Electron holography of field-emitting carbon nanotubes

Enhancing performance of electron holography with mathematical and machine learning-based denoising techniques

Electron holography is a useful tool for analyzing functional properties, such as electromagnetic fields and strains of materials and devices. The performance of electron holography is limited by the 'shot noise' inherent in electron micrographs (holograms), which are composed of a finite number of electrons. A promising approach for addressing this issue is to use mathematical and machine learning-based image-processing techniques for hologram denoising. With the advancement of information science, denoising methods have become capable of extracting signals that are completely buried in noise, and they are being applied to electron microscopy, including electron holography. However, these advanced denoising methods are complex and have many parameters to be tuned; therefore, it is necessary to understand their principles in depth and use them carefully. Herein, we present an overview of the principles and usage of sparse coding, the wavelet hidden Markov model and tensor decomposition, which have been applied to electron holography. We also present evaluation results for the denoising performance of these methods obtained through their application to simulated and experimentally recorded holograms. Our analysis, review and comparison of the methods clarify the impact of denoising on electron holography research.

Nanoscale Three-Dimensional Charge Density and Electric Field Mapping by Electron Holographic Tomography

The operation of nanoscale electronic devices is related intimately to the three-dimensional (3D) charge density distributions within them. Here, we demonstrate the quantitative 3D mapping of the charge density and long-range electric field associated with an electrically biased carbon fiber nanotip with a spatial resolution of approximately 5 nm using electron holographic tomography in the transmission electron microscope combined with model-based iterative reconstruction. The approach presented here can be applied to a wide range of other nanoscale materials and devices.

Unveiling the Nottingham Inversion Instability during the thermo-field emission from refractory metal micro-protrusions

The electron emission by micro-protrusions has been studied for over a century, but the complete explanation of the unstable behaviors and their origin remains an open issue. These systems often evolve towards vacuum breakdown, which makes experimental studies of instabilities very difficult. Modeling studies are therefore necessary. In our model, refractory metals have shown the most striking results for discontinuities or jumps recorded on the electron emitted current under high applied voltages. Herein, we provide evidence on the mechanisms responsible for the initiation of a thermal instability during the field emission from refractory metal micro-protrusions. A jump in the emission current at steady state is found beyond a threshold electric field, and it is correlated to a similar jump in temperature. These jumps are related to a transient runaway of the resistive heating that occurs after the Nottingham flux inversion. That causes the hottest region to move beneath the apex, and generates an emerging heat reflux towards the emitting surface. Two additional conditions are required to initiate the runaway. The emitter geometry must ensure a large emission area and the thermal conductivity must be high enough at high temperatures so that the heat reflux can significantly compete with the heat diffusion towards the thermostat. The whole phenomenon, that we propose to call the Nottingham Inversion Instability, can explain unexpected thermal failures and breakdowns observed with field emitters.

Probing local order in multiferroics by transmission electron microscopy

The ongoing trend toward miniaturization has led to an increased interest in the magnetoelectric effect, which could yield entirely new device concepts, such as electric field-controlled magnetic data storage. As a result, much work is being devoted to developing new robust room temperature (RT) multiferroic materials that combine ferromagnetism and ferroelectricity. However, the development of new multiferroic devices has proved unexpectedly challenging. Thus, a better understanding of the properties of multiferroic thin films and the relation with their microstructure is required to help drive multiferroic devices toward technological application. This review covers in a concise manner advanced analytical imaging methods based on (scanning) transmission electron microscopy which can potentially be used to characterize complex multiferroic materials. It consists of a first broad introduction to the topic followed by a section describing the so-called phase-contrast methods, which can be used to map the polar and magnetic order in magnetoelectric multiferroics at different spatial length scales down to atomic resolution. Section 3 is devoted to electron nanodiffraction methods. These methods allow measuring local strains, identifying crystal defects and determining crystal structures, and thus offer important possibilities for the detailed structural characterization of multiferroics in the ultrathin regime or inserted in multilayers or superlattice architectures. Thereafter, in Section 4, methods are discussed which allow for analyzing local strain, whereas in Section 5 methods are addressed which allow for measuring local polarization effects on a length scale of individual unit cells. Here, it is shown that the ferroelectric polarization can be indirectly determined from the atomic displacements measured in atomic resolution images. Finally, a brief outlook is given on newly established methods to probe the behavior of ferroelectric and magnetic domains and nanostructures during in situ heating/electrical biasing experiments. These in situ methods are just about at the launch of becoming increasingly popular, particularly in the field of magnetoelectric multiferroics, and shall contribute significantly to understanding the relationship between the domain dynamics of multiferroics and the specific microstructure of the films providing important guidance to design new devices and to predict and mitigate failures.

