Kinetic roughening of the GaAs(001) surface during plasma etching by H and CH@sub 3@ radicals was investigated using atomic force microscopy in combination with RHEED and Auger spectroscopy. The evolution of the surface morphology was tracked as a function of etching time, temperature, and plasma composition. Large changes in the form of the surface roughness were observed and reflect variations in the surface dynamics which induce correlations from point-to-point on the surface. These changes involved not only the length scale of surface features, but also distinctive variations in the anisotropy between [110] and [-110], particularly as a function of surface temperature. Surface height data were analyzed to extract height correlation functions, which provided dynamic and roughness scaling exponents for comparison with theory. Measured height-difference correlation functions displayed two distinct roughness scaling regimes with a crossover that increased from ~ 30 nm to ~ 150 nm with increasing surface temperature between 500 K and 700 K. At short length scales, a roughness coefficient of ~ 0.7 was typically observed, while a logarithmic dependence was generally observed at larger length scales. Calculated height-correlation functions based on continuum models that include competition between short length-scale surface diffusion and long-range desorption dynamics reproduce this crossover behavior and offer the potential for extracting information on changing surface dynamics as a function of etch conditions.