Electron Microscopy

Interdiscriplinary Project together with GFE (Gemeinschaftslabor für Elektronenmikroskopie, RWTH Aachen).

Electron Probe Microanalysis

epma_sketch

Electron Probe Microanalysis (EPMA) is an imaging technique used for the quantitative analysis of the composition of solid material samples at the micro- to nanometer scale. The sample is excited by a focussed beam of electrons which induces multiple relaxation processes inside the sample. In EPMA the emission of characteristic x-rays is of special focus. If an electron which is induced by the beam strikes a bound electron which occupies an atomic shell of an atom inside the specimen, the bound electron is ejected from its shell and the atom is left with a vacancy. Outer shell electrons fill this vacancy by emitting a quantized x-ray with an energy corresponding to the energy level difference of the originating and the target shell. The energy levels of electron shells are characteristic for a specific atom, hence the energy of the emitted x-ray provides information about the composition of the material sample. In EPMA the intensity of characteristic x-radiation, which are the observed values, is considered in the form of k-ratios.

Inverse Problem of Reconstruction

interaction_volume The determination of material structure and composition forms the inverse problem of reconstruction in EPMA. The crucial ingredients to the inverse problem of reconstruction are the definition of a material model, that maps material parameters to a material composition function (in space) and a accurate model of the physical processes that induce and attenuate the characteristic radiation. Then the reconstruction can be formalized as follows:

"Find the set of parameters such that the modeled k-ratios reproduce the experimental k-ratios as good as possible."

Our model combinatines a model for electron transport in inhomogeneous media based on the radiative transfer equation together with a subsequent model for x-ray generation and attenuation.

The material parametrization plays a essential role in the reconstruction problem. In the one hand, the set of parameters that is reconstructed (layer thicknesses, weight fractions, size and shape of material imperfections) defines the questions posed to the reconstruction algorithm. On the other hand, it alleviates the inherent ill-posed structure of the inverse problem. For a reliable/unambiguous reconstruction result, the inclusion of prior knowledge about the material, which experimenters usually have, is necessary.

reconstructions