In electron optics, calculation of the electric field plays a major role in all computations and simulations. Accurate field calculation methods such as the finite element method (FEM), boundary element method and finite difference method, have been used for years. However, such methods are computationally very expensive and make the computer simulation challenging or even infeasible when trying to apply automated design of electrostatic lens systems with many free parameters. Hence, for years, electron optics scientists have been searching for a fast and accurate method of field calculation to tackle the aforementioned problem in the design and optimization of electrostatic electron lens systems. This paper presents a novel method for fast electric field calculation in electrostatic electron lens systems with reasonably high accuracy to enable the electron-optical designers to design and optimize an electrostatic lens system with many free parameters in a reasonably short time. The essence of the method is to express the off-axis potential in an axially symmetrical coordinate system in terms of derivatives of the axial potential up to the fourth order, and equate this to the potential of the electrode at that axial position. Doing this for a limited number of axial positions, we get a set of equations that can be solved to obtain the axial potential, necessary for calculating the lens properties. We name this method the fourth-order electrode method because we take the axial derivatives up to the fourth order. To solve the equations, a quintic spline approximation of the axial potential is calculated by solving three sets of linear equations simultaneously. The sets of equations are extracted from the Laplace equation and the fundamental equations that describe a quintic spline. The accuracy and speed of this method is compared with other field calculation methods, such as the FEM and second order electrode method (SOEM). The new field calculation method is implemented in design/optimization of electrostatic lens systems by using a genetic algorithm based optimization program for electrostatic lens systems developed by the authors. The effectiveness of this new field calculation method in optimizing optical parameters of electrostatic lens systems is compared with FEM and SOEM and the results are presented. It should be noted that the formulation is derived for general axis symmetrical electrostatic electron lens systems, however the examples shown in this paper are with cylindrical electrodes due to the simplicity of the implementation in the software.

Structures fabricated using focused electron beam-induced deposition (FEBID) have sloped sidewalls because of the very nature of the deposition process. For applications this is highly undesirable, especially when neighboring structures are interconnected. A new technique combining FEBID and focused electron beam-induced etching (FEBIE) has been developed to fabricate structures with vertical sidewalls. The sidewalls of carbon FEBID structures have been modified by etching with water and it is shown, using transmission electron microscopy imaging, that the sidewall angle can be tuned from outward to inward by controlling the etch position on the sidewall. A surprising under-etching due to the emission of secondary electrons from the deposit was observed, which was not indicated by a simple model based on etching. An analytical model was developed to include continued etching once the deposit has been removed at the exposed pixel. At this stage the secondary electrons from the substrate then cause the adsorbed water molecules to become effective in etching the deposit from below, resulting in under-etched structures. The evolution of the sidewall angle during etching has also been experimentally observed in a scanning electron microscope by continuously monitoring the secondary electron detector signal.

In the Multi beam source (MBS) of our Multi Beam Scanning Electron Microscope (MBSEM), an aperture lens array (ALA) splits the emission cone of the Schottky field emitter into multiple beamlets. When the apertures in the ALA are close to each other, the ALA can introduce aberrations to these beamlets through the electrostatic interaction of neighbouring apertures with each aperture's lens field. When the apertures are arranged in a square grid pattern, the aberration causes fourfold astigmatism. The effect on the beam spot is analyzed through a combination of 3D simulations and experimental validation. To counterbalance the fourfold astigmatism, a correction scheme is proposed in which a slightly non-round profile is applied to the aperture lenses.

Le Poole describes his odyssey in electron microscopy, beginning with his early studies that led up to his application in 1939 to H.B. Dorgelo to build an electron microscope. Gradual progress was made after the German invasion of Holland. Successes and disappointments are both recorded. Post-war meetings are invoked, especially the first international congress on electron microscopy in Delft in 1949.