Single Electron Precision in the Measurement of Charge Distributions on Electrically Biased Graphene Nanotips Using Electron Holography

We use off-axis electron holography to measure the electrostatic charge density distributions on graphene-based nanogap devices that have thicknesses of between 1 and 10 monolayers and separations of between 8 and 58 nm with a precision of better than a single unit charge. Our experimental measurements, which are compared with finite element simulations, show that wider graphene tips, which have thicknesses of a single monolayer at their ends, exhibit charge accumulation along their edges. The results are relevant for both fundamental research on graphene electrostatics and applications of graphene nanogaps to single nucleotide detection in DNA sequencing, single molecule electronics, plasmonic antennae, and cold field emission sources.

Quantitative measurement of nanoscale electrostatic potentials and charges using off-axis electron holography: Developments and opportunities

Off-axis electron holography has evolved into a powerful electron-microscopy-based technique for characterizing electromagnetic fields with nanometer-scale resolution. In this paper, we present a review of the application of off-axis electron holography to the quantitative measurement of electrostatic potentials and charge density distributions. We begin with a short overview of the theoretical and experimental basis of the technique. Practical aspects of phase imaging, sample preparation and microscope operation are outlined briefly. Applications of off-axis electron holography to a wide range of materials are then described in more detail. Finally, challenges and future opportunities for electron holography investigations of electrostatic fields and charge density distributions are presented.

Two-dimensional mapping of the electric field distribution inside vacuum microgaps observed in a scanning electron microscope

In this paper, we present an in-situ measurement method to directly observe the distribution of the local electric field between vacuum microgaps. The measurement was performed in-situ inside a high resolution scanning electron microscope (SEM), and the nature of the local electric field was characterized through secondary electron contrast images with the aid of Rutherford scattering theory. Based on the regular fringes in these contrast images, the distribution of the local electric field could be extracted from the contour lines of the fringes while the magnitude of the local electric field could be evaluated qualitatively by the gradient of the contour lines. The finite element method (FEM) simulation and the three-electrodes imaging experiment were also conducted, and the obtained two-dimensional electric field distribution agreed well with the FEM simulation, suggesting that the in-situ visualization technique could be useful for determining the local field enhancement behavior for various geometrical configurations and microscale structures. A physical mechanism for the local electric field mapping is suggested. This study demonstrates the potential of SEM imaging for obtaining information about the local electric field within microelectronic structures and devices.

Advanced Electron Holography Applied to Electromagnetic Field Study in Materials Science

Advances and applications of electron holography to the study of electromagnetic fields in various functional materials are presented. In particular, the development of split-illumination electron holography, which introduces a biprism in the illumination system of a holography electron microscope, enables highly accurate observations of electromagnetic fields and the expansion of the observable area. First, the charge distributions on insulating materials were studied by using split-illumination electron holography and including a mask in the illumination system. Second, the three-dimensional spin configurations of skyrmion lattices in a helimagnet were visualized by using a high-voltage holography electron microscope. Third, the pinning of the magnetic flux lines in a high-temperature superconductor YBa₂ Cu₃ O_7-y was analyzed by combining electron holography and scanning ion microscopy. Finally, the dynamic accumulation and collective motions of electrons around insulating biomaterial surfaces were observed by utilizing the amplitude reconstruction processes of electron holography.

