III. RESULTS AND DISCUSSION

As stated in Sec. I, growth in argon reduces the overall Si sublimation rate from the SiC surface, leading to more homogeneous graphene films with larger domain sizes than attainable under high-vacuum. ^{Reference Wu, Ye, Capano, Xuan, Sui, Qi, Cooper, Shen, Pandey, Prakash and Reifenberger18,Reference Sutter24,Reference Virojanadara, Syväjarvi, Yakimova, Johansson, Zakharov and Balasubramanian25} There is great interest in graphene on the C-face of SiC because its transport properties are superior to those on the Si-face. ^{Reference Hass, Feng, Li, Li, Zong, de Heer, First, Conrad, Jeffrey and Berger26–Reference Tedesco, VanMil, Myers-Ward, McCrate, Kitt, Campbell, Jernigan, Culbertson, Eddy and Gaskill29} Although the number of graphene layers on the C-face is usually large (often tens of layers thick), individual layers are electronically decoupled due to stacking disorder, resulting in high electron mobility and 2D-like electronic properties. ^{Reference de Heer, Berger, Wu, First, Conrad, Li, Li, Sprinkle, Hass, Sadowski, Potemski and Martinez27,Reference Hass, Feng, Millán-Otoya, Li, Sprinkle, First, de Heer, Conrad and Berger30,Reference Hass, Varchon, Millán-Otoya, Sprinkle, Sharma, de Heer, Berger, First, Magaud and Conrad31} However, comparisons of carrier mobility between Si- and C-face samples grown in vacuum, and C-face samples grown in vacuum and low-pressure Ar ambient presented in Table I, illustrate that growth in argon does not guarantee high-mobility graphene on the carbon face of SiC.

TABLE I.

Mobility data for graphene under various processing conditions.

Immediately evident from the data is the lack of a systematic variation in C-face mobility as a function of pressure. If the premise for growing in Ar is to reduce Si sublimation, than growth in 1 mbar argon is expected to yield a higher average mobility than growth in vacuum, all other parameters are equal. To better understand this mobility data, and to gain a measure of the reproducibility of graphene synthesis, the structure of these films is investigated by GIXD.

A specular scan in Fig. 3(a) of the Si-face graphene layer displays a broad peak with a Gaussian shape centered at q _z = 1.873 Å⁻¹, and a small lower Q peak, which is a finite-size peak (Kiessing fringe). The main peak has a (full-width at half maximum) FWHM = 0.283 Å⁻¹ corresponding to a 2.22-nm (7 monolayers) thick graphene film with an interlayer spacing of 3.355 Å, nearly identical to the interplanar spacing of Bernal-stacked graphite (d = 3.354 Å). Specular scans of C-face graphene films (samples B, C, and D) are best fit with two Gaussian peaks having very different FWHM values [Figs. 3(b)–3(d)]. This suggests the graphene thickness distribution is bimodal, with films possessing thick and thin regions, in agreement with previous reports. ^{Reference Jernigan, VanMil, Tedesco, Tischler, Glaser, Davidson, Campbell and Gaskill28,Reference Luxmi, Guowei, Feenstra and Fisher32} Using the Scherrer equation, film thicknesses are estimated based on curve fitting. Thin and thick regions are approximately 15 and 46 monolayers in sample B, 14 and 42 monolayers in sample C, and 12 and 32 monolayers in sample D [Figs. 3(b)–3(d)]. The number of monolayers in the thicker regions decreases faster (from 46 to 32 layers) than in the thinner film regions (from 15 to 12 layers) as argon pressure increases, indicating higher Ar pressure reduces thickness nonuniformity.

FIG. 3.

X-ray specular scan of (a) sample A (Si-face, vacuum), (b) sample B (C-face, vacuum), (c) sample C (C-face, 1 mbar Ar), and (d) sample D (C-face, 10 mbar Ar). Curve fitting (red traces) of the spectra around q _z = 1.873 Å⁻¹ using a single Gaussian for sample A, and two Gaussian curves (green traces) for sample B, C, and D. The blue dashed lines correspond to the d-spacing of Bernal-stacked graphite (q _z = 1.873 Å⁻¹, d = 3.354 Å).

A rough estimate of the relative amount of thin and thick regions on any one sample can be obtained by calculating the area ratios under the Gaussian peaks. The calculated ratios of thick:thin regions are 1.3:1, 1:1, and 1.1:1 for sample B (vacuum), sample C (1 mbar Ar), and sample D (10 mbar Ar), respectively. The lack of dependence of thickness ratio on argon pressure may indicate variations in defect distributions in the substrate are a dominant factor in determining thickness uniformity.

Figure 4 is an x-ray topograph that reveals dislocations in 4H–SiC starting materials. Although no single topograph can image all dislocations, the (10 $\bar 1$ 8) x-ray topograph reveals all screw dislocations with Burgers vector [000n]. This topograph is taken in reflection to image dislocations close to the surface. Specular scans of Fig. 3 are collected using a small incidence angle, and long sections of the surface (several mm²) contribute to the diffraction data. In locations with high dislocation density, Si–C bonds are more highly strained, and the activation barrier for Si sublimation is lower. It is reasonable to expect thickness variations in light of the dislocation density variations shown in Fig. 4.

