Université de droit, d’économie et des sciences d’Aix-Marseille

Faculté des sciences et techniques de saint-Jérôme

&

university of Debrecen

Theses of Co-directed PhD Thesis

France-Hungary

by

Zoltán ERDÉLYI

Doctor of Philosophy

In the subject of:

materials Science

Approved 12 October 2001 in presence of committee:

Dezső BEKE (Supervisor)
Jean BERNARDINI (Supervisor)
István SZABÓ
Christophe GIRARDEAUX
Géza TICHY (Referee)
Vassilis PONTIKIS (Referee)

The dawn of nano-scale science can be traced to the classic talk of Richard Feynman gave on December 29th, 1959 at the annual meeting of the American Physical Society at the California Institute of Technology. In this lecture, Feynman suggested that there exists no fundamental reason to prevent the controlled manipulation of matter at the scale of individual atoms and molecules. Twenty-one years later, Eigler and co-workers constructed the first man-made object atom-by-atom with the aid of a scanning tunnelling microscope. This was just 2400 years after Democritus postulated atoms to be the fundamental building blocks of the visible world. The field derives its name from the SI-prefix nano, meaning 1/1,000,000,000 of something. A nanometre is thus 1/1,000,000,000 of a metre, which is around 1/50,000 of the diameter of a human hair or the space occupied by 3-4 atoms placed end-to-end.

Recent fundamental investigations and the applied research in materials science concentrate in many aspects on the physics and technology of nanostructures. The new properties of materials at nano-scale dimensions manifest itself in peculiar mechanical, chemical, magnetic, optic and biological characteristics. The possible applications cover a wide range from the construction of materials for micro- and nanoelectronics to biomedical applications. Applications of these require, however, the knowledge of parameters and physical laws valid at nano-scale.

We have studied three systems experimentally: Si-Ge, Ni-Cu and Cu-Ag. There is a complete mutual solubility in the first two systems. The mutual diffusion coefficients (Si in Ge and vice versa; Ni in Cu and vice versa) are strongly influenced by the chemical composition of the alloy, especially at low temperatures. There is, however, a miscibility gap in the Cu-Ag system.

Our samples were prepared by magnetron sputtering (Debrecen) (Si-Ge and Cu-Ag) except for the Cu-Ni, which were evaporated in-situ under ultra high vacuum.

We have analysed these samples by Small Angle X-Ray Diffraction (Debrecen), Auger Electron Spectroscopy (traditional – Marseille, depth profiling – Budapest) and Rutherford backscattering (Debrecen).

Grain boundaries are, generally, diffusion short circuits; consequently, the major part of material transport will occur by grain-boundary diffusion in nanomaterials where a large amount of atoms can lie on grain or interphase boundaries (50% for a grain size equal to 5 nm; 20% for a grain size equal to 10 nm). An interesting question arose during the interpretation of the already existing data on grain-boundary diffusion in nanocrystalline materials: whether the grain-boundary diffusion coefficients measured in these alloys are identical to those obtained in microcrystalline state or not? An answer to this question would solve a fundamental problem concerning to the structure of GB in these materials weather it is a well defined and more or less ordered one as in coarse grained materials or a disordered like frozen-gas structure.

1. We tried to answer this question by comparing the temperature dependence of Ag grain-boundary diffusion in Cu measured by Auger electron spectroscopy in C-kinetics regime (Hwang-Balluffi method) with triple products determined previously in polycrystalline samples using radio tracer technique in B-kinetics regime. From this comparison the activation energy of the surface segregation factor was also determined, which is in a good agreement with surface segregation energies of Ag in Cu(Ag) bulk alloys published in the literature. These results as a whole suggest that there is no difference between nanostructured and bulk polycrystals from the point of view of grain-boundary material transport.

The diffusion in nanostructures has other challenging features even if the role of structural defects (dislocations, phase- or grain-boundaries) can be neglected. This can be the case for diffusion in amorphous materials, in epitaxially grown highly ideal thin films or multilayers where diffusion along short circuits can be ignored and "only" principal difficulties, related to nanoscale effects, raise.

