Critical interdependent effects have been observed in the growth of AlGaAs/InGaAs quantum-well structures by molecular beam epitaxy. It is shown that statistical experimental design is an effective method for quickly optimizing complex device structures. This technique is very useful for the optimization of processes with a large number of interdependent parameters, and allows for the clear visualization and separation of complex interwoven effects. In the present work, we show the importance of the oxide desorption process for the optimal growth of AlGaAs-containing structures. ©1997 American Institute of Physics.