KPFM measurements reveal variations in the graphene coverage as contributing to the different step heights observed. shows a typical step structure for a sample prepared in an argon atmosphere. Of the two topographic steps () only one coincides with a change in contact potential (). The underlying surface structure is analyzed in and represented in an atomic ball-and-stick scheme in . The left step is a substrate step of three bilayers of SiC with a height of 0.75 nm, indicated by the three blue blocks representing the bilayers. The right step is a substrate bilayer step combined with a change in graphene coverage from single to double layer. The resulting topographic step height is 0.09 nm, the change in contact potential 130 mV. Such analysis is supported by the fact that steps with a height that is a multiple of the SiC bilayer height never coincide with a change in contact potential. The interface layer introduced in has been reported as a graphitic layer covalently bound to the SiC substrate [4
]. While its influence on the electronic structure and contact potential is under discussion, it has no influence on the step heights between graphene-covered terraces.
Figure 3 (a) Topographic image showing two steps found typically on samples prepared in an argon atmosphere. (b) Corresponding image of the contact potential difference. Note that only the small step in (a) coincides with a shift in contact potential. (c) Topography (more ...)
Rendering the data sets into a pseudo-three-dimensional representation provides an intuitive understanding of the structure and composition of the sample [22
]. shows results for a sample prepared in UHV. The topography data is rendered and overlayed with a colour scale representing the local contact potential. Most parts of the sample show a bluish colour indicating single-layer graphene coverage. Some smaller terraces exhibit a higher contact potential represented in red, which indicates double-layer graphene. Double-layer graphene spots are regularly observed to grow over a SiC bilayer substrate step. No change in contact potential is observed without a corresponding change in step height. The much simpler surface structure of samples prepared in an argon atmosphere is demonstrated in . The identification of surface areas such as the one in by KPFM allows subsequent experiments to be aimed at a direct comparison between single and double layer graphene, for example, in friction experiments.
Rendered images of graphene layers on SiC(0001) prepared in (a) UHV and (b) an argon atmosphere. The colour represents the local contact potential. Bluish colour indicates single-layer graphene, reddish colour double-layer graphene.
While this visualization method allows for a quick identification of the surface structure, we will now introduce two-dimensional histograms as a complementary data representation. These histograms are very useful for a quantitative analysis of the complex structures of samples prepared in UHV.
Histograms represent the distribution of values in a given data set. Here we are using two-dimensional histograms to represent the data contained in multichannel NC-AFM frames. Several signal values are assigned to each pixel of a scanned frame, e.g., topography and contact-potential values. Using topography and contact potential as axes of a two-dimensional scatter plot, the frequency of occurrence of each pair of topography and contact-potential values is represented by a colour scheme. In this way, topography and contact potential can be graphically correlated while their quantitative values can be directly read from the plot. In order to make two such histograms comparable, topography and contact-potential values are given with respect to the values found in one reference area of the scan frame. A scan frame recorded with 512 lines of 512 pixels provides 262144 data points for this scatter plot, enough for a distinct representation of the relationship between topography and contact potential. shows two-dimensional histograms based on the data sets already presented in the rendered images in .
Figure 5 Two-dimensional histograms based on the data set for the rendered images in . The colour scheme represents the number of data couples that fall into the respective topography and contact-potential bin; (a) sample prepared in UHV, (b) in an argon (more ...)
The sample prepared in UHV is analyzed in . Two distinct groups of clustered data points are lined up vertically, reflecting the coverage by single and double-layer graphene. Within each group, a distinct step height of 0.75 nm is dominant, which corresponds to half the unit cell of 6H-SiC(0001). The step height between single- and double-layer graphene terraces is typically 0.42 nm, indicated by green arrows in . It has been suggested that half a unit cell of SiC(0001) is consumed for the growth of one layer of graphene. This relation suggests itself as the density of carbon atoms is very similar for one half of a unit cell of SiC and one layer of graphene. The step height of 0.42 nm is then given as the difference between 0.75 nm for half a unit cell and 0.33 nm for the height of one layer of graphene.
The sample prepared in an argon atmosphere is analyzed in , its structure with wide terraces and few steps is reflected in the observation of only two narrow clusters of data points in the histogram. The two groups correspond to a height difference of 0.64 nm, i.e., about 0.33 nm less than four SiC(0001) bilayers, which is again the step height of the graphene layer. Therefore we conclude that the lower terrace is depressed by four SiC bilayers but is covered by one additional graphene layer compared to the upper terrace. The extra SiC bilayer decomposed for the structure in as compared to is indicated by the grey arrow.