We have studied the influence of the growth conditions on the Si incorporation in AlN films grown by plasma-assisted molecular-beam epitaxy. Nitrogen-rich growth conditions allow controlled incorporation of Si up to a concentration of 5.2×1021 cm-3, determined by elastic recoil detection analysis, whereas Si incorporation is supressed under Al-rich growth conditions. The structural and morphological properties determined by x-ray diffraction and atomic force microscopy were not affected up to Si concentrations of 1.2×1021 cm-3. The electrical conductivity for the N-rich growth regime first increases with Si concentration followed by a decrease due to an increase of the activation energy up to 570 meV for a Si content of 1.2×1021 cm-3. For higher silicon concentrations, we have observed a sharp decrease in activation energy and an increase in conductivity by four orders of magnitude, attributed to the onset of impurity band conduction. [ABSTRACT FROM AUTHOR]