Electron holographic observations of the electrostatic field associated with thin reverse-biased p-n junctions

How space-charge behaviour at grain boundaries in electroceramic oxides is modified by two restricted equilibria

Determining the space-charge potential at grain boundaries in oxides by various experimental methods bears the promise of providing a comprehensive, quantitative description of interfacial defect chemistry. In this study, we draw attention to the problem of unifying data measured in different temperature ranges. We focus on unifying data from elevated-temperature electrical methods, such as impedance spectroscopy and current-voltage measurements, with data from room-temperature imaging techniques, such as Scanning Probe Microscopy (SPM), Transmission Electron Microscopy (TEM), and Atom Probe Tomography (APT). By means of continuum simulations, we calculate the space-charge potential Φ0 at grain boundaries in the model electroceramic oxide acceptor-doped SrTiO3, taking into account, first, a restricted equilibrium that leads to frozen-in acceptor-dopant profiles, and subsequently, a restricted equilibrium that leads to frozen-in bulk oxygen-vacancy concentrations. Our results indicate non-trivial differences between experimental values of Φ0 obtained from electrical and from imaging methods, differences that arise from the different measurement temperatures and that are aggravated by the restricted equilibria. We also show that grain-boundary widths determined from elemental acceptor-cation profiles will not, on principle, agree with the electrical width extracted from impedance spectroscopy data.

Low-dose measurement of electric potential distribution in organic light-emitting diode by phase-shifting electron holography with 3D tensor decomposition

To improve the performance of organic light-emitting diodes (OLEDs), it is essential to understand and control the electric potential in the organic semiconductor layers. Electron holography (EH) is a powerful technique for visualizing the potential distribution with a transmission electron microscope. However, it has a serious issue that high-energy electrons may damage the organic layers, meaning that a low-dose EH is required. Here, we used a machine learning technique, three-dimensional (3D) tensor decomposition, to denoise electron interference patterns (holograms) of bilayer OLEDs composed of N,N'-di-[(1-naphthyl)-N,N'-diphenyl]-(1,1'-biphenyl)-4,4'-diamine (α-NPD) and tris-(8-hydroxyquinoline)aluminum (Alq3), acquired under a low-dose rate of 130 e- nm-2 s-1. The effect of denoising on the phase images reconstructed from the holograms was evaluated in terms of both the phase measurement error and the peak signal-to-noise ratio. We achieved a precision equivalent to that of a conventional measurement that had an exposure time 60 times longer. The electric field within the Alq3 layer decreased as the cumulative dose increased, which indicates that the Alq3 layer was degraded by the electron irradiation. On the basis of the degradation of the electric field, we concluded that the tolerance dose without damaging the OLED sample is about 1.7 × 105 e- nm-2, which is about 0.6 times that of the conventional EH. The combination of EH and 3D tensor decomposition denoising is capable of making a time series measurement of an OLED sample without any effect from the electron irradiation.

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.

Extended Charge Layers in Metal-Oxide-Semiconductor Nanocapacitors Revealed by Operando Electron Holography

The metal-oxide-semiconductor (MOS) capacitor is one of the fundamental electrical components used in integrated circuits. While much effort is currently being made to integrate new dielectric or ferroelectric materials, capacitors of silicon dioxide on silicon remain the most prevalent. It is perhaps surprising therefore that the electric field within such a capacitor has never been measured, or mapped out, at the nanoscale. Here we present results from operando electron holography experiments showing the electric potential across a working MOS nanocapacitor with unprecedented sensitivity and reveal unexpected charging of the dielectric material bordering the electrodes.

Phase-shifting electron holography for accurate measurement of potential distributions in organic and inorganic semiconductors

Phase-shifting electron holography (PS-EH) is an interference transmission electron microscopy technique that accurately visualizes potential distributions in functional materials, such as semiconductors. In this paper, we briefly introduce the features of the PS-EH that overcome some of the issues facing the conventional EH based on Fourier transformation. Then, we present a high-precision PS-EH technique with multiple electron biprisms and a sample preparation technique using a cryo-focused-ion-beam, which are important techniques for the accurate phase measurement of semiconductors. We present several applications of PS-EH to demonstrate the potential in organic and inorganic semiconductors and then discuss the differences by comparing them with previous reports on the conventional EH. We show that in situ biasing PS-EH was able to observe not only electric potential distribution but also electric field and charge density at a GaAs p-n junction and clarify how local band structures, depletion layer widths and space charges changed depending on the biasing conditions. Moreover, the PS-EH clearly visualized the local potential distributions of two-dimensional electron gas layers formed at AlGaN/GaN interfaces with different Al compositions. We also report the results of our PS-EH application for organic electroluminescence multilayers and point out the significant potential changes in the layers. The proposed PS-EH enables more precise phase measurement compared to the conventional EH, and our findings introduced in this paper will contribute to the future research and development of high-performance semiconductor materials and devices.

