Papers by Author: Z. Erdélyi

Abstract: General description of the interplay between the Kirkendall shift (as a special way of relaxation) and diffusion induced driving forces in diffusion intermixing of binary systems is given. It is shown that, if the Kirkendall shift is negligible, a steady state Nernts-Planck regime is established with diffusion coefficient close to the slower diffusivity, independently of the type of the diffusion induced field and also independently whether this is a single field or a combination of different fields (e.g. stress field and extra chemical potential of non-equilibrium vacancies). Deviations from parabolic kinetics are expected only before or after this steady state stage. Using the results of our previous paper, on development and relaxation of diffusion induced stresses, it is illustrated that the setting of time of the Nernst-Planck regime is very short: intermixing on the scale of few tenths of nanometer is enough to reach it. It is also illustrated that this stage is realized even in the case of asymmetric interdiffusion (in one side of the diffusion zone the diffusion is orders of magnitude higher than in the other), when the stress distribution has a more complex form (having a sharp peak at the interface). Surprisingly the steady state is longer than it would be expected from the relaxation time of Newtonian flow: This is so because the composition profile is not static but changes fast in the timescale of the stress relaxation, and thus the stress re-develops continuously.

Abstract: The influence of hydrogen on the structural stability of multilayers made of ultrathin (3 nm) Si and Ge amorphous layers submitted to annealing to activate Si and Ge intermixing has been studied by TEM and AFM. By energy dispersive microanalysis the interdiffusion of Si and Ge has been observed. The Si/Ge multilayers, however, underwent remarkable structural degradation because of the formation of hydrogen bubbles which give rise to surface bumps and eventually craters when the bubbles blow up because of too high internal pressure in samples with high H content and annealed at high temperatures. The hydrogen forming the bubbles comes from the rupture of the Si-H and Ge-H bonds activated by the thermal energy of the annealing and by the energy released by the recombination of thermally generated electron hole pairs.

Abstract: In a set of recent papers we have shown that the diffusion asymmetry in diffusion couples (the diffusion coefficient is orders of magnitude larger in one of the parent materials) leads to interesting phenomena: i) sharp interface remains sharp and shifts with non Fickian (anomalous) kinetics [1-5], ii) originally diffuse interface sharpens even in ideal (completely miscible) systems [6,7], iii) an initially existing thin AB phase in A/AB/B diffusion couple can be dissolved [8], iv) there exists a crossover thickness (typically between few nanometers and 1m) above which the interface shift turns back to the Fickian behaviour [9], v) the growth rate of a product of solid state reaction can be linear even if there is no any extra potential barrier present (which is the classical interpretation of the “interface reaction control” for linear kinetics) [10]. These latter results will be summarized and reformulated according to the usual expression for linear-parabolic law containing the interdiffusion coefficient, D, and interface transfer coefficient, K. Relation between the activation energies of D and K will be analyzed and compared with available experimental data.

Abstract: Diffusion controlled processes play a crucial role in the degradation of technical materials. At low temperatures the most significant of them is the diffusion along grain boundaries. In thin film geometry one of the best methods for determining the grain boundary (GB) diffusion coefficient of an impurity element is the Hwang-Balluffi method, in which a surface sensitive technique is used to follow the surface accumulation kinetics. Results of grain boundary diffusion measurements, carried out in our laboratory by this method in three different materials systems (Ag/Pd, Ag/Cu and Au/Ni) are reviewed. In case of Ag diffusion along Pd GBs the surface accumulation was followed by AES method. The data points can be well fitted by an Arrhenius function with an activation energy Q=0.99eV

Abstract: Depending on the thermodynamic, structural and diffusion properties of the system, a thin deposit dissolves into a substrate by different mechanisms. In this communication these different behaviours, investigated by surface analytical techniques (AES, XPS, STM, UPS, etc) [ - ], are reviewed. The experiments were also supported by computer simulations. The obtained results are compared and it is summarized how different parameters influence the dissolution of a thin film in a substrate. Furthermore, it is show that i) the volume dissolution kinetics is different on the atomic-/nano-scale than on the microscopic scale due to the diffusion asymmetry ii) the volume and GB diffusion in one measurement can be separated and iii) pure (C-kinetic) GB diffusivities can be determined from thin film kinetics measurements performed under adequate conditions.

Abstract: X-ray standing wave technique has been used to measure the kinetics of CoSi intermetallic phase growth in a-Si/Co/a-Si sandwich structure. The a-Si/Co/a-Si arrangement were placed into a waveguide structure formed by two Ta films. X-ray fluorescence and extended X-ray absorption fine structure analysis has been used in a combination with X-ray standing wave technique for depth profiling with sub-nanometer resolution of specimens annealed at 493K for different annealing time. The position and the thickness of the growing CoSi intermetallic phase have been monitored.

