Electron Interferometry Research Articles

Mesoscopic Interferometers for Electron Waves

Mesoscopic interferometers are electronic analogues of optical interferometers, with “quantum point contacts” playing the role of optical beam splitters. Mesoscopic analogues of two-slit, Mach-Zehnder and Fabry-Perot interferometers have been built. A fundamental difference between electron and photon interferometry is that electron interferometry is nonlocal.

Optical system for double-biprism electron holography

A novel system of electron interferometry and holography using two electron biprisms has been developed. The first biprism is installed in the image plane of the objective lens and the second one is set behind the first magnifying lens, inside the shadow area of the first biprism. The system can independently control two important parameters for interferograms and holograms, the fringe spacing and interference width. Thus, it gives us more flexibility on performing electron interferometry and holography. The good performance of the system was demonstrated using a 1MV field-emission electron microscope. We introduce a variety of optical set-ups for the system and explain the advantages of each set-up in detail, with experimental results.

Analysis of sidewall quality in through-wafer deep reactive-ion etching

The quality of channel sidewalls resulting from through-wafer deep reactive-ion etching is analysed using scanning electron microscopy, atomic-force microscopy and interferometry. Sidewall quality and profile are highly dependent on the width of the etched channel. Channels narrower than 100 μm show generally good sidewall smoothness, though with a bowed profile. This profile leads to ion-induced damage towards the bottom of the channel sidewall. Wider channels, in contrast, exhibit overpassivation of the sidewalls with a region of thick polymer build-up followed by vertical striations and a very rough surface, but with an overall vertical profile. Redeposition of the passivation from the trench bottom to the sidewalls as suggested by other researchers is supported by our observations.

Double-biprism electron interferometry

Electron holography based on two electron biprisms was developed. The upper biprism was installed just on the image plane of the objective lens, and the lower one was set between the crossover point and image plane of the magnifying lens. This system was able to control two important parameters of the hologram—fringe space and width of interference region—independently. The system enabled us to perform electron holography and interferometry more flexibly. We confirmed the good performance of the system and did preliminary applications using a 1-MV field-emission electron microscope.

Analysis of sidewall quality in through-wafer deep reactive-ion etching

The quality of channel sidewalls resulting from through-wafer deep reactive-ion etching is analysed using scanning electron microscopy, atomic-force microscopy and interferometry. Sidewall quality and profile are highly dependent on the width of the etched channel. Channels narrower than 100 μm show generally good sidewall smoothness, though with a bowed profile. This profile leads to ion-induced damage towards the bottom of the channel sidewall. Wider channels, in contrast, exhibit overpassivation of the sidewalls with a region of thick polymer build-up followed by vertical striations and a very rough surface, but with an overall vertical profile. Redeposition of the passivation from the trench bottom to the sidewalls as suggested by other researchers is supported by our observations.

A Point Projection Microscope for Electron Interferometry in the Reflection Mode

A Point Projection Microscope for Electron Interferometry in the Reflection Mode

Phase recovery and lensless imaging by iterative methods in optical, X-ray and electron diffraction.

Thomas Young's quantitative analysis of interference effects provided the confidence needed to revive the wave theory of light, and firmly established the concept of phase in optics. Phase plays a similarly fundamental role in matter-wave interferometry, for which the field-emission electron microscope provides ideal instrumentation. The wave-particle duality is vividly demonstrated by experimental 'Young's fringes' using coherent electron beams under conditions in which the flight time is less than the time between particle emission. A brief historical review is given of electron interferometry and holography, including the Aharonov-Bohm effect and the electron Sagnac interferometer. The simultaneous development of phase-contrast imaging at subnanometre spatial resolution has greatly deepened our understanding of atomic processes in biology, materials science and condensed-matter physics, while electron holography has become a routine tool for the mapping of electrostatic and magnetic fields in materials on a nanometre scale. The encoding of phase information in scattered farfield intensities is discussed, and non-interferometric, non-crystallographic methods for phase retrieval are reviewed in relationship to electron holography. Examples of phase measurement and diffraction-limited imaging using the hybrid input-output iterative algorithm are given, including simulations for soft X-ray imaging, and new experimental results for coherent electron and visible-light scattering. Image reconstruction is demonstrated from experimental electron and visible-light Fraunhofer diffraction patterns. The prospects this provides for lensless imaging using particles for which no lenses exist (such as neutrons, condensates, coherent atom beams and X-rays) are discussed. These new interactions can be expected to provide new information, perhaps, for example, in biology, with the advantage of less damage to samples.