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.

Visualization of different carrier concentrations in n-type-GaN semiconductors by phase-shifting electron holography with multiple electron biprisms

Phase-shifting electron holography (PS-EH) using a transmission electron microscope (TEM) was applied to visualize layers with different concentrations of carriers activated by Si (at dopant levels of 1019, 1018, 1017 and 1016 atoms cm-3) in n-type GaN semiconductors. To precisely measure the reconstructed phase profiles in the GaN sample, three electron biprisms were used to obtain a series of high-contrast holograms without Fresnel fringes generated by a biprism filament, and a cryo-focused-ion-beam (cryo-FIB) was used to prepare a uniform TEM sample with less distortion in the wide field of view. All layers in a 350-nm-thick TEM sample were distinguished with 1.8-nm spatial resolution and 0.02-rad phase-resolution, and variations of step width in the phase profile (corresponding to depletion width) at the interfaces between the layers were also measured. Thicknesses of the active and inactive layers at each dopant level were estimated from the observed phase profile and the simulation of theoretical band structure. Ratio of active-layer thickness to total thickness of the TEM sample significantly decreased as dopant concentration decreased; thus, a thicker TEM sample is necessary to visualize lower carrier concentrations; for example, to distinguish layers with dopant concentrations of 1016 and 1015 atoms cm-3. It was estimated that sample thickness must be more than 700 nm to make it be possible to detect sub-layers by the combination of PS-EH and cryo-FIB.

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.

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.

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.

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.

Noise estimation for off-axis electron holography

Off-axis electron holography provides access to the phase of the elastically scattered wave in a transmission electron microscope at scales ranging from several hundreds of nanometres down to 0.1nm. In many cases the reconstructed phase shift is directly proportional to projected electric and magnetic potentials rendering electron holography a useful and established characterisation method for materials science. However, quantitative interpretation of experimental phase shifts requires quantitative knowledge about the noise, which has been previously established for some limiting cases only. Here, we present a general noise transfer formalism for off-axis electron holography allowing to compute the covariance (noise) of reconstructed amplitude and phase from characteristic detector functions and general properties of the reconstruction process. Experimentally, we verify the presented noise transfer formulas for two different cameras with and without objects within the errors given by the experimental noise determination.

Three-dimensional reconstructions of electrostatic potential distributions with 1.5-nm resolution using off-axis electron holography

Three-dimensional (3D) reconstruction experiments were carried out by observing high-resolution 3D electrostatic potential distributions of Pt nanoparticles using off-axis electron holographic tomography. These Pt nanoparticles were mounted on the surfaces of amorphous silicon pillars. In order to realize high-resolution observation, we developed a mechanically stable 3D specimen holder with small specimen drifts and vibrations. From the 3D electrostatic potential distribution data of Pt nanoparticles (2.0 nm in diameter), we obtained the resolution of 1.5 nm.

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.

Electron holographic observation of micro-magnetic fields current-generated from single carbon coil

A carbon coil was evaluated for use as a micro-solenoid in a small magnetic device. A single carbon coil was lifted out of the aggregate using a tungsten fine probe in a focused ion beam (FIB) system and was wired to two small electrodes in the specimen holder of a transmission electron microscope (TEM). A direct current was supplied to the single carbon coil. A micro/nano-magnetic field generated from the coil was directly observed by electron holography. A computer simulation of electron holography was also done to quantitatively analyze the magnetic field. Details on the FIB technique, the electron holographic observation and the simulation are described.

