New Atom Probe Tomography Reconstruction Algorithm for Multilayered Samples 251


hemispherical radii are simply found as R = V/Eβ0 and we do not care about the shape of the specimen beyond the field of view θV; the layer beneath may be evaporating but its presence is implicitly taken into account by the voltage evolution. The third hemispherical apex radius is found by the same relationship, but when reaching the interface, the normal angle is smaller than θV. Thus, the shape of the second layer is computed until the field of view is reached, as explained in the Model section (field ratio and tangential continuity set, respectively, the a and b parameters of the blue Delaunay surface). The fourth and fifth hemispherical radii are found by R = V/Eβ, where Eβ is that corresponding to the second layer. Indeed, at this stage the first layer has totally disappeared. In practical, Eβ simply equates to Eβ0 divided by the set of field ratios of the interfaces above it at the beginning of the evaporation. This version of the algo- rithm is particularly suited if the sample geometry is poorly known, or if a lot of interfaces are present and are evaporated at the same time.


APPLICATION


Simulated Analyses To evaluate the effectiveness of the new reconstruction algorithm, it was first tested on data sets generated by numerical simulations of the evaporation of bilayer speci- mens. Simulations were performed with the meshless simulation method that was described in Rolland et al. (2015b). The virtual sample is a hexagonal compact structure embedded in a tip with an apex radius of 20nm and a null shank angle, with the axis oriented along the [0001] direc- tion, and contains two distinct layers. Two distinct simula- tions were performed, corresponding to the basic high on


(a hemispherical seated on the truncated cone), that comes with an increase of the radius of curvature. In turns, the magnification is decreasing and the analyzed volume is widening until the low field layer reaches its steady-state morphology. The opposite argumentation may be applied to the low on high field case. Standard cone angle reconstruction was first applied to


low and low on high evaporation field cases. The evaporation field ratio between the top layer and the bottom layer was set to 1.25 and 0.8, respectively. Field evaporation of the sample was simulated and ions trajectories were computed toward a virtual detector placed 10cm away from the tip. Ions impacts falling outside a circle of radius 6 cmcentered on the detector were deleted from the simulation output to mimic the experimental limited field of view. The obtained impacts list was then used as if it was the experimental data set to reconstruct. The initial positions of the collected ions on the detector are reported in Figures 5a and 5d for the high on low and low and high case, respectively. Those volumes would correspond to perfect reconstructions of the analyzed volume. We shall now briefly explain the origin of the latter profile. During the transition from the high to low field layer,


there is a decrease of both layers’ radii of curvature (Fig. 1d, first row). This results in an increase of the magnification, and thus to a decrease of the specimen surface area seen by the detector. The analyzed volume is pinched at the interface (Fig. 5a). Right after the top high field layer (thin red layer on the Fig. 1d, first row and third column) has totally evapo- rated, the low field layer is protruding with a small radius of curvature. It progressively returns to its steady-state shape


radius of curvature and field of view (Fig. 5b for high on low field and Fig. 5e for low on high field). Interfaces were introduced in the algorithm with the prescribed field ratio corresponding to each simulation. Qualitatively, the obtained volumes are in good agreement with the simulation based reconstructions presented in Larson et al. (2012). The bias on the analyzed depth is reduced (39.5nm for high on low field and 44.6nmfor low on high field) because the new algorithm takes into account the volume pinching and widening that occur in the high on low and low on high situations, respec- tively. Moreover, the spatial resolution is clearly improved right below the interface, with atomic planes being partially resolved. To quantify this improvement, the average in-depth position errors (z difference between an atom in the recon- struction and the same atom in the analyzed volume, i.e. ori- ginal position before field evaporation) were computed for both standard and new reconstruction methods. In the high on lowcase (respectively lowon high case), this erroramounts to 2nm (respectively 0.95nm) with standard reconstruction and 0.23nm (respectively 0.28) with the new reconstruction. However, note that the volume pinching and widening are not as pronounced as they should, so that there is still a bias in the analyzed depth. To reproduce the perfect reconstruction geometry, one should progressively increase, respectively decrease, the curvature ratio for the high on low and low on high case when approaching the interface. This effect may be attributed to variations of the β factor on the emitter surface.


the data sets, with the initial radius of curvature and field of view deduced from the top part of the perfect reconstruc- tions, when the interface has not yet influenced the tip morphology. Reconstructed volumes are reported for the high on low and low on high configuration in Figures 5c and 5d. The analyzed depth is underestimated for the high on low case (37.2nm instead of 42.4 nm) and overestimated for the low on high case (46.8nm instead of 45.3 nm). In addition, the interface is bent upward and downward for the former and latter cases, respectively. Also, in both cases the atomic planes are dramatically distorted on the side of the volume, right below the interface. The cone angle version of the new reconstruction algo- rithm was then used on the same data, with the same initial


Experimental Data Set


The new algorithm was also tested on an experimental data set to prove its applicability to real experiments. The sample is made up of a In0.15Al0.85N layer of 35nm embedded between two GaN layers. As the geometry of the sample is not well-known and exhibits a variation of the shank angle, as evidenced by the different slopes at the beginning and at


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