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
Accurate and traceable calibration of lateral standards (1D and 2D gratings) is a basic metrological task for nano- and microtechnology. Both the mean pitch and the uniformity of the gratings should be measured quantitatively. Although optical diffractometers are effective for measuring the mean pitch, they are not able to measure the uniformity of gratings. In this study, the calibration of gratings is performed using a metrological large range scanning probe microscope with optimized measurement strategies. Two different kinds of data evaluation methods, a gravity centre method and a Fourier transform method, have been developed and investigated. Cosine error, a significant error source of the measurement, is analysed and corrected. Calibrations on several 1D gratings have been carried out. The calibrated mean pitch values have an excellent agreement with those measured by optical diffractometry. Nevertheless, irregularities of the gratings were only deduced from the SPM results. Finally, the usage of the 1D/2D gratings for the calibration of a typical SPM is illustrated.
Two-dimensional (2D) gratings are widely used for calibrating the xy-plane of nearly all kinds of microscopes. The mean pitch, orthogonality and local pitch uniformity of the 2D gratings have to be calibrated prior to usage. In this paper, a method of accurate calibration of 2D gratings using a metrological large-range scanning force microscope is presented. A new measurement strategy is proposed, where the 2D gratings are measured in two narrow rectangular areas for determining all desired measurands and a small square area for viewing the grids in detail. The proposed strategy greatly shortens the measurement time, reduces the drift and eases the data processing procedure. Different data evaluation methods are introduced. Several 2D gratings with mean pitches from 100 nm to 10 µm have been calibrated, the results agree well with the values determined by an optical diffractometer. The expanded uncertainty (k = 2) of the mean pitch was approximately 15 pm for a 2D grating with a nominal mean pitch of 1000 nm, i.e. a relative uncertainty of 1.5 × 10−5.
We demonstrate a device concept to fabricate resistance standards made of quantum Hall series arrays by using p-type and n-type graphene. The ambipolar nature of graphene allows fabricating series quantum Hall resistors without complex multi-layer metal interconnect technology, which is required when using conventional GaAs two-dimensional electron systems. As a prerequisite for a precise resistance standard we confirm the vanishing of longitudinal resistance across a p-n junction for metrological relevant current levels in the range of a few microamperes.Graphene is an electronic material which, since its discovery in 2004, has triggered an avalanche of theoretical and experimental studies. 1 Its band structure gives rise to a number of fascinating properties, making it a promising material for next generation electronic devices. 2 Especially for electrical metrology graphene has unique advantages: since the quantum Hall effect persists up to room temperature, 3 and since the Landau level spacing in a small magnetic field B decreases only with the square root of B, graphene offers the exciting possibility of a resistance standard working at 4.2 K or higher, and in a magnetic field of only 1 or 2 Tesla. 4,5 In metrology the quantum Hall effect is used to realize a value of electrical resistance with relative measurement uncertainty of a few parts in 10 9 or better, typically employing GaAs based heterostructures hosting a 2-dimensional electron system (2DES). Parallel or series quantum Hall arrays could cover a wider resistance scale than just the singular value of 12.9 kΩ. Such quantum Hall arrays are technically feasible, but they are not used in practice, mainly due to the technical difficulties to produce arrays which reliably allow a low measurement uncertainty. Here we present a device concept which avoids these difficulties by exploiting the unique feature of graphene that it can support a 2-dimensional hole system (2DHS) as well as a 2-dimensional electron system in the same device. We support our concept by demonstrating that the prerequisite for a quantum Hall series resistance standard, the vanishing of longitudinal resistance across the series connection, is met even at the high current levels required in practice.The technique of connecting quantum Hall devices in series or in parallel, to obtain multiples or fractions of the resistance h/2e², was first demonstrated by Delahaye. 6 For the case of a series connection, the principle is illustrated in FIG. 1(a). Twice the value of the single-Hall-bar resistance R H = h/2e² is measured between terminals 5 and 5' because the voltage drop in the connection (2-2') is practically zero as can be shown by an equivalent circuit model of a quantum Hall device. 7 The model predicts that in Hall-bars with multiple inter-connections the current in each additional connection is smaller than in the preceding one by a factor ε/(ε+2) with ε = R c /R H , where R c is the interconnect resistance. When ε << 1, three interconnects between successive Hall bars already suffi...
We present a new method for the complete three-dimensional (3D) calibration of scanning probe microscopes (SPM) and other high-resolution microscopes, e.g., scanning electron microscopes (SEM) and confocal laser scanning microscopes (CLSM), by applying a 3D micrometre-sized reference structure with the shape of a cascade slope-step pyramid. The 3D reference structure was produced by focused ion beam induced metal deposition. In contrast to pitch featured calibration procedures that require separate lateral and vertical reference standards such as gratings and step height structures, the new method includes the use of landmarks, which are well established in calibration and measurement tasks on a larger scale. However, the landmarks applied to the new 3D reference structures are of sub-micrometre size, the so-called ‘nanomarkers’. The nanomarker coordinates are used for a geometrical calibration of the scanning process of SPM as well as of other instrument types such as SEM and CLSM. For that purpose, a parameter estimation routine involving three scale factors and three coupling factors has been developed that allows lateral and vertical calibration in only one sampling step. With this new calibration strategy, we are able to detect deviations of SPM lateral scaling errors as well as coupling effects causing, e.g., a lateral coordinate shift depending on the measured height position of the probe.
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