Energy-filtered Convergent-beam Electron Diffraction Research Articles

Differential quantitative analysis of background structure in energy-filtered convergent-beam electron diffraction patterns

Measurements of electronic structure in solids by quantitative convergent-beam electron diffraction (QCBED) will not reach their ultimate accuracy or precision until the contribution of the background to the reflections in energy-filtered CBED patterns is fully accounted for. Apart from the well known diffuse background that arises from thermal diffuse scattering of electrons, there is a component that has a much higher angular frequency. The present work reports experimental evidence that this component mimics the angular distribution of the elastically scattered electrons within each reflection. A differential approach to QCBED is suggested as a means of quantitatively accounting for the background in energy-filtered CBED data.

Observations of flow in Inx Ga1-xAs multilayers

Work elsewhere has shown that the hardnesses of coherent InxGa1-xAs multilayer structures in which the misfit stresses are controlled by varying the indium content in each layer are influenced by the thicknesses and the coherency strains in the layers. These results have been interpreted in terms of the length-scale for flow being greater than the layer thickness and associated with deformation size effects. However, nanoindentation of InxGa1-x As suggests an influence of the flow stress of the individual layers on the overall multilayer flow stress. Consequently, initiation of flow in the weaker layer is expected. A deformed multilayer has been characterized by measurement of the lattice rotations measured from energy-filtered convergent beam electron diffraction (CBED) patterns recorded in scanning transmission electron microscopy (STEM) mode. Based on the movement of Kikuchi lines as a result of rotations of the lattice the local orientation of the crystal can be extracted, allowing the local orientations to be estimated. The small probe-size in CBED of ∼1 nm used here ensures the region sampled is smaller than the thickness of the individual layers. These measurements have been used to construct a map of the axes of rotation in the lattice which demonstrates the ability to distinguish the individual layers.

Composition analysis of semiconductor quantum wells by energy filtered convergent-beam electron diffraction

We show how energy-filtered convergent-beam electron diffraction (EFCBED) patterns can be used to determine the chemical composition of buried semiconductor strained quantum wells. Our method is based on a quantitative analysis of the intensities of high-order Bragg lines in the transmitted disc of EFCBED patterns taken from plan-view samples. This analysis makes it possible to determine the displacement vector R introduced between the top and bottom parts of the matrix by the deformation of the quantum well and consequently to determine its composition. This is illustrated in the case of an In x Ga 1− x As quantum well buried in a GaAs matrix. A detailed analysis of the effect of experimental parameters on Bragg lines intensity is performed. In particular, the importance of the choice of the diffraction vector is pointed out. The relative uncertainty on the measurement of the indium content x is found to be lower than 5% and a possible occurrence of slight compositional fluctuations in the (0 0 1) growth plane is pointed out.

Direct strain measurement in a 65nm node strained silicon transistor by convergent-beam electron diffraction

Using the energy-filtered convergent-beam electron diffraction (CBED) technique in a transmission electron microscope, the authors report here a direct measurement of the lattice parameters of uniaxially strained silicon as close as 25nm below the gate in a 65nm node p-type metal-oxide-semiconductor field-effect transistor with SiGe source and drain. It is found that the dominant strain component (0.58%) is compressive along the source-drain direction. The compressive stress is 1.1GPa along this direction. These findings demonstrate that CBED can serve as a strain metrology technique for the development of strained silicon device technology.

Analysis of Nano-scale Strain Near Shallow Trench Isolation Structures by Energy-filtered Convergent Beam Electron Diffraction

Extended abstract of a paper presented at Microscopy and Microanalysis 2006 in Chicago, Illinois, USA, July 30 – August 3, 2006

Analysis of Nanoscale Stress in Strained Silicon Materials and Microelectronics Devices by Energy-Filtered Convergent Beam Electron Diffraction

The convergent beam electron diffraction (CBED) technique of transmission electron microscopy (TEM) has excellent capabilities for strain detection at high spatial resolution. Here we report strain measurements in a bulk s-Si/SiGe/Si wafer and in a strained 35nm PMOS device in which SiGe acts as the source and drain. CBED measurements of the composition of the relaxed SiGe buffer are in quantitative agreement with Raman spectroscopy. For the PMOS device, CBED measured a uniaxial compressive stress of 1.12GPa in the channel. However, it was found that even in the cross-sectional TEM samples with thicknesses greater than 300nm, the intrinsic surface strain relaxation was often so severe that no recognizable high-order Laue zone lines in the CBED patterns could be collected. The amorphorization of both free surfaces of the TEM sample to a range of about 80nm is proposed to minimize the impact of surface strain relaxation for future study.

