GaN atomic electric fields from a segmented STEM detector: Experiment and simulation.

Atomic electric fields in a thin GaN sample are measured with the centre-of-mass approach in 4D-scanning transmission electron microscopy (4D-STEM) using a 12-segmented STEM detector in a Spectra 300 microscope. The electric fields, charge density and potential are compared to simulations and an experimental measurement using a pixelated 4D-STEM detector. The segmented detector benefits from a high recording speed, which enables measurements at low radiation doses. However, there is measurement uncertainty due to the limited number of segments analysed in this study.

Dose efficient annular bright field contrast with the ISTEM method: A proof of principle demonstration.

The ISTEM mode for TEM has been demonstrated to have several advantages in regard to resolution and precision. While previous works primarily focussed on the advantages due to the reduced spatial coherence, the actual image contrast, i.e. how bright or dark certain atom columns are imaged, has mostly been of secondary concern. The present work sets out to achieve the contrast of annular bright field STEM in ISTEM, producing the high contrast of light elements, for which this method is popular. It is shown from theoretical considerations that using an annular condenser aperture this aim can be realised. The optimal size of this aperture is found by simulative studies. It is then manufactured from platinum foil and installed in an image-aberration corrected microscope. ABF-like ISTEM images of strontium titanate in [100] projection are acquired. The pure oxygen columns are clearly resolved with significant contrast. The image pattern is indeed identical to what is achieved by ABF STEM. A close look at the image formation also shows that the dose needed for a given signal-to-noise ratio is at least a quarter smaller for ABF-like ISTEM compared to ABF STEM, assuming detectors of similar detective quantum efficiency.

Accuracy and precision of position determination in ISTEM imaging of BaTiO3.

In this paper we study the effect of lens aberrations (spherical aberration and astigmatism), beam tilt, contamination and shot noise on the accuracy and precision of position determination in imaging scanning transmission electron microscopy (ISTEM) on the example of BaTiO3. ISTEM images are simulated as a function of sample thickness and defocus starting from a nearly perfect microscope setting. A defocus range was identified, in which atom column positions were reliably visible and could be decently measured. By averaging over this defocus and thickness range a figure of merit was defined and used to study the influence of above mentioned disturbing effects as a function of their strength. It turned out that column positions might become inaccurate, but distances are measured accurately. These were used to obtain recommendations for the experimental setup to measure the atomic arrangement that induces ferroelectric switching of BaTiO3.

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.

Using molecular dynamics for multislice TEM simulation of thermal diffuse scattering in AlGaN.

For simulation of transmission electron microscopic images and diffraction patterns, the accurate inclusion of thermal diffuse scattering by phonons is important. In the frozen phonon multislice algorithm, this is possible, if thermal displacements according to the realistic, quantum mechanical distribution can be generated. For pure crystals, quantum mechanical calculations based on DFT yield those displacements. But for alloys one is usually restricted to the Einstein approximation, where correlations between atoms are neglected. In this article, molecular dynamics simulations are discussed and used as an alternative method for displacement calculation. Employing an empirical Stillinger-Weber type potential, classical motion is used as an approximation for the quantum mechanical dynamics. Thereby, correlations and possible static atomic displacements are inherently included. An appropriate potential is devised for AlGaN by fitting to force constant matrices determined from DFT and elastic constants of AlN and GaN. A comparison shows that the empiric potential reproduces phonon dispersions and displacement expectations from DFT references. The validity for alloys is successfully demonstrated by comparison to DFT calculations in special quasirandom structures. Subsequently, molecular dynamics were used in multislice simulations of both conventional and scanning TEM images. The resulting images are in very good agreement with DFT based calculations, while a slight yet significant deviation from Einstein approximation results can be seen, which can be attributed to the neglect of correlations in the latter. The presented potential hence proves to be a useful tool for accurate TEM simulations of AlGaN alloys.

Quantitative HAADF STEM of SiGe in presence of amorphous surface layers from FIB preparation.

