Reflection high‐energy electron diffraction (RHEED) intensity oscillations have been used during molecular beam epitaxy (MBE) to accurately determine threshold layer thicknesses for two‐dimensional (2D) growth of InxGa1−xAs on GaAs for a wide range of substrate temperatures and indium compositions. InxGa1−xAs/GaAs single quantum wells were also grown by MBE and studied using low‐temperature photoluminescence (PL) spectroscopy. PL peak energy, intensity, and linewidth measurements provided information on the critical layer thicknesses for the formation of dislocations which, under our experimental conditions, were the same as the threshold layer thicknesses for 2D growth measured from the damping behavior of RHEED intensity oscillations.