Abdelouahab OUAHAB

 Département des Sciences Physiques, Université Kasdi Merbah,

 Ouargla, BP 501, Route de Ghardaïa, 30000, Algeria.



 L’interface Au/YBCO est représentée par un modèle simple montrant le contact entre deux surface d’une interface épitaxiale avec la relation d’orientation Au(111)/YBCO(001) où  la direction [011]Au est  parallèle à  [100]YBCO; la surface de terminaison du YBCO étant le plan CuO.  Un modèle plus simple de l’interface celui Au(001)/YBCO(001) est est utilisé pour calculer les énergies d’interaction entre la couche métallique est le substrat oxyde en fonction de la distance de séparation entre les deux surfaces pour différentes configurations en utilisant la théorie de la fonctionnelle de la densité. La configuration ayant l’énergie d’interaction la plus élevée est celle qui correspond à la situation dans laquelle les atomes d’or sont situés sur les sites oxygène de la surface du supraconducteur.


 The Au/YBCO interface is represented by a simple model showing the contact of two surfaces of an epitaxial interface with the orientation relationship Au(111)/YBCO(001) where [011]Au is parallel to [100]YBCO for which termination surface of the substrate corresponds to the CuO layer of YBCO. A simplest model with different configuration Au(001)/YBCO(001) is used to calculate the interaction energies using pseudopotential DFT approach as a function of the separation distance between the metallic film and the surface of the superconductive substrate in different configurations. The configuration with the highest interaction energy at the interface Au/YBCO(001) was found to correspond to the deposition of Au film in such way that the Au atoms of the interfacial monolayer are top oxygen atoms of the substrate surface.


 Since superconductive materials have been discovered in the end of the 1980s application and theoretical studies have been carried out to develop techniques to fabricate superconductive materials and devices. Among superconductive materials the YBCO (YBa2Cu3O7-x) was the first high critical temperature superconductor HTC with a working temperature of about 77 K. Applications of superconductive materials have been since developed and covered many fields such as NMR devices (working at strong magnetic fields in the range of 3-5 tesla assured by the high currents reaching 104 -106 A/cm2 [1-3]), microwave devices [4, 5] Josephson devices [6-15], YBCOsilicon hybrid/integrated electronics and microelectronics device applications [13], HTS based transmission cables [15, 16], motors, generators, SMES, transformers, high-field magnets, high critical temperature magnets [17], electric power application, [18-21], superconducting magnetic energy storage system [22] and fault current limiter [23]. The YBCO superconductive material belongs to the crystallographic family of ceramics known to be very rigid but fragile and chemically unstable when its surface is exposed to atmospheric air [24]. In addition this superconductive ceramics need to be wired to the electric circuit which is mainly realised by metallic contacts. These contacts must have very good quality to ensure carrying high electric currents. Mechanical supporting the superconductive material is ensured by oxide [4, 25, 26] or by metallic substrates [1, 6, 7, 28 -31]. Among these laters, the gold and silver were the first to be used in such contacts and substrates [6, 27]. The structure of the interface between superconductor and metal controls the electric quality of the contacts [32, 33]. In order to get such metallic contacts with YBCO superconductor metal, has to be deposed on perfect superconductor surface to avoid structural defects. This can be achieved by metal evaporation or sputtering which can yield abrupt interfaces on large surfaces can be realised. A stepped interfaces can be seen also with a step difference of a multiple of constant height which corresponds to the parameter c of the unit cell of YBCO [34] suggesting that a preferential termination of the YBCO (probably CuO one) is in contact with the metal at the interface. Several metal/oxide interfaces have been studied theoretically in the aim to determine their atomic and electronic structure. The examples the Ag/MgO [35], Pd/MgO [36], Ag/Al2O3 [37] can be cited here. These studies were carried out using DFT calculations which become more and more involved in the field of theoretical condensed matter studies nowadays. However, such studies are not available for the Au/YBCO interface. To get more comprehension of the atomic structure of this interface we attempt to study the structure of the Au(100)/YBCO(001) interface by the use of DFT calculations in order to determine the surface potential energy (SPE) which can be used to describe the interatomic interactions between the two sides of the interface. The SPE can be used then to simulate the interface structure at a mesoscopic scale. Such work has been done for other interfaces [37, 38]. <Q           The paper will be organized like follows: we represent a model of the Aug/YBCO interface which we use then to calculate interaction energies between the metal Ag and the superconductor and a description of the calculation details. The results will be presented in a separate section followed by discussions and a conclusion.


 The metallic film of gold is generally deposited on termination surface of the superconductor. This is similar to the Ag/YBCO interface for which a similar study is reported elsewhere [39]. We have presented a in this study a model based on the epitaxial relationship revealed X ray diffraction at the interface. The model we present here is not very different. The X ray showed that the epitaxial relationship at the interface is of the form Ag(111)/YBCO(001) where [110]Ag//[100]YBCO.