The chemical composition of four Si1-xGex layers grown on silicon was determined from quantitative scanning transmission electron microscopy (STEM). The chemical analysis was performed by a comparison of the high-angle annular dark field (HAADF) intensity with multislice simulations. It could be shown that amorphous surface layers originating from the preparation process by focused-ion beam (FIB) at 30 kV have a strong influence on the quantification: the local specimen thickness is overestimated by approximately a factor of two, and the germanium concentration is substantially underestimated. By means of simulations, the effect of amorphous surface layers on the HAADF intensity of crystalline silicon and germanium is investigated. Based on these simulations, a method is developed to analyze the experimental HAADF-STEM images by taking the influence of the amorphous layers into account which is done by a reduction of the intensities by multiplication with a constant factor. This suggested modified HAADF analysis gives germanium concentrations which are in agreement with the nominal values. The same TEM lamella was treated with low-voltage ion milling which removed the amorphous surface layers completely. The results from subsequent quantitative HAADF analyses are in agreement with the nominal concentrations which validates the applicability of the used frozen-lattice based multislice simulations to describe the HAADF scattering of Si1-xGex in STEM.

Materials characterisation by angle-resolved scanning transmission electron microscopy.

Solid-state properties such as strain or chemical composition often leave characteristic fingerprints in the angular dependence of electron scattering. Scanning transmission electron microscopy (STEM) is dedicated to probe scattered intensity with atomic resolution, but it drastically lacks angular resolution. Here we report both a setup to exploit the explicit angular dependence of scattered intensity and applications of angle-resolved STEM to semiconductor nanostructures. Our method is applied to measure nitrogen content and specimen thickness in a GaNxAs1-x layer independently at atomic resolution by evaluating two dedicated angular intervals. We demonstrate contrast formation due to strain and composition in a Si- based metal-oxide semiconductor field effect transistor (MOSFET) with GexSi1-x stressors as a function of the angles used for imaging. To shed light on the validity of current theoretical approaches this data is compared with theory, namely the Rutherford approach and contemporary multislice simulations. Inconsistency is found for the Rutherford model in the whole angular range of 16-255 mrad. Contrary, the multislice simulations are applicable for angles larger than 35 mrad whereas a significant mismatch is observed at lower angles. This limitation of established simulations is discussed particularly on the basis of inelastic scattering.

Nanoscopic Insights into InGaN/GaN Core-Shell Nanorods: Structure, Composition, and Luminescence.

Nitride-based three-dimensional core-shell nanorods (NRs) are promising candidates for the achievement of highly efficient optoelectronic devices. For a detailed understanding of the complex core-shell layer structure of InGaN/GaN NRs, a systematic determination and correlation of the structural, compositional, and optical properties on a nanometer-scale is essential. In particular, the combination of low-temperature cathodoluminescence (CL) spectroscopy directly performed in a scanning transmission electron microscope (STEM), and quantitative high-angle annular dark field imaging enables a comprehensive study of the nanoscopic attributes of the individual shell layers. The investigated InGaN/GaN core-shell NRs, which were grown by metal-organic vapor-phase epitaxy using selective-area growth exhibit an exceptionally low density of extended defects. Using highly spatially resolved CL mapping of single NRs performed in cross-section, we give a direct insight into the optical properties of the individual core-shell layers. Most interesting, we observe a red shift of the InGaN single quantum well from 410 to 471 nm along the nonpolar side wall. Quantitative STEM analysis of the active region reveals an increasing thickness of the single quantum well (SQW) from 6 to 13 nm, accompanied by a slight increase of the indium concentration along the nonpolar side wall from 11% to 13%. Both effects, the increased quantum-well thickness and the higher indium incorporation, are responsible for the observed energetic shift of the InGaN SQW luminescence. Furthermore, compositional mappings of the InGaN quantum well reveal the formation of locally indium rich regions with several nanometers in size, leading to potential fluctuations in the InGaN SQW energy landscape. This is directly evidenced by nanometer-scale resolved CL mappings that show strong localization effects of the excitonic SQW emission.

Direct Measurement of Polarization-Induced Fields in GaN/AlN by Nano-Beam Electron Diffraction.

The built-in piezoelectric fields in group III-nitrides can act as road blocks on the way to maximizing the efficiency of opto-electronic devices. In order to overcome this limitation, a proper characterization of these fields is necessary. In this work nano-beam electron diffraction in scanning transmission electron microscopy mode has been used to simultaneously measure the strain state and the induced piezoelectric fields in a GaN/AlN multiple quantum well system.

Effects of instrument imperfections on quantitative scanning transmission electron microscopy.