Phononic Origins of Friction in Carbon Nanotube Oscillators

Phononic coupling can have a significant role in friction between nanoscale surfaces. We find frictional dissipation per atom in carbon nanotube (CNT) oscillators to depend significantly on interface features such as contact area, commensurability, and by end-capping of the inner core. We perform large-scale phonon wavepacket MD simulations to study phonon coupling between a 250 nm long (10,10) outer tube and inner cores of four different geometries. Five different phonon polarizations known to have dominant roles in thermal transport are selected, and transmission coefficient plots for a range of phonon energies along with phonon scattering dynamics at specific energies are obtained. We find that the length of interface affects friction only through LA phonon scattering and has a significant nonlinear effect on total frictional force. Incommensurate contact does not always give rise to superlubricity: the net effect of two competing interaction mechanisms shown by longitudinal and transverse phonons decides the role of commensurability. Capping of the core has no effect on acoustic phonons but destroys the coherence of transverse optical phonons and creates diffusive scattering. In contrast, the twisting and radial breathing phonon modes have perfect transmission at all energies and can be deemed as the enablers of ultralow friction in CNT oscillators. Our work suggests that tuning of interface geometries can give rise to desirable friction properties in nanoscale devices.

The dissipation of field emitting carbon nanotubes in an oxygen environment as revealed by in situ transmission electron microscopy

In this work, we report the first direct experimental observations of carbon nanotubes (CNT) field emitting in an oxygen environment, using aberration-corrected environmental transmission electron microscopy in combination with an electrical biasing specimen holder under low-dose, field-free imaging conditions. Our studies show that while the CNTs remain stable during high vacuum field emission, they experience abrupt decreases in length, also termed "burn-back", when field-emitting in an oxygen environment at around 30 Pa pressure. Furthermore, we perform correlative field-free and aberration-corrected, high-resolution transmission electron microscopy imaging to understand how the structure of the CNTs - particularly the opening of the nanotube caps - is influenced by its gas environment during field emission. This work provides significant insight into the mechanism of carbon nanotube behavior under non-ideal field emission conditions.

Quantitative 3D electromagnetic field determination of 1D nanostructures from single projection

One-dimensional (1D) nanostructures have been regarded as the most promising building blocks for nanoelectronics and nanocomposite material systems as well as for alternative energy applications. Although they result in confinement of a material, their properties and interactions with other nanostructures are still very much three-dimensional (3D) in nature. In this work, we present a novel method for quantitative determination of the 3D electromagnetic fields in and around 1D nanostructures using a single electron wave phase image, thereby eliminating the cumbersome acquisition of tomographic data. Using symmetry arguments, we have reconstructed the 3D magnetic field of a nickel nanowire as well as the 3D electric field around a carbon nanotube field emitter, from one single projection. The accuracy of quantitative values determined here is shown to be a better fit to the physics at play than the value obtained by conventional analysis. Moreover the 3D reconstructions can then directly be visualized and used in the design of functional 3D architectures built using 1D nanostructures.

Calibration for medium resolution off-axis electron holography using a flexible dual-lens imaging system in a JEOL ARM 200F microscope

In this work the calibration of a medium resolution off-axis electron holography using a dual-lens imaging system in a JEOL ARM 200F is shown. The objective dual-lens configuration allows adjusting the field of view from 35nm to 2.5μm. Subsequently, the parameters used in phase shift reconstruction were calibrated considering biprism voltage versus fringe spacing (σ) and versus fringe width (W). The reliability of the transmission electron microscope performance using these parameters was achieved using gold nanoparticles of known size and adjusting the excitation voltage of the lenses.

Diagnosing nanoelectronic components using coherent electrons

We present the direct observation, using off-axis electron holography (EH), of the electric potential distribution in the vicinity of a single carbon nanotube electrically biased by two closely spaced contacts. When our results are combined with finite element modeling, we demonstrate the ability to separately observe the electrostatic potential drops across the metal contacts at the interface with the nanotube and along the length of the nanotube itself. We demonstrate that the uneven resistivity of different contacts can cause an asymmetric EH phase shift, which can readily be identified and quantified. EH thus offers a unique and precise approach for in-depth understanding and quick diagnosis of many similar nanoscale electronic devices.

