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Method Development

Further development and extension of X-Ray Diffraction Laminography

In the last years, X-ray diffraction laminography (XDL) has been developed at IPS/KIT for the 3D imaging of defect structures in crystalline samples [Hänschke 2012]. It was successfully applied to weakly absorbing materials like silicon (Si) to capture complex arrangments of dislocations in 3D.

Within the STROBOS-CODE project, the partners aim on extending the basic methodology by correlative measurement and analysis procedures, see Fig. 1. By combining XDL with complementary methods a comprehensive characterization of crystalline defects and the associated lattice strain can be obtained, e.g. linking the 3D structure (on the mesoscopic length scale between micrometers and millimeters) of dislocation patterns to microscopic aspects like the Burgers Vector distribution.

Fig. 1: Proposed workflow for the comprehensive characterization of defect investigation in crystalline specimen, here shown at the example of a complex dislocation structure in a silicon wafer.

The basic principle of XDL is similar to conventional computed tomography: A set of 2D projection images is recorded from different view directions. To take advantage of Bragg diffraction contrast it is crucial to rotate the sample about a selected reciprocal crystal vector. Suitable reconstruction algorithms then provide a 3D picture of the investigated crystal volume. In order to extend XDL with time-resolving in situ capabilites, a sufficiend speed-up of the measurement procedure is key. Within STROBOS-CODE this is being achieved by the development, implementation, and optimization of dedicated instrumentation and reconstruction algorithms.

Recently, for example, the number of projection images required for successful 3D reconstruction could be considereably reduced: While for the conventional reconstruction techniques like filtered back projection about 700 projections within a 130°-angle range were necessary to achieve a sufficiently accurate 3D reconstruction of a complex dislocation network, applying adopted algebraic reconstruction techniques (e.g. DART) the required number of projections could be reduced to 50, meaning a speed-up by a factor of 14. This speed-up enabled new measurement schemes, e. g. capturing the nucleation, generation and propagation of dislocations by performing a gradual annealing of the sample alternating with XDL-scans. This makes it possible to image the evolution of dislocations into complex structures with a spatial resolution on the micrometer scale in crystal volumes of several mm3 of size.


Quantitative full-field X-ray diffraction imaging

The STROBOS-CODE instrumentation is designed to be fully compatible with a broad range of X-ray diffraction imaging acquisition schemes, in particular with so-called rocking curve imaging (RCI). Within STROBOS-CODE also the general theoretical aspects of quantitative data analysis are being investigated and corresponding procedures and algorithms are derived, implemented and tested, providing access to the local 2D/3D crystalline properties, see for example Fig. 2. In combination and correlated with XDL data, for example, this will allow linking the nucleation and evolution of dislocations to the driving strain fields.

 Fig. 2: Feasibility study for the quantitative analysis of RCI data acquired from multiple (here 16) view directions, in this way providing access to the local tilt (amount and direction) and strain, together with a estimation of the error.