Analysis of Nano-scale Stress in Strained Silicon Materials and Microelectronics Devices by Energy-filtered Convergent Beam Electron Diffraction

not Available.

Radial Distribution Function Analyses of Amorphous Carbon Films Containing Silicon and Hydrogen by Energy-Filtered Diffraction and EXELFS

Short-range order in amorphous materials is most commonly characterized with the use of radial distribution functions (RDFs). Two analytical electron microscopy methods were used in this study to measure RDFs from amorphous carbon films containing different levels of silicon and hydrogen (Si-aC:H): energy-filtered convergent-beam electron diffraction (EFCBED) and extended electron energy-loss fine structure (EXELFS) analyses. The films were deposited in an industrial-scale system onto a thin adhesive titanium layer on silicon substrates by reactive sputtering of carbon with a feed gas of tetramethyl silane (TMS) and argon, to produce a series of films with different Si and H contents (Si/C = 0, 0.04, 0.10, and 0.18).

Radial distribution function analyses of amorphous carbon thin films containing various levels of silicon and hydrogen

Short-range order in amorphous carbon thin films containing silicon and hydrogen (Si-aC:H) was characterized using radial distribution functions (RDFs). RDFs describe the average number of neighbors located a distance r away from an arbitrary atom in the sample. Two methods in the transmission electron microscope (TEM) were used in this study to obtain RDFs: energy-filtered convergent-beam electron diffraction (EFCBED) and extended electron energy-loss fine structure (EXELFS) analyses. Four Si-aC:H film samples were prepared in cross section for TEM using a focused ion beam system. Both EFCBED and EXELFS techniques were used to study the same samples. RDF interpretation included estimation and comparison of near-neighbor distances, average bond angles, and coordination numbers as a function of sample composition. Key RDF characteristics were correlated to thin film material properties.

In situ observation of oxygen deficiency occurring during electron irradiation in high Tc superconductor YBa2Cu3Oy.

The decreasing process of oxygen in YBa2Cu3Oy is investigated through high resolution electron microscopy (HREM) and convergent beam electron diffraction (CBED). Measurements of the axial length in HREM images show that oxygen content y decreases faster near a twin boundary than at the inner part of a twin lamella. The transformation from an orthorhombic to a tetragonal phase starts at a twin boundary and the transformed region propagates to an inner region of lamella. Lattice strains are observed near boundaries between transformed and non-transformed regions. The transformation is almost complete within 30 s during observation of HREM images at 400 kV and at room temperature. A value of y was quantitatively measured by analysing observed intensities of energy-filtered CBED patterns with the dynamical theory. The value of y decreases from 6.9 to 6.5 when 200 kV electrons are irradiated for 160 s in a microscope at 108 K. More precise analysis of the intensities provides information on charge distribution along the c-axis as well as local oxygen content at a spatial resolution of several nanometres.

Refinement of crystal structural parameters using two-dimensional energy-filtered CBED patterns.

A new method to refine crystal structural parameters using convergent-beam electron diffraction (CBED), which is applicable to nanometre-size crystal structure analysis, is proposed. This method is based on the fitting between theoretical calculations and experimental intensities of energy-filtered two-dimensional CBED patterns containing higher-order Laue-zone (HOLZ) reflections. The use of HOLZ reflections is essential for the method because small displacements of atoms can be sensitively detected using HOLZ reflections with large reciprocal vectors. For this purpose, a new Omega-filter transmission microscope (JEM-2010FEF), which can take energy-filtered CBED patterns up to a high angle with a small distortion, and a new analysis program to refine structural parameters, which is based on many-beam Bloch-wave calculations and nonlinear least-squares fitting, have been developed. As a test example, a positional parameter and isotropic and anisotropic Debye-Waller factors of CdS have been refined. Two-dimensional CBED patterns calculated with the refined parameters show very good agreement with the experimental ones, and the refined values of the parameters also agree well with the result of a single-crystal X-ray diffraction experiment. Important problems of the analysis procedure are discussed item by item.

