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Investigating the CVD synthesis of graphene on Ge(100): towards layer by layer growth

Germanium is emerging as the substrate of choice for the growth of graphene in CMOS-compatible processes. For future application in next generation devices the accurate control over the properties of high-quality graphene synthesized on Ge surfaces, such as number of layers and domain size, is of paramount importance. Here we investigate the role of the process gas flows on the CVD growth of graphene on Ge(100). The quality and morphology of the deposited material is assessed by using microRaman spectroscopy, x-ray photoemission spectroscopy, scanning electron and atomic force microscopies. We find that by simply varying the carbon precursor flow different growth regimes - yielding to graphene nanoribbons, graphene monolayer and graphene multilayer - are established. We identify the growth conditions yielding to a layer-by-layer growth regime and report on the achievement of homogeneous monolayer graphene with an average intensity ratio of 2D and G bands in the Raman map larger than 3.


INTRODUCTION
Since its isolation, graphene has attracted a huge interest due to its unique electronic structure and exceptional electronic and mechanical properties. Scalable and controlled synthesis of high quality graphene is the main request for several potential applications. Chemical Vapor Deposition (CVD) has been predicted as the leading growth technique for large-scale deposition of graphene films 1 and has emerged as the dominant method to synthesize continuous films of "electronic grade". Even though CVD graphene on metal has reached high standards of quality, 2-6 the compatibility with mainstream silicon microelectronics requires the growth of metal-free graphene on CMOS compatible semiconductor 1,7 . Germanium is a perfect candidate as substrate since high quality single crystal epitaxial Ge on Si is routinely available 8 and it does not form a stable carbide 9 . The successful growth of graphene on Ge could enable the integration in the CMOS platform of graphene-based optoelectronic devices as high performance transistors, [10][11][12] terahertz emitters, 13 and electro-optical modulators 14 .
Large area single crystal graphene films on the Ge(110) substrate are achieved 15 exploiting the anisotropic surface symmetry of Ge(110) 16 . However, the development of a CMOS integrated graphene electronics requires the successful growth of high quality graphene on the Ge (100) surface. In Refs. [17][18][19] the CVD growth of graphene on Ge(100) substrates and Ge/Si(100) was demonstrated. Despite the variety of graphene features reported in literature, [17][18][19][20][21][22] the process conditions yielding to the development of monolayer, multilayer, or graphene nanoribbons have not been yet well established to-date, hindering the development of wafer scale graphenebased optoelectronics, where the control over the morphology and structure of the deposited graphene is mandatory 23,24 .
The catalyzed CVD growth of graphene is determined by a specific sequence of processes, i.e. the formation of active carbon species on the substrate, the graphene domain nucleation, and the domain lateral growth. In all these processes hydrogen plays an active role, promoting 4 the activation of surface-bound carbon and acting as an etching agent that controls the size and morphology of the resulting graphene domains. 25,26 The different relevance of these processes at different stages of the growth depends essentially on the ratio in the process gas mixture of the H2 carrier gas with the carbon-containing hydride (e.g. CH4) on the substrate surface, where the catalysis and diffusion of the C species take place.
In this work we investigate the processes at the basis of the different CVD growth regimes of graphene on Ge(100) by varying the methane flow, the H2:CH4 flow ratio, and the deposition time. The joint use of complementary experimental techniques, both spectroscopic and morphological, allowed an exhaustive characterization of the "as grown" materials (without the need of graphene transfer on other substrates) at different stages and conditions of the synthesis. We demonstrate that by simply varying the methane flow is possible to tune the growth so to obtain either graphene nanoribbons, graphene monolayer and graphene multilayer.
The role of the different processes bringing to the formation of graphene on Ge(100), from nucleation to domain lateral growth and etching, domain merging and multilayer development in the different growth conditions are established. Notably, this work leads to the identification of a layer-by-layer growth regime which allows for the synthesis of high quality monolayer graphene in a controllable and reliable manner. As the presented process is developed in a commercially available reactor, it might be easily reproduced and its adoption in industrial production appears feasible. The report of a layer-by-layer growth on Ge substrates and in a commercially available reactor is a first step towards a larger accessibility of high quality graphene whose properties can be tuned by controlling the number of layers.

