## 1 Introduction  
Heteroepitaxy of III-nitrides is one of the most widely developed techniques for the manufacturing of devices for optoelectronics (light-emitting diodes [1, 2], laser diodes [3, 4], ultraviolet emitters [5]) and high-frequency power electronics [6, 7]. Due to the lack of cheap GaN or AlN wafers of sufficient size, GaN-based structures are usually deposited on various foreign substrates such as sapphire, 4H-SiC (0001) or silicon (111). The main drawback of sapphire is its low thermal conductivity, whereas silicon carbide substrates are still rather expensive. Silicon wafers are more manufacturable and significantly cheaper [8]. They have sufficient size (up to 8 inches) and higher thermal conductivity than Al\({}_{2}\)O\({}_{3}\). The ability to manufacture GaN-based devices in fully depreciated 6- or 8-inch wafer silicon fabrication plants provides the cost competitiveness of GaN-on-Si technology [9]. Despite all the successes, obtaining III-nitrides on Si substrates is still problematic due to the differences in lattice constants (18%) and thermal expansion coefficients (46%) of these materials [10]. Thus, GaN-on-Si technology requires a complex buffer design including different transition layers and superlattices [11, 12] to reduce the dislocation density and residual stresses.  
In some recent works, researchers regarded graphene as a suitable 2D buffer, which facilitated the high-quality epitaxy of III-nitrides layers on a silicon substrate via both the MOCVD [13, 14, 15, 16] and MBE techniques [17, 18, 19]. Graphene has a hexagonal crystal lattice comparable to the (0001) plane of a GaN (AlN) crystal in the wurtzite phase. In addition, graphene is thermally stable and can be transferred to an arbitrary substrate. The Van der Waals interaction at the III-nitride/graphene interface provides reliable binding despite some lattice constants mismatch. In addition, gallium atoms can migrate on the graphene surface due to the sufficiently low migration barrier (12 meV) [20]. On the other hand, the nucleation on the pristine graphene is very difficult due to the absence of dangling bonds on its surface [21]. Islands of nuclei appear primarily at the graphene wrinkles. This effect leads to poor morphology and high defect density in GaN epilayers. Oxygen [22] or nitrogen [23,24] plasma pretreatment can be applied to promote GaN nucleation and growth on the graphene surface. In addition, the work function, surface potential, surface oxidation and chemical activity of few-layer graphene highly depend on the number of layers. Therefore, number of layers influence on the density and activity of nucleation sites.  
Despite the growing interest in the graphene-assisted epitaxy of III-nitrides, there are only a few studies considering the dependence of the nucleation process on the number of graphene layers [21,25,26,27]. The only work devoted to the growth of GaN by MBE on graphene-coated SiO\({}_{2}\) substrates was conducted by [25]. However, the authors of [25] considered only XRD data. In our previous works [18,28], GaN and AlN graphene-assisted epitaxy using the PA-MBE method on an amorphous substrate was demonstrated. In the present paper, we investigate the epitaxy of GaN/AlN on few-layer and multilayer CVD graphene. The effect of the number of graphene sheets, surface properties and defectiveness of the 2D buffer on the quality of the resulting III-nitrides epitaxial layers are considered in detail. A theoretical study of the AlN-graphene interaction conducted using the density functional theory complements the experimental results.