Atom probe tomography quantification of carbon in silicon.

Atom Probe Tomography (APT) was used to quantify carbon in implanted silicon at two various electric fields (~ 15 and 20 V/nm). Using equal proportions of implanted 12C and 13C, the numerous molecular ions that were observed were identified and their contribution to the carbon content statistically derived. Much more accurate carbon quantification was obtained in the lowest electric field analysis by comparing APT with Secondary Ion Mass Spectroscopy profiles. This was assigned to a lower amount of molecular ion dissociations. Furthermore, the number of self-interstitials trapped per carbon atom in clusters was derived. This value of interest for the microelectronics industry regarding dopant diffusion and implantation induced defects was estimated close to one, in agreement with the expected stoichiometry of the SiC phase present in the phase diagram. However, this was obtained only when using low electric field conditions.

Detecting Dissociation Dynamics of Phosphorus Molecular Ions by Atom Probe Tomography.

Dissociation processes involving phosphorus cations were investigated during laser-assisted atom probe tomography of crystalline indium phosphide (InP). This technique not only allows the formation of medium-sized phosphorus cations by means of femtosecond laser pulses under ultrahigh vacuum and high electric field conditions but also allows one to study the time-resolved dissociation dynamics. Data reveal the formation of cations up to P232+ and their subsequent dissociation into two smaller Pk+ cations (k > 2). The use of a time- and position-sensitive detector combined with numerical calculations provided information related to the molecule orientation, decay time, and kinetic energy release during dissociation phenomena. Results suggest that the dissociation processes are most likely due to the emission of Pk2+ cations in excited states and their subsequent decay in low field regions during their flight toward the detector. This study provides operative guidelines to obtain information on dissociation processes using a tomographic atom probe as a reaction microscope and indicates the current capabilities and limitations of such an approach.

A photonic atom probe coupling 3D atomic scale analysis with in situ photoluminescence spectroscopy.

Laser enhanced field evaporation of surface atoms in laser-assisted Atom Probe Tomography (APT) can simultaneously excite photoluminescence in semiconductor or insulating specimens. An atom probe equipped with appropriate focalization and collection optics has been coupled with an in situ micro-photoluminescence (µPL) bench that can be operated during APT analysis. The photonic atom probe instrument we have developed operates at frequencies up to 500 kHz and is controlled by 150 fs laser pulses tunable in energy in a large spectral range (spanning from deep UV to near IR). Micro-PL spectroscopy is performed using a 320 mm focal length spectrometer equipped with a CCD camera for time-integrated and with a streak camera for time-resolved acquisitions. An example of application of this instrument on a multi-quantum well oxide heterostructure sample illustrates the potential of this new generation of tomographic atom probes.

Compositional accuracy of atom probe tomography measurements in GaN: Impact of experimental parameters and multiple evaporation events.

A systematic study of the biases occurring in the measurement of the composition of GaN by Atom Probe Tomography was carried out, in which the role of surface electric field and laser pulse intensity has been investigated. Our data confirm that the electric field is the main factor influencing the measured composition, which exhibits a deficiency of N at low field and a deficiency of Ga at high field. The deficiency of Ga at high field is interpreted in terms of preferential evaporation of Ga. The detailed analysis of multiple evaporation events reveals that the measured composition is not affected by pile-up phenomena occurring in detection system. The analysis of correlation histograms yields the signature of the production of neutral N2 due to the dissociation of GaN32+ ions. However, the amount of N2 neutral molecules that can be detected cannot account for the N deficiency found at low field. Therefore, we propose that further mechanisms of neutral N evaporation could be represented by dissociation reactions such as GaN+→ Ga++ N and GaN2+→ Ga2++ N.

Kinetic theory of diffusion-limited nucleation.

We examine binary nucleation in the size and composition space {R,c} using the formalism of the multivariable theory [N. V. Alekseechkin, J. Chem. Phys. 124, 124512 (2006)]. We show that the variable c drops out of consideration for very large curvature of the new phase Gibbs energy with composition. Consequently nuclei around the critical size have the critical composition, which is derived from the condition of criticality for the canonical variables and is found not to depend on surface tension. In this case, nucleation kinetics can be investigated in the size space only. Using macroscopic kinetics, we determine the general expression for the condensation rate when growth is limited by bulk diffusion, which accounts for both diffusion and capillarity and exhibits a different dependence with the critical size, as compared with the interface-limited regime. This new expression of the condensation rate for bulk diffusion-limited nucleation is the counterpart of the classical interface-limited result. We then extend our analysis to multicomponent solutions.

An analytical model accounting for tip shape evolution during atom probe analysis of heterogeneous materials.