FIG. 4.

X-ray reflection topograph from (10 $\bar 1$ 8) diffraction peak. Lighter features on dark background are defects near the SiC surface. Low defect area is located at “1” and a highly defective region is located at “2.” Total area is 1 × 1 cm.

Peak positions of graphene films on the C-face in Fig. 3 are observed at smaller q _z compared to Bernal-stacked graphite (q _z = 1.873 Å⁻¹). Hence, the d-spacing of graphene layers on the C-face (about 3.400 and 3.367 Å for sample B; about 3.400 and 3.364 Å for sample C, and about 3.409 and 3.360 Å for sample D) is markedly larger than on the Si-face (about 3.355 Å). This interlayer expansion of C-face graphene layers contributes to a higher mobility usually measured compared to mobility measured from Si-face graphene. ^{Reference Hass, Feng, Li, Li, Zong, de Heer, First, Conrad, Jeffrey and Berger26,Reference Tedesco, VanMil, Myers-Ward, McCrate, Kitt, Campbell, Jernigan, Culbertson, Eddy and Gaskill29,Reference Hass, Feng, Millán-Otoya, Li, Sprinkle, First, de Heer, Conrad and Berger30}

Azimuthal (phi) scans of in-plane graphene (100) peaks in Fig. 5 are used to determine the in-plane texture of the films, with ϕ = 0° defined along the [ $10\bar 10$ ] direction of SiC. The sharp peak at ϕ = 30° with a narrow FWHM (=0.25° for sample A) confirmed that graphene layers are epitaxial and displayed the expected crystallographic relationship with respect to the SiC substrate. A phi scan away from the graphene (100) peak coincided with the baseline intensity in Fig 5(a), showing there is no randomly oriented graphene on the Si-face of SiC [Fig. 5(a)]. In vacuum-grown C-face graphene (sample B), ^{Reference de Heer, Berger, Wu, First, Conrad, Li, Li, Sprinkle, Hass, Sadowski, Potemski and Martinez27,Reference Sprinkle, Hicks, Tejeda, Taleb-Ibrahimi, Fèvre, Bertran, Tinkey, Clark, Soukiassian, Martinotti, Hass and Conrad33} there is a measurable diffraction signal up to approximately 10° off the main peak in the phi scan [Fig. 5(b)]. The graphene (100) diffraction away from 30° becomes more prominent in Ar-grown graphene films (samples C and D) even though these films have a smaller number of layers than the vacuum-grown sample [Figs. 5(c) and 5(d)]. This observation demonstrates that Ar-grown samples have more in-plane disordered graphene. As a result, these layers become more electronically decoupled and behave more like a single sheet of graphene. ^{Reference Hass, Feng, Millán-Otoya, Li, Sprinkle, First, de Heer, Conrad and Berger30,Reference Hass, Varchon, Millán-Otoya, Sprinkle, Sharma, de Heer, Berger, First, Magaud and Conrad31} Stacking disorder reduces van der Waals interactions between graphene layers, which leads to an increase of the interlayer spacing of graphene, ^{Reference Hass, Feng, Millán-Otoya, Li, Sprinkle, First, de Heer, Conrad and Berger30,Reference Hass, Varchon, Millán-Otoya, Sprinkle, Sharma, de Heer, Berger, First, Magaud and Conrad31,Reference Franklin34,Reference Baskin and Meyer35} in agreement with the specular scans [Figs. 3(b)–3(d)]. Specular diffraction data show the thinner regions in samples B, C, and D have larger interlayer stacking distances than graphite. The thicker regions, on the other hand, have interlayer spacing closer to that of Bernal-stacked graphite. To explain these observations, it is hypothesized that graphene layers initially form with randomly stacked layers on the C-face because of inadequately controlled sublimation leading to high initial growth rates. As layers grow thicker, the interlayer spacing relaxes to a value closer to that of Bernal-stacked graphite.

FIG. 5.

X-ray azimuthal phi-scan of the (100) in-plane peak around ϕ = 30° with respect to the underlying SiC lattice along the [ $10\bar 10$ ] direction of SiC in (a) sample A (Si-face, vacuum), (b) sample B (C-face, vacuum), (c) sample C (C-face, 1 mbar Ar), and (d) sample D (C-face, 10 mbar Ar).