Accurate structure refinement and measurement of crystal charge distribution using convergent beam electron diffraction.

The method for accurate structure refinement from energy-filtered convergent-beam electron diffraction (CBED) patterns is described with emphasis on recent progress in using imaging filters and 2-D detectors. Details are given about the underlying theoretical model and the statistical analysis of experimental data. The relationship between crystal potential and charge density is also derived for crystals at thermal equilibrium. The method is applied to the refinement of Si (111) and (222) structure factors using various goodness-of-fit (GOF) criteria. Results show that the refinement method is robust and highly accurate. The importance of the experimentally measured structure factors is illustrated through the study of the charge density in MgO. With the measured structure factors, it is possible to obtain details about the charge redistribution due to crystal bonding.

The quantitative characterization of SiGe layers by analysing rocking profiles in CBED patterns.

Convergent beam electron diffraction is used for the quantitative determination of layer thickness, composition and strain in pseudomorphic Si/SiGe two- and three-layer systems grown by molecular beam epitaxy. By using plan-view specimens, we are able to avoid the influence of surface relaxation which generally complicates the determination of strains in cross-sectional specimens. For quantitative strain determination, rocking curves of Bragg lines in energy-filtered convergent beam electron diffraction patterns are analysed. The experimentally obtained rocking curves are compared with kinematical calculations by a computerized fit procedure. The resulting layer parameters are then further refined by a dynamical simulation. Results for the strains obtained with this technique are in good agreement with theoretical values. With this method layer thickness is measured down to monolayer precision. The accuracy of the strain analysis depends on the sequence and thickness of the layers.

Corrections for Multiple Scattering in Integrated Electron Diffraction Intensities. Application to Determination of Structure Factors in the [001] Projection of AlmFe

Approximate methods are described for treating dynamical scattering effects in integrated electron diffraction intensities from unknown structures. In the application to AlmFe, (hk0) structure factors have been determined by combining data from two electron diffraction techniques: energy-filtered convergent-beam electron diffraction (CBED) profiles from the (h00) and (hh0) systematic rows and integrated intensity collected by the precession technique in the [001] projection. The ab initio determination of the (h00) and (hh0) structure factors was based on accurate intensity measurements and n-beam dynamical scattering calculations for the systematic row. The remaining (hk0) structure factors were determined from integrated intensities by means of two-beam-like intensity expressions and the effect of other beams was accounted for by a dynamical potential.

Effects of Debye-Waller factors and compositional uncertainties on the 200 structure factor refinement eta in-TiAl

The effects of uncertainties in Debye-Waller factors and chemical composition on 200 structure factor refinement in eta-TiAl have been investigated. Energy-filtered convergent-beam electron diffraction has been used to record 200 rocking curves from two different thicknesses of a thin foil taken from a Ti-51.3 1Al alloy (all compositions in atomic per cent). The structure factor has been refined by matching rocking curves determined by experiment to those theoretically calculated using the Bloch wave formalism of the dynamical theory of electron diffraction. The influence of uncertainties in the Debye-Waller factors and sample composition have been assessed: for samples deviating from stoichiometry, the need to use accurate site-specific Debye-Waller factors has been demonstrated. Also, to extract accurate structure factors, it is necessary to make use of homogeneous samples, the compositions of which must be known to better than 0.2%, a rather restrictive limitation.

