New results are reported from an ongoing international research effort to accurately determine the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The surfaces of two 28 Si-enriched spheres were decontaminated and reworked in order to produce an outer surface without metal contamination and improved sphericity. New measurements were then made on these two reconditioned spheres using improved methods and apparatuses. When combined with other recently refined parameter measurements, the Avogadro constant derived from these new results has a value of N A = 6.022 140 76(12) × 10 23 mol -1 . The X-ray crystal density method has thus achieved the target relative standard uncertainty of 2.0 × 10 -8 necessary for the realization of the definition of the new kilogram.

We present a new fabrication method for epitaxial graphene on SiC which enables the growth of ultrasmooth defect-and bilayer-free graphene sheets with an unprecedented reproducibility, a necessary prerequisite for wafer-scale fabrication of high quality graphene-based electronic devices. The inherent but unfavorable formation of high SiC surface terrace steps during high temperature sublimation growth is suppressed by rapid formation of the graphene buffer layer which stabilizes the SiC surface. The enhanced nucleation is enforced by decomposition of polymer adsorbates which act as a carbon source. With most of the steps well below 0.75 nm pure monolayer graphene without bilayer inclusions is formed with lateral dimensions only limited by the size of the substrate. This makes the polymer assisted sublimation growth technique the most promising method for commercial wafer scale epitaxial graphene fabrication. The extraordinary electronic quality is evidenced by quantum resistance metrology at 4.2 K with until now unreached precision and high electron mobilities on mm scale devices. Main TextThe success of graphene as a basis for new applications depends crucially on the reliability of the available technologies to fabricate large areas of homogenous high quality graphene layers. Epitaxial growth on metals as well as on SiC substrates is employed with specific benefits and drawbacks.Single graphene layers epitaxially grown on SiC offer a high potential for electronic device applications. They combine excellent properties, e.g. high electron mobilities, with the opportunity for wafer-scale fabrication and direct processing on semi-insulating substrates without the need to transfer the graphene to a suitable substrate (Avouris & Dimitrakopoulos 2012). Some progress has been achieved during the recent years. In particular, high temperature sublimation growth under Ar atmosphere (Virojanadara et al. 2008),(Emtsev et al. 2009 or by confinement control (Heer et al. 2011), (Real et al. 2012) was a breakthrough for synthesizing large-area graphene on SiC substrates.The coverage of graphene bilayers could be reduced from wide stripes formed along the terraces to small micrometer-sized bilayer patches (Virojanadara et al. 2009). Further it was found that beyond pure sublimation growth from SiC graphene formation can be assisted by additional carbon supply from external sources (Al-Temimy et al. 2009;Moreau et al. 2010). In particular, by using propane in

A new single crystal from isotopically enriched silicon was used to determine the Avogadro constant N A by the x-ray-crystal density method. The new crystal, named Si28-23Pr11, has a higher enrichment than the former 'AVO28' crystal allowing a smaller uncertainty of the molar mass determination. Again, two 1 kg spheres were manufactured from this crystal. The crystal and the spheres were measured with improved and new methods. One sphere, Si28kg01a, was measured at NMIJ and PTB with very consistent results. The other sphere, Si28kg01b, was measured only at PTB and yielded nearly the same Avogadro constant value. The mean result for both 1 kg spheres is N A = 6.022 140 526(70) × 10 23 mol −1 with a relative standard uncertainty of 1.2 × 10 −8 . This value deviates from the Avogadro value published in 2015 for the AVO28 crystal by about 3.9(2.1) × 10 −8 . Possible reasons for this difference are discussed and additional measurements are proposed.

Self-assembled monolayers of aromatic molecules on copper substrates can be converted into high-quality single-layer graphene using low-energy electron irradiation and subsequent annealing. This two-dimensional solid state transformation is characterized on the atomic scale and the physical and chemical properties of the formed graphene sheets are studied by complementary microscopic and spectroscopic techniques and by electrical transport measurements. As substrates, Cu(111) single crystals and the technologically relevant polycrystalline copper foils are successfully used.

Non-destructive chemical functionalization of graphene for applications in electronic devices (e.g., sensors or transducers) is achieved via assembly of carbon nanomembrane (CNM)/single-layer graphene (SLG) van der Waals heterostructures. The CNMs are 1 nm-thick, dielectric molecular sheets terminated with functional amino groups. The structure and performance of heterostructured field-effect transistors (FETs) are characterized by photoelectron/Raman spectroscopy and by electric transport measurements in vacuum, ambient conditions and water.

Within the scope of re-determining the Avogadro constant, the content of impurities in ultra-pure, mono-isotopically enriched silicon ‘Si28’ was measured by infrared spectrometry. The calibration factors required for the calculation of the concentrations from the maximum absorption coefficients had to be determined in this context for the isotopically enriched material. For this purpose a model was prepared, which enables conversion of the factors for Si with natural isotopic abundance. On the basis of these results, the concentrations of the three most decisive impurities in the enriched material were determined. These are oxygen atoms on interstitial sites and substituting carbon and boron atoms which occupy silicon sites. Whereas carbon and oxygen were measured in accordance with standardized procedures modified for the particular metrological use, the absorption measurement of the boron was carried out differently to the conventional standard. The concentrations determined for the three types of crystal impurities are high enough to make a correction of the lattice parameter for the ‘Si28’ material necessary.

The electrical transport properties of epitaxial graphene layers are correlated with the SiC surface morphology. In this study we show by atomic force microscopy and Raman measurements that the surface morphology and the structure of the epitaxial graphene layers change significantly when different pretreatment procedures are applied to nearly on-axis 6H-SiC(0 0 0 1) substrates. It turns out that the often used hydrogen etching of the substrate is responsible for undesirable high macro-steps evolving during graphene growth. A more advantageous type of sub-nanometer stepped graphene layers is obtained with a new method: a high-temperature conditioning of the SiC surface in argon atmosphere. The results can be explained by the observed graphene buffer layer domains after the conditioning process which suppress giant step bunching and graphene step flow growth. The superior electronic quality is demonstrated by a less extrinsic resistance anisotropy obtained in nano-probe transport experiments and by the excellent quantization of the Hall resistance in low-temperature magneto-transport measurements. The quantum Hall resistance agrees with the nominal value (half of the von Klitzing constant) within a standard deviation of 4.5 × 10(-9) which qualifies this method for the fabrication of electrical quantum standards.

A metrological challenge is currently underway to replace the present definition of the kilogram. One prerequisite for this is that the Avogadro constant, N A , which defines the number of atoms in a mole, needs to be determined with a relative uncertainty of better than 2 × 10 −8 . The method applied in this case is based on the x-ray crystal density experiment using silicon crystals. The first attempt, in which silicon of natural isotopic composition was used, failed. The solution chosen subsequently was the usage of silicon highly enriched in 28 Si from Russia. First, this paper reviews previous efforts from the very first beginnings to an international collaboration with the goal of producing a 28 Si single crystal with a mass of 5 kg, an enrichment greater than 0.9999 and of sufficient chemical purity. Then the paper describes the activities of a follow-up project, conducted by PTB, to produce a new generation of highly enriched silicon in order to demonstrate the quasi-industrial and reliable production of more than 12 kg of the 28 Si material with enrichments of five nines. The intention of this project is also to show the availability of 28 Si single crystals as a guarantee for the future realisation of the redefined kilogram.