2. For example, one of the most important differences for diffusion in such crystalline materials – as compared to diffusion for long distances (orders of magnitude longer than the atomic spacing) – is that the continuum approach cannot be automatically applied. The validity of the continuum model shifts as the function of the strength of the concentration dependence of the diffusion coefficients, and in many real multilayer systems with typical modulation length of few nanometers, it can break down.
3. Furthermore, at short diffusion distances in case of interdiffusion, due to the composition dependence of the diffusion coefficients, the shape of the interface can be also different from the well-known interfaces obtained in bulk samples. We have found from simulations in multilayers A/B where the diffusion coefficients of A (B) atoms in B (A) are very different, which leads strongly (exponential) concentration dependent diffusion coefficients during the homogenisation, that large asymmetry is observed in the evolution of the concentration profiles. A fast homogenisation takes place on the side where the diffusion is faster, and here the distribution is practically flat. Thus only the amplitude of the composition modulation decreases with time and the interface remains sharp and shifts. The Auger depth profiling technique provided direct evidence for this in amorphous Si-Ge system []. Furthermore, we found that there is a difference between the results obtained from the continuum and discrete models: the shape of the moving boundary changes with time in the discrete model and it shows a layer-by layer dissolution kinetics, while in the continuum model the interface remains atomic sharp.
4. Investigating the combined effects of stress and non-linearity due to the concentration dependence of the diffusion coefficients, it was shown that in the Si-Ge system not only the concentration but also the pressure distribution is also very asymmetrical [, ]. Furthermore, stress effects do not modify the behaviour of the composition profile and the time evolution of the X-ray intensity curve; only its ‘slope’, which is proportional to the diffusivity, has been changed. Consequently stress effects can slow down the homogenisation in multilayers.
5. Moreover, in these materials, at short diffusion times, when the gradient of concentration is large, the usual parabolic law of diffusion can be violated, leading to a linear law even if there is no reaction control at al. We have investigated the effect of segregation on the dissolution of a thin Ni layer (3-14 eq-ML) into a semi-infinite Cu substrate []. Our simulations indicated a step-wise character of dissolution in accordance with the results obtained in multilayers and an interesting interference between the segregation and dissolution. Because of the strong concentration dependence of the diffusion coefficients of the diffusing species, the interface remains sharp and shifts until it reaches the next-to-the-last layer. In this part of the dissolution a concentration dependent diffusion on discrete lattice controls the process. We have seen that the thickness of Ni decreases linearly with time, indicating the strong non-linearity, deviation from the continuum description and violation of the parabolic law. This was also experimentally confirmed from Auger measurements of dissolution of Ni into semi-infinite Cu substrate. In the final stage of the dissolution, due to the driving force for segregation, the process continues by the saturation of Cu in the top layer. The change of the concentration of the second layer (first underlayer) occurs according to the segregation isotherm. Finally, after the saturation of the surface layer by Cu, the final homogenisation takes place by complete dissolution of the second layer.

