Diamond-like carbon (DLC) is a metastable form of amorphous carbon with significant sp3 bonding. DLC is a semiconductor with a high mechanical hardness, chemical inertness, and optical transparency. This review will describe the deposition methods, deposition mechanisms, characterisation methods, electronic structure, gap states, defects, doping, luminescence, field emission, mechanical properties and some applications of DLCs. The films have widespread applications as protective coatings in areas, such as magnetic storage disks, optical windows and micro-electromechanical devices (MEMs).

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Diamond-like amorphous carbon

We show that the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations. The model leads to the following characteristic form for the depth dependence of the hardness: H H 0 1+ h ∗ h where H is the hardness for a given depth of indentation, h, H0 is the hardness in the limit of infinite depth and h ∗ is a characteristic length that depends on the shape of the indenter, the shear modulus and H0. Indentation experiments on annealed (111) copper single crystals and cold worked polycrystalline copper show that this relation is well-obeyed. We also show that this relation describes the indentation size effect observed for single crystals of silver. We use this model to derive the following law for strain gradient plasticity: ( σ σ 0 ) 2 = 1 + l χ , where σ is the effective flow stress in the presence of a gradient, σ0 is the flow stress in the absence of a gradient, χ is the effective strain gradient and l a characteristic material length scale, which is, in turn, related to the flow stress of the material in the absence of a strain gradient, l ≈ b( μ σ 0 ) 2 . For materials characterized by the power law σ 0 = σ ref e 1 n , the above law can be recast in a form with a strain-independent material length scale l. ( builtσ σ ref ) 2 = e 2 n + l χ l = b( μ σ ref ) 2 = l ( σ 0 σ ref ) 2 . This law resembles the phenomenological law developed by Fleck and Hutchinson, with their phenomenological length scale interpreted in terms of measurable material parametersbl].

Indentation size effects in crystalline materials: A law for strain gradient plasticity

Couple stress based strain gradient theory for elasticity

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scale structures. In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors. This set enables the application of the higher-order equilibrium conditions to strain gradient elasticity theory and reduces the number of independent elastic length scale parameters from five to three. On the basis of this new strain gradient theory, a strain gradient elastic bending theory for plane-strain beams is developed. Solutions for cantilever bending with a moment and line force applied at the free end are constructed based on the new higher-order bending theory. In classical bending theory, the normalized bending rigidity is independent of the length and thickness of the beam. In the solutions developed from the higher-order bending theory, the normalized higher-order bending rigidity has a new dependence on the thickness of the beam and on a higher-order bending parameter, bh. To determine the significance of the size dependence, we fabricated micron-sized beams and conducted bending tests using a nanoindenter. We found that the normalized beam rigidity exhibited an inverse squared dependence on the beam's thickness as predicted by the strain gradient elastic bending theory, and that the higher-order bending parameter, bh, is on the micron-scale. Potential errors from the experiments, model and fabrication were estimated and determined to be small relative to the observed increase in beam's bending rigidity. The present results indicate that the elastic strain gradient effect is significant in elastic deformation of small-scale structures.

Experiments and theory in strain gradient elasticity

Indentations of micron size into the (100), (110) and (111) surfaces of Mo and W single crystals have been studied using the scanning tunneling microscopy (STM). Results on geometrical parameters of indents are presented and discussed in connection with the mechanism of plastic flow and the indentation size effect.

