Giant Secondary Grain Growth in Cu Films on Sapphire

Single crystal metal films on insulating substrates are attractive for microelectronics and other applications, but they are difficult to achieve on macroscopic length scales. The conventional approach to obtaining such films is epitaxial growth at high temperature using slow deposition in ultrahigh vacuum conditions. Here we describe a different approach: sputter deposition at modest temperatures followed by annealing to induce secondary grain growth. We show that polycrystalline as-deposited Cu on \alpha-Al2O3(0001) can be transformed into Cu(111) with centimeter-sized grains. Employing optical microscopy, x-ray diffraction, and electron backscatter diffraction to characterize the films before and after annealing, we find a particular as-deposited grain structure that promotes the growth of giant grains upon annealing. To demonstrate one potential application of such films, we grow graphene by chemical vapor deposition on wafers of annealed Cu and obtain epitaxial graphene grains of 0.2 mm diameter.

Vapor-phase thin film deposition, first enabled by the invention of modern vacuum technology about a century ago [1], has developed into an essential component of many modern technologies. Advances in electron diffraction and microscopy over the past century provided tools for probing the crystalline structure of thin films and spurred investigation of the fundamental processes that determine grain size and orientation [2]. Thus grain growth and epitaxy have become central topics in thin film research. In applications of thin films, much effort is spent manipulating grain structure to achieve specific mechanical, electrical, magnetic, optical, and chemical properties. Examples include magnetic recording media [3], electrochemical catalysts [4], and interconnects for microelectronics whose resistance to electromigration depends on film texture and grain size [5]. A common challenge for metals and semiconductors grown on insulating substrates is to obtain a desired orientation of grains (such as <111> perpendicular to the film plane) along with macroscopic grain sizes ( 100 µm in the plane of the film). The conventional approach to this challenge to is to seek conditions that produce large epitaxial grains during growth. An alternative approach, and the one that is the focus of this work, is to deposit a polycrystalline film and then produce large epitaxial grains by annealing. Although the basic idea was clearly described almost 25 years ago by C. V. Thompson et al., who called it "epitaxial grain growth" [6], it has remained relatively unexplored since then. Here we show that this approach can produce films with individual grains with area > 1 cm 2 .
The work described here was motivated by a desire to produce Cu(111) films that approach the ideal of a single crystal and that are suitable as substrates for chemical vapor deposition (CVD) of graphene and hexagonal boron nitride (h-BN) at temperatures near 1000 • C. Copper is the most commonly used substrate for graphene CVD because its negligible carbon solubility enables growth of precisely one layer over a wide range of growth conditions. It can also be readily etched away to allow transfer of the graphene to other substrates for further device fabrication steps [7]. Although polycrystalline Cu foils are typically used, the Cu(111) surface provides a hexagonal template with a relatively small lattice mismatch (3.8% and 2.2% for graphene and h-BN, respectively) that allows epitaxial growth with low, uniform strain [8]. Previous work on bulk single crystals has shown that graphene has less rotational disorder when grown on Cu(111) than on Cu(100) [9,10]. Exploiting the benefits of Cu(111) for commercial, wafer-scale production of graphene will require a process for producing crystalline films on a suitable substrate. A particularly attractive substrate is α-Al 2 O 3 (0001). It is widely used by manufacturers of radio-frequency electronics and lightemitting diodes in the form of wafers with diameters up to 200 mm, it is physically and chemically stable under graphene CVD conditions, and it can likely be reused after metal etching to release the graphene layer.
There is a large body of work pertaining to Cu on α-Al 2 O 3 , which is a model system for epitaxy, adhesion, and other properties of metal-ceramic interfaces [11]. On the α-  [12][13][14], substrate temperature [11], deposition rate [11], and other conditions [15]. We show here that a particular mixture of OR I and OR II in as-deposited Cu films enables giant grain growth upon annealing.