EXPERIMENTAL METHODS
Graphene was grown on Ge(100) substrates by employing a commercially available 4" coldwall CVD reactor (Aixtron BM). The Ge(100) substrates were cut into 1x1 cm 2 pieces from a 5 4" wafers (N-type Sb-doped, n=10 16 cm -3 , <100>+/-0.1°, double side polished) and cleaned with ultrasonic bath in isopropyl alcohol followed by rinsing in de-ionized water. The substrates were then placed at the center of the BM growth chamber and heated up to the deposition temperature in H2 and Ar gas mixture. Once the growth temperature was reached, the carbon precursor (i.e., CH4) was introduced in the chamber. In the reported experiments H2 and Ar flows were set at 200 and 800 sccm respectively, while the CH4 flow varied in the 1-10 sccm range. The growth was performed at 100 mbar and at T=930°C, only few degrees below the Ge surface melting. As a matter of fact good quality graphene on Ge can be achieved only employing growth temperatures in a small range close to the Ge melting. To ensure good reproducibility and a homogeneous temperature on the whole Ge surface the substrate heating is carried out by a multi-step temperature ramp. After graphene deposition the system was cooled down to room temperature in H2 and Ar. No differences were appreciated performing the cooling process in either an H2:Ar mixture or in pure Ar.
Raman spectroscopy (Renishaw inVia confocal Raman microscope) was performed using an excitation wavelength of 532 nm, a 100x objective, a laser spot size of 1 µm and a step size of 1 µm for area mapping. The intensity ratio of the 2D, G and D bands were evaluated by using the integrated area of the peaks.
The sample morphology was investigated by means of SEM (FEI Helios 600 Nanolab DualBeam) and AFM (Veeco CP-II) operating in tapping mode. The xn coverage fraction of domains with n-layers of graphene (n-LG) was evaluated from a standard analysis of the SEM images performed by setting user-defined threshold levels for the grey scale intensity. For all the samples n-LG domain size distribution, domain average size (defined as the square root of the area) and its standard deviation were determined. The domain size analysis has been 6 performed also on AFM data on the samples that do not exhibit the Ge nano-texturing induced by the graphene growth. In this case the threshold intervals for the height values associated to n-LG were extracted from line-profile analysis. The results of the two methods are in good agreement in all the analyzed samples.
The XPS measurements were carried out using a monochromatic Al Kα source (hν=1486.6 eV) and a concentric hemispherical analyzer operating in retarding mode (Physical Electronics Instruments PHI), with overall resolution of 0.4 eV. The C1s core level area intensity of each sample has been normalized to that acquired in the same experimental conditions on a commercial single layer graphene (SLG), a CVD-deposited graphene on copper foil and transferred on a SiO2 substrate, purchased from Graphenea.

