Sebastien Ducourtieux

Flake thickness is one of the defining properties of graphene-related 2D materials (GR2Ms), and therefore requires reliable, accurate, and reproducible measurements with well-understood uncertainties. This is needed regardless of the production method or manufacturer because it is important for all GR2M products to be globally comparable. An international interlaboratory comparison on thickness measurements of graphene oxide flakes using atomic force microscopy has been completed in technical working area 41 of versailles project on advanced materials and standards. Twelve laboratories participated in the comparison project, led by NIM, China, to improve the equivalence of thickness measurement for two-dimensional flakes. The measurement methods, uncertainty evaluation and a comparison of the results and analysis are reported in this manuscript. The data and results of this project will be directly used to support the development of an ISO standard.

In order to evaluate the uncertainty budget of the LNE’s mAFM, a reference instrument dedicated to the calibration of nanoscale dimensional standards, a numerical model has been developed to evaluate the measurement uncertainty of the metrology loop involved in the XYZ positioning of the tip relative to the sample. The objective of this model is to overcome difficulties experienced when trying to evaluate some uncertainty components which cannot be experimentally determined and more specifically, the one linked to the geometry of the metrology loop. The model is based on object-oriented programming and developed under Matlab. It integrates one hundred parameters that allow the control of the geometry of the metrology loop without using analytical formulae. The created objects, mainly the reference and the mobile prism and their mirrors, the interferometers and their laser beams, can be moved and deformed freely to take into account several error sources. The Monte Carlo method is then used to determine the positioning uncertainty of the instrument by randomly drawing the parameters according to their associated tolerances and their probability density functions (PDFs). The whole process follows Supplement 2 to ‘The Guide to the Expression of the Uncertainty in Measurement’ (GUM). Some advanced statistical tools like Morris design and Sobol indices are also used to provide a sensitivity analysis by identifying the most influential parameters and quantifying their contribution to the XYZ positioning uncertainty. The approach validated in the paper shows that the actual positioning uncertainty is about 6 nm. As the final objective is to reach 1 nm, we engage in a discussion to estimate the most effective way to reduce the uncertainty.

This article reports on the evaluation of an uncertainty budget associated with the measurement of the mean diameter of a nanoparticle (NP) population by Atomic Force Microscopy. The measurement principle consists in measuring the height of a spherical-like NP population to determine the mean diameter and the size distribution. This method assumes that the NPs are well-dispersed on the substrate and isolated enough to avoid measurement errors due to agglomeration phenomenon. Since the measurement is directly impacted by the substrate roughness, the NPs have been deposited on a mica sheet presenting a very low roughness. A complete metrological characterization of the instrument has been carried out and the main error sources have been evaluated. The measuring method has been tested on a population of SiO ₂ NPs. Homemade software has been used to build the height distribution histogram taking into account only isolated NP. Finally, the uncertainty budget including main components has been established for the mean diameter measurement of this NP population. The most important components of this uncertainty budget are the calibration process along Z -axis, the scanning speed influence and then the vertical noise level.

In the frame of developing a thermally passive atomic force microscope head, a new kind of 2D displacement sensor based on a four quadrant optic fibre bundle has been implemented. The aim is to replace the quad cell photodiode used in the optical beam deflection method to detect cantilever deflection. The use of the bundle as a position sensor has already been modelled and experimentally evaluated in a previous work. This article reports on the implementation of the bundle as a deflection sensor for atomic force microscopy. The main motivation for such a development was to reduce the heat sources in the instrument. To reach this goal the photodiode and its conditioning circuit used for the measurement of cantilever deflection has been externalized from the AFM head. For the same reason, the laser diode and its electronic driver have been deported using optic fibre. To test the AFM head prototype in real conditions, approach curves and AFM images have been performed. The results show that the bundle is very well suited for AFM applications that require very low heat sources such as metrological AFM where each error source has to be managed.

This article is the first step in the development of a hybrid metrology combining AFM and SEM techniques for measuring the dimensions of a nanoparticle population in 3D space ( X , Y , Z ). This method exploits the strengths of each technique on the same set of nanoparticles. AFM is used for measuring the nanoparticle height and the measurements along X and Y axes are deduced from SEM images. A sampling method is proposed in order to obtain the best deposition conditions of SiO ₂ and gold nanoparticles on mica or silicon substrates. Only the isolated nanoparticles are taken into account in the histogram of size distribution. Moreover, a semi-automatic Matlab routine has also been developed to process the AFM and SEM images, measure and count the nanoparticles. This routine allows the user to exclusively select the isolated nanoparticles through a control interface. The measurements have been performed on spherical-like nanoparticles to test the method by comparing the results obtained with both techniques.

We report on the observation of strong backscattering of charge carriers in the quantum Hall regime of polycrystalline graphene, grown by chemical vapor deposition, which alters the accuracy of the Hall resistance quantization. The temperature and magnetic field dependence of the longitudinal conductance exhibits unexpectedly smooth power-law behaviors, which are incompatible with a description in terms of variable range hopping or thermal activation but rather suggest the existence of extended or poorly localized states at energies between Landau levels. Such states could be caused by the high density of line defects (grain boundaries and wrinkles) that cross the Hall bars, as revealed by structural characterizations. Numerical calculations confirm that quasi-one-dimensional extended nonchiral states can form along such line defects and short circuit the Hall bar chiral edge states.

We report on a study of the quantum Hall effect in large area Hall bars made of polycrystalline graphene grown by chemical vapor deposition and then transferred on SiO ₂ /Si substrate. The longitudinal conductivity σ _xx measured near Landau Level filling factors ±2, ±6 evidences a strong backscattering of carriers even at T=0.3 K and B=19 T. It results that the Hall resistance is not quantized at the metrological level. σ _xx increases (decreases) as a function of the temperature (magnetic induction) following unexpected power laws that are not compatible with usual backscattering mechanisms like variable range hopping or inter-Landau level activation. With the support of structural characterizations and numerical simulations, we discuss the role of line defects (wrinkles and grain boundaries) crossing the Hall bar which can short-circuit the counter-propagating edge states.