Stefan Parviainen

Atomistic simulations of field assisted evaporation in atom probe tomography

Atom probe tomography (APT) is an extremely powerful technique for determining the three-dimensional structure and chemical composition of a given sample. Although it is designed to provide images of material structure with atomic scale resolution, reconstruction artifacts, well-known to be present in reconstructed images, reduce their accuracy. No existing simulation technique has been able to describe the origin of these artifacts. Here we develop a simulation technique which allows for atomistic simulations of the atom emission process in the presence of high electric fields in APT experiments. Our code combines hybrid concurrent electrodynamics—molecular dynamics and a Monte Carlo approach. We use this technique to demonstrate the atom-level origin of artifacts in APT image reconstructions on examples of inclusions and voids in investigated samples. The results show that even small variations in the surface topology give rise to distortions in the local electric field, limiting the accuracy of conventional APT reconstruction algorithms.

Investigation of the thermal stability of Cu nanowires using atomistic simulations

We present a method for determining the melting point of copper nanowires based on classical molecular dynamics simulations and use it to investigate the dependence of the melting point on wire diameter. The melting point is determined as the temperature at which there is a significant change in the fraction of liquid atoms in the wire, according to atomic bond angle analysis. The results for the wires with diameters in the range 1.5 nm to 20 nm show that the melting point is inversely proportional to the diameter while the cross-sectional shape of the wire does not have a significant impact. Comparison of results obtained using different potentials show that while the absolute values of the melting points may differ substantially, the melting point depression is similar for all potentials. The obtained results are consistent with predictions based on the semi-empirical liquid drop model.

Application of the general thermal field model to simulate the behaviour of nanoscale Cu field emitters

Strong field electron emission from a nanoscale tip can cause a temperature rise at the tip apex due to Joule heating. This becomes particularly important when the current value grows rapidly, as in the pre-breakdown (the electrostatic discharge) condition, which may occur near metal surfaces operating under high electric fields. The high temperatures introduce uncertainties in calculations of the current values when using the Fowler–Nordheim equation, since the thermionic component in such conditions cannot be neglected. In this paper, we analyze the field electron emission currents as the function of the applied electric field, given by both the conventional Fowler–Nordheim field emission and the recently developed generalized thermal field emission formalisms. We also compare the results in two limits: discrete (atomistic simulations) and continuum (finite element calculations). The discrepancies of both implementations and their effect on final results are discussed. In both approaches, the electric field, electron emission currents, and Joule heating processes are simulated concurrently and self-consistently. We show that the conventional Fowler–Nordheim equation results in significant underestimation of electron emission currents. We also show that Fowler–Nordheim plots used to estimate the field enhancement factor may lead to significant overestimation of this parameter especially in the range of relatively low electric fields.

Local changes of work function near rough features on Cu surfaces operated under high external electric field

Metal surfaces operated under high electric fields produce sparks even if they are held in ultra high vacuum. In spite of extensive research on the topic of vacuum arcs, the mystery of vacuum arc origin still remains unresolved. The indications that the sparking rates depend on the material motivate the research on surface response to extremely high external electric fields. In this work by means of density-functional theory calculations we analyze the redistribution of electron density on {100} Cu surfaces due to self-adatoms and in presence of high electric fields from −1 V/nm up to −2 V/nm (−1 to −2 GV/m, respectively). We also calculate the partial charge induced by the external field on a single adatom and a cluster of two adatoms in order to obtain reliable information on charge redistribution on surface atoms, which can serve as a benchmarking quantity for the assessment of the electric field effects on metal surfaces by means of molecular dynamics simulations. Furthermore, we investigate the modif...

