Marco Beleggia

Dipolar Magnetism in Ordered and Disordered Low-Dimensional Nanoparticle Assemblies

Magnetostatic (dipolar) interactions between nanoparticles promise to open new ways to design nanocrystalline magnetic materials and devices if the collective magnetic properties can be controlled at the nanoparticle level. Magnetic dipolar interactions are sufficiently strong to sustain magnetic order at ambient temperature in assemblies of closely-spaced nanoparticles with magnetic moments of ≥ 100 μB. Here we use electron holography with sub-particle resolution to reveal the correlation between particle arrangement and magnetic order in self-assembled 1D and quasi-2D arrangements of 15 nm cobalt nanoparticles. In the initial states, we observe dipolar ferromagnetism, antiferromagnetism and local flux closure, depending on the particle arrangement. Surprisingly, after magnetic saturation, measurements and numerical simulations show that overall ferromagnetic order exists in the present nanoparticle assemblies even when their arrangement is completely disordered. Such direct quantification of the correlation between topological and magnetic order is essential for the technological exploitation of magnetic quasi-2D nanoparticle assemblies.

Convenient contrast enhancement by a hole-free phase plate

Decrease of the irradiation dose needed to obtain a desired signal-to-noise ratio can be achieved by Zernike phase-plate imaging. Here we present results on a hole-free phase plate (HFPP) design that uses the incident electron beam to define the center of the plate, thereby eliminating the need for high precision alignment and with advantages in terms of ease of fabrication. The Zernike-like phase shift is provided by a charge distribution induced by the primary beam, rather than by a hole in the film. Compared to bright-field Fresnel-mode imaging, the hole-free phase plate (HFPP) results in two- to four-fold increase in contrast, leading to a corresponding decrease in the irradiation dose required to obtain a desired signal-to-noise ratio. A local potential distribution, developed due to electron beam-induced secondary-electron emission, is the most likely mechanism responsible for the contrast-transfer properties of the HFPP.

Direct measurement of the charge distribution along a biased carbon nanotube bundle using electron holography

Nanowires and nanotubes can be examined in the transmission electron microscope under an applied bias. Here we introduce a model-independent method, which allows the charge distribution along a nanowire or nanotube to be measured directly from the Laplacian of an electron holographic phase image. We present results from a biased bundle of carbon nanotubes, in which we show that the charge density increases linearly with distance from its base, reaching a value of ∼0.8 electrons/nm near its tip.

Magnetostatics of the uniformly polarized torus

We provide an exhaustive description of the magnetostatics of the uniformly polarized torus and its derivative self-intersecting (spindle) shapes. In the process, two complementary approaches have been implemented, position-space analysis of the Laplace equation with inhomogeneous boundary conditions and a Fourier-space analysis, starting from the determination of the shape amplitude of this topologically non-trivial body. The stray field and the demagnetization tensor have been determined as rapidly converging series of toroidal functions. The single independent demagnetization-tensor eigenvalue has been determined as a function of the unique aspect ratio α of the torus. Throughout the range of values of the ratio, corresponding to a multiply connected torus proper, the axial demagnetization factor Nz remains close to one half. There is no breach of smoothness of Nz(α) at the topological crossover to a simply connected tight torus (α=1). However, Nz is a non-monotonic function of the aspect ratio, such that substantially different pairs of corresponding tori would still have the same demagnetization factor. This property does not occur in a simply connected body of the same continuous axial symmetry. Several self-suggesting practical applications are outlined, deriving from the acquired quantitative insight.

A formula for the image intensity of phase objects in Zernike mode.

I present an analytical expression for the image intensity of a phase object visualized in Zernike phase contrast mode. The formula is valid for periodic and non-periodic weak and strong objects, and accounts for the effects of finite illumination. The expression provided is intended as a generalization of the standard reference formula given in the Born and Wolf [Principles of Optics, sixth ed., Pergamon Press, New York, 1980, p. 427] textbook as well as of the formalism employed to evaluate imaging doses in Zernike mode [M. Malac, M. Beleggia, R. Egerton, Y. Zhu, Ultramicroscopy 108 (2008) 126]. I illustrate the usefulness of the improved expression by means of three examples: a sinusoidal phase grating, a Gaussian object, and a phase step. The optimal Zernike phase angle yielding maximum image contrast is found to be object-dependent and not necessarily equal to pi/2. Phase plate optimization criteria are derived and presented for two of the examples considered.