Here, we demonstrate ultrafast scanning electron microscopy (SEM) for making ultrafast movies of mechanical oscillators at resonance with nanoscale spatiotemporal resolution. Locking the laser excitation pulse sequence to the electron probe pulses allows for video framerates over 50 MHz, well above the detector bandwidth, while maintaining the electron beam resolution and depth of focus. The pulsed laser excitation is tuned to the oscillator resonance with a pulse frequency modulation scheme. We use an atomic force microscope cantilever as a model resonator, for which we show ultrafast real-space imaging of the first and even the 2 MHz second harmonic oscillation as well as verification of power and frequency response via the ultrafast movies series. We detect oscillation amplitudes as small as 20 nm and as large as 9 μm. Our implementation of ultrafast SEM for visualizing nanoscale oscillatory dynamics adds temporal resolution to the domain of SEM, providing new avenues for the characterization and development of devices based on micro- and nanoscale resonant motion.

We have analyzed the possibilities of wave front shaping with miniature patterned electron mirrors through the WKB approximation. Based on this, we propose a microscopy scheme that uses two miniature electron mirrors on an auxiliary optical axis that is in parallel with the microscope axis. A design for this microscopy scheme is presented for which the two axes can be spatially separated by as little as 1 mm. We first provide a mathematical relationship between the electric potential and the accumulated phase modulation of the reflected electron wave front using the WKB approximation. Next, we derive the electric field in front of the mirror, as a function of a topographic or pixel wise excited mirror pattern. With this, we can relate the effect of a mirror pattern onto the near-field phase, or far field intensity distribution and use this to provide a first optical insight into the functioning of the patterned mirror. The equations can only be applied numerically, for which we provide a description of the relevant numerical methods. Finally, these methods are applied to find mirror patterns for controlled beam diffraction efficiency, beam mode conversion, and an arbitrary phase and amplitude distribution. The successful realization of the proposed methods would enable arbitrary shaping of the wave front without electron–matter interaction, and hence we coin the term virtual phase plate for this design. The design may also enable the experimental realization of a Mach–Zehnder interferometer for electrons, as well as interaction-free measurements of radiation sensitive specimen.

The use of electron mirrors in aberration correction and surface-sensitive microscopy techniques such as low-energy electron microscopy has been established. However, in this work, by implementing an easy to construct, fully electrostatic electron mirror system under a sample in a conventional scanning electron microscope (SEM), we present a new imaging scheme which allows us to form scanned images of the top and bottom surfaces of the sample simultaneously. We believe that this imaging scheme could be of great value to the field of in-situ SEM which has been limited to observation of dynamic changes such as crack propagation and other surface phenomena on one side of samples at a time. We analyze the image properties when using a flat versus a concave electron mirror system and discuss two different regimes of operation. In addition to in-situ SEM, we foresee that our imaging scheme could open up avenues towards spherical aberration correction by the use of electron mirrors in SEMs without the need for complex beam separators.

The design of an electrostatic electron optical system with five electrodes and two objective functions is optimized using multiobjective genetic algorithms (MOGAs) optimization. The two objective functions considered are minimum probe size of the primary electron beam in a fixed image plane and maximum secondary electron detection efficiency at an in-lens detector plane. The time-consuming step is the calculation of the system potential. There are two methods to do this. The first is using COMSOL (finite element method) and the second is using the second-order electrode method (SOEM). The former makes the optimization process very slow but accurate, and the latter makes it fast but less accurate. A fully automated optimization strategy is presented, where a SOEM-based MOGA provides input systems for a COMSOL-based MOGA. This boosts the optimization process and reduces the optimization times by at least ∼10 times, from several days to a few hours. A typical optimized system has a probe size of 11.9 nm and a secondary electron detection efficiency of 80%. This new method can be implemented in electrostatic lens design with one or more objective functions and multiple free variables as a very efficient, fully automated optimization technique.

High resolution dense lines patterned by focused electron beam-induced deposition (FEBID) have been demonstrated to be promising for lithography. One of the challenges is the presence of interconnecting material, which is often carbonaceous, between the lines as a result of the Gaussian line profile. We demonstrate the use of focused electron beam-induced etching (FEBIE) as a scanning electron microscope (SEM)-based direct-write technique for the removal of this interconnecting material, which can be implemented without removing the sample from the SEM for post processing. Secondary electron (SE) imaging has been used to monitor the FEBIE process, and atomic force microscopy (AFM) measurements confirm the fabrication of well separated FEBID lines. We further demonstrate the application of this technique for removing interconnecting material in high resolution dense lines using backscattered electron (BSE) imaging to monitor the process.