Conventional and back-side focused ion beam milling for off-axis electron holography of electrostatic potentials in transistors

Off-axis electron holography is used to characterize a linear array of transistors, which was prepared for examination in cross-sectional geometry in the transmission electron microscope (TEM) using focused ion beam (FIB) milling from the substrate side of the semiconductor device. The measured electrostatic potential is compared with results obtained from TEM specimens prepared using the more conventional 'trench' FIB geometry. The use of carbon coating to remove specimen charging effects, which result in electrostatic fringing fields outside 'trench' specimens, is demonstrated. Such fringing fields are not observed after milling from the substrate side of the device. Analysis of the measured holographic phase images suggests that the electrically inactive layer on the surface of each FIB-milled specimen typically has a thickness of 100 nm.

Off-axis electron holography of unbiased and reverse-biased focused ion beam milled Si p-n junctions

Off-axis electron holography is used to measure electrostatic potential profiles across a silicon p-n junction, which has been prepared for examination in the transmission electron microscope (TEM) in two different specimen geometries using focused ion beam (FIB) milling. Results are obtained both from a conventional unbiased FIB-milled sample and using a novel sample geometry that allows a reverse bias to be applied to an FIB-milled sample in situ in the TEM. Computer simulations are fitted to the results to assess the effect of TEM specimen preparation on the charge density and the electrostatic potential in the thin sample.

Off-axis electron holography without Fresnel fringes

A new method for forming an electron hologram without Fresnel fringes caused by an electron biprism is presented. Adding a fine filament to the ordinary setup for off-axis electron holography directly prevented Fresnel diffraction at the electron biprism and eliminated 70% of the phase error due to the Fresnel diffraction. This made it possible to obtain a hologram having uniform interference fringes, and to reconstruct a clear phase image of a weak electric-field.

Mapping of process-induced dopant redistributions by electron holography

We present and review dopant mapping examples in semiconductor device structures by electron holography and outline their potential applications for experimental investigation of two-dimensional (2D) dopant diffusion on the nanometer scale. We address the technical challenges of the method when applied to transistor structures with respect to quantification of the results in terms of the 2D p-n junction potential and critically review experimental boundary conditions, accuracy, and potential pitfalls. By obtaining maps of the inner electrostatic potential before and after anneals typically used in device processing, we demonstrate how the "vertical" and "lateral" redistribution of boron during device fabrication can directly be revealed. Such data can be compared with the results of process simulation to extract the fundamental parameters for dopant diffusion in complex device structures.

Influence of the elliptical illumination on acquisition and correction of coherent aberrations in high-resolution electron holography

In high-resolution off-axis electron holography, the interpretable lateral resolution is extended up to the information limit of the electron microscope by means of a correcting phase plate in Fourier space. A plane illuminating electron wave is generally assumed. However, in order to improve spatial coherence, which is essential for holography, the object under investigation is illuminated with an elliptically shaped electron source. This special illumination imposes a variation of beam directions over the field of view. Therefore, due to the interaction of beam tilt and coherent wave aberration, the effective aberrations vary over the field of view yielding a loss of isoplanicity. Consequently, in the past the aberrations were only corrected successfully for a small part of the field of view. However, a thorough analysis of the holographic imaging process shows that the imaging artifacts introduced by the elliptical illumination can be corrected under reconstruction by means of a phase curvature, which models the illuminating wave front. Applied in real space, this phase curvature is seamlessly incorporated into the correction process for coherent wave aberration resulting in an improvement of interpretable lateral resolution up to the information limit for the whole field of view.

Electron interference: mystery and reality

Interference of electron waves has developed from a fascinating phenomenon in basic physics to a key method for the highly sophisticated investigation of both electric and magnetic structures in solid-state materials. After more than 20 years of development, electron holography in the transmission electron microscope is now a very powerful technique for the analysis of micro-fields down to atomic dimensions. The applications extend from highly sensitive measurements in semiconductor technology to the quantitative characterization of atomic structures.

Hologram simulation for off-axis electron holography

Hologram simulation for electron holography using an electron biprism is described. An electron hologram is superimposed by Fresnel fringes originating from the electron biprism, which affects both the amplitude and the phase of the object wave and the reference wave. In this simulation, we consider the effects of Fresnel diffraction as well as the electron-wave phase shift due to the electromagnetic field produced by the specimen. We also take into account the phase shift due to the inner potential of the specimen, the amplitude modulation due to the absorption of the incident electrons by the specimen, reference-wave distortion caused by the electromagnetic fields, coherency of the electron wave, and quantum noise of the detected electrons. Simulated and experimentally obtained holograms and reconstructed images are compared for the cases of a charged latex spherical particle and a single magnetic-domain spherical particle placed on a carbon film.