Observation of electrostatic fields by electron holography: The case of reverse-biased p-n junctions

A simple and intuitive model for long-range 3D potential distributions of in-operando TEM-samples: Comparison with electron holographic tomography

Electron holography is a powerful tool to investigate the properties of micro- and nanostructured electronic devices. A meaningful interpretation of the holographic data, however, requires an understanding of the 3D potential distribution inside and outside the sample. Standard approaches to resolve these potential distributions involve projective tilt series and their tomographic reconstruction, in addition to extensive simulations. Here, a simple and intuitive model for the approximation of such long-range potential distributions surrounding a nanostructured coplanar capacitor is presented. The model uses only independent convolutions of an initial potential distribution with a Gaussian kernel, allowing the reconstruction of the entire potential distribution from only one measured projection. By this, a significant reduction of the required computational power as well as a drastically simplified measurement process is achieved, paving the way towards quantitative electron holographic investigation of electrically biased nanostructures.

Measuring Electrical Resistivity at the Nanoscale in Phase-Change Materials

Electrical resistivity is the key parameter in the active regions of many current nanoscale devices, from memristors to resistive random-access memory and phase-change memories. The local resistivity of the materials is engineered on the nanoscale to fit the performance requirements. Phase-change memories, for example, rely on materials whose electrical resistance increases dramatically with a change from a crystalline to an amorphous phase. Electrical characterization methods have been developed to measure the response of individual devices, but they cannot map the local resistance across the active area. Here, we propose a method based on operando electron holography to determine the local resistance within working devices. Upon switching the device, we show that electrical resistance is inhomogeneous on the scale of only a few nanometers.

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.

Quantitative Characterization of Nanometer-Scale Electric Fields via Momentum-Resolved STEM

Most of today's electronic devices, like solar cells and batteries, are based on nanometer-scale built-in electric fields. Accordingly, characterization of fields at such small scales has become an important task in the optimization of these devices. In this study, with GaAs-based p-n junctions as the example, key characteristics such as doping concentrations, polarity, and the depletion width are derived quantitatively using four-dimensional scanning transmission electron microscopy (4DSTEM). The built-in electric fields are determined by the shift they introduce to the center-of-mass of electron diffraction patterns at subnanometer spatial resolution. The method is applied successfully to characterize two p-n junctions with different doping concentrations. This highlights the potential of this method to directly visualize intentional or unintentional nanoscale electric fields in real-life devices, e.g., batteries, transistors, and solar cells.

Interference and interferometry in electron holography

This paper reviews the basics of electron holography as an introduction of the holography part of this special issue in Microscopy. We discuss the general principle of holography and interferometry regarding measurements and analyses of phase distributions, first using the optical holography. Next, we discuss physical phenomena peculiar to electron waves that cannot be realized by light waves and principles of electromagnetic field detection and observation methods. Furthermore, we discuss the interference optical systems of the electron waves and their features, and methods of reconstruction of the phase information from electron holograms, which are essential for realization of practical electron holography. We note that following this review application of electron holography will be discussed in detail in the papers of this special issue.

Simulation-Trained Sparse Coding for High-Precision Phase Imaging in Low-Dose Electron Holography

We broaden the applicability of sparse coding, a machine learning method, to low-dose electron holography by using simulated holograms for learning and validation processes. The holograms, with shot noise, are prepared to generate a model, or a dictionary, that includes basic features representing interference fringes. The dictionary is applied to sparse representations of other simulated holograms with various signal-to-noise ratios (SNRs). Results demonstrate that this approach successfully removes noise for holograms with an extremely small SNR of 0.10, and that the denoised holograms provide the accurate phase distribution. Furthermore, this study demonstrates that the dictionary learned from the simulated holograms can be applied to denoising of experimental holograms of a p-n junction specimen recorded with different exposure times. The results indicate that the simulation-trained sparse coding is suitable for use over a wide range of imaging conditions, in particular for observing electron beam-sensitive materials.