Conductance-phase determination in double-slit transmission across a quantum dot using a Hilbert transform method

Recent mesoscopic two-arm experiments involving quantum dots, electron interferometry, and Aharonov-Bohm effects have enabled measurements of both electron transmission probabilities and phases. Unexpected features in the phases as function of the gap voltage U have stimulated several theoretical works. It is shown in this paper that the phases (f ) and conductances (|C|), appearing both in the experimental and in theoretical studies, are interrelated through integral expressions, causing f and $\mathrm{ln}(|C|)$ to be Hilbert transforms. The empirically found interrelations imply certain analytical properties of the U dependence of wave functions in mesoscopic systems.

Fabrication of single self-supported metallic nanometric wires

The fabrication of self-supported ultrathin metallic wires is described. The initial material is a Pt/Rh (10%) wire embedded inside a 50 μm diameter Ag sheath. The thinning procedure which includes mechanical, chemical, annealing, and ion milling processes, leads to diameters down to 60 nm. Each wire is curved then fixed on a dedicated support suited to all the successive preparation steps. This mechanical attachment permits a precise positioning of such a wire at micrometric distances from a flat surface and therefore, its use as an electron biprism in low-energy electron interferometry experiments. The wire thinning is limited by the creation of cusps on the wire shape.

Measurements of neutral density based on emissivity in the Alcator C-Mod divertor

Neutral density profiles have been derived along the outboard divertor target of Alcator C-Mod and inside the last closed flux surface (LCFS). Local emission rates are obtained by a tomographic inversion of measured brightness profiles. Electron temperatures and densities provided by a divertor Langmuir probe array are then used to calculate the local neutral density, , from the emissivity profile. For points inside the LCFS, electron cyclotron emission (ECE) and interferometry data were used for electron density and temperature, respectively. Along the divertor target, steep gradients in neutral density persist during regular ohmic attached discharges, with . Plasma detachment leads to values of that can reach up to several times in the bottom of the divertor with much shallower pressure gradients to the midplane. Modelling of the parallel plasma momentum decrease due to charge exchange (CX) and elastic ion - neutral collisions indicates that neutral densities well below those observed are sufficient to explain the measured drop in parallel plasma pressure. This suggests that significant momentum is carried by the neutrals in the divertor resulting in decreased efficiency of momentum transfer between ions and neutrals.

The phase constancy of electron waves traveling through Boersch's electrostatic phase plate

We draw attention to the observation that an electrostatic phase plate, originally proposed by Boersch in 1947, introduces a uniform phase shift. The device consists of a ring electrode, shielded by earthed electrodes. The phase shift of the electron wave traveling through the interior of the ring is uniform and constant independent of the radius of the ring for a very low applied voltage. This can be shown by considering the Laplace equation, which is satisfied by the electrostatic scalar potential subjected to the boundary conditions. The phase shift, which is proportional to the potential integrated along the optic axis, is constant inside the ring as if there were a thin film of uniform thickness. With such a device in the back focal plane of the objective lens, a phase contrast electron microscope could be constructed. The device could also be used as a constant phase shifter for electron interferometry.