Quantitative in situ magnetization reversal studies in Lorentz microscopy and electron holography

A generalized procedure for the in situ application of magnetic fields by means of the excitation of the objective lens for magnetic imaging experiments in Lorentz microscopy and electron holography is quantitatively described. A protocol for applying magnetic fields with arbitrary in-plane magnitude and orientation is presented, and a freeware script for Digital Micrograph(™) is provided to assist the operation of the microscope. Moreover, a method to accurately reconstruct hysteresis loops is detailed. We show that the out-of-plane component of the magnetic field cannot be always neglected when performing quantitative measurements of the local magnetization. Several examples are shown to demonstrate the accuracy and functionality of the methods.

In-situ observation and relocation method of nanomaterial samples based on microscope systems

Taking poly(lactic acid) microbubbles and purple membranes as examples, a general in situ observation and relocation method of nanomaterial samples based on microscope systems was reported. First, a four-grade coordinate with different precisions was marked around a substrate by UV lithography. Second, using optical microscope and scanning probe microscope, special positions of poly(lactic acid) microbubbles and purple membranes were observed, respectively. Third, the four-grade coordinate value corresponded to the special sample position, and the distance between the special position and coordinate edge were recorded, respectively. Finally, the special position can be easily found again, or the sample in the special position can be manipulated and secondary processed based on the recorded coordinate value and distance, after the sample was removed and then was reset on the sample stage of microscope. The in situ observation and relocation method can be applied in different microscope systems and different sample substrates, and will have potential applications in the manipulation and the secondary process of micro- and nano-devices.

Dark-field electron holography for the measurement of geometric phase

The genesis, theoretical basis and practical application of the new electron holographic dark-field technique for mapping strain in nanostructures are presented. The development places geometric phase within a unified theoretical framework for phase measurements by electron holography. The total phase of the transmitted and diffracted beams is described as a sum of four contributions: crystalline, electrostatic, magnetic and geometric. Each contribution is outlined briefly and leads to the proposal to measure geometric phase by dark-field electron holography (DFEH). The experimental conditions, phase reconstruction and analysis are detailed for off-axis electron holography using examples from the field of semiconductors. A method for correcting for thickness variations will be proposed and demonstrated using the phase from the corresponding bright-field electron hologram.

Electron tomography and holography in materials science

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.

Site-specific fabrication of Fe particles for carbon nanotube growth

We report a method for site-specific fabrication of Fe catalyst particles on silica (SiO(2)) substrate by electron beam induced decompositionat 650 (EBID) of iron nonacarbonyl. The unobstructed, atomic level in situ observations of the catalyst particles, recorded degrees C in 8-15 mTorr of acetylene, reveal the structural transformations during reduction, sintering, carburization of Fe nanoparticles and subsequent CNT growth.

Direct observation of field emission in a single TaSi2 nanowire

The electric potential change in a single TaSi2 nanowire during field emission was visualized by means of electron holography. During the field emission, the interference fringes of the electron hologram were blurred locally between the TaSi2 nanowire and anode. This phenomenon was interpreted as being due to a change in the electric potential of approximately 1 V in the TaSi2 nanowire after each ballistic emission. The experiments on the single TaSi2 nanowire field emission behavior provide the useful information for understanding the field emission in the nano-field-emitting device.

Electron field emission characteristics and field evaporation of a single carbon nanotube

Direct transmission electron microscope (TEM) observations of the field emission and evaporation process of emitting carbon nanotubes (CNTs) shown that the tip structure of the CNT is in general composed of irregular shaped graphitic sheets which extend typically more than 10 nm from the end of the CNT. It is found that the irregular shaped graphitic sheets at the tip of the CNT may greatly enhance the field emission characteristics of the CNT when compared with that having an ideal circular edge. The field evaporation of the CNT proceeds typically via the removal of the irregular shaped graphitic sheets from the tip of the CNT, and field emission characteristics of a CNT depend far more sensitively on the tip structure than on the geometric length of the CNT.