Microindentations on W and Mo oriented single crystals: An STM study

Grazing-angle x-ray reflectivity (XRR) is described as an efficient, nondestructive, parameter-free means to measure the mass density of various types of amorphous carbon films down to the nanometer thickness range. It is shown how XRR can also detect layering if it is present in the films, in which case the reflectivity profile must be modeled to derive the density. The mass density can also be derived from the valence electron density via the plasmon energy, which is measured by electron energy-loss spectroscopy (EELS). We formally define an interband effective electron mass ${m}^{*},$ which accounts for the finite band gap. Comparison of XRR and EELS densities allows us to fit an average ${m}^{*}=0.87m$ for carbon systems, m being the free-electron mass. We show that, within the Drude-Lorentz model of the optical spectrum, ${m}^{*}=[1\ensuremath{-}{n(0)}^{\ensuremath{-}2}]m,$ where $n(0)$ is the refractive index at zero optical frequency. The fraction of ${\mathrm{sp}}^{2}$ bonding is derived from the carbon K-edge EELS spectrum, and it is shown how a choice of ``magic'' incidence and collection angles in the scanning transmission electron microscope can give ${\mathrm{sp}}^{2}$ fraction values that are independent of sample orientation or anisotropy. We thus give a general relationship between mass density and ${\mathrm{sp}}^{3}$ content for carbon films.

Density, sp 3 fraction, and cross-sectional structure of amorphous carbon films determined by x-ray reflectivity and electron energy-loss spectroscopy

The effect of nitrogen addition on the structural and electronic properties of hydrogenated amorphous carbon (a-C:H) films has been characterized in terms of its composition, sp3 bonding fraction, infrared and Raman spectra, optical band gap, conductivity, and paramagnetic defect. The variation of conductivity with nitrogen content suggests that N acts as a weak donor, with the conductivity first decreasing and then increasing as the Fermi level moves up in the band gap. Compensated behavior is found at about 7 at. % N, for the deposition conditions used here, where a number of properties show extreme behavior. The paramagnetic defect density and the Urbach tailwidth are each found to decrease with increasing N content. It is unusual to find alloy additions decreasing disorder in this manner.

Nitrogen modification of hydrogenated amorphous carbon films

Successful control of the conductivity of tetrahedrally bonded amorphous carbon (ta-C) by incorporation of N during film growth is reported. N is introduced into the films during growth by injecting N 2 gas into a plasma stream formed by a carbon cathodic vacuum arc. X-ray-photoemission-spectroscopy studies of films prepared over a range of N 2 partial pressures show that the N concentration varies from 2% to below the detection limit. Spectroscopic studies using electron-energy-loss spectroscopy confirm that the ta-C films with N contents up to 1 at. % retain their predominantly tetrahedral amorphous structure

Nitrogen doping of highly tetrahedral amorphous carbon

The momentum and energy dependence of the matrix elements for direct and indirect transitions across the band gap is studied both theoretically and experimentally. The accepted theory for the inelastic scattering cross section of fast electrons by condensed matter is extended to show how the nature of a transition can change the shape of the measured energy-loss spectrum in the region of the onset. For the case of direct transitions the matrix element acts only as a multiplicative factor to the joint density of states (JDOS), and so an $(E\ensuremath{-}{E}_{g}{)}^{1/2}$ term is observed in the spectrum. The matrix elements for indirect transitions are shown to be dependent on the momentum transferred by the incident fast electron to the crystal electrons. The product of the indirect matrix element and the JDOS contributes an $(E\ensuremath{-}{E}_{g}{)}^{3/2}$ term to the spectrum. To test this theory it is shown that the matrix-element-weighted joint density of states should be extracted from the electron-energy-loss spectra via a Kramers-Kronig transformation. An objective method is proposed for plotting the data to determine both the principal band gaps and their direct or indirect nature. The method is tested and succeeds in well-known cases. It is now possible with the electron microscope to measure these fundamental electronic properties of semiconductors and insulators accurately by electron spectroscopy.

L. M. Brown

Papers

Microindentations on W and Mo oriented single crystals: An STM study

Density, sp 3 fraction, and cross-sectional structure of amorphous carbon films determined by x-ray reflectivity and electron energy-loss spectroscopy

Nitrogen modification of hydrogenated amorphous carbon films

Nitrogen doping of highly tetrahedral amorphous carbon

Direct and indirect transitions in the region of the band gap using electron-energy-loss spectroscopy