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First principle calculations are performed using the super cell method with pseudopotentials and plane waves based on the Density Functional Theory (DFT) for the surface structural properties at T = 0 K . Thin slabs of 7 - 13 atomic layers of the clean Nb and Ta (001) surfaces are considered and relaxations, surface energies, and work functions of the fully relaxed slabs are presented. Consistent results are obtained with the Generalized Gradient Approximation (GGA) and the Local Density Approximation (LDA) for the exchange-correlation functional and they compare well with experimental and other theoretical works.

This decade is seeing tremendous change in the electronics market with the development and commercialization of new technologies in mobile communication, personal computers and the Internet. Niobium and tantalum compounds are being used successfully in a variety of different applications in the electronic and electro-optic markets. The need for miniaturization and high-performance electronic components is leading to more research in nanostructured materials. Characterizing the fundamental properties of these nanoscale constructions is of prime importance. The surface structural properties are of immense importance when artificial fabrication of materials with desirable properties is sought. Owing to the large advancements in thin film depositing techniques and the technological importance of the transition metals, study of the surface energetics of the transition metals is a rapidly growing field. It is essential to have detailed information on the relaxed geometry and energetics of the system to understand completely the factors influencing the epitaxy of interfaces and multilayers. Reliable information on the clean (bare) surface properties is necessary before multi-layer or interface studies can be performed. The growing use of Nb and Ta in nanotechnology requires a clear understanding of the surface properties of these metals. In this paper the surface energies and work functions of the Nb, and Ta (001) relaxed surfaces at zero Kelvin are reported using the total energy pseudopotential method under DFT. Norm conserving pseudopotentials with a plane wave basis set is used to vastly reduce computer time and still maintain the desired accuracy. DFT has the double advantage of being able to treat many problems to sufficiently high accuracy, as well as being computationally simple [1-4]. Over the last forty years or so DFT has gained tremendous popularity and it is currently one of the most widely used methods for “ab initio” calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions.

The purpose of the present work is to take into account a complete relaxation of the atomic positions for the calculation of the surface properties. Since, most of the existing first principles calculations [5-7] have assumed truncated bulk geometry of the surface this is highly desirable. In addition this is the first study of these systems with the DFT-total energy pseudopotential method. The agreement of the results with those obtained by other methods proves the reliability of this method and is also one of the motivations.

The Niobium and Tantalum (001) surfaces are modeled by periodic slabs consisting of 7 to 13 layers, separated by several layers of vacuum, equivalent to almost 70% - 75% of the slab thickness. On account of the large and persistent relaxations at the relatively open (001) surfaces, especially transition metals performing the calculations for slabs of 7 - 13 atomic layers helps to check the convergence of the results. Even though, for all practical purposes the 9 or 11-layer slab is thick enough to avoid perturbation connected with the finite/periodic geometry and can represent well all the surfaces considered.

All calculations are performed using the ABINIT software package with norm conserving pseudopotentials [

The lattice constants used in this study of the Nb and Ta (001) surfaces are calculated from first principles, self consistently, both for the GGA and LDA calculations. The optimized lattice constant values, the cutoff energy and the k-point grid are listed in

The structural relaxation of the clean Nb and Ta (001) surfaces is performed for the various atomic layer slabs and the percentage relaxations of the atomic layers are calculated using the relation:

where is the distance between two successive layers in the relaxed surface structure and ∆Bulk is the interlayer bulk distance. The GGA relaxation results are summarized in

^{a}Percentage difference in lattice constants—present calculations and experimental results [

Other works ∆_{12}: −13.9 (DFT-GGA) [

results of other theoretical and experimental works including that of LEED for the topmost layer relaxation are presented at the end of each surface data [13-18]. The relaxation behavior of the different surfaces is in close agreement to other works. It can be noticed that the topmost layer relaxation converges excellently with the number of layers for Nb and for Ta within an uncertainty of ±0.1.

The formation energy of a solid surface can be extracted from thin slab calculations if the bulk energy per atom is known. The surface energy is calculated using the relation:

where E_{n} is the energy per unit cell of the n layer slab and E_{B} is the bulk energy of the infinite solid per unit cell. The factor of half arises from the 2 surfaces of the slab. A direct application of the formula (2) usually leads to a linear divergence with the increasing slab thickness if E_{B} is determined from an independent bulk calculation [_{B} is taken as an average of the energy increment values for the unrelaxed slabs of n layers and n ± 1 layers. For example to calculate the surface energy of the 7 layer slab, the average of the total energy difference of the 6 layer and 8 layer slabs from the 7 layer slab is taken as the bulk energy.

The results of other calculations have been included alongside for comparison. There is good agreement with the work of Vitos et al. for the Niobium surface [

The work function corresponds to the minimum amount of energy needed to remove an electron from the metal and for a metallic slab may be expressed as the difference between the electrostatic potential barrier height in the vacuum, V_{es}, and the Fermi energy, E_{F}

In metals, the work function and ionization energy are the same. The work function of a surface is strongly affected by the condition of the surface. The presence of minute amounts of contamination (less than a monolayer of atoms or molecules), or the occurrence of surface reactions (oxidation or similar) can change the work function substantially. Theoretical first principles determinations of work function are therefore very useful. The calculated work functions for the relaxed surfaces in GGA are listed in

and Ta surfaces. There is also good agreement with other ab-initio calculations and experiment. The small discrepancies can be attributed to the neglect of relaxations in the