Breaking the spherical and chromatic aberration barrier in transmission electron microscopy

Since the invention of transmission electron microscopy (TEM) in 1932 (Z. Physik 78 (1932) 318) engineering improvements have advanced system resolutions to levels that are now limited only by the two fundamental aberrations of electron lenses; spherical and chromatic aberration (Z. Phys. 101 (1936) 593). Since both aberrations scale with the dimensions of the lens, research resolution requirements are pushing the designs to lenses with only a few mm space in the pole-piece gap for the specimen. This is in conflict with the demand for more and more space at the specimen, necessary in order to enable novel techniques in TEM, such as He-cooled cryo electron microscopy, 3D-reconstruction through tomography (Science 302 (2003) 1396) TEM in gaseous environments, or in situ experiments (Nature 427 (2004) 426). All these techniques will only be able to achieve Angstrom resolution when the aberration barriers have been overcome. The spherical aberration barrier has recently been broken by introducing spherical aberration correctors (Nature 392 (1998) 392, 418 (2002) 617), but the correction of the remaining chromatic aberrations have proved to be too difficult for the present state of technology (Optik 57 (1980) 73). Here we present an alternative and successful method to eliminate the chromatic blur, which consists of monochromating the TEM beam (Inst. Phys. Conf. Ser. 161 (1999) 191). We show directly interpretable resolutions well below 1A for the first time, which is significantly better than any TEM operating at 200 KV has reached before.     

Low-energy foil aberration corrector

A spherical and chromatic aberration corrector for electron microscopes is proposed, consisting of a thin foil sandwiched between two apertures. The electrons are retarded at the foil to almost zero energy, so that they can travel ballistically through the foil. It is shown that such a low-voltage corrector has a negative spherical aberration for not too large distances between aperture and foil, as well as a negative chromatic aberration. For various distances the third- and fifth-order spherical aberration coefficients and the first- and second-order chromatic aberration coefficients are calculated using ray tracing. Provided that the foils have sufficient electron transmission the corrector is able to correct the third-order spherical aberration and the first-order chromatic aberration of a typical low-voltage scanning electron microscope. Preliminary results show that the fifth-order spherical aberration and the second-order chromatic aberration can be kept sufficiently low.     

A method of dynamic chromatic aberration correction in low-voltage scanning electron microscopes

A time-of-flight concept that dynamically corrects for chromatic aberration effects in scanning electron microscopes (SEMs) is presented. The method is predicted to reduce the microscope's chromatic aberration by an order of magnitude. The scheme should significantly improve the spatial resolution of low-voltage scanning electron microscopes (LVSEMs). The dynamic means of correcting for chromatic aberration also allows for the possibility of obtaining high image resolution from electron guns that have relatively large energy spreads.     

Optimum HRTEM image contrast at 20 kV and 80 kV--exemplified by graphene

The dependence of high-resolution transmission electron microscopy (HRTEM) image contrast of graphene on the adjustable parameters of an aberration-corrected microscope operated at 80 and 20 kV has been calculated and, for 80 kV, compared with measurements. We used density functional theory to determine the projected atom potential and obtained the image intensity by averaging over the energy distribution of the imaging electrons, as derived from the electron energy loss spectroscopy measurements. Optimum image contrast has been determined as a function of energy spread of the imaging electrons and chromatic aberration coefficient, showing that significant improvement of contrast can be achieved at 80 kV with the help of a monochromator, however at 20 kV only with chromatic aberration correction and bright atom contrast conditions.     