Here, we experimentally demonstrate interaction-free measurements with electrons using a novel electron Mach-Zehnder interferometer. The flexible two-grating electron interferometer is constructed in a conventional transmission electron microscope and achieves high contrast in discrete output detectors, tunable alignment with independently movable beam splitters, and scanning capabilities for imaging. With this path-separated electron interferometer, which closely matches theoretical expectations, we demonstrate electron interaction-free measurements with an efficiency of 14±1%. Implementing this quantum protocol in electron imaging opens a path toward interaction-free electron microscopy.

Electron beams can be reflected by an electrode that is at a more negative potential than the cathode from which the beam is emitted. We want to design a mirror with a flat mirror electrode where the electrons are reflected at a plane very close to the electrode. The wave front of an electron can then be shaped when the mirror contains a surface topography or modulated potential. However, electron beams reflected by flat electron mirrors are usually characterized by high coefficients of chromatic and spherical aberration. When the mirror is combined with an electrostatic lens to form a tetrode mirror system, the situation deteriorates even further. This places a restrictive limit on the maximum aperture angle of the beam, and consequently also limits the attainable resolution at the image plane. We have numerically studied the dependence of these aberrations as a function of design parameters of the tetrode mirror consisting of a ground, lens, cap, and mirror electrode, and limited ourselves to only using flat electrodes with round apertures, at fixed electrode spacing. It turns out that the third order spherical aberration can be made negative. The negative third order aberration is then used to partially compensate the positive fifth order aberration. This way, a system configuration is obtained that, at 2 keV beam energy, provides a diffraction limited resolution of 7.6 nm at an image plane 25 mm from the mirror at beam semi-angles of 2.3 mrad, enabling an illumination radius of 40 μm at the mirror. The presented tetrode mirror design could spark innovative use of patterned electron mirrors as phase plates for electron microscopy in general, and for use as coherent beam splitters in Quantum Electron Microscopy in particular. An appendix presents a method to calculate the spot size of a focused beam in the presence of both third and fifth order spherical aberration coefficients, which is also applicable to Scanning (Transmission) Electron Microscopes with aberration correctors.

The analytical theory of statistical Coulomb interactions allows to determine the trajectory displacement in a single rotationally symmetrical beam with well-behaved spatial and angular particle distributions. This can be used to estimate the trajectory displacement in a multi-beam system using the so called fully-filled segment approximation. This approach predicts full compensation of trajectory displacement for a specific setup of the system. We show that this prediction is not consistent with Monte Carlo simulations and we develop a new approach to the calculation, showing that two independent trajectory displacement contributions are present in a multi-beam system. We support this calculation with Monte Carlo simulations as well as with experimental data from a multi-beam system.

Electrostatic beam blankers are an alternative to photo-emission sources for generating pulsed electron beams for Time-resolved Cathodoluminescence and Ultrafast Electron Microscopy. While the properties of beam blankers have been extensively investigated in the past for applications in lithography, characteristics such as the influence of blanking on imaging resolution have not been fully addressed. We derive general analytical expressions for the spot displacement and loss in resolution induced by deflecting the electron beam in a blanker. In particular, we analyze the sensitivity of both measures to how precise the conjugate focus is aligned in between the deflector plates. We then work out the specific case of a beam blanker driven by a linear voltage ramp as was used in recent studies by others and by us. The result shows that the spot displacement and focus blur can be reduced to the same order as the electron beam probe size, even when using a beam blanker of millimeter or larger scale dimensions. An interesting result is that, by the right choice of the focus position in the deflector, either the spot displacement from the stationary position can be minimized, or the blur can be made zero but not both at the same time. Our results can be used both to characterize existing beam blanker setups and to design novel blankers. This can further develop the field of time-resolved electron microscopy by making it easier to generate pulses with a typical duration of tens of picoseconds in a regular scanning electron microscope at high spatial resolution.

