NdF3 layers were grown on Si(1 1 1) substrates at 400, 550 and 700 degrees C by molecular beam epitaxy. Investigation by reflection high-energy electron diffraction (RHEED) in situ showed that the NdF3 layers had good crystalline quality. The orientational relationship between NdF3 layers and Si(1 1 1) substrates was confirmed to be NdF3(0 0 0 2) < 1 1 (2) over bar 0 >\\Si(1 1 1)< 1 1 0 > by X-ray rocking curve (XRC) analysis. The morphology of NdF3 layers and insights into their growth mechanism were obtained by atomic force microscopy (AFM). The flatness of the epitaxial layers and the microcracks due to mismatch of thermal expansion coefficient are discussed as a function of growth temperature, layer thickness, and size of scanned area.