Microstructures of AlN thin films on Si substrates grown by plasma assisted molecular beam epitaxy were analyzed with various growth temperatures and substrate orientations. Reflection high energy electron diffraction (RHEED) patterns were checked for the in-situ monitoring of the growth condition. X-ray diffraction(XRD), double crystal X-ray diffraction (DCXD), and transmission electron microscopy/diffraction (TEM/TED) techniques were employed to characterize the microstructure of the films after growth. On Si(100) sub-strates, AlN thin films were grown mostly along the hexagonal c-axis orientation at temperature higher than $850^{circ}C$. On the other hand the AlN films on Si(111) were epitaxially grown with directional coherencies in AlN(0001)/Si(111), AlN(1100)/Si(110), and AlN(1120)/Si(112). The microstructure of AlN thin films on Si(111) substrates, with a full width at half maximum of almost 3000 arcsec at 2$ heta$=$36.2^{circ}$, showed that the single crystal films were grown, even if they includ a lot of crystal defects such as dislocations and stacking faults.