Grain growth in thin films can occur during deposition and during subsequent processing steps such as annealing [16]. The equilibrium state of a film is determined by the interplay of various energies: film-substrate interface, film free surface, grain boundary, and strain. The actual state of a film is also affected by kinetic processes such as diffusion, thus substrate temperature and the energy of arriving species during deposition are important in determining grain size and orientation. Due to the interplay among various energies, conventional grain growth stagnates when the average grain size is about 3× the film thickness [16]. In some cases, particularly for Cu and other fcc metals where grain boundaries are mobile at relatively low temperatures, grains can grow larger than the stagnation limit through a process known as secondary grain growth [17]. This occurs when grains of a particular low energy orientation grow at the expense of a matrix of other, stagnated grains. Although secondary grain growth can occur during deposition, it is typically exploited during subsequent annealing [6], as we do here. In Cu films sputtered onto amorphous SiO 2 , secondary grain growth driven by minimization of strain energy has produced grains ∼ 10 µm to ∼ 100 µm across with a (100) orientation [18,19]. In our epitaxial Cu films, the fact that a (111) orientation is favored indicates surface and interface energies dominate over strain energies [16,20].
Annealing can cause a thin film to break into discontinuous islands, a phenomenon known 3 as dewetting or agglomeration [21,22]. The process, which is driven by minimization of the total energy of the film/substrate system, typically begins with the development of thermal grooves at grain boundaries in the film [23]. These grooves deepen at a rate that increases with temperature, and dewetting occurs when the grooves reach the substrate, so thinner films become discontinuous at lower temperatures. For films exposed to temperatures near the bulk melting point, as is the case when Cu (melting point of 1084 • C) is used for CVD of graphene, dewetting is a major limitation on the survivability of the film. Fortunately, grain growth and dewetting are competing processes [16]. As we show here, the growth of giant grains at temperatures somewhat below 1000 • C allows Cu films to endure subsequent graphene growth conditions with minimal dewetting.
In this paper, we present an extensive investigation of grain size and orientation for Cu films sputtered onto α-Al 2 O 3 (0001) substrates at a wide range of temperatures, and then annealed at temperatures near 1000 • C. We characterize our films using x-ray diffraction (XRD) and electron backscatter diffraction (EBSD) to measure crystallinity, and optical microscopy to show film properties over large areas. We also report results for large domain graphene growth by CVD on these films, characterized by optical microscopy and Raman spectroscopy. Our findings show that an appropriate combination of deposition and annealing temperatures can produce Cu(111) single crystal films, free of twinning and thermal grooves, over macroscopic length scales. Such films offer an ideal substrate for epitaxial CVD of graphene, h-BN, and possibly other materials. . The dark lines apparent in Fig. 1b,d,e are thermal grooves that mark the edges of grain boundaries in the Cu film (see [24] and Supplementary Fig. S2 for confirmation of this correspondence). Since these films are 450 nm thick, conventional grain growth stagnation would limit grains to roughly 3× the film thickness, or 1.5 µm. The actual grains are much larger than this limit, and for T d = 80 • C the grains exceed the image size. Figure 1g  for EBSD maps of the rare grain boundaries that remain after annealing.) The dark spots OR I and OR II in the azimuthal scan (Fig. 2c). The peaks every 60 • instead of 120 • in the azimuthal scans indicate both OR I and OR II consist of twins that are related by an in-plane rotation of 60 • . This twinning, which is expected because the OR between a (111) cubic film and a hexagonal substrate is equivalent for a 60 • in-plane rotation, has limited the crystallinity of Cu(111) in several graphene CVD studies [24][25][26][27]. For T d ≥ 100 • C, the film texture is purely (111), the rocking curve has no tails, and the azimuthal scan shows a single OR. The changes in these three features point to a sudden transition to improved epitaxy between T d = 80 • C and T d = 100 • C. Surprisingly, it is just below this transition where giant grain growth is most pronounced, i.e., better as-deposited epitaxy does not necessarily promote giant grain growth upon annealing.  in the ND map (Fig. 3c), and the ND+RD map shows only OR II grains (Fig. 3f ). For T d = 80 • C, which favors giant grain growth upon annealing, the as-deposited film is marked by a nonuniform distribution of grain sizes: the ND map in Fig. 3b shows several (111) grains that are much larger than their neighbors, and the ND+RD map in Fig. 3e shows that these large grains are exclusively OR II. The pole figure has 12 spots due to twinning in both the OR II grains (pink and green in Fig. 3e) and in the smaller OR I grains (yellow in Fig. 3e). The variation of colors for OR II grains is due to in-plane misalignment about the nominal epitaxial direction of up to several degrees. This is consistent with the broad OR II peaks in the XRD azimuthal scans in Fig. 2c.