Towards quantitative electrostatic potential mapping of working semiconductor devices using off-axis electron holography

Pronounced improvements in the understanding of semiconductor device performance are expected if electrostatic potential distributions can be measured quantitatively and reliably under working conditions with sufficient sensitivity and spatial resolution. Here, we employ off-axis electron holography to characterize an electrically-biased Si p-n junction by measuring its electrostatic potential, electric field and charge density distributions under working conditions. A comparison between experimental electron holographic phase images and images obtained using three-dimensional electrostatic potential simulations highlights several remaining challenges to quantitative analysis. Our results illustrate how the determination of reliable potential distributions from phase images of electrically biased devices requires electrostatic fringing fields, surface charges, specimen preparation damage and the effects of limited spatial resolution to be taken into account.

Direct Evidence of the Anisotropic Structure of Vortices Interacting with Columnar Defects in High-Temperature Superconductors through the Analysis of Lorentz Images

Two types of Fresnel contrasts of superconducting vortices in a Lorentz micrograph, corresponding to pinned and unpinned vortices, were obtained by a newly developed 1 MV field-emission transmission electron microscope on a Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212) thin specimen containing tilted linear columnar defects introduced by heavy ion irradiation. The main features of the Fresnel contrasts could be consistently interpreted by assuming that the vortices are pinned along the tilted columnar defects and by using a layered or an anisotropic model to calculate the phase shift of the electron wave. The confirmed validity of both models strongly indicates that superconducting vortices in high-critical temperature (high- T c ) layered materials have an anisotropic structure.

Electron Holography of Magnetic Materials

Transmission electron microscopy (TEM) involves the use of high-energy (60-3000 keV) electrons that have passed through a thin specimen to record images, diffraction patterns or spectroscopic information from a region of interest. Many different TEM techniques have been developed over the years into highly sophisticated methodologies that have found widespread application across scientific disciplines. Because the TEM has an unparalleled ability to provide structural and chemical information over a range of length scales down to atomic dimensions, it has developed into an indispensable tool for scientists who are interested in understanding the properties of nanostructured materials and in manipulating their behavior (Smith, 2007). State-of-the-art TEMs are now equipped with spherical and chromatic aberration correctors and can provide interpretable image resolutions of 0.05 nm (Erni et al., 2009). However, in addition to conventional TEM techniques that can be used to provide structural and compositional information about materials, the TEM also allows magnetic and electrostatic fields in specimens to be imaged with nanometer spatial resolution. One of the most powerful techniques for providing this information is electron holography, which was originally proposed as a means to compensate for lens aberrations and to improve electron microscope resolution (Gabor, 1949). Electron holography is still the only technique that provides direct access to the phase shift of the electron wave that has passed through a thin specimen, in contrast to more conventional TEM techniques that record only spatial distributions of image intensity. Electron holography has only recently become widely available on commercial electron microscopes. The earliest studies using electron holography were restricted by the limited brightness and coherence of the tungsten filaments that were used as electron sources (Haine & Mulvey, 1952). The availability of high brightness, stable, coherent field emission electron guns now allows electron holography to be applied to a wide variety of materials such as quantum well structures, magnetic thin films, semiconductor devices, natural rocks and biominerals.

Towards quantitative off-axis electron holographic mapping of the electric field around the tip of a sharp biased metallic needle

We apply off-axis electron holography and Lorentz microscopy in the transmission electron microscope to map the electric field generated by a sharp biased metallic tip. A combination of experimental data and modelling provides quantitative information about the potential and the field around the tip. Close to the tip apex, we measure a maximum field intensity of 82 MV/m, corresponding to a field k factor of 2.5, in excellent agreement with theory. In order to verify the validity of the measurements, we use the inferred charge density distribution in the tip region to generate simulated phase maps and Fresnel (out-of-focus) images for comparison with experimental measurements. While the overall agreement is excellent, the simulations also highlight the presence of an unexpected astigmatic contribution to the intensity in a highly defocused Fresnel image, which is thought to result from the geometry of the applied field.

Low-dose performance of parallel-beam nanodiffraction

We evaluate the low-dose performance of parallel nano-beam diffraction (NBD) in the transmission electron microscope as a method for characterizing radiation sensitive materials at low electron irradiation dose. A criterion, analogous to Roses, is established for detecting a diffraction spot with desired signal-to-noise ratio. Our experimental data show that a dose substantially lower than in high-resolution bright-field imaging is sufficient to determine structure and orientation of individual nanoscale objects embedded in amorphous matrix. In an instrument equipped with a cold field-emission gun it is possible to form a probe with sub-3 nm diameter and sub-0.3 mrad convergence angle with sufficient beam current to record a diffraction pattern with less than 0.2 s acquisition time. The interpretation of NBD patterns is identical to that of selected area diffraction patterns. We illustrate the physical principles underlying good low-dose performance of NBD by means of a phase grating. The electron irradiation dose needed to detect a diffraction peak in NBD is found proportional to 1/N2, where N is the number of lattice planes contributing to the peak.