Design of electrostatic phase elements for sorting the orbital angular momentum of electrons

The orbital angular momentum (OAM) sorter is a new electron optical device for measuring an electron's OAM. It is based on two phase elements, which are referred to as the "unwrapper" and "corrector" and are placed in Fourier-conjugate planes in an electron microscope. The most convenient implementation of this concept is based on the use of electrostatic phase elements, such as a charged needle as the unwrapper and a set of electrodes with alternating charges as the corrector. Here, we use simulations to assess the role of imperfections in such a device, in comparison to an ideal sorter. We show that the finite length of the needle and the boundary conditions introduce astigmatism, which leads to detrimental cross-talk in the OAM spectrum. We demonstrate that an improved setup comprising three charged needles can be used to compensate for this aberration, allowing measurements with a level of cross-talk in the OAM spectrum that is comparable to the ideal case.

Accurate measurement of electric potentials in biased GaAs compound semiconductors by phase-shifting electron holography

The innate electric potentials in biased p- and n-type GaAs compound semiconductors and the built-in potential were successfully measured with high accuracy and precision by applying in situ phase-shifting electron holography to a wedge-shaped GaAs specimen. A cryo-focused-ion-beam system was used to prepare the 35°-wedge-shaped specimen with smooth surfaces for a precise measurement. The specimen was biased in a transmission electron microscope, and holograms with high-contrast interference fringes were recorded for the phase-shifting method. A clear phase image around the p-n junction was reconstructed even in a thick region (thickness of ~700 nm) at a spatial resolution of 1 nm and precision of 0.01 rad. The innate electric potentials of the unbiased p- and n-type layers were measured to be 12.96 ± 0.17 V and 14.43 ± 0.19 V, respectively. The built-in potential was determined to be 1.48 ± 0.02 V. In addition, the in situ biasing measurement revealed that the measured electric-potential difference between the p and n regions changed by an amount equal to the voltage applied to the specimen, which indicates that all of the external voltage was applied to the p-n junction and that no voltage loss occurred at the other regions.

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 techniques for in situ observation of solid-state lithium ion conductors

Advanced techniques for overcoming problems encountered during in situ electron holography experiments in which a voltage is applied to an ionic conductor are reported. The three major problems encountered were 1) electric-field leakage from the specimen and its effect on phase images, 2) high electron conductivity of damage layers formed by the focused ion beam method, and 3) chemical reaction of the specimen with air. The first problem was overcome by comparing experimental phase distributions with simulated images in which three-dimensional leakage fields were taken into account, the second by removing the damage layers using a low-energy narrow Ar ion beam, and the third by developing an air-tight biasing specimen holder.

Restoration of singularities in reconstructed phase of crystal image in electron holography

Off-axis electron holography can be used to measure the inner potential of a specimen from its reconstructed phase image and is thus a powerful technique for materials scientists. However, abrupt reversals of contrast from white to black may sometimes occur in a digitally reconstructed phase image, which results in inaccurate information. Such phase distortion is mainly due to the digital reconstruction process and weak electron wave amplitude in some areas of the specimen. Therefore, digital image processing can be applied to the reconstruction and restoration of phase images. In this paper, fringe reconnection processing is applied to phase image restoration of a crystal structure image. The disconnection and wrong connection of interference fringes in the hologram that directly cause a 2π phase jump imperfection are correctly reconnected. Experimental results show that the phase distortion is significantly reduced after the processing. The quality of the reconstructed phase image was improved by the removal of imperfections in the final phase.

Direct observation of dopant distribution in GaAs compound semiconductors using phase-shifting electron holography and Lorentz microscopy

Phase-shifting electron holography and Lorentz microscopy were used to map dopant distributions in GaAs compound semiconductors with step-like dopant concentration. Transmission electron microscope specimens were prepared using a triple beam focused ion beam (FIB) system, which combines a Ga ion beam, a scanning electron microscope, and an Ar ion beam to remove the FIB damaged layers. The p-n junctions were clearly observed in both under-focused and over-focused Lorentz microscopy images. A phase image was obtained by using a phase-shifting reconstruction method to simultaneously achieve high sensitivity and high spatial resolution. Differences in dopant concentrations between 1 × 10(19) cm(-3) and 1 × 10(18) cm(-3) regions were clearly observed by using phase-shifting electron holography. We also interpreted phase profiles quantitatively by considering inactive layers induced by ion implantation during the FIB process. The thickness of an inactive layer at different dopant concentration area can be measured from the phase image.