Visualizing charge carrier flow over interfaces or near surfaces meets great challenges concerning resolution and vastly different time scales of bulk and surface dynamics. Ultrafast or four-dimensional scanning electron microscopy (USEM) using a laser pump electron probe scheme circumvents the optical diffraction limit, but disentangling surface-mediated trapping and ultrafast carrier dynamics in a single measurement scheme has not yet been demonstrated. Here, we present lock-in USEM, which simultaneously visualizes fast bulk recombination and slow trapping. As a proof of concept, we show that the surface termination on GaAs, i.e., Ga or As, profoundly influences ultrafast movies. We demonstrate the differences can be attributed to trapping-induced surface voltages of approximately 100-200 mV, which is further supported by secondary electron particle tracing calculations. The simultaneous visualization of both competing processes opens new perspectives for studying carrier transport in layered, nanostructured, and two-dimensional semiconductors, where carrier trapping constitutes a major bottleneck for device efficiency.

In electron optics, the design of electron lens systems is still a challenge. To optimize such systems, the objective function which should be calculated, depends on the electric potential distribution in the space created by the lenses. To obtain the electric potential, the existing methods are generally based on some mathematical techniques which need to mesh the space of the lens system and derive the electric potential at all mesh points. Hence, calculation of the objective function for such systems are computationally expensive. Therefore, applying a fully automatic optimization routine has not yet been feasible, especially for lens systems with many free variables. Hence, the study of objective-function landscape of such problems has not yet been performed. One of the questions of interest for optical designers, that has not been studied in the literature, is whether this problem can be solved by a local optimizer or is it necessary to apply a global optimizer. Recently we succeeded in implementing a method (based on a so-called SOEM (Second Order Electrode Method) technique) which calculates the electric potential in a fast and reasonably accurate way. In this paper, that method, is implemented to perform the study of local versus global optimization for electron lens design. The global optimization method here is performed by GA (Genetic Algorithm). The objective function is taken to be the probe size of the electron beams at the image plane. The results of our study show that the objective function of this problem has many local minima and the optimization of such problems cannot be handled by a local optimizer. GA is shown to perform well by overcoming these multiple-local minima to arrive at a global minima.

To allow researchers to fabricate micro- and nano-devices on a small scale, without having to use complex cleanroom facilities, a single tool is proposed in which a variety of typical cleanroom techniques and processes is combined. This ‘cleanroom’ in SEM tool, based on a scanning electron microscope (SEM), integrates several add-on tools, such as a miniature plasma source for sputtering and cleaning purposes, a miniature thermal evaporator for metal deposition, and facilities to enable in-situ selective atomic layer deposition. The cleanroom techniques and processes selected for integration in the ‘cleanroom’ in SEM tool are discussed, and the design and fabrication of the add-on tools are presented. Finally the proofs of principle of the plasma source, evaporator and in-situ selective ALD process are experimentally demonstrated.

Electron sources for high-resolution applications such as microscopy and lithography are characterized by their brightness and energy spread rather than by their total emission current. In fact, most of the emitted current is cut out by apertures and only nanoamps or at most microamps actually reach the sample or wafer. This chapter reviews the physics and practical properties of the electron sources that are typically used in microscopy and lithography. It is an extension of topics addressed in [1] with special emphasis on application aspects and their emitter requirements. Recent developments are reviewed. The relations between the source properties and the resolution and throughput of these instruments is derived and discussed.

Large area electron microscopy (EM) imaging has long been difficult due to fundamental limits in throughput for conventional electron microscopes. New developments in transmission electron microscopy and multi-beam scanning electron microscopy (MBSEM) imaging have however made it possible to generate large EM datasets [1,2,3]. This article describes a transmission imaging technique that is suitable for a MBSEM as it allows for a relatively straightforward way of separating the signals generated by each beam. The technique places a thin (50nm-200nm) tissue section directly on top of a coated scintillator. The electrons that are transmitted through the section generate light in the scintillator which is collected by a high NA objective and imaged onto a photon detector. This article gives a model for the contrast-to-noise (CNR) and signal-to-noise (SNR) ratio that is to be expected for this imaging technique. These parameters were calculated using Monte-Carlo simulations. It was found that the CNR increases when decreasing landing energy and SNR increases with increasing landing energy. These two trends cause that there is an intermediate energy where imaging performance is best. The energy of this optimum was calculated for various levels of heavy metal staining, section thickness, coating material, coating thickness and light collection efficiency. The model was verified experimentally on a synthetic sample.