Electrodynamics—molecular dynamics simulations of the stability of Cu nanotips under high electric field

The shape memory effect and pseudoelasticity in Cu nanowires is one possible pair of mechanisms that prevents high aspect ratio nanosized field electron emitters to be stable at room temperature and permits their growth under high electric field. By utilizing hybrid electrodynamics molecular dynamics simulations we show that a global electric field of 1 GV/m or more significantly increases the stability and critical temperature of spontaneous reorientation of nanosized Cu field emitters. We also show that in the studied tips the stabilizing effect of an external applied electric field is an order of magnitude greater than the destabilization caused by the field emission current. We detect the critical temperature of spontaneous reorientation using the tool that spots the changes in crystal structure. The method is compatible with techniques that consider the change in potential energy, has a wider range of applicability and allows pinpointing different stages in the reorientation processes.

Thermal stability of interface voids in Cu grain boundaries with molecular dynamic simulations

By means of molecular dynamic simulations, the stability of cylindrical voids is examined with respect to the diffusion bonding procedure. To do this, the effect of grain boundaries between the grains of different crystallographic orientations on the void closing time was studied at high temperatures from 0.7 up to 0.94 of the bulk melting temperature (). The diameter of the voids varied from 3.5 to 6.5 nm. A thermal instability occurring at high temperatures at the surface of the void placed in a grain boundary triggered the eventual closure of the void at all examined temperatures. The closing time has an exponential dependence on the examined temperature values. A model based on the defect diffusion theory is developed to predict the closing time for voids of macroscopic size. The diffusion coefficient within the grain boundaries is found to be overall higher than the diffusion coefficient in the region around the void surface. The activation energy for the diffusion in the grain boundary is calculated based on molecular dynamic simulations. This value agrees well with the experimental given in the Ashby maps for the creep in copper via Coble GB diffusion.

Reconstructing APT Datasets: Challenging the Limits of the Possible

Atom probe tomography (APT) has been successfully used in materials science for several decades for probing local compositional variations. In metals, the capacity to measure reliable composition at the nanoscale in 3D was successfully demonstrated in the early nineties [I, 2]. By using a few geometric ingredients, a reconstruction recipe was proposed at this time that surprisingly produced on selected materials, 3D images with an atomic scale precision of the distribution of atoms with elemental identification [3). The ability to localize precisely the 3-D coordinates of individual atoms in direct space of materials is expected to find important applications in materials science and engineering, nanoscience, physics and chemistry. It is particularly crucial in semiconductor industry, to design optical devices or electronic devices, such as light-emitting diodes (LEDs), or transistors. This ideal picture of near-perfect 3D microscope however faces two issues. First, the precision of images may vary strongly from one material to another. Compared to an optical or an electron microscope, the spatial resolution loss is not diffraction limited, since image is produced from the inverse projection of ion trajectories, ions been produced by field evaporation of surface atoms. Precision is perturbed by slight deviations of the trajectories of ions from their initial positions at the specimen surace to the ion detector. A real understanding of this trajectory taking into account first the quantum interaction of atoms/ions with the specimen surface under the presence of the strong electric field existing on the surface is mandatory. The interplay between quantum processes, and more classical deviations induced by the distribution of the electric field close to the surface is extremely complex. In metals, most of the deviations thought to be induced by the field, as it was recently demonstrated experimentally by field ion microscopy in tungsten (fig. I). In oxides, quantum effects such as in-flight dissociation of molecules may degrade significantly the spatial precision (fig. 2) [4]. The second issue concerns the global distortions induced by the presence in the sample of phases very different in term of the critical fields required to extract surface atoms. This is a current case when analyzing devices composed of complex structures of metals, oxides and semiconductors materials. The surface of the sample ideally modelled with a constant curvature radius evolves dynamically under the process of field evaporation in a complex 3D surface. The direct consequence is the presence of distortions in the projected image. After the evaporation of each atom, the field distribution around the sample must be evaluated, to understand the projection law that should necessary be taken into account to generate an accurate reconstruction [5, 6). To overcome this cumbersome calculation, an alternative model, much simpler, was developed to reproduce the imaging process in simple configurations. In multilayers systems, it was demonstrated that most of the distortions could be reduced using a fast and efficient reconstruction algorithm that predicts the analytical shape of the emitting surface all along the evaporation process [7]. If a complementary technique can be used on the same sample to verify the morphology or provide complementary information before APT analysis, then this can also greatly…