An introduction to the transport properties of graphene combining experimental results and theoretical analysis is presented. In the theoretical description simple intuitive models are used to illustrate important points on the transport properties of graphene. The concept of chirality, stemming from the massless Dirac nature of the low energy physics of the material, is shown to be instrumental in understanding its transport properties: the conductivity minimum, the electronic mobility, the effect of strain, the weak (anti-)localization, and the optical conductivity.

Colloquium: The transport properties of graphene: An introduction

The rapid development of electron tomography, in particular the introduction of novel tomographic imaging modes, has led to the visualization and analysis of three-dimensional structural and chemical information from materials at the nanometre level. In addition, the phase information revealed in electron holograms allows electrostatic and magnetic potentials to be mapped quantitatively with high spatial resolution and, when combined with tomography, in three dimensions. Here we present an overview of the techniques of electron tomography and electron holography and demonstrate their capabilities with the aid of case studies that span materials science and the interface between the physical sciences and the life sciences.

Electron tomography and holography in materials science

It has been possible to produce photon vortex beams — optical beams with spiralling wavefronts — for some time, and they have found widespread application as optical tweezers, in interferometry and in information transfer, for example. The production of vortex beams of electrons was demonstrated earlier this year (
 http://go.nature.com/4H2xWR
 ) in a procedure involving the passage of electrons through a spiral stack of graphite thin films. The ability to generate such beams reproducibly in a conventional electron microscope would enable many new applications. Now Jo Verbeeck and colleagues have taken a step towards that goal. They describe a versatile holographic technique for generating these twisted electron beams, and demonstrate their potential use as probes of a material's magnetic properties. It was demonstrated recently that passing electrons through a spiral stack of graphite thin films generates an electron beam with orbital angular momentum — analogous to the spiralling wavefronts that can be introduced in photon beams and which have found widespread application. Here, a versatile holographic technique for generating these twisted electron beams is described. Moreover, a demonstration is provided of their potential use in probing a material's magnetic properties. Vortex beams (also known as beams with a phase singularity) consist of spiralling wavefronts that give rise to angular momentum around the propagation direction. Vortex photon beams are widely used in applications such as optical tweezers to manipulate micrometre-sized particles and in micro-motors to provide angular momentum1,2, improving channel capacity in optical3 and radio-wave4 information transfer, astrophysics5 and so on6. Very recently, an experimental realization of vortex beams formed of electrons was demonstrated7. Here we describe the creation of vortex electron beams, making use of a versatile holographic reconstruction technique in a transmission electron microscope. This technique is a reproducible method of creating vortex electron beams in a conventional electron microscope. We demonstrate how they may be used in electron energy-loss spectroscopy to detect the magnetic state of materials and describe their properties. Our results show that electron vortex beams hold promise for new applications, in particular for analysing and manipulating nanomaterials, and can be easily produced.

Production and application of electron vortex beams

The understanding and management of strain is of fundamental importance in the design and implementation of materials. The strain properties of nanocrystalline materials are different from those of the bulk because of the strong influence of their surfaces and interfaces, which can be used to augment their function and introduce desirable characteristics. Here we explain how new X-ray diffraction techniques, which take advantage of the latest synchrotron radiation sources, can be used to obtain quantitative three-dimensional images of strain. These methods will lead, in the near future, to new knowledge of how nanomaterials behave within active devices and on unprecedented timescales.

Coherent X-ray diffraction imaging of strain at the nanoscale.

Nanoporous anodic aluminium oxide: Advances in surface engineering and emerging applications

Strained silicon is now an integral feature of the latest generation of transistors and electronic devices because of the associated enhancement in carrier mobility. Strain is also expected to have an important role in future devices based on nanowires and in optoelectronic components. Different strategies have been used to engineer strain in devices, leading to complex strain distributions in two and three dimensions. Developing methods of strain measurement at the nanoscale has therefore been an important objective in recent years but has proved elusive in practice: none of the existing techniques combines the necessary spatial resolution, precision and field of view. For example, Raman spectroscopy or X-ray diffraction techniques can map strain at the micrometre scale, whereas transmission electron microscopy allows strain measurement at the nanometre scale but only over small sample areas. Here we present a technique capable of bridging this gap and measuring strain to high precision, with nanometre spatial resolution and for micrometre fields of view. Our method combines the advantages of moire techniques with the flexibility of off-axis electron holography and is also applicable to relatively thick samples, thus reducing the influence of thin-film relaxation effects.

Nanoscale holographic interferometry for strain measurements in electronic devices

Aberration-corrected high-resolution transmission electron microscopy (HRTEM) is used to measure strain in a strained-silicon metal-oxide-semiconductor field-effect transistor. Strain components parallel and perpendicular to the gate are determined directly from the HRTEM image by geometric phase analysis. ${\mathrm{Si}}_{80}{\mathrm{Ge}}_{20}$ source and drain stressors lead to uniaxial compressive strain in the Si channel, reaching a maximum value of $\ensuremath{-}1.3%$ just below the gate oxide, equivalent to 2.2 GPa. Strain maps obtained by linear elasticity theory, modeled with the finite-element method, agree with the experimental results to within 0.1%.

/pdf/direct-mapping-of-strain-in-a-strained-silicon-transistor-by-4zf8jvpgnp.pdf

Direct mapping of strain in a strained silicon transistor by high-resolution electron microscopy.

We present a derivation of the orbital and spin sum rules for magnetic circular dichroic spectra measured by electron energy loss spectroscopy in a transmission electron microscope. These sum rules are obtained from the differential cross section calculated for symmetric positions in the diffraction pattern. Orbital and spin magnetic moments are expressed explicitly in terms of experimental spectra and dynamical diffraction coefficients. We estimate the ratio of spin to orbital magnetic moments and discuss first experimental results for the Fe ${L}_{2,3}$ edge.

/pdf/experimental-application-of-sum-rules-for-electron-energy-drxbumuyvr.pdf

Experimental application of sum rules for electron energy loss magnetic chiral dichroism

Quantitative analysis of HOLZ line splitting in CBED patterns of epitaxially strained layers

https://hal.archives-ouvertes.fr/hal-00678407/document

Florent Houdellier

Papers

Nanoscale holographic interferometry for strain measurements in electronic devices

Direct mapping of strain in a strained silicon transistor by high-resolution electron microscopy.

Experimental application of sum rules for electron energy loss magnetic chiral dichroism

Quantitative analysis of HOLZ line splitting in CBED patterns of epitaxially strained layers

New carbon cone nanotip for use in a highly coherent cold field emission electron microscope