The brightest beam in science: New directions in electron microscopy and interferometry

An ultrasharp electron field-emission source, with emission region on the order of atomic size (i.e., fraction of a nanometer), produces a bright, strongly self-focused, highly coherent electron beam—indeed the brightest particle beam currently known to science. Employed in the configuration of a point-production microscope, this ‘‘nanotip’’ source facilitates low-energy electron imaging of fragile structures at atomic-scale resolution. When slightly out of focus, the microscope serves as perhaps the world’s simplest electron interferometer providing Fresnel diffraction patterns from which important information like effective source size, source brightness, and beam degeneracy can be determined. One remarkable feature of point sources is the perfect (i.e., aberration-free), lensless imaging of periodic structures at a denumerable set of focal planes with complete suppression of nonperiodic detail. The high degeneracy and coherent emission of an electron pointlike source can be exploited in new types of quantum interferometry involving correlated electrons.

On the mean inner potential in high- and low-energy electron diffraction

New electron microscopies spanning the energy range from millivolts to kilovolts image different beam-energy-dependent potentials. We review the theories of the average value of the mean inner potential of a solid in order to understand its role in image interpretation and its relationship to charge density and atom positions in crystals. Three common definitions of this quantity are compared, that from high-volatge transmission electron interferometry, the theory of surface dipole layers and the work function, and that from low-energy electron diffraction (LEED). Energy-dependent corrections due to exchange and virtual inelastic scattering are proposed for LEED, photoelectron holography (PEH), the low-energy electron microscope (LEEM) and the point-projection microscope (PPM) operating in the sub-kilovolt range. A calculation of the mean free path of low-energy electrons as a function of their energy is also reproduced.

Imaging extrinsic defects at the NiSi2/Si(111) metal–semiconductor interface

The scanning tunneling microscope is used to image properties of the buried NiSi2/Si(111) metal–semiconductor interface using electron interferometry. This technique reveals the presence of multiple domains in conductance images that are not visible in topographic images. The multiple domains are explained in terms of silicide regions of different thicknesses that are separated by step domain boundaries at the buried interface. The possible influence of these extrinsic defects on the formation of the Schottky barrier and on local real space characterization techniques used to measure Schottky barrier heights are discussed.

Study of ferroelectric domain wall structures using electron holographic techniques

Abstract In this paper we will discuss our recent experimental results, using electron holography and electron interferometry, of studies of ferroelectric domain walls in BaTiO3 and PLZT thin specimens.

Scanning tunnelling microscopy

Scanning tunnolling microscop! (STM) is a rclativcly new tccbnique. originating as it does from pioneering work of Binnig and Rohrcr in the early 1980s ‘. The concept is relatively simple. J~tst place ;I slurp tungsten tip close to a conducting surl~lcc. so close that the W:ILC‘ functions of the closest tip atom and the surface atoms overlap. Apply ;I potential diffcrcncc between tip and surface and a tunnelling current will flow. By varying the potential and/‘or separation. the local density of states can be probed. By scanning the tip, a picture of the surface topography can be formed from variations in the tunnelhng current or from variations in tip height, necessary to maintain constant tunnelling current and thcrcforc constant tip’surl‘acc separation. One of ~hc first applications of STM, and certainly one that caused the most impact, was the unequivocal solution of the problem of the atomic arrangement of the rcconstructcd (7 x 7) surface of silicon( I I1 )‘. In die Tcw years since lhal pionccrins work, the uses of STM have burgeoned. As well as atomic resolution of topography. Mark function and local density of states. STM has been used. for cx~mplc, to obscrvc charge densit) WIVC~~. for magnetic imaging ‘. for observing spin polarized clcctrons’. for dctcrmining metallic udhcsion/friction”. for electron interferometry’ and for determining electrochemical reactivity’. I am sure 0lal I ha\e not listed aII variations as new methods seem to cmcrge each month. An important nc\v atom probe tcchniquc that has cmergcd from STM and is now reaching maturity is atomic force microscopy (AFM)“. This depends on mechanical interaction when ;I minute force is applied bctwccn ;I tip on a scnsitivc cantilckcr and a surface. The dcflcction of the cantilever is amplified by. for cxamplc. an optical Ic\,cr. and dctcctcd to build LIP an im;lgc of the surface potential. AFM is particularly LISCI‘UI I'OI insulating surfaces and for determining surface friction. Atomic resolution is possible. although AFM cannot quite achieve the rcsolulion of STM. In this reCec I \\ill only discuss STM : theory. instrumcntaCon and c.xamplcs of rcccnt rccults.