Phase contrast image simulations for electron holography of magnetic and electric fields

The research on flux line lattices and pancake vortices in superconducting materials, carried out within a long and fruitful collaboration with Akira Tonomura and his group at the Hitachi Advanced Research Laboratory, led us to develop a mathematical framework, based on the reciprocal representation of the magnetic vector potential, that enables us to simulate realistic phase images of fluxons. The aim of this paper is to review the main ideas underpinning our computational framework and the results we have obtained throughout the collaboration. Furthermore, we outline how to generalize the approach to model other samples and structures of interest, in particular thin ferromagnetic films, ferromagnetic nanoparticles and p-n junctions.

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.

Mapping the electrical properties of semiconductor junctions--the electron holographic approach

The need to determine the electrical properties of semiconductor junctions with high spatial resolution is as pressing now as ever. One technique that offers the possibility of quantitative high-resolution mapping of two- and three-dimensional electrostatic potential distributions is off-axis electron holography. In this study, we review some of the issues associated with interpreting phase shifts measured using off-axis electron holography, and we describe how a quantitative determination of the dopant-related electrostatic potential can be achieved for device structures. Issues that include the presence of surface "dead" layers, external electrostatic fringing fields, variations in specimen thickness and dynamical diffraction are discussed, and their impact on the quantification of results obtained using off-axis electron holography is examined.

On specimen tilt for electron holography of semiconductor devices

Electron holography can be successfully used for potential mapping on a nanometer scale. It relies on the fact that the phase of the electron wave is proportional to the electrostatic potential in the specimen. However, this proportionality is valid only in a kinematical condition, which is achieved by proper specimen orientation with respect to the electron beam. In this report, we examine experimentally in detail the specimen orientations of silicon devices that minimize dynamical diffraction. The tilt of the specimen from the edge-on position to a favorable orientation causes certain interfaces in the specimen to smear. We describe the smearing by a transfer function and compare it to wave transfer function of the microscope. The maximal specimen tilt alphamax that does not cause smearing greater than the resolution r of the microscope is alphamax = arctan(5.70r/t), where t is the specimen thickness.

Specimen preparation for electron holography of semiconductor devices

A reliable and quick method of preparing specimens for electron holography of semiconductor devices is described in detail. The method is based on conventional mechanical grinding and polishing, and argon-ion milling, providing a large ( approximately 100 microm) area of electron transparency, no curtaining and thin dead layers on the surfaces of specimens. The vacuum area, necessary for the reference wave, is cut into the specimen by a focused ion beam. The advantages and disadvantages are discussed. The method has a yield greater than 90%, of tests of more than 20 specimens of MOS transistors.

Semiconductor dopant profiling by off-axis electron holography

Silicon wafers with a complex but known dopant profile were used to explore possible methods for improving the reliability of off-axis electron holography for quantitative determination of electrostatic potential profiles in doped semiconductor devices. The variability of results from nominally identical structures was attributed to local charging and associated external fields, forcing the development of a more robust approach to hologram analysis that incorporated an additional phase correction factor rather than rely on vacuum for phase flattening. Consistent results in close agreement with simulated profiles based on measured dopant distributions could then be obtained. Carbon coating was shown to be effective in reducing accumulation of charge caused by emission of secondary electrons. Overall, this work demonstrates that reliable potential profiles from unbiased samples should be obtainable on a routine basis provided that regions suitable for flattening of the phase profile can be identified.

Quantitative electron holography of biased semiconductor devices

Electron holography is used to measure electrostatic potential profiles across reverse-biased Si p-n junctions in situ in the transmission electron microscope. A novel sample geometry based on focused ion-beam milling is developed, and results are obtained for a range of sample thicknesses and bias voltages to allow the holographic contrast to be interpreted. The physical and electrical nature of the sample surface, which is affected by sample preparation and electron beam irradiation, is discussed.

An introduction to off-axis electron holography

The technique of off-axis electron holography is introduced and reviewed. The history of the topic is discussed briefly looking at the origin of electron holography and the reasons for its growth in recent years around the world. The formation and numerical reconstruction of the hologram is discussed in detail on a theoretical and practical level. The spread of holography is illustrated through a number of applications ranging from ultra high resolution studies of crystal structures, the imaging of magnetic and electric fields, the determination of sample composition and morphology and the use of holography for imaging biological specimens.