An analytical model describing the field evaporation dynamics of a tip made of a thin layer deposited on a substrate is presented in this paper. The difference in evaporation field between the materials is taken into account in this approach in which the tip shape is modeled at a mesoscopic scale. It was found that the non-existence of sharp edge on the surface is a sufficient condition to derive the morphological evolution during successive evaporation of the layers. This modeling gives an instantaneous and smooth analytical representation of the surface that shows good agreement with finite difference simulations results, and a specific regime of evaporation was highlighted when the substrate is a low evaporation field phase. In addition, the model makes it possible to calculate theoretically the tip analyzed volume, potentially opening up new horizons for atom probe tomographic reconstruction.

Critical nucleus composition in a multicomponent system.

The properties of a critical nucleus are derived using the capillarity theory in the framework of classical nucleation. An analytical solution for the composition of a critical nucleus is given for low supersaturation. The theory is valid for any multicomponent systems. It is found that the deviation in nucleus composition from the equilibrium tie-line is mainly due to the difference in the Hessian of the Gibbs energy of the phases and the magnitude of the deviation in composition from equilibrium is order of the supersaturation. Despite our analysis strictly holds for low supersaturation, this suggests strong deviations near the spinodal line.

Point process statistics in atom probe tomography.

We present a review of spatial point processes as statistical models that we have designed for the analysis and treatment of atom probe tomography (APT) data. As a major advantage, these methods do not require sampling. The mean distance to nearest neighbour is an attractive approach to exhibit a non-random atomic distribution. A χ(2) test based on distance distributions to nearest neighbour has been developed to detect deviation from randomness. Best-fit methods based on first nearest neighbour distance (1 NN method) and pair correlation function are presented and compared to assess the chemical composition of tiny clusters. Delaunay tessellation for cluster selection has been also illustrated. These statistical tools have been applied to APT experiments on microelectronics materials.

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.

Minimum free-energy pathway of nucleation.

Nucleation in a two-component incompressible system was studied by examining the topology of the free-energy landscape. The properties of a single nucleus during nucleation were derived from the minimum free-energy pathway (MFEP) within the Cahn-Hilliard continuum theory of nucleation. MFEPs were computed using the string method. In particular, we have provided a detailed description of the nucleation process for a regular solution (T/T(c) = 0.8656) for increasing supersaturation up to the spinodal line. Two original results were found in terms of the physics of nucleation. A universal two-step behaviour was found whatever the supersaturation: nuclei sharply enrich up to equilibrium and then grow. Embryos show diffuse interfaces along the MFEP. The width of interfaces quickly saturates to its value at the critical nuclei and stays constant afterwards.

Clustering and local magnification effects in atom probe tomography: a statistical approach.

Local magnification effects and trajectory overlaps related to the presence of a second phase (clusters) are key problems and still open issues in the assessment of quantitative composition data in three-dimensional atom probe tomography (APT) particularly for tiny solute-enriched clusters. A model based on the distribution of distance of first nearest neighbor atoms has been developed to exhibit the variations in the apparent atomic density in reconstructed volumes and to correct compositions that are biased by local magnification effects. This model was applied to both simulated APT reconstructions and real experimental data and shows an excellent agreement with the expected composition of clusters.

Clustering and nearest neighbour distances in atom probe tomography: the influence of the interfaces.

The statistical 1NN method is an elegant way to derive the composition of small B-enriched clusters in a random AB solid solution from 3D atomic fields. An extension of this method is proposed that includes the contribution of interface region and provides an estimate of the core composition of clusters. This model is applied to boron-implanted silicon containing boron-enriched clusters. A comparison with the previous model is performed. This new approach gives relevant information, i.e. the core composition of clusters and the cluster-matrix interface width.

Clustering and pair correlation function in atom probe tomography.

The measurement of the composition of small clusters from 3D maps as provided by atom probe tomography or Monte-Carlo simulations is a very tricky issue. A method based on pair correlation functions was developed. The analytical expression of the pair correlation function as a function of the phase composition, the number density and the size of spherical particles for a two-phase mono-dispersed system has been established. A best-fit procedure applied to experimental pair correlation function is shown to be a simple, fast and elegant way to determine the concentration of clusters and that of the parent phase as well as the radius and the number density of clusters. Application to carbon-doped silicon demonstrates the validity of this approach. Results were found very close to those derived by other means. This method was also applied to boron clustering in implanted silicon where clusters are not visible in 3D images. The advantage of this approach over other methods such as erosion or cluster identification is discussed.

Clustering and nearest neighbour distances in atom-probe tomography.