Several instrumental imperfections of transmission electron microscopes are characterized and their effects on the results of quantitative scanning electron microscopy (STEM) are investigated and quantified using simulations. Methods to either avoid influences of these imperfections during acquisition or to include them in reference calculations are proposed. Particularly, distortions inflicted on the diffraction pattern by an image-aberration corrector can cause severe errors of more than 20% if not accounted for. A procedure for their measurement is proposed here. Furthermore, afterglow phenomena and nonlinear behavior of the detector itself can lead to incorrect normalization of measured intensities. Single electrons accidentally impinging on the detector are another source of error but can also be exploited for threshold-less calibration of STEM images to absolute dose, incident beam current determination and measurement of the detector sensitivity.

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.

Homogeneity and composition of AlInGaN: A multiprobe nanostructure study.

The electronic properties of quaternary AlInGaN devices significantly depend on the homogeneity of the alloy. The identification of compositional fluctuations or verification of random-alloy distribution is hence of grave importance. Here, a comprehensive multiprobe study of composition and compositional homogeneity is presented, investigating AlInGaN layers with indium concentrations ranging from 0 to 17at% and aluminium concentrations between 0 and 39 at% employing high-angle annular dark field scanning electron microscopy (HAADF STEM), energy dispersive X-ray spectroscopy (EDX) and atom probe tomography (APT). EDX mappings reveal distributions of local concentrations which are in good agreement with random alloy atomic distributions. This was hence investigated with HAADF STEM by comparison with theoretical random alloy expectations using statistical tests. To validate the performance of these tests, HAADF STEM image simulations were carried out for the case of a random-alloy distribution of atoms and for the case of In-rich clusters with nanometer dimensions. The investigated samples, which were grown by metal-organic vapor phase epitaxy (MOVPE), were thereby found to be homogeneous on this nanometer scale. Analysis of reconstructions obtained from APT measurements yielded matching results. Though HAADF STEM only allows for the reduction of possible combinations of indium and aluminium concentrations to the proximity of isolines in the two-dimensional composition space. The observed ranges of composition are in good agreement with the EDX and APT results within the respective precisions.

Conventional transmission electron microscopy imaging beyond the diffraction and information limits.

There are mainly two complementary imaging modes in transmission electron microscopy (TEM): Conventional TEM (CTEM) and scanning TEM (STEM). In the CTEM mode the specimen is illuminated with a plane electron wave, and the direct image formed by the objective lens is recorded in the image plane. STEM is based on scanning the specimen surface with a focused electron beam and collecting scattered electrons with an extended disk or ring-shaped detector. Here we show that combination of CTEM imaging with STEM illumination generally allows extending the point resolution of CTEM imaging beyond the diffraction limit. This new imaging mode improves imaging characteristics, is more robust against chromatic aberration, exhibits direct structural imaging with superior precision, visualizes light elements with excellent contrast, and even allows us to overcome the conventional information limit of a microscope.

Influence of static atomic displacements on composition quantification of AlGaN/GaN heterostructures from HAADF-STEM images.

In an earlier publication Rosenauer et al. introduced a method for determination of composition in AlGaN/GaN heterostructures from high-angle annular dark field (HAADF) images. Static atomic displacements (SADs) were neglected during simulation of reference data because of the similar covalent radii of Al and Ga. However, SADs have been shown (Grillo et al.) to influence the intensity in HAADF images and therefore could be the reason for an observed slight discrepancy between measured and nominal concentrations. In the present study parameters of the Stillinger-Weber potential were varied in order to fit computed elastic constants, lattice parameters and bonding energies to experimental ones. A reference data set of HAADF images was simulated, in which the new parameterization was used to account for SADs. Two reference samples containing AlGaN layers with different Al concentrations were investigated and Al concentrations in the layers determined based on the new data set. We found that these concentrations were in good agreement with nominal concentrations as well as concentrations determined using alternative techniques such as strain state analysis and energy dispersive X-ray spectroscopy.

Quantitative strain and compositional studies of InxGa1-xAs Epilayer in a GaAs-based pHEMT device structure by TEM techniques.