First experimental test of a new monochromated and aberration-corrected 200 kV field-emission scanning transmission electron microscope

The first 200 kV scanning transmission electron microscope (STEM) with an imaging energy filter, a monochromator and a corrector for the spherical aberration (Cs-corrector) of the illumination system has been built and tested. The STEM/TEM concept with Koehler illumination allows to switch easily between STEM mode for analytical and TEM mode for high-resolution or in situ studies. The Cs-corrector allows the use of large illumination angles for retaining a sufficiently high beam current despite the intensity loss in the monochromator. With the monochromator on and a 3 microm slit in the dispersion plane that gives 0.26 eV full-width at half-maximum (FWHM) energy resolution we have obtained so far an electron beam smaller than 0.20 nm in diameter (FWHM as measured by scanning the spot quickly over the CCD) which contains 7 pA current and, according to simulations, should be around 0.12 nm in true size. A high-angle annular dark field (ADF) image with isotropic resolution better than 0.28 nm has been recorded with the monochromator in the above configuration and the Cs-corrector on. The beam current is still somewhat low for electron energy-loss spectroscopy (EELS) but is expected to increase substantially by optimising the condenser set-up and using a somewhat larger condenser aperture.     

The influence of objective lens aberrations in energy-loss spectrometry

The conditions under which the energy resolution and collection efficiency in electron energy-loss spectrometry are limited by the spherical and chromatic aberrations of the objective lens have been studied. It is shown that, for the optimum settings of the pre-spectrometer optics, the energy resolution will be of the same order in diffraction mode as it is in magnification mode. The influence of the aberrations on the practice of energy-loss spectroscopy is discussed, and it is demonstrated that the chromatic aberration can act as a broadband filter for energy-loss electrons.     

Adaptive aberration correction using a triode hyperbolic electron mirror

A converging electron mirror can be used to compensate spherical and chromatic aberrations in an electron microscope. This paper presents an analytical solution to a novel triode (three electrode) hyperbolic mirror as an improvement to the well-known diode (two electrode) hyperbolic mirror for aberration correction. A weakness of the diode mirror is a lack of flexibility in changing the chromatic and spherical aberration coefficients independently without changes in the mirror geometry. In order to remove this limitation, a third electrode can be added. We calculate the optical properties of the resulting triode mirror analytically on the basis of a simple model field distribution. We present the optical properties-the object/image distance, z(0), and the coefficients of spherical and chromatic aberration, C(s) and C(c), of both mirror types from an analysis of electron trajectories in the mirror field. From this analysis, we demonstrate that while the properties of both designs are similar, the additional parameters in the triode mirror improve the range of aberration that can be corrected. The triode mirror is also able to provide a dynamic adjustment range of chromatic aberration for fixed spherical aberration and focal length, or any permutation of these three parameters. While the dynamic range depends on the values of aberration correction needed, a nominal 10% tuning range is possible for most configurations accompanied by less than 1% change in the other two properties.     

Transmission electron microscopy with a liquid flow cell

The imaging of microscopic structures at nanometre-scale spatial resolution in a liquid environment is of interest for a wide range of studies. Recently, a liquid flow transmission electron microscopy (TEM) holder equipped with a microfluidic cell has been developed and shown to exhibit flow of nanoparticles through an electron transparent viewing window. Here we demonstrate the application of the flow cell system for both scanning and conventional transmission electron microscopy imaging of immobilized nanoparticles with a resolution of a few nanometres in liquid water of micrometre thickness. The spatial resolution of conventional TEM bright field imaging is shown to be limited by chromatic aberration due to multiple inelastic scattering in the water, and we demonstrate that the liquid in the cell can be displaced by a gas phase that forms under intense electron irradiation. Our data suggest that under appropriate conditions, TEM imaging with a liquid flow cell is a promising method for understanding the in situ behaviour of nanoscale structures in a prescribed and dynamically changing chemical environment.     