CH4 flow influence on the growth kinetics
To gain insight into the graphene CVD growth on the Ge(100) surface we investigated the influence of the CH4 flow on the growth kinetics by synthesizing graphene films at fixed deposition time tD=60 min varying the CH4 flow F in the 1-10 sccm range. The resulting H2:CH4 flow ratio R varied from R=200 down to R=20.
The Raman spectra of the samples grown at different F and their analysis are shown in Figure   1. In all the samples the Raman spectra exhibit the typical graphene features, i.e. 2D and G bands located at ~ 2700 and ~ 1600 cm -1 , and the D peak related to the presence of residual defects in the film at ~1350 cm -1 (see Figure 1a).   Their asymmetric shape characterized by a relatively high length/width aspect ratio is promoted by the Ge(100) surface anisotropy. 21 Nanoribbons cover about 35 % of the Ge surface and have an average aspect ratio α=6 and an average length Rl=150 nm. Their typical shape measured by AFM is highlighted at the bottom of Figure 3a. Its height of 1 nm is consistent with a single layer feature. 17 The relatively high intensity ratio between D and G peaks (ID/IG) (see Figure 1c) in the Raman spectrum is ascribable to the small size of nanoribbons. As a matter of fact, the nanoribbon boundaries give a large contribution to the defect-related D peak being their size smaller with respect to the laser spot diameter (~1µm). If the deposition time tD is doubled keeping the same growth conditions, the surface coverage increases to about 60%. In some regions of the sample the nanoribbons merge and the ID/IG intensity ratio decreases down to ~0.7.
For F=2 sccm a single layer graphene film covers completely the Ge substrate. As a matter of fact, the SEM image of Figure 2b 27 The I2D/IG intensity ratio µ-Raman map and the relative histogram are reported in Figure 1e and 1f, respectively. The I2D/IG distribution has an average value and a standard deviation equal to 3.1 and 0.55, respectively. It is well known that the I2D/IG ratio decreases with the graphene charge doping. 28 Raman spectroscopy can be used to evaluate the doping level and the amount of strain in graphene by analyzing the 2D-and G-band positions. 29 In order to estimate the charge density in Fig. 1g we report the 2D vs G peak positions in Raman spectra taken in different surface regions of the sample grown at F= 2 sccm. The charge density can be estimated using the strain and doping deconvolution reported in Ref. 29 . The figure shows that the experimental data are not positioned on the charge neutrality line. Although the analysis does not allow to distinguish between holes and electrons we can estimate a charge density of the order of 1 ´ 10 13 cm -2 . This value is comparable with the electron density found in Ref. 19 by Hall measurements. The same analysis reveals also the presence of a compressive biaxial strain e ~-0.3% similar to that observed in Ref. 19 . We point here out that in our samples the obtained average I2D/IG intensity ratio is larger and the standard deviation is smaller than those reported in literature [17][18][19] demonstrating the high quality and uniformity of our single layer graphene.
For F=5 sccm single, bi-and trilayer graphene domains coexist on the Ge surface as shown in Figure 2c. The growth mode observed in this condition is similar to that reported in Ref. 18 . The average bilayer and trilayer domain sizes are 330±60 nm and 170±70 nm, respectively. Less than 10% of the Ge surface is left exposed. The measured Raman features (I2D/IG =2 and G2D = 41 cm -1 ) are compatible with the presence of mono-and multilayer graphene domains. The AFM image of Figure 3c shows that the Ge substrate is nano-textured. The height oscillations of the nano-faceting are larger than the graphene layer spacing and do not allow a reliable detection of n-LG domains from the AFM topography.
where n is the number of the graphene layers, lef f =lcosϑ=3.2 monolayers 30 is the effective electron escape depth, ϑ=30° is the detection angle, i.e. the angular displacement of the detector slit measured respect to the normal to the sample surface. nanoribbons partially cover the Ge surface, an additional carbon component at higher binding energy Eb= 285.8 eV due to C contamination appears. As a matter of fact, a peak with the same line shape and binding energy is present in the XPS spectrum of a Ge substrate exposed for tD=60 min only to hydrogen and argon, i.e. at F=0. This C contamination component appears in the XPS spectra whenever a significant fraction of the germanium surface remains uncovered.
In Figure 4c we compare the experimental IC/IC SLG ratios to the theoretical ones calculated using the xn values of Figure 4a and eq.(1). Their good agreement for each sample confirms the reliability of the xn values estimated from morphological data.

Growth time evolution of graphene layers at CH4 flow F=2 sccm
The above reported analysis demonstrates that the use of F=2 sccm and R=100 corresponds to a "special" growth condition in which the combined effect of carbon activation, graphene domains growth, and etching is optimized for the development of a continuous graphene 13 monolayer. Therefore, we have selected these process conditions to investigate the growth evolution as a function of the deposition time.
The morphology of the films deposited for tD=30 and 120 min, i.e. before and after the development of the continuous graphene monolayer discussed in the previous section, is shown in Figure 5. For tD=30 min the SEM image (Figure 5a) evidences the presence of small graphene grains on the Ge surface with a coverage fraction of about 25%. They have an average size of 55±20 nm and a density of ~10÷20 µm -2 . The AFM topography (Figure 5b) demonstrates that at this stage of the growth the Ge surface is not nanostructured and has a rms surface roughness of 0.26 nm.
The surface area where graphene grain thickness is ~1 nm (delimited by the grey lines in the AFM image) is consistent with the 25% coverage of graphene grains evidenced by SEM.
14 The Raman spectrum of the sample ( Figure 6) reflects with the "seed-like" stage of the graphene domain evolution. As a matter of fact, the defect band D has very high intensity (ID/IG=1.9). Although the I2D/IG=3 confirms the monolayer nature of the grains the width of the 2D bands is relatively large (G2D=51.8 cm -1 ) suggesting that defects impact also this parameter.