Applications of electron holography to ferromagnetic and superconductive materials

Electromagnetic fields are not observable with conventional electron microscopy: The fields deflect an incident electron beam but no contrast is produced in the electron micrograph for the fields since all the electrons deflected at an object point are focused into a single image point through the electron lens. The information about the electomagnetic fields is included in the deflection distribution or the phase distribution of an electron beam, which is lost in electron micrographs. Electron interferometry has been carried out since 1950s using a transmission electron microscope equipped with an electron biprism to make ultra-fine measurements. The advent of a "coherent" field-emission electron beam has greatly expanded the range of applications and possibilities: Electric and magnetic fields are directly observed as equipotential lines and magnetic lines of force in an electron-holographic interference micrograph. Precision in phase measurement has increased to 2π/50 thanks to a phase amplification technique peculiar to holography.In magnetic field observation, contour fringes in an interference micrograph directly indicate projected magnetic lines of force in h/e flux units. An example of a magnetic field micrograph is shown in Fig. 1.

Transmission electron spectroscopy and interferometry of electroceramic oxides

Research on ferroelectricity and related phenomena has come a long way since the discovery of hysteretic nonlinearity of polarization in "Rochelle Salt" by J. Valasek in 1920's. Ever since the discovery, microstructural issues have dominated the field. With the current trends in using ferroelectric and related oxides in nanocrystalline and thin film forms, techniques for microstructural analysis for such specimens are becoming more sophisticated.We are currently investigating nanocrystalline TiO2 as a model system to examine size dependency of electronic structure in nanocrystals, as reflected in their energy loss spectra. Electron beam evaporated nanocrystals of TiO2 (size ranging from 2 - 10 nm) have been examined with transmission EELS with a ~ 0.8 nm electron probe of our HF-2000 FE TEM. The particles were dispersed on a holey carbon grid and those protruding into the holes were analyzed for changes in valence and core loss spectra as a function of nominal particle size. The plasmon loss energies were observed to increase with decrease in particle size.

Atomic-Force Microscopy with piezoresistive cantilevers

The atomic force microscope (AFM) works by measuring the deflection of a cantilever as it is scanned over a sample. A sharp tip at the end of the cantilever is responsible for the high lateral resolution achieved with the AFM. There are several ways to measure the deflection of the cantilever. The technique used to measure the deflection of the cantilever most often dictates the mechanical complexity and stability of the instrument. Electron tunneling, interferometry and capacitive sensors have been used successfully. The most common way to measure the cantilever deflection is by means of an optical deflection detector.The piezoresistivc cantilever offers a new way to measure the deflection of the cantilever, with performances comparable to the performances of other deflection detectors, and with the advantage that the sensor is incorporated in the cantilever. This simplifies the design and operation of the microscope In particular, the piezoresistive cantilever facilitates the use and often improves the performances of an AFM when operated in ultra high vacuum (UHV), at low temperature, or when used to image large samples.

Particle in a variable-size box: The influence of the tip in thin-film electron interferometry.

The influence of the scanning-tunneling-microscopy tip on the conductance spectra measured in thin-film electron interferometry is considered, and is discussed in terms of coupled quantum wells. One of the wells is formed by the linear potential drop between the tip and sample, which gives rise to vacuum-field-emission resonances. The spectra of field-emission resonances are shown to be very sensitive to the properties of the tip, and can be understood in terms of confining the electron to triangular potential wells of different sizes. The other potential well is formed within the thin-film adlayer, and its spectrum should be largely independent of the properties of the tip. We consider the spectrum of the coupled system, and discuss it in terms of perturbation theory where we observe the tendency of the levels to repel each other when they are closely spaced in energy, and to cause level splitting when the levels are degenerate.