Energy loss spectroscopic profiling across linear interfaces: the example of amorphous carbon superlattices

Energy loss spectroscopic profiling is a way to acquire, in parallel, spectroscopic information across a linear feature of interest, using a Gatan imaging filter (GIF) fitted to a transmission electron microscope (TEM). This technique is capable of translating the high spatial resolution of a bright field image into a sampling of the spectral information with similar resolution. Here we evaluate the contributions of chromatic aberration and the various acquisition parameters to the spatial sampling resolution of the spectral information, and show that this can reach 0.5 nm, in a system not ordinarily capable of forming electron probes smaller than 2 nm. We use this high spatial sampling resolution to study the plasmon energy variation across amorphous carbon superlattices, in order to extract information about their structure and electronic properties. By modelling the interaction of the relativistic incident electrons with a dielectric layer sandwiched between outer layers, we show that, due to the screening of the interfaces and at increased collection angles, the plasmon energy in the sandwiched layer can still be identified for layer thicknesses down to 5 A. This allows us to measure the change in the well bandgap as a function of well width and to interpret it in terms of the changes in the sp2 -fractions due to the deposition method, as measured from the carbon K-edges, and in terms of quantum confinement of the well wavefunction by the adjacent barriers.     

A new aberration-corrected,energy-filtered LEEM/PEEM instrument. I. Principles and design

We describe a new design for an aberration-corrected low energy electron microscope (LEEM) and photo electron emission microscope (PEEM), equipped with an in-line electron energy filter. The chromatic and spherical aberrations of the objective lens are corrected with an electrostatic electron mirror that provides independent control over the chromatic and spherical aberration coefficients C_c and C₃, as well as the mirror focal length, to match and correct the aberrations of the objective lens. For LEEM (PEEM) the theoretical resolution is calculated to be ∼1.5 nm (∼4 nm). Unlike previous designs, this instrument makes use of two magnetic prism arrays to guide the electron beam from the sample to the electron mirror, removing chromatic dispersion in front of the mirror by symmetry. The aberration correction optics was retrofitted to an uncorrected instrument with a base resolution of 4.1 nm in LEEM. Initial results in LEEM show an improvement in resolution to ∼2 nm.     

Top-bottom effect in energy-selecting transmission electron microscopy

Energy-selecting TEM can avoid the chromatic error of large specimen thicknesses when selecting an energy window at the most probable energy loss. The resolution is limited by the spatial beam broadening for structures at the top (electron entrance) of the specimen layer. A test experiment with polystyrene spheres of 1.1 μm in diameter shows a blurring of 8 nm when imaging with ΔE = 250 eV and E = 80 keV.     

Prospects for aberration-free electron microscopy

Future aberration-corrected electron microscopes that will enable sub-Angstroem spatial and sub-eV energy resolution are outlined . The sub-Angstroem transmission electron microscope (SATEM) only compensates for the spherical aberration and reduces the chromatic aberration disc by means of a monochromator. In order to correct for both aberrations, two novel correctors, the ultracorrector and the superaplanator are proposed which will yield a resolution limit of about 0.5A and a large field of view of more than 4 x 10(6) image points. The superaplanator is best suited for obtaining an achromatic aplanat required for the realization of the high-performance in situ electron microscope of the TEAM project.     

Contrast in the electron spectroscopic imaging mode of a TEM. I. Influence of zero-loss filtering on scattering contrast

Measured values of the transmission of amorphous films as a function of the objective aperture and film thickness can be described by a single-scattering theory for unfiltered and zero-loss filtered images in the electron spectroscopic imaging mode of a transmission electron microscope. The theory can be applied to estimate the gain of contrast by zero-loss filtering for specimen structures larger and smaller than the chromatic aberration disc.     

Differential algebraic method for aberration analysis of typical electrostatic lenses

In this paper up to fifth-order geometric and third-order chromatic aberration coefficients of typical electrostatic lenses are calculated by means of the charged particle optics code, COSY INFINITY, based on the differential algebraic (DA) method. A two-tube immersion lens and a symmetric einzel lens have been chosen as two examples, whose axial potential distributions are numerically calculated by a FORTRAN program using the finite difference method. The DA results are in good agreement with those evaluated by the aberration integrals in electron optics. The DA method presented here can easily be extended to aberration analysis of other numerically computed electron lenses, including magnetic lenses.     

