We have investigated the transport of carriers in GaAs using time resolved optical spectroscopy with picosecond resolution. Carriers are optically created to the sample surface by an ultra-fast laser pulse. They diffuse and drift throught a thick GaAs layer, until they are captured by an InGaAs quantum well, where they recombine with holes from a p-type doped layer at an inner InGaP barrier. Our study was performed with a set of samples with different GaAs layer thickness. As the GaAs thickness increases, the emission from the quantum well is delayed and its decay slows down significantly. We have investigated the effect of an applied DC field between the surface and the In GaAs quantum well. The transient of the quantum well emission is mostly independent of the applied DC voltage up to field of the order of 20 KV /cm, including both polarities. This is a clear indication that the carrier transport is dominated by ambipolar diffusion due to the Coulomb interaction that strongly couples photoinjected electrons and holes. On the other hand, the decay of the GaAs emission varies significantly when a DC gate voltage is applied such as a current appears at the structure.