 Gold and silver are noble metals, and their crystallographic structure is FCC. Furthermore, their chemical structure unit cell parameters are very close to each other: both belong to the column of the periodic table and the unit cell parameter is 4.08 A° and 4.09 for gold and silver respectively. Taking these considerations into account, a simple geometric model of the Au/YBCO is illustrated on figure 2. This model is similar to the Ag/YBCO one and is based on the assumption that the metallic film is deposited on the 'natural termination' of the superconductive substrate, and takes into account the miss-much between the two materials. In fact, the Au has the CFC unit cell with the cell parameter of 4.08A° which very close the silver unit cell parameter, and the YBCO crystallographic structure is perovkstie type with parameters a, b and c equal to 3.81 (3.82)  A°, 3.88 (3.89) A°, and 3.67 (3.68)  A° respectively [40-42]. When the two surfaces of both material are brought close to each other to form the interface we can envisage that an atom of Au taken as a reference in top oxygen atom and going along the direction of the a axis of the YBCO surface, the next Au atom to oxygen will coincide with the third atom. In the b direction, the coincidence will be with the fifth Au atom as we can see in figure 3. The nearest neighbour distance for the Au (111) surface is and; the two distance of first coincidence in the a and b directions can be determined by these two equations:

Where na and nb are the numbers of unit cell distances in the a and b directions respectively; they are deduced from the last equation and are equal to 3 and 5 respectively. Our model shows that the best coincidence takes place as follows: In the [100] direction YBCO, if an Au atom of the metallic interfacial layer is top an oxygen atom of the CuO termination surface of oxygen, the next Au atom is distant by 4x2.8911.56 A°. Because of the difference between the metallic and the oxide lattice parameters, the distance between oxygen coincident atoms of the YBCO surface is 3 x 3.81=11.43 A°. This is little bit different in [010] direction: The Au-Au distance is 4x5.0120.04 A° in front of 5x3.88=19.4 A° for O-O distance. To have an epitaxial deposition of Au(111) on YBCO with CuO termination surface, a dilation of the Au (111) surface parameters of 1.12 % and 3.12 % receptively is necessary. The aim of our study is to obtain interaction energies between the metallic film and superconductor substrate. We have used a supercell containing only one unit cell of YBCO and five monolayers of the metal film which gives more realistic situation since the metallic film is thicker and hence avoiding surface effects on interaction energies. The number of atoms in the supercell reduces to only 26 atoms. Note that the (111) and the (100) face for the metallic film are quite similar for this situation, for this reason the model proposed here belongs to the interface Au(100)/YBCO(001) rather than Au(111)/YBCO(001). The mismatch between the metal and the substrate changes to 7 % for the direction a and to 5 % for the b direction of the YBCO respectively. In DFT calculations, the physical system are modelled by a supercell that represents the physical system conserving as long


as possible its geometrical configuration and chemical composition. If we use the above dimensions of the superconductor as a substrate to depose the metallic film, and taking into account that one unit cell of YBCO counts 10 atoms, the supercell counts 3 x 5 x 10 atoms for the substrate. If we use only three monolayers to represent the Au (111) film we need to use at least three monolayers of Au atoms to simulate a thick metallic film, the three monolayers count 3 x 16 = 48 Au atoms. The total number of atoms in the supercell of our model counts now 198 atoms. This a huge unit cell for the DFT calculations since the computer memory and calculations require powerful machines unfortunately unavailable for us. These values of the mismatch in the last model are quite large compared to model systems of metal/oxide DFT calculations such as Ag/MgO(100) interface in which the mismatch is less than 3 % [38]. However it is reported in many studies of similar interfaces like Pd/MgO and Ni/MgO where the mismatch is about 7.6 and 16 % respectively [43]. Moreover, the largest mismatch reported in DFT studies is 18 % for the NiO/Ni interface [44]. More first principle studies of complicated interfaces are reported like the Cu/Al2 O3(0001) interface in which the mismatch is 7.3 % [45].


 The geometrical configuration of the Au/YBCO interface was presented by a simple model made by the contact of two surfaces of an epitaxial interface of the orientation relationship Au(111)/YBCO(001) where [011]Au is parallel to [100]Y BCO. To calculate the interaction energies at this interface, a simplest model with different configuration Au/YBCO(001) is presented and used to calculate the interaction energies using  DFT pseudopotential. The proposed model of the interface is used to get an estimation of the interaction energies and their dependence on the separation distance between the metallic film and the surface of the superconductive substrate with CuO termination. The relative horizontal positions of the interfacial Au monolayer with respect to the substrate surface atoms representing three different situations of high symmetries on the surface: (1) Au atoms are top oxygen atoms,(2) Au atoms are top copper atoms, and (3) Au atoms are top intermediate sites. The calculated interaction energies show that the most stable configuration of the interface Au/YBCO(001) is that corresponding to the situation in which the Au film so that the Au atoms of the metallic interfacial monolayer are top oxygen atoms of the substrate surface with an interaction energy of about 1.09 eV/u.s. and a separation distance of about 2.20 A°.


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