We report the results of molecular dynamics simulation of a spatiotemporal evolution of the locally photoexcited electrons and holes localized in two separate layers. It is shown that the ring-shaped spatial pattern of luminescence forms due to the strong in-layer Coulomb interaction at high photoexcitation power. In addition, the results predict (i) stationary spatial oscillations of the electron density in quasi one-dimensional case and (ii) dynamical phase transition in the expansion of two-dimensional electron cloud when threshold electron concentration is reached. A possible reason of the oscillations and a theoretical interpretation of the transition are suggested.