chemical potential during growth explains the formation of the ordered surface structures.