1. D.L. Beke, G.A. Langer, M. Kiss-Varga, A. Dudas, P. Nemes, L. Daróczi, Gy. Kerekes, Z. Erdélyi, Thermal stability of amorphous and crystalline multilayers produced by magnetron sputtering, Vacuum, 1998, 50, No. 3-4, 373-383 [0.51]
2. D.L. Beke, P. Nemes, Z. Erdélyi, I.A. Szabó, G.A. Langer, Stress effects and non-linearities in diffusional mixing of multilayers, Materials Reserach Society Symposium Proceedings: Diffusion Mechanisms in Crystalline Materials Editors: Y. Mishin, G. Vogl, N. Ciwern, R. Catlow, D. Farkas MRS Warrendale, Pennsylvania, USA, 1998, 527, 99-110
3. Z. Erdélyi, D.L. Beke, P. Nemes, G.A. Langer, On the range of validity of the continuum approach for nonlinear diffusional mixing of multilayers, Phil.Mag. A, 1999, 79, No 8, 1757-1768 [1.915]
4. Zs. Tôkei, Z. Erdélyi, Ch. Girardeaux, A. Rolland, Effect of sulphur content and pre-annealing treatments on nickel grain-boundary diffusion in high-purity copper, Phil.Mag. A, 2000, 80, No. 5, 1075-1083 [1.915]
5. D.L. Beke, A. Dudas, A. Csik, G.A. Langer, M. Kis-Varga, L. Daróczi, Z. Erdélyi, On the thermal stability of multilayers, Functional Materials, 1999, 6, No. 3, 539-544
6. A. Dudás, G.A. Langer, D.L. Beke, M. Kis-Varga, L. Daróczi, Z. Erdélyi, Thermal stability of Mo-V epitaxial multilayers, Journal of App. Phys., 1999, 86, No. 4, 2008-2013 [2.275]
7. D.L. Beke, Z. Erdélyi, P. Bakos, Cs. Cserháti, I.A. Szabó, Segregation Induced Phase Transformations in Nanostructures, The Japan Institute of Metals, Proc. Vol. 12, 1297-1300 (1999)
8. Z. Erdélyi, Ch. Girardeaux, G.A.Langer, L. Daróczi, A. Rolland, D.L. Beke, Determination of grain-boundary diffusion coefficients by Auger Electron Spectroscopy, Applied Surface Science, 162-163, 213-218 (2000) [1,195]
9. A. Simon, A. Csik, F. Pászti, Á.Z. Kiss, D.L. Beke, L. Daroczi, Z. Erdélyi, G.A. Langer, Study of interdiffusion in amorphous Si/Ge multilayers by Rutherford backscattering spectrometry, Nuclear Instruments and Methods in Physics Research B, 2000, 161-163, 472-476 [1.118]
10. G.Erdélyi, Z. Erdélyi, D.L. Beke, J. Bernardini, C. Lexellent, Pressure dependence of Ni self-diffusion in NiTi near equatomic alloy, Phys. Rev. B, 2000, 62, No. 13, 1-4 [3.008]
11. A. Csik, D.L. Beke, G.A. Langer, Z. Erdélyi, L. Daróczi, K. Kapta, M. Kiss-Varga, Non-linearity due to the strong concentration dependence of diffusion in amorphous Si-Ge multilayers, Vacuum, 61, No. 2-4, 297-301 (2001) [0.51]
12. Z. Erdélyi, Ch. Girardeaux, G.A. Langer, D.L. Beke, A. Rolland, J. Bernardini, Determination of grain-boundary diffusion of Ag in nanocrystalline Cu by Hwang-Balluffi method, Journal of Applied Physics, 89, No. 7, 3971-3975 (2001) [2.275]
13. A. Csik, G.A. Langer, D.L Beke, Z. Erdélyi, M. Menyhárd, A. Sulyok, Investigation of interdiffusion in amorphous Si/Ge multilayers by Auger depth profiling technique, Journal of Applied Physics, 89, No. 1, 804-806 (2001) [2.275]
14. D.L. Beke, A. Csik, G.A. Langer, Z. Erdélyi, Z. Papp, Diffusion and thermal stability in multilayers, Def. and Diff. Forum, 194-199, 1403-1416 (2001) [0.712]
15. G. Erdélyi, Z. Erdélyi, D.L. Beke, Pressure dependence of self diffusion in B2 intermetallic phases, Def. and Diff. Forum, 194-199, 473-480 (2001) [0.712]
16. Z. Erdélyi, Ch. Girardeaux, J. Bernardini, D.L. Beke, A. Rolland, Experimental and theoretical study of type C grain boudary and volume diffusion by AES in metal/metal structures, Def. and Diff. Forum, 194-199, 1161-1166 (2001) [0.712]
17. J. Nyéki, Ch. Girardeaux, Z. Erdélyi, G.A. Langer, G. Erdélyi, D.L. Beke, A. Rolland, AES study of surface segregation of Ge in amorphous Si_1-x thin film alloys, Surface Science (2000), in press
18. Z. Erdélyi, Ch. Girardeaux, Zs. Tôkei, D.L. Beke, Cs. Cserháti, A. Rolland, Investigation of the interplay of nickel dissolution and copper segregation in Ni/Cu(111) system by Auger dissolution kinetics, Surface Science (2000), in press
19. Z. Erdélyi, D. L. Beke, J. Bernardini, Ch. Girardeaux and A. Rolland, Investigations of Diffusion Kinetics by Auger Electron Spectroscopy, Defects and Diffusion in Metals - Annual Retrospective 2001, Defect and Diffusion Forum, (2001), in press

