The surface roughness of gallium arsenide ͑001͒ films produced by metalorganic vapor-phase epitaxy has been studied as a function of temperature and growth rate by in situ scanning tunneling microscopy. Height-height correlation analysis reveals that the root-mean-height difference follows a power-law dependence on lateral separation, i.e., ⌫(L)ϭkL a , up to a critical distance L c , after which it remains constant. For layer-by-layer growth, the roughness exponent, ␣, equals 0.25 Ϯ0.05, whereas the critical distance increases from 50 to 150 nm as the substrate temperature increases from 825 to 900 K. The roughness exponent jumps to 0.65Ϯ0.1 upon transitioning to three-dimensional island growth. By relating the height-height correlation analysis to the Einstein diffusivity relationship, the activation energy for gallium surface diffusion has been estimated: E d ϭ1.35Ϯ0.1 eV.