Strain analysis from nano-beam electron diffraction: Influence of specimen tilt and beam convergence.

Strain analyses from experimental series of nano-beam electron diffraction (NBED) patterns in scanning transmission electron microscopy are performed for different specimen tilts. Simulations of NBED series are presented for which strain analysis gives results that are in accordance with experiment. This consequently allows to study the relation between measured strain and actual underlying strain. A two-tilt method which can be seen as lowest-order electron beam precession is suggested and experimentally implemented. Strain determination from NBED series with increasing beam convergence is performed in combination with the experimental realization of a probe-forming aperture with a cross inside. It is shown that using standard evaluation techniques, the influence of beam convergence on spatial resolution is lower than the influence of sharp rings around the diffraction disc which occur at interfaces and which are caused by the tails of the intensity distribution of the electron probe.

Optimization of NBED simulations for disc-detection measurements.

Nano-beam electron diffraction (NBED) is a method which can be applied to measure lattice strain and polarisation fields in strained layer heterostructures and transistors. To investigate precision, accuracy and spatial resolution of such measurements in dependence of properties of the specimen as well as electron optical parameters, simulations of NBED patterns are required which allow to predict the result of common disc-detection algorithms. In this paper we demonstrate by focusing on the detection of the central disc in crystalline silicon that such simulations require to take several experimental characteristics into account in order to obtain results which are comparable to those from experimental NBED patterns. These experimental characteristics are the background intensity, the presence of Poisson noise caused by electron statistics and blurring caused by inelastic scattering and by the transfer quality of the microscope camera. By means of these optimized simulations, different effects of specimen properties on disc detection - such as strain, surface morphology and compositional changes on the nanometer scale - are investigated and discussed in the context of misinterpretation in experimental NBED evaluations. It is shown that changes in surface morphology and chemical composition lead to measured shifts of the central disc in the NBED pattern of tens to hundreds of µrad. These shifts are of the same order of magnitude or even larger than shifts that could be caused by an electric polarisation field in the range of MV/cm.

Theoretical study of precision and accuracy of strain analysis by nano-beam electron diffraction.

Measurement of lattice strain is important to characterize semiconductor nanostructures. As strain has large influence on the electronic band structure, methods for the measurement of strain with high precision, accuracy and spatial resolution in a large field of view are mandatory. In this paper we present a theoretical study of precision and accuracy of measurement of strain by convergent nano-beam electron diffraction. It is found that the accuracy of the evaluation suffers from halos in the diffraction pattern caused by a variation of strain within the area covered by the focussed electron beam. This effect, which is expected to be strong at sharp interfaces between materials with different lattice plane distances, will be discussed for convergent-beam electron diffraction patterns using a conventional probe and for patterns formed by a precessing electron beam. Furthermore, we discuss approaches to optimize the accuracy of strain measured at interfaces. The study is based on the evaluation of diffraction patterns simulated for different realistic structures that have been investigated experimentally in former publications. These simulations account for thermal diffuse scattering using the frozen-lattice approach and the modulation-transfer function of the image-recording system. The influence of Poisson noise is also investigated.

Comparison of intensity and absolute contrast of simulated and experimental high-resolution transmission electron microscopy images for different multislice simulation methods.

The Stobbs factor problem, a major difference of absolute contrast between experimental and simulated high resolution transmission electron microscopy images has been reported frequently. In this respect, some modifications to the multislice simulation techniques were proposed to improve the correspondence to the experiment. The influence of different suggestions on the simulated contrast is investigated by numerical simulations. The agreement between experiment and simulations is then checked by comparison with high-resolution micrographs of crystalline gold. The experimental data is therefore compared to simulated intensities computed for the thickness and orientation of the specimen measured by refinements of diffraction patterns. The agreement of both intensity and contrast is investigated and the remaining contrast discrepancy is determined. The results show a good agreement for a small objective aperture, while for a larger aperture a difference of contrast by a factor of 1.2 can still be observed. Without any aperture, the deviation between experiment and simulations is largest.