Technology and metrology of new electronic materials and devices

Scaling of the metal oxide semiconductor (MOS) field-effect transistor has been the basis of the semiconductor industry for nearly 30 years. Traditional materials have been pushed to their limits, which means that entirely new materials (such as high-kappa gate dielectrics and metal gate electrodes), and new device structures are required. These materials and structures will probably allow MOS devices to remain competitive for at least another ten years. Beyond this timeframe, entirely new device structures (such as nanowire or molecular devices) and computational paradigms will almost certainly be needed to improve performance. The development of new nanoscale electronic devices and materials places increasingly stringent requirements on metrology.

In situ transmission electron microscopy observations of individually selected freestanding carbon nanotubes during field emission

For the successful application of carbon nanotubes (CNTs) as electron sources in various applications it is important to understand the relation between the morphology of the CNT and its emission properties. A method was developed to study individual, freestanding and pre-selected CNTs with high-resolution transmission electron microscopy (TEM). The technique provided important parameters of the CNT, such as the number of carbon walls and the nature of its apex. The resolution with which the freestanding apices were imaged depended linearly on the ratio of the length and the radius. CNTs were also imaged in situ in the TEM while emitting electrons. It was found that the structure of a CNT was highly stable below a certain threshold emission current of typically 2 microA, while various structural changes occurred above the threshold, leading to either damaging or repair of the structure at the apex of the CNT.

On the transport of intensity technique for phase retrieval

The Transport of Intensity technique is becoming a viable alternative to electron holography for phase retrieval in Transmission Electron Microscopy. However, several issues are still to be clarified in order to ascertain the applicability of the technique; among them, the controversy regarding its geometrical or wave-optical nature, as related to the phase detection limit. We show here that the Transport of Intensity is a wave-optical technique that works in a special regime of small defocus where the image intensity is linear with the defocus parameter. By a simple analytical example we show that the Transport of Intensity correctly reconstructs the electron optical phase shift even when the phase is smaller than pi, a value defining the boundary between the geometrical and wave approaches. Another example is given, the reconstruction of a phase jump, accompanied with experimental support showing that phase retrieval by Electron Holography and Transport of Intensity techniques yields results in good agreement.

Carbon nanotube electron sources and applications

In this review we give an overview of the present status of research on carbon nanotube (CNT) field emitters and their applications. Several different construction principles of field-emission devices with CNTs are summarized. The emission mechanism is introduced and a detailed overview is given of the measured emission properties and related topics of CNT electron sources. We give also several examples of field-emission devices with CNT electron emitters that are presently being investigated in the academic world as well as in industry. Carbon nanotube electron sources clearly have interesting properties, such as low voltage operation, good stability, long lifetime and high brightness. The most promising applications are the field-emission display and high-resolution electron-beam instruments. But several hurdles remain, such as the manufacture of an electron source or an array of electron sources with exactly the desired properties in a reproducible manner.

Carbon nanotube electrostatic biprism: principle of operation and proof of concept

During in situ transmission electron microscopy (TEM) field emission experiments, carbon nanotubes are observed to strongly diffract the imaging TEM electron beam. We demonstrate that this effect is identical to that of a standard electrostatic biprism. We also demonstrate that the nanotube biprism can be used to capture electron-holographic information.

Quantum-mechanical investigation of field-emission mechanism of a micrometer-long single-walled carbon nanotube

A quantum-mechanical simulation is carried out to investigate the charge distribution and electrostatic potential along a 1 microm long (5,5) single-walled carbon nanotube under realistic field-emission experimental conditions. A single layer of carbon atoms is found sufficient to shield most of the electric field except at the tip where strong field penetration occurs. The penetration leads to a nonlinear decrease of potential barrier for emission, which is equally responsible for the low threshold voltage besides the well-known geometrical field enhancement factor.

Electron field emission properties of closed carbon nanotubes

Recent experiments have shown that carbon nanotubes exhibit excellent electron field emisson properties with high current densities at low electric fields. Here we present theoretical investigations that incorporate geometrical effects and the electronic structure of nanotubes. The electric field is dramatically enhanced near the cap of a nanotube with a large variation of local field distribution. It is found that deviation from linear Fowler-Nordheim behavior occurs due to the variation of the local field in the electron tunneling region. The maximum current per tube is of the order of 10 microA. Local and microscopic aspects of field emission from nanotubes are also presented.