The measurement of chemical composition of tiny clusters is a tricky problem in both atom-probe tomography experiments and atomic simulations. A new approach relying on the distribution of the first nearest neighbour (1NN) distances between solute atoms in the 3D space composed of A and B atoms was developed. This new approach, the 1NN method, is shown to be an elegant way to get the composition of tiny B-enriched clusters embedded in a random AB solid solution. The theoretical statistical distributions of first neighbour distances P(r) for both random solid solution and solute-enriched clusters finely dispersed in a depleted matrix are established. It is shown that the most probable distance of P(r) gives directly the phase composition. Applications of this model to both one-phase SiGe alloy and boron-doped silicon containing small clusters indicate that this new approach is quite reliable.

Atomic-scale redistribution of Pt during reactive diffusion in Ni (5% Pt)-Si contacts.

The NiSi silicide that forms by reactive diffusion between Ni and Si active regions of nanotransistors is used nowadays as contacts in nanoelectronics because of its low resistivity. Pt is added to the Ni film in order to stabilise the NiSi phase against the formation of the high-resistivity NiSi(2) phase and agglomeration. In situ X-ray diffraction (XRD) experiments performed on material aged at 350 degrees C (under vacuum) showed the complete consumption of the Ni (5 at% Pt) phase, the regression of Ni(2)Si phase as well as the growth of the NiSi phase after 48 min. Pt distribution for this heat treatment has been analysed by laser-assisted tomographic atom probe (LATAP). An enrichment of platinum in the middle of the NiSi phase suggests that Pt is almost immobile during the growth of NiSi at the two interfaces: Ni(2)Si/NiSi and NiSi/Si. In the peak, platinum was found to substitute for Ni in the NiSi phase. Very small amounts of Pt were also found in the Ni(2)Si phase close to the surface and at the NiSi/Si interface.

Three-dimensional atom mapping of boron in implanted silicon.

The redistribution of boron in highly implanted 100 silicon (10keV; 5x10(15)at/cm(2)) annealed at 600 degrees C for 1h was studied using both laser-assisted wide-angle atom probe (LaWaTAP) and secondary ion mass spectrometry (SIMS). As expected, the concentration was found to increase steeply to 10(21) boron atoms/cm(3) at a distance close to 35nm and to decrease slowly to 10(19)/cm(3), a value close to the boron level of the silicon substrate. For depth under 75nm, the implantation profile of boron as given by LaWaTAP was found very close to that given by SIMS investigations without any calibration of the LaWaTAP data. For larger depth, the LaWaTAP profile is observed above that of SIMS. Detection limits of LaWaTAP for low dopant concentrations are discussed. The contribution of the background noise in the spectrum and sampling errors are considered. Fine-scale fluctuations not detected in SIMS profile and related to clustering were evidenced in LaWaTAP maps and profiles. Numerous boron clusters lying on {001} planes parallel to the implanted surface, a few nanometer in size, were identified and interpreted as boron interstitial clusters (BICs), in agreement with Cristiano et al. observations. They contained between 50 and 300 atoms (Si and B). This is much higher than that generally assumed in particular in ab-initio modelling where a few atoms BICs are considered. These clusters contained 7at% of boron in average.

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.

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.

Optical and thermal processes involved in ultrafast laser pulse interaction with a field emitter.

In the interaction between ultrafast laser pulses and a field emitter both optical and thermal processes are involved. In this paper, these physical process, and their timescales, are experimentally explored. Simple models are proposed to explain the observed experimental behaviour, and the influence of various parameters are investigated. In the case of optical processes, it is shown that the optical field is greatly enhanced at the tip apex, and that field evaporation could be induced by an optical non-linear effect called optical rectification. In the case of thermal processes, it is shown that the temperature rise because of light absorption can be determined and that the cooling process of the tip surface can be studied by pump probe measurements.

Application of Fourier transform and autocorrelation to cluster identification in the three-dimensional atom probe.

Because of the increasing number of collected atoms (up to millions) in the three-dimensional atom probe, derivation of chemical or structural information from the direct observation of three-dimensional images is becoming more and more difficult. New data analysis tools are thus required. Application of a discrete Fourier transform algorithm to three-dimensional atom probe datasets provides information that is not easily accessible in real space. Derivation of mean particle size from Fourier intensities or from three-dimensional autocorrelation is an example. These powerful methods can be used to detect and image nano-segregations. Using three-dimensional 'bright-field' imaging, single nano-segregations were isolated from the surrounding matrix of an iron-copper alloy. Measurement of the inner concentration within clusters is, therefore, straightforward. Theoretical aspects related to filtering in reciprocal space are developed.