In GaAs-based pseudomorphic high-electron mobility transistor device structures, strain and composition of the In x Ga1-x As channel layer are very important as they influence the electronic properties of these devices. In this context, transmission electron microscopy techniques such as (002) dark-field imaging, high-resolution transmission electron microscopy (HRTEM) imaging, scanning transmission electron microscopy-high angle annular dark field (STEM-HAADF) imaging and selected area diffraction, are useful. A quantitative comparative study using these techniques is relevant for assessing the merits and limitations of the respective techniques. In this article, we have investigated strain and composition of the In x Ga1-x As layer with the mentioned techniques and compared the results. The HRTEM images were investigated with strain state analysis. The indium content in this layer was quantified by HAADF imaging and correlated with STEM simulations. The studies showed that the In x Ga1-x As channel layer was pseudomorphically grown leading to tetragonal strain along the [001] growth direction and that the average indium content (x) in the epilayer is ~0.12. We found consistency in the results obtained using various methods of analysis.

Measurement of indium concentration profiles and segregation efficiencies from high-angle annular dark field-scanning transmission electron microscopy images.

We investigated segregation of indium in an InxGa1-xAs/GaAs heterostructure via high-angle annular dark field-scanning transmission electron microscopy (HAADF-STEM), where contrast strongly depends on the nuclear charges of the scattering atoms (Z-contrast). Indium concentration maps have been deduced from HAADF-STEM images by comparing normalized measured intensities with multislice simulations in the frozen lattice approach. Segregation coefficients were derived following the segregation model of Muraki et al.. This is demonstrated for HAADF-STEM images recorded in [100] and [110] zone-axes. Determined indium concentrations and segregation coefficients are compared with results from composition analysis by lattice fringe analysis (CELFA) measurements and energy-dispersive X-ray analysis (EDX).

Optimization of the preparation of GaN-based specimens with low-energy ion milling for (S)TEM.

We report on optimization of electron transparent GaN based specimens for transmission electron microscopy (TEM) and scanning TEM (STEM) studies by combining focused ion beam thinning and low-energy (≤500 eV) Ar-ion milling. Energy dependent ion milling effects on GaN based structures are investigated and the quality of ion milled samples is compared with that of specimens prepared by wet chemical etching. Defects formed during ion milling lead to amorphization of the specimen. The experimental results are compared with Monte-Carlo simulations using the SRIM (stopping and range of ions in matter) software. Specimen thickness was deduced from high-angle annular dark field STEM images by normalization of measured intensities with respect to the intensity of the scanning electron probe and comparison with multislice simulations in the frozen lattice approach. The results show that the thickness of the amorphous surface layer can be successfully reduced below 1 nm by low energy ion milling, leading to a homogeneous image contrast in TEM and STEM, so that good conditions for quantitative analysis can be achieved. For an ion energy of 400 eV the thickness measurements resulted in an etching rate of about 6-8 nm/min.

Composition mapping in InGaN by scanning transmission electron microscopy.

We suggest a method for chemical mapping that is based on scanning transmission electron microscopy (STEM) imaging with a high-angle annular dark field (HAADF) detector. The analysis method uses a comparison of intensity normalized with respect to the incident electron beam with intensity calculated employing the frozen lattice approximation. This procedure is validated with an In(0.07)Ga(0.93)N layer with homogeneous In concentration, where the STEM results were compared with energy filtered imaging, strain state analysis and energy dispersive X-ray analysis. Good agreement was obtained, if the frozen lattice simulations took into account static atomic displacements, caused by the different covalent radii of In and Ga atoms. Using a sample with higher In concentration and series of 32 images taken within 42 min scan time, we did not find any indication for formation of In rich regions due to electron beam irradiation, which is reported in literature to occur for the parallel illumination mode. Image simulation of an In(0.15)Ga(0.85)N layer that was elastically relaxed with empirical Stillinger-Weber potentials did not reveal significant impact of lattice plane bending on STEM images as well as on the evaluated In concentration profiles for specimen thicknesses of 5, 15 and 50 nm. Image simulation of an abrupt interface between GaN and In(0.15)Ga(0.85)N for specimen thicknesses up to 200 nm showed that artificial blurring of interfaces is significantly smaller than expected from a simple geometrical model that is based on the beam convergence only. As an application of the method, we give evidence for the existence of In rich regions in an InGaN layer which shows signatures of quantum dot emission in microphotoluminescence spectroscopy experiments.