Standard deviations of composition measurements in atom probe analyses-Part II: 3D atom probe.

In a companion paper [F. Danoix, G. Grancher, A. Bostel, D. Blavette, Surf. Interface Anal. this issue (previous paper).], the derivation of variances of the estimates of measured composition, and the underlying hypotheses, have been revisited in the the case of conventional one dimensional (1D) atom probes. In this second paper, we will concentrate on the analytical derivation of the variance when the estimate of composition is obtained from a 3D atom probe. As will be discussed, when the position information is available, compositions can be derived either from constant number of atoms, or from constant volume, blocks. The analytical treatment in the first case is identical to the one developed for conventional 1D instruments, and will not be discussed further in this paper. Conversely, in the second case, the analytical treatment is different, as well as the formula of the variance. In particular, it will be shown that the detection efficiency plays an important role in the determination of the variance.

Standard deviations of composition measurements in atom probe analyses. Part I conventional 1D atom probe.

Atom probe is a very powerful instrument to measure concentrations on a sub nanometric scale [M.K. Miller, G.D.W. Smith, Atom Probe Microanalysis, Principles and Applications to Materials Problems, Materials Research Society, Pittsburgh, 1989]. Atom probe is therefore a unique tool to study and characterise finely decomposed metallic materials. Composition profiles or 3D mapping can be realised by gathering elemental composition measurements. As the detector efficiency is generally not equal to 1, the measured compositions are only estimates of actual values. The variance of the estimates depends on which information is to be estimated. It can be calculated when the detection process is known. These two papers are devoted to give complete analytical derivation and expressions of the variance on composition measurements in several situations encountered when using atom probe. In the first paper, we will concentrate on the analytical derivation of the variance when estimation of compositions obtained from a conventional one dimension (1D) atom probe is considered. In particular, the existing expressions, and the basic hypotheses on which they rely, will be reconsidered, and complete analytical demonstrations established. In the second companion paper, the case of 3D atom probe will be treated, highlighting how the knowledge of the 3D position of detected ions modifies the analytical derivation of the variance of local composition data.

The shape of field emitters and the ion trajectories in three-dimensional atom probes

The lateral resolution of three-dimensional atom probes is mainly controlled by the aberrations of the ion trajectories near the specimen surface. For the first time, a simulation program has been developed to reconstruct the ion trajectories near a sharp hemispherical electrode defined at the atomic scale. Surface atoms submitted to the highest field were removed one by one. The consecutive gradual change of the surface topology was taken into account in the calculation of ion trajectories. As the tip was 'field evaporated', the initial spherical shape of the emitter was observed to transform gradually into a polygonal shape. When the tip reached its equilibrium shape, the field distribution at the tip surface was found to be much more uniform compared to the initial distribution. The calculated distribution of ion impacts on the detector exhibits the presence of depleted zones both at the centre of low index poles and along <001> zone axes. These predictions are in excellent agreement with experiments.

A new approach to the interpretation of atom probe field-ion microscopy images.

The field distribution and the ion trajectories close to the tip surface are known to mainly control the contrast of field-ion microscopy and the resolution of the three-dimensional atom probe. The proper interpretation of images provided by these techniques requires the electric field and the ion trajectories to be determined accurately. A model has been developed in order to compute the ion trajectories close to a curved emitting surface modelled at the atomic scale. In this model, both the gradual change of the tip surface and the chemical nature of atoms were taken into account. Predictions and results given by this approach are shown to be in excellent agreement with experiments. The calculated electric field at the tip surface is consistent with field-ion microscopy contrasts. The preferential retention of surface atoms and the order of evaporation were correctly simulated. The ion trajectories were successfully described. In this way, the crucial problem of trajectory overlap and local magnification could be investigated. These simulations not only lead to a new understanding of the physical basis of image formation, but also have a predictive value.

Improvement of the mass resolution of the atom probe using a dual counter-electrode.

As compared to other techniques, the mass resolution of the 3D atom probe is rather poor. This low mass resolution derives from the spread in energy of field-evaporated ions. In this work, the single counter-electrode used to remove atoms from the specimen was replaced with a dual counter-electrode. A positive standing voltage V(PA) is applied on the electrode facing the specimen while the second electrode is grounded. As a result, ions experience a post-acceleration between electrodes that lowers energy deficits of ions resulting in an improvement in the mass resolution. This paper reports the study of the resulting improvement in mass resolution as a function of the post-acceleration voltage. It is also shown that, because of the evaporation pulse, ions also undergo a dynamic post-deceleration in the between electrodes. This post-deceleration contributes to the mass resolution increase. Our results show that this very simple device makes it possible to significantly improve the mass resolution of the atom probe. For a low post-acceleration voltage, the mass resolution is 800 FWHM and 200 at full-width tenth-maximum.

Effects of incidence angles of ions on the mass resolution of an energy compensated 3D atom probe.

We have used a first-order reflectron lens in an optical tomographic atom probe in order to improve the mass resolution. Calculations have been performed to determine the effect of second-order errors in ion energy and incidence angle on the performance of the lens. By applying a correction procedure based on the results of these calculations, we have been able to improve experimental mass resolution by 30%.

Advance in multi-hit detection and quantization in atom probe tomography.

The preferential retention of high evaporation field chemical species at the sample surface in atom-probe tomography (e.g., boron in silicon or in metallic alloys) leads to correlated field evaporation and pronounced pile-up effects on the detector. The latter severely affects the reliability of concentration measurements of current 3D atom probes leading to an under-estimation of the concentrations of the high-field species. The multi-hit capabilities of the position-sensitive time-resolved detector is shown to play a key role. An innovative method based on Fourier space signal processing of signals supplied by an advance delay-line position-sensitive detector is shown to drastically improve the time resolving power of the detector and consequently its capability to detect multiple events. Results show that up to 30 ions on the same evaporation pulse can be detected and properly positioned. The major impact of this new method on the quantization of chemical composition in materials, particularly in highly-doped Si(B) samples is highlighted.

Pragmatic reconstruction methods in atom probe tomography.

Data collected in atom probe tomography have to be carefully analysed in order to give reliable composition data accurately and precisely positioned in the probed volume. Indeed, the large analysed surfaces of recent instruments require reconstruction methods taking into account not only the tip geometry but also accurate knowledge of geometrical projection parameters. This is particularly crucial in the analysis of multilayers materials or planar interfaces. The current work presents a simulation model that enables extraction of the two main projection features as a function of the tip and atom probe instrumentation geometries. Conversely to standard assumptions, the image compression factor and the field factor vary significantly during the analysis. An improved reconstruction method taking into account the intrinsic shape of a sample containing planar features is proposed to overcome this shortcoming.

The spatial resolution of 3D atom probe in the investigation of single-phase materials

The resolution of three-dimensional atom probe (3DAP) is known to be mainly controlled by the aberrations of the ion trajectories near the surface of the specimen. A model has been developed to compute the ion trajectories in 3D near a sharp hemispherical electrode defined at the atomic scale. Simulations were applied on one-phase binary alloys. The influence of the evaporation fields of chemical species is studied. Simulated desorption images are consistent with experiments in both ordered alloys and random solid solution. An extra loss in the lateral resolution is observed in disordered alloys as compared to pure metals. The predicted order of evaporation provided by this model is in excellent agreement with experiments. The stacking sequence of atomic planes reconstructed from simulated data is shown to be disturbed in a similar way as observed in real experiments with 3DAP.