**1. Introduction to van der Waals epitaxy**

Heteroepitaxial growth of III–V semiconductor on complementary metal-oxide-semiconduc‐ tor (CMOS)-compatible substrates has been a subject of research over the last 40 years [1–10]. Unfortunately, these long-period and extensive scientific efforts devoted to the direct growth of III–V materials on such target substrates have resulted in little success. The primary obstacle to success is the lattice and thermal expansion mismatches between semiconductor com‐ pounds of interest and the substrate materials. Therefore, the heteroepitaxy of high-quality three-dimensional (3D) materials requires an alternative technique, which can eliminate the limitation of inherent lattice matching [11–15].

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Thanks to the two-dimensional (2D)-layered materials whose unique and promising proper‐ ties enable to open up a new route of heteroepitaxy without the aforementioned constraints. Recently, the so-called van der Waals epitaxy (vdWE), a new paradigm of epitaxial growth for III–V semiconductors, has been the focus of significant research interest, which is evidenced by a search in Google Scholar, leading to 12,200 hits in the years 2011 through 2015 [16–21]. Needless to say, this new research area of heteroepitaxy is mainly dictated by the surface properties of emerging 2D materials, which also have many novel electrical, optical, thermal, and mechanical properties [22–34].

Recently, different research groups already used few 2D atomic-layered materials as a semiconductor substrate for the growth of 3D semiconductors [35–37]. Among them, gra‐ phene, hexagonal boron nitride (hBN), transition metal dichalcogenides (TMDs), and topo‐ logical insulator materials are the most frequently used ones. The main reason why these 2D materials are advantageous to be used as a semiconductor substrate is that the overgrown film materials float on top of the dangling-bonds-free 2D substrate surface instead of being rigidly bound to it, thereby mitigating lattice and thermal mismatch between 3D materials and the underlying 2D substrate. Besides, due to the crystalline surface with triangular lattice or honeycomb atomic arrangement, 2D materials are structurally compatible with many 3D semiconductors of zinc-blend (ZB), wurtzite (WZ), and diamond crystal structures. Further‐ more, most of the 2D materials are thermally stable, which exhibit high decomposition temperature, thus making it an ideal material of choice for many fabrication processes.

The integration of III–V semiconductors on 2D materials is feasible using the epitaxial growth by molecular beam epitaxy (MBE) or metal organic chemical vapor phase deposition (MOCVD). Layered materials can be grown directly on the target substrates using either chemical vapor deposition (CVD) or MBE [38, 39]. Then, the layered material can be mechan‐ ically transferred onto any substrate after being grown if needed. Graphene is found to be one of the most popular 2D materials for van der Waals (vdW) epitaxial growth. A number of studies are undertaken to achieve high-quality MBE-grown GaAs nanowires (NWs) on a graphene/silicon substrate. High-density, vertical, coaxially heterostructured InAs/InGaAs NWs on graphene over a wide tunable ternary compositional range is demonstrated using MOCVD.

Using graphene as a 2D material for relieving thermal/lattice mismatch, the proof-of-principle demonstrations for the epitaxial growth of GaAs [36, 40], InAs [41], and GaN [23, 42, 43] on silicon substrates are already presented in several studies. Hence, these early demonstrations show a great promise of vdW heteroepitaxy for integrating III–V semiconductors on silicon using 2D materials as a buffer layer. Both nanostructures and thin films of these compound semiconductors are addressed by these preliminary studies. Most importantly, the results obtained from these studies motivate to realize high-quality epitaxial thin film or nanostruc‐ tures of other III–V semiconductors, for example, InP, GaSb, InAs on silicon using graphene buffer layers. In such a way, the epitaxial growth on 2D material platform will have significant implications for a wide variety of optoelectronic devices, such as light-emitting devices [26, 42] and a new generation of solar cells for flexible applications [44].

Given the significant research interest in vdW heteroepitaxy for III–V compound semicon‐ ductors utilizing 2D materials, there is an obvious need for a comprehensive book chapter, which describes the recent progress and research activities. The aim of this chapter is to give a precise picture of the current status of vdW heteroepitaxy for 3D semiconductors on 2D materials, targeting mainly for optoelectronic device applications.

In this chapter, the difference between vdWE associated with layered materials and conven‐ tional epitaxy is first briefly discussed in Section 2. The work of several groups worked on nanowires grown on graphene using vdW epitaxial growth is then described in Section 3. Different types of grown 3D III–V thin films on 2D materials already demonstrated are mentioned in Section 4. Finally, a summary on the future prospects of the vdW epitaxy concept in case of growth of 3D materials on a layered material substrate is presented in Section 5.