低色差GRIN棒透镜的设计原则

对梯度折射率(GRIN)棒透镜色差的影响因素进行了讨论,根据Fantone模型,在光学玻璃Nd-V图中直观地表示了离子交换法制备低色差GRIN棒透镜时交换离子对的选择原则和基础玻璃光学性能确定原则.分析表明,以具有常用光学性质的玻璃作为基础玻璃,可以通过Na⁺/Li⁺交换或K⁺/Cs⁺交换获得低色差GRIN棒透镜,而K⁺/Tl⁺交换和Na⁺/Ag⁺交换所制作的GRIN棒透镜具有很大的色差.上述原则对低色差GRIN棒透镜的制作具有指导意义.     

High-order and multipole aberrations by aberration integral and direct ray-tracing methods

This paper describes methods for computing high-order aberrations and multipole aberrations in electron optical systems. Two approaches are discussed – the first involves obtaining aberration integrals for the high-order aberration coefficients, in terms of paraxial rays and axial field functions, while the second method uses direct ray-tracing through fields computed accurately by finite element or finite difference methods. The methods are illustrated by several examples, including a wide-angle focusing and deflection system with fifth-order aberrations, a combined magnetic and electrostatic lens, a ‘supertip’ ion source, an electron mirror with negative spherical and chromatic aberration, and a chromatically corrected quadrupole lens.     

High resolution at low beam energy in the SEM: resolution measurement of a monochromated SEM

The resolution of secondary electron low beam energy imaging of a scanning electron microscope equipped with a monochromator is quantitatively measured using the contrast transfer function (CTF) method. High-resolution images, with sub-nm resolutions, were produced using low beam energies. The use of a monochromator is shown to quantitatively improve the resolution of the SEM at low beam energies by limiting the chromatic aberration contribution to the electron probe size as demonstrated with calculations and images of suitable samples. Secondary electron image resolution at low beam energies is ultimately limited by noise in the images as shown by the CTFs.     

Studies of a magnetically focused electrostatic mirror. II. Aberration corrections

A magnetically focused electrostatic mirror is shown to be able to correct the spherical and chromatic aberrations of a probe forming system simultaneously. The probe forming system comprises a uniform magnetic lens and a uniform electrostatic mirror. Previous theoretical investigations showed that the spherical and chromatic aberration coefficients of these two components are the same values but with opposite sign, whose combination will therefore be free from aberrations. The experimental arrangement used a solenoid to produce a uniform magnetic field, and a series of plate electrodes to produce a uniform electrostatic field. These fields are shown to satisfy the experimental requirements. By deliberately changing the extraction voltage to defocus the electron beam, the author is able to observe correction of chromatic aberration by one order of magnitude. By deliberately changing the lens field and the mirror field, the author is able to observe the reduction of the asymmetry caused by the spherical aberration, which the author believes also indicates correction by one order of magnitude.     

Design of an aberration corrected low-voltage SEM

The low-voltage foil corrector is a novel type of foil aberration corrector that can correct for both the spherical and chromatic aberration simultaneously. In order to give a realistic example of the capabilities of this corrector, a design for a low-voltage scanning electron microscope with the low-voltage foil corrector is presented. A fully electrostatic column has been designed and characterised by using aberration integrals and ray tracing calculations. The amount of aberration correction can be adjusted relatively easy. The third order spherical and the first order chromatic aberration can be completely cancelled. In the zero current limit, a FW50 probe size of 1.0 nm at 1 kV can be obtained. This probe size is mainly limited by diffraction and by the fifth order spherical aberration.     

Double aberration correction in a low-energy electron microscope

The lateral resolution of a surface sensitive low-energy electron microscope (LEEM) has been improved below 4 nm for the first time. This breakthrough has only been possible by simultaneously correcting the unavoidable spherical and chromatic aberrations of the lens system. We present an experimental criterion to quantify the aberration correction and to optimize the electron optical system. The obtained lateral resolution of 2.6 nm in LEEM enables the first surface sensitive, electron microscopic observation of the herringbone reconstruction on the Au(1 1 1) surface.