Abstract: Epitaxial, coherent Mo/V multilayers were deposited by magnetron sputtering on (001) oriented MgO substrates at 873K (sample MoV-T), 923K (sample MoV-U) and 973K (sample MoV-V), respectively. In order to estimate the concentration profiles in our multilayers, a superlattice refinement modelling procedure has been used on high-angle XRD symmetric scans. The Mo/V interfaces were always sharper than V/Mo ones (in this notation the order of element reflects the sequence of deposition: e.g. the Mo/V interface was formed by the deposition of the V on the Mo surface). Furthermore the interface diffuseness was only slightly different at the lowest substrate temperature, but the difference increased with increasing temperature and an abrupt concentration jump could be observed at the Mo/V interface in the sample, sputtered at the 973 K. This indicates that during deposition the interfacial mixing by impact exchange events is important and thermally activated processes (surface diffusion and/or jumps driven by segregation) are less effective. With increasing substrate temperature the thickness of the V/Mo interfaces were unchanged while the Mo/V interface became shaper and sharper i.e. thermally activated jumps were more active during deposition of V atoms. Thus in forming Mo/V interfaces the segregation tendency of V to the Mo surface results in enhanced exchanges between V atoms (buried in the near surface layers of the Mo substrate) and surface Mo atoms, leading to more sharper interface with increasing temperature. On the other hand during the formation of the V/Mo interfaces the chemical thickness of the interface, provided again by impact exchanges, was practically unchanged.

Abstract: Solid state reactions between amorpous Si and crystalline Co have been investigated by synchrotron radiation at Bessy (Berlin, Germany). The multilayered samples (with 10 periods of a-Si(15 nm)/Co(15 nm) layers) were produced by magnetron sputtering and isothermally heat treated at temperatures between 523 and 593 K. From the time evolution of the XRD spectra first the growth rate of the CoSi phase as well as the decay rate of the Co layer we determined (at 523 and 543 K). The kinetics were described by a power law; tk, and for the growth of CoSi k=0.65 while for the loss of the Co the k=0.77 was obtained, respectively. At higher temperatures (at 573 and 593 K) the formation and growth of the Co2Si layer, at the expense of the Co and already existing CoSi layers, was observed with exponents of about 1 for all the above kinetics. These results, together with the results of resistance kinetics measurements, in similar multilayered as well as bi-layered samples at similar temperatures, providing similar exponents will be presented. Possibility of the interface reaction control and/or the effect of the diffusion asymmetry (which was recently published for the interpretation of solid state reactions with non-parabolic kinetics on the nanoscale) will be discussed.

Abstract: Solid state reactions between amorphous Si and crystalline Co have been investigated by 4W electrical resistance and TEM. Multilayered (with 10 periods of 5nm a-Si/5nm Co and 10 nma- Si/10nm Co layers) as well as tri-layered samples (20nm a-Si/3nmCoSi/6nm Co) were produced by magnetron sputtering and isothermally heat treated at different temperatures between 473 and 523K. From the time evolution of the normalized resistance the kinetics of the process were determined by fitting a power law, tk, and k was between 0.8 and 1. Possibility of the interface reaction control and/or the effect of the diffusion asymmetry (which was recently published for the non-parabolic interface shifts on the nanoscale) will be discussed.

Abstract: In nanostructured materials, where the density of grain- and interphase-boundaries is high, the diffusion and kinetics of surface segregation, i.e. the effective material flow is always influenced by the contributions of these boundaries [1]. Diffusion on the nano/atomic scales in multilayers, thin films has many challenging features even if the role of structural defects can be neglected and ‘only’ the effects related to the nano/atomic scale arise. Different examples for diffusional nanoscale effects discovered recently by the authors will be given in this paper. We show that the continuum descriptions of diffusion cannot be applied automatically on such short distances, the classical continuum approximations (Fick's laws) cannot describe correctly the atomic movements. [2-4] They predict faster kinetics than the atomistic models and the interface shift is always proportional to the square-root of time (x ∝ t1/2 ⇒ x2 ∝ t: parabolic or Fickian kinetics). As we will show, however, the kinetics can be even linear (x ∝ t) on the nano/atomic scale. [3, 4] Furthermore, the continuum descriptions foretell infinitely fast kinetics as the time goes to zero (v=dx/dt∝1/t1/2), which is a long standing paradox of diffusion theory. We will show a possible resolution of this paradox. [5] Moreover, we will show that an initially diffused interface can sharpen even in completely miscible systems. [6, 7]