Although the large grain size for OR II in Fig. 3e indicates OR II is favored over OR I during deposition, the XRD data of Fig. 2f [15]. The different in-plane strain expected for the two ORs, tensile for OR I and compressive for OR II [28], is qualitatively consistent with this finding: since Cu expands more rapidly than α-Al 2 O 3 (0001) as temperature increases, the strain energy of an OR under tensile strain will decrease and that of an OR under compressive strain will increase.
To examine the intermediate stages of giant grain growth, we used shorter annealing times and lower annealing temperatures. For a T d = 80 • C film annealed for ∼ 1 min at 750 • C, we found exclusively OR II grains (Supplementary Fig. S4). After annealing for 20 min at 800 • C, we found individual OR I grains starting to consume the surrounding matrix of OR II grains (Supplementary Fig. S2). Figure 4 shows the boundary between a giant OR I 4c,d, show that the upper region is a single OR I grain (no twinning) whereas the matrix contains both OR II twins. It is clear that the process of giant grain growth involves OR I grains consuming OR II grains upon annealing. In order for this to occur, the as-deposited film must contain a fraction of both orientation relationships, because if there are no OR I seed grains present (as is the case with T d = 100 • C) or if the film is already exclusively OR I (T d ≥ 270 • C), the film will stagnate with the as-deposited orientation relationship, creating thermal grooves between twins and eventually severe dewetting (Supplementary Fig. S1).
Deposition at T d = 80 • C provides a mix of grain orientations that promotes growth of giant OR I grains before significant dewetting occurs, thus stabilizing the Cu film and allowing it to survive graphene CVD conditions. Annealing of a T d = 80 • C film deposited through a shadow mask to create isolated 100 µm Cu islands showed the density of OR I seed grains is only about one per mm 2 (Supplementary Fig. S6).
Graphene grown by CVD (see Methods) is shown in Fig. 5. We have optimized the  [27]. Since the Cu is epitaxial with the sapphire substrate, this enables alignment of macroscopic features such as sample edges with zig-zag and armchair directions in graphene nanostructures. Figure 5b shows the dendritic nature of the island perimeter. This type of growth is similar to graphene growth at low pressures where the H 2 /CH 4 ratio is close to 1. Figure 5c is a Raman spectrum of the graphene after transfering a continuous graphene film to a 300 nm oxidized Si substrate using PMMA and thermal release tape. The I G' /I G peak ratio is 2.3, with Lorentzian FWHM peak widths of 12 cm -1 and 27 cm -1 for the G and G' peaks, respectively, and the D peak is small. All these features indicate a high quality, monolayer graphene film.
We have demonstrated a route to single crystal Cu(111) films over centimeter length scales based on dramatic secondary grain growth of a favored orientation of Cu on α-Al 2 O 3 (0001).
Our XRD and EBSD results show in detail the particular as-deposited grain structure that promotes giant grain growth upon annealing. Although this work has focused on Cu films thick enough to survive graphene CVD conditions, we expect similar phenomena to occur at lower temperatures for thinner films, based on standard grain growth models. Furthermore, materials other than Cu should also be suitable for giant grain growth if the required asdeposited grain structure can be obtained. A promising candidate is Al on α-Al 2 O 3 (0001), since films having a mixture of OR I and OR II have already been demonstrated [11].  XRD and EBSD. X-ray diffraction was performed using a Cu Kα source and a 4-circle goniometer with an instrument resolution of 0.0001 • . All measurements were performed using parallel beam optics with a maximum beam divergence of 0.15 • , which sets the minimum rocking curve linewidth achievable in the experiment. A powder Si sample was used to correct any offsets in the 2θ angle. Symmetric θ − 2θ scans were used to determine the out-of-plane crystalline axes. Once the (111) reflection was found, the tilt angle was scanned to generate the (111) rocking curve. In-plane azimuthal scans of the (220) reflection were taken with the grazing incidence angle adjusted to the value of maximum intensity (typically about 0.5 • above the critical angle). At this angle, the entire 5 mm x 6 mm sample is illuminated by the x-rays. Once the (220) peak was located, an azimuthal scan about the sample normal axis was taken to determine the in-plane angular distribution of the [220]
For EBSD measurements, all films were oriented with [1120] Al 2 O 3 parallel to the RD direction. The SEM accelerating voltage was 20 kV, the chip was tilted 70 • towards the detector, and diffraction patterns were collected with 4 × 4 binning over a hexagonal array of ≈ 500 nm pixels.
Graphene growth, transfer, and characterization. Before graphene growth, the