DISCUSSION
In the CVD growth of graphene on metallic surfaces the catalysis of methane on the surface and the successive formation of CHx active species enhanced by the presence of H produce a carbon-adatom species supersaturated surface, where the graphene nucleation takes place. 32 Graphene nuclei grow further by consuming the adsorbed carbon species. The occurrence of successive nucleation depends on the balance between the production rate of carbon growth species from catalyzed methane decomposition and their consumption rate due to nucleation and growth or to recombination and desorption. The domain lateral growth rate and shape are also influenced by the H etching that removes the C atoms bound to the graphene boundaries. 16 Our findings suggest that the same growth model reported in Ref. 32 can be applied to the CVD growth of graphene on Ge. We attribute this to the similarities existing between the C-Ge and C-Cu material systems: similar catalytic activity, extremely low solubility of carbon, absence of a stable carbide. 9,17 The time evolution of the xn coverage fractions and of the Raman spectra points out that at F= 2 sccm and R=100 the growth proceeds in a layer-by-layer regime suggesting that in these process conditions the C adatom species (CHx ) concentration before nucleation is just above the critical supersaturation level. The nucleation and grow th of graphene grain deplete the adsorbed carbon species and their concentration is reduced to a level where the nucleation rate can be negligible and only monolayered domain enlargement takes place up to coalescence.
After domain merging and completion of the first graphene layer the initial supersaturation condition leading to novel nucleation is restored and the second graphene layer begins to form.
The high reproducibility of the continuous graphene monolayer achievement at tD=60 min in several deposition runs points to the occurrence of a rest period between the completion of the first layer and the nucleation of the second one, that is to restore the supersaturation conditions. At present, our data do not allow to unambiguously conclude whether the 2-LG nucleates on top (wedding cake structures WC) or underneath (inverted wedding cake structures IWC) the first one.
For low CH4 flow (F=1 sccm) the graphene growth slows down. As a matter of fact, the growth rate at F=1 sccm (5.4x10 -3 -LG/min) is significantly smaller than half the rate at F=2 sccm (1.7x10 -2 -LG/min). Taking into account that the higher H2:CH4 ratio should increase the production rate of carbon growth species 25 the sub-linear behavior of the growth rate can be ascribed to the effect of hydrogen etching. Although hydrogen etching has the capability of "drawing" the shape of the graphene domains 25 , the role of hydrogen on the development of the graphene nanoribbons observed at F=1 sccm is still not clear. As a matter of fact graphene nanoribbons were recently obtained in UHV by using ethylene without H2. 21 Comparing the previously published data 20,21 with our findings, we can observe that all these nanoribbon growth regimes are characterized by a small growth rate.
For the highest methane flows investigated (F≥5 sccm), we found the coexistence of uncovered, 1-, 2-and 3-LG regions on the Ge surface. In these growth conditions the increase of C adatom species concentration leads to a strong supersaturation on the Ge(100) surface.
The production rate of carbon growth species by catalyzed methane decomposition is much larger than their total consumption rate allowing the further nucleation of graphene domains. 32 This growth mode has been reported in Ref. 18 for graphene growth on Ge(100) at atmospheric pressure. However, we do not observe the minimum in the nucleation probability of the second layer they found at intermediate CH4 flow: in our samples the higher is the flow the higher is the multilayer nucleation and the smaller the domain size. The difference can reside in the more accurate control of temperature in our growths. While we fixed T=930 °C, in Ref. 18 the growth temperature was between 910 and 930 °C, a range in which temperature variations have a strong impact in the graphene synthesis.

CONCLUSIONS
We investigated the CVD growth of graphene on Ge(100) as a function of the methane flow, H2:CH4 flow ratio and deposition time. The combined analysis of the Raman, XPS and SEM/AFM data allowed us to tune the growth in order to obtain graphene nanoribbons, a layer by layer growth and multilayer graphene synthesis by simply varying the CH4 flow. A layer-bylayer growth regime occurred for F=2 sccm and R=100. Employing these "special" growth conditions we obtained the reliable and well controlled growth of graphene monolayer with average I2D/IG ratio larger than 3, a value exceeding the state of the art for graphene synthesis on

Funding Sources
The work was partially supported by the European Union Seventh Framework Program under grant agreement n° 604391 Graphene Flagship