Atom probe reconstruction with a locally varying tip shape

In this thesis, a new approach for the reconstruction of data taken from an atom probe tomography experiment is presented. The goal of the study is to develop an algorithm, which is able to overcome well-known drawbacks of the conventional reconstruction technique, mainly caused by local magnification effects. At the same time, the algorithm should be easy to use and also fast enough, so that it might be routinely used as an improved alternative to the established reconstruction technique. The idea is based on the already existing possibility to simulate an entire atom probe experiment on a realistic length. Since the successive calculation of ion trajectories starting at the emitter surface and hitting the detector after a flight of a few centimeters can be realized, the concept is designed to invert the field evaporation process by making use of this trajectory calculation. To this end, the detected emitter volume needs to be rebuilt from the bottom to the top, which is an important difference compared to the conventional technique. In a first test, this inversion of the simulated experiment is demonstrated for a few prominent example cases. The decisive criterion for the positioning of an atom at a specific lattice site on the current emitter surface is the accordance of the impact position of the corresponding calculated trajectory with the measured coordinates on the detector. For every possible surface position, first an ion trajectory is calculated and its detector impact position is compared to the measured impact position. Finally, the best-matching trajectory defines the reconstruction coordinates. The approach is performed for some prominent example emitter structures with strongly varying evaporation fields of the involved material, which is known for causing tremendous artifacts in the reconstruction derived by the standard technique. In this first attempt, the algorithm is restricted to a rigid lattice, which means that detected atoms can only be positioned at sites belonging to the former lattice of the emitter. In a second step, the restriction to a rigid lattice is dropped. In this way, the reconstruction algorithm describes a more realistic scenario, since the exact lattice structure and its orientation might be unknown in the majority of experiments. The possibilities and limitations of the approach are discussed. It is found that an additional criterion for the determination of the reconstruction coordinates is needed in this case, since the algorithm is very sensitive to the misplacement of atoms. The stability can be significantly improved by the consideration of an inter-atomic potential, which acts as a filter that exclusively allows surface sites with a sufficiently high amount of neighbor atoms. For a perfect detector efficiency the algorithm yields promising results, but a decrease of the efficiency towards realistic values gives rise to artifacts. As a consequence of these numerical experiments, a new concept has been developed, which neglects the consideration of exact ion trajectories in order to make the algorithm more stable and fast. This third approach assumes rotational symmetry for the investigated emitter volume. An absolutely new characteristic of the technique is the capability to extract the shape of a field emitter directly from the observed pattern of ion impacts on the detector. This feature is a very important difference to the conventional technique, which assumes a constant spherical emitter shape. To the best of the authors knowledge, such a technique with this capability did not exist before. The promising features are demonstrated for several simulated but nevertheless realistic emitter structures. The improved quality of the reconstruction that can be achieved by the application of the here developed technique is shown by direct comparison to the result of the established reconstruction approach. The impressive benefits are illustrated for relevant emitter structures containing either precipitates or layers of different materials with strongly varying evaporation fields (44% or 56% relative variation). In addition, a simple modification of the technique is described, which yields homogenized atomic densities in the reconstructed volumes. Without this modification, the emitter surface is treated like a rigid curved plane, which is shifted upwards with every reconstructed atom during reconstruction. Once the surface is no longer considered to be rigid, individual parts can be lifted separately, yielding a significantly homogenized atomic density. Finally, the new concept of shape extraction is extended for the application to arbitrary emitter structures. The main idea of extracting the information about the emitter shape from the local density of measured events on the detector is maintained. In order to extend the approach to the application to structures without rotational symmetry, a relation between the local density of events on the detector and the Gaussian curvature on the emitter surface is derived. With the help of an iterative finite difference method, the Gaussian curvature at several positions on the tip surface is set. Consequently, a reasonable description of the emitter surface can be obtained and the reconstruction of an arbitrary data set can be performed. The concept is tested and discussed for a simulated example emitter structure