The growth of AlGaAs has been known to exhibit a region of substrate temperatures where rough growth morphologies are observed. A number of mechanisms had been proposed to explain this forbidden window of growth temperatures. Here, these mechanisms are examined, with emphasis on the growth of the binary, AlAs, in order to rule out effects due to differences in diffusion and desorption of Ga and Al. Reflection high energy electron diffraction is used to monitor the growth of AlAs in both solid source and gas source MBE as a function of substrate temperatures. Even without Ga present, 3D features are observed at intermediate substrate temperatures. Above and below these temperatures, RHEED intensity oscillations are observed, indicating layer-by-layer growth. This reentrant behavior is observed when using As4 or when using As2 produced from arsine, but not using As2 produced from elemental arsenic. Oxygen is not observed to incorporate differently in AlAs layers grown in the different temperature regimes. Atomic hydrogen is observed to smoothen the growth morphology. To explain the results we consider potential barriers to adatom diffusion at step edges. The temperature boundaries of the reentrant behavior were measured versus the incident Al flux. The Al flux dependence of the boundaries is consistent with the existence of diffusion barriers at step edges.