Angle‐resolved Scanning Transmission Electron Microscopy (
ARSTEM
) for materials analysis
Authors: Müller‐Caspary Knut , Oppermann Oliver , Grieb Tim , Rosenauer Andreas , Schowalter Marco , Krause Florian F. , Mehrtens Thorsten , Potapov Pavel , Beyer Andreas , Volz Kerstin 
Published: December 2016

Many solid‐state properties leave characteristic fingerprints in the angular dependence of electron scattering. STEM is dedicated to probe scattered intensity at atomic resolution, but it drastically lacks angular resolution due to detectors integrating over broad solid angles. By developing a setup which is capable of recording STEM images for dedicated acceptance angles of annular detectors, we firstly report the simultaneous measurement of specimen thickness, chemical composition and strain in a GaN
x
As
1‐x
/GaAs layer at atomic resolution. Our analysis exploits two angle ranges, namely A: 42‐66 and B: 82‐141mrad which exhibit different dependencies on nitrogen content x and specimen thickness as shown by the simulation in Fig.1a. To acquire images for dedicated angle settings, we developed a motorised, software‐controlled iris aperture (Fig.2a) mounted above the Fischione 3000 ring detector in a Titan 80/300 (S)TEM, which is used to control the outer acceptance angle of the detector as depicted by the detector scans in the inset. Consequently, a STEM image formed by electrons scattered to the angular interval [α,β] is obtained by the difference I(β)‐I(α) between 2 images taken at iris radii α and β.

For GaNAs, we recorded four 2Kx2K high‐resolution STEM (HRSTEM) images with iris radii 42, 66, 82 and 141 mrad, performed a Voronoi segmentation with respect to atomic columns and averaged the intensity within the Voronoi cells. By mapping the Voronoi intensity with respect to their cell index and correlating the images, specimen drift was compensated for. Subtracting respective images yields the data in Fig.1b,c for the desired angular ranges. The GaNAs layer is imaged with high contrast for the angular range of 42‐66 mrad whereas it is invisible for a detector acceptance of 82‐141 mrad. By simultaneously comparing Fig.1b,c with simulations [1], the local nitrogen content and specimen thickness were obtained as shown in Fig.1d,e. Hence our method overcomes the common problem to interpolate thickness from regions with known composition. Finally, profiles across the GaNAs layer (not shown) reveal an average N content of x=2.5% and a mean thickness of 186nm. The nitrogen content is verified by X‐ray studies and strain state analysis in one of the HRSTEM images. The total acquisition took 5:40min here whereas a 1kHz camera would have needed 70min to obtain this data.

Secondly, we imaged a Ge
x
Si
1‐x
/Si field effect transistor using a dense sampling of the scattering angles between 16 and 255 mrad at two specimen thicknesses of 50 and 150 nm. Two different camera lengths with each 16 outer acceptance angles were used as shown in the radial sensitivity curves in Fig.2b, obtained by scanning the beam over the detector with iris aperture. Fig.2c exemplarily shows several images recorded at the larger camera length. The first image for the range [16,22 mrad] completely lacks chemical contrast in favour of strain‐dominated intensity modulations in the vicinity of the Ge‐containing source S and drain D stressors. Towards image 4 for [16,34 mrad] strain and the onset of Z‐contrast determine the image contrast comparably, the latter caused by the 2 times larger atomic number of Ge compared to Si. In subsequent images Z‐contrast dominates the signal revealing the two composition regimes of Ge with x=22% and x=37% which we determined using EDX with the chemiSTEM system.

By subsequently subtracting the images we obtain the explicit angular dependence of scattered intensity for pure Si and the two Ge regimes in Fig.3a‐c. Obviously the scattered intensity increases with both thickness and Ge content over the broad angle range covered here. Particular attention is to be drawn at the theoretical models included for comparison in Fig.3: δ denotes the exponent obtained for assuming the Rutherford model where intensity is proportional to Z
δ
. The variety of δ values shows that there is no consistent trend as to a composition, thickness and angle‐dependence, so that the Rutherford theory is inapplicable to our STEM data. Moreover, frozen‐lattice multislice simulations for strain‐relaxed (alloy) supercells are shown by the dashed lines. Although perfect agreement is found for angles above 35mrad, significant deviations are observed at smaller angles. This mismatch of contemporary simulations, which are fully elastic except for phonon scattering, is discussed in detail with respect to further inelastic scattering on the basis of the angular dependence measured from energy‐filtered diffraction patterns.