1. D.L. Beke, G.A. Langer, M. Kiss-Varga, A. Dudas, P. Nemes, L. Daróczi, Gy. Kerekes, Z. Erdélyi, 7th Joint Vacuum Conference of Hungary, Austria, Croatia and Slovenia, May 26-29, 1997 Debrecen (Hungary)
2. D.L. Beke, P. Nemes, Z. Erdélyi, I.A. Szabó, G.A. Langer, MRS Spring Meeting, San Francisco (USA),1998. 13-16.March
3. D.L. Beke, A. Dudas, A. Csik, G.A. Langer, M. Kis-Varga, L. Daróczi, Z. Erdélyi, Physics and Technology of Nanostructured, Multicomponent Materials, Ungvár (Ukrain), 1998. 24-26 September
4. D.L. Beke, Z. Erdélyi, P. Bakos, Cs. Cserháti, I.A. Szabó, International Conference on Solid-Solid Phase Transformations, Kyoto (Japan), May 1999
5. Z. Erdélyi, Ch. Girardeaux, G.A.Langer, L. Daróczi, A. Rolland, D.L. Beke, The 5^th international conference on Atomically Controlled Surfaces, Interfaces and Nanostructures, Aix-en-Provence (France), 1999
6. Z. Erdélyi, Ch. Girardeaux, G.A.Langer, L. Daróczi, A. Rolland, D.L. Beke, Second International Workshop on Surface and Grain Boundary Segregation, Duesseldorf (Germany), 1999
7. Cs. Cserháti Z. Erdélyi, D.L. Beke, I.A. Szabó, P. Bakos, Second International Workshop on Surface and Grain Boundary Segregation, Duesseldorf (Germany), 1999
8. Z. Erdélyi, Ch. Girardeaux, D.L. Beke, Zs. Tôkei, Cs. Cserháti, A. Rolland, 18^th European Conference on Surface Science, Vienna, 1999
9. A. Simon, A. Csik, F. Pászti, Á.Z. Kiss, D.L. Beke, L. Daróczi, Z. Erdélyi, G.A. Langer, 4th International Conference on ION BEAM ANALYSIS and 6th European Conference on ACCELERATORS IN APPLIED RESEARCH AND TECHNOLOGY (IBA-14\ECAART-6), 1999
10. Z. Erdélyi, Diffusion dans des films minces et multicouches, Journée des doctorants 2000, Marseille (France), Marseille-Luminy (France), January 2000
11. Z. Erdélyi, Etude des effets conjugués de la dissolution de nickel et de la ségrégation du cuivre dans le systčme Ni/Cu(111), talk at Université Aix-Marseille I, Marseille-Luminy (France), February 2000
12. D.L. Beke, A. Csik, G.A. Langer, Z. Erdélyi, Z. Papp, Multilayers, Fifth International Conference on Diffusion in Materials, Paris (France), July 17-21 2000
13. G. Erdélyi, Z. Erdélyi, Z. Kátai, D.L. Beke, Fifth International Conference on Diffusion in Materials, Paris (France), July 17-21 2000
14. Z. Erdélyi, Ch. Girardeaux, J. Bernardini, D.L. Beke, A. Rolland, Fifth International Conference on Diffusion in Materials, Paris (France), July 17-21 2000
15. Z. Erdélyi, Dépôt d’un film mince de Ni sur Cu(111): effets conjugués de la dissolution et de la ségrégation, talk at Université Aix-Matseille III, Marseille (France), March 2001
16. Z. Erdélyi, Nemlineáris diffúzió és szegregáció nanoskálán, Tavaszi Szél 2001, Gödöllő (Magyarország) 2001. április 20-22.