Low-Order Structure-Factor Amplitude and Sign Determination of an Unknown Structure AlmFe by Quantitative Convergent-Beam Electron Diffraction

An iterative method for the determination of structure-factor amplitudes and phases of crystals with unknown structure is proposed. The method is based on the quantitative evaluation of energy-filtered convergent-beam electron diffraction (CBED) patterns. It has been applied to the metastable phase AlmFe (m = 4.2–4.4), which was found as primary particles in commercial aluminium alloys. When the rocking curves of reflections along a (100) systematic row are fitted, a number of structure-factor amplitudes and signs of h00-type reflections of AlmFe have been determined successfully. The accuracy of the structure-factor amplitudes is better than 5% for the strong reflections and about 10% for the weak reflections. The aim of this method is to provide accurate structure-factor data, including both amplitudes and phases, for ab initio structure determination and refinement of unknown structures by using electron diffraction techniques.

The use of Bethe potentials in zone-axis CBED pattern matching

In recent years quantitative diffraction techniques have been developed which can obtain accurate low-order structure factors by matching theoretical calculations to experimental energy-filtered Convergent Beam Electron Diffraction (CBED) patterns. These techniques rely on the calculation of accurate diffraction intensities which requires lengthy computation. We have previously described a method of reducing computing times using perturbation theory. In this paper we describe a modification to our original zone-axis pattern matching method to include Bethe potentials. The modifications to the pattern matching process are described and the results of structure factor measurements for Si [110] patterns using Bethe potentials are discussed.

Structure factor measurement in TiAl and silicon

The accurate measurement of low order structure factors is required for the determination of the electron charge density distribution in crystals. In this work the energy-filtered convergent beam electron diffraction (CBED) rocking curve method has been used for accurate structure factor measurements. This CBED method for structure factor refinement involves matching of the experimental CBED intensities to those calculated using dynamical electron diffraction theory. The CBED experiments were conducted with a Philips EM420 Transmission Electron Microscope coupled with a custom built energy-filtering attachment enabling single electron counting. The theoretical pattern matching was performed using FORTRAN programs which were developed by Swaminathan. Initially the experimental plan involved an attempt to refine structure factors of TiAl by two dimensional Bloch wave calculations. The results of this project have been reported elsewhere. Subsequently it proved impossible to obtain results with sufficient precision for TiAl reproducibly, i.e. less than 0.1%, from samples of different thicknesses.

Contrast of HOLZ lines in energy-filtered convergent-beam electron diffraction patterns from silicon

Higher-order Laue-zone (HOLZ) lines were investigated in convergent-beam electron diffraction patterns from silicon near the low-indexed zone axes [100], [110] and [111]. The visibility of these lines depends on the effective structure potentials of the reflections from the first Laue zone depending on their Debye–Waller factor. The contrast of the HOLZ lines is strongly reduced by inelastically scattered electrons. They can be excluded by an imaging Ω filter for energy losses above 2 eV. The diffraction patterns were compared with many-beam calculations. Without absorption, an excellent agreement could be achieved for the [111] and [100] zone axes, while the simulation of the [110] zone-axis pattern needed a calculation with absorption. The reason for this observation is explained in the Bloch-wave picture. Calculations with absorption, however, lead to artefacts in the intensity distribution of the [100] HOLZ pattern. In order to obtain agreement with the experiment, the Debye–Waller factor had to be modified in different ways for the different zone axes. This corresponds to a strong anisotropy of the Debye–Waller factor. To confirm this observation, the temperature dependence of the intensity distributions of the HOLZ patterns was investigated between 50 and 680 K. At room temperature, the parameter D in the Debye–Waller factor exp(−Ds2) was determined as 0.13, 0.26 and 0.55 Å2 for the zone axes [100], [111] and [110], respectively. The reliability of the conclusions is discussed.

Direct retrieval of crystal structure factors in THEED

A linear model and a non-linear quadratic model for transmission high-energy electron diffraction (THEED) have been developed and applied to invert crystal structure factors directly from energy-filtered convergent beam electron diffraction (CBED) intensities. The models are based on perturbation theory of high-energy electron diffraction, and the unperturbated reference structure factors are constructed from an assembly of neutral atoms. The single and double diffraction approximations used in the linear and quadratic models are shown to be good approximations for describing the redistributed charge scattering in crystals, and the inverted crystal structure factors are shown to be unique for all practical sample thicknesses used in THEED.