High-resolution in-plane GIXD is used to study the structure of graphene in the film plane. All samples display the typical features of the graphene unit cell as shown in radial scans along the graphene (100) and (110) directions. ^{Reference Lee, Toney, Ko, Randel, Jung, Munakata, Lu, Geballe, Beasley, Sinclair, Manoharan and Salleo23,Reference Hass, Feng, Li, Li, Zong, de Heer, First, Conrad, Jeffrey and Berger26,Reference de Heer, Berger, Wu, First, Conrad, Li, Li, Sprinkle, Hass, Sadowski, Potemski and Martinez27,Reference Wallace36} The radial peaks of graphene on the Si-face (sample A) are shifted toward larger q _r (=smaller a _G) compared to the expected values for graphite (q _r = 2.553 Å⁻¹, a _G = 2.461 Å, and q _r = 5.106 Å⁻¹, a _G/2 = 1.2305 Å) [Fig. 6(a)], suggesting graphene layers are under biaxial compressive strain at room temperature. The compressive strain of this graphene film is isotropic and calculated to be 0.31%. This isotropic compressive strain can be attributed to the large difference in thermal expansion coefficients between graphene and SiC (α_G < α_SiC), ^{Reference Röhrl, Hundhausen, Emtsev, Seyller, Graupner and Ley37,Reference Ferralis, Maboudian and Carraro38} which affects the electronic properties of graphene films. ^{Reference Robinson, Wetherington, Tedesco, Campbell, Weng, Stitt, Fanton, Frantz, Snyder, VanMil, Jernigan, Myers-Ward, Eddy and Gaskill39–Reference Huang, Yan, Heinz and Hone41} Such strain information averaged over relatively large areas of graphene on SiC (≈mm² for these experiments) cannot be obtained with characterization tools that probe local structures such as Raman spectroscopy. ^{Reference Röhrl, Hundhausen, Emtsev, Seyller, Graupner and Ley37,Reference Ferralis, Maboudian and Carraro38,Reference Robinson, Puls, Staley, Stitt and Fanton42} In contrast to graphene on the Si-face (sample A), radial scans of graphene on the C-face samples display peaks located very close (within 0.05%) to that of unstrained graphite [Figs. 6(b)–6(d)], indicating that a relaxation of the compressive strain has occurred in these thicker films. The lattice constant of graphene films converges to that of bulk graphite as layer thickness increases and forms wrinkles or ridge structures, which are usually observed in thermally grown epitaxial graphene on the C-face caused by thermal stresses built-up upon cooling. ^{Reference Bolen, Shen, Gu, Colby, Stach, Ye and Capano20,Reference Luxmi, Guowei, Feenstra and Fisher32,Reference Tedesco, Jernigan, Culbertson, Hite, Yang, Daniels, Myers-Ward, Eddy, Robinson, Trumbull, Wetherington, Campbell and Gaskill43–Reference Colby, Bolen, Capano and Stach45}

FIG. 6.

X-ray radial scan of (a) sample A (Si-face, vacuum), (b) sample B (C-face, vacuum), (c) sample C (C-face, 1 mbar Ar), and (d) sample D (C-face, 10 mbar Ar) across the (11) rod of graphene reciprocal lattice. Curve fitting (red traces) of the spectra around q _r = 5.106 Å⁻¹ using two Gaussians (green traces) for all samples. The blue dashed lines correspond to one half of the lattice constant of the unit cell in unstrained graphene (q _r = 5.106 Å⁻¹, a _G/2 = 1.2305 Å).

Peaks in the radial scans contain much information about the microstructure of graphene. A complete and systematic analysis of their shape and position as a function of processing conditions is beyond the scope of this manuscript. Nevertheless, qualitative statements can be made. The width of the radial scan across the (11) rod is broader in Si-face graphene compared to C-face graphene. This observation strongly suggests Si-face graphene is smaller grained in-plane compared to C-face graphene. The larger coherence length contributes to the (generally) higher carrier mobility of graphene on the C-face graphene compared to mobility on the Si-face graphene, in agreement with previous reports. ^{Reference Sutter24,Reference Hass, Feng, Li, Li, Zong, de Heer, First, Conrad, Jeffrey and Berger26,Reference de Heer, Berger, Wu, First, Conrad, Li, Li, Sprinkle, Hass, Sadowski, Potemski and Martinez27,Reference Zhou, Gweon, Fedorov, First, de Heer, Lee, Guinea, Castro Neto and Lanzara46} Furthermore, on C-face graphene, peaks in the same radial scans show a pronounced asymmetry. Such a peak shape (i.e., the existence of a “tail” at q _r higher than the peak q _r) suggests the grain structure has two distributions coexisting in the film with differently sized domains having slightly different lattice parameters. The angular resolution of the scans does not permit accurate deconvolution of components, but it is reasonable that the high-q _r tail is due to a population of smaller compressively strained crystallites. Interestingly, the film that displays the lowest mobility (sample C) has the largest population of small crystallites (coherence length on the order of ∼30 nm) as evidenced by the broader, more intense tail. Samples B and D, on the other hand, have different average mobility, but their in-plane grain structure appears similar. The higher mobility of the film grown in the Ar atmosphere (9000 cm²/Vs) may be attributed to the more pronounced rotational disorder which increases isolation of individual graphene layers. It should be added that a more complete analysis would entail measuring these parameters in all crystallographic orientations. These results, nevertheless, indicate that graphene film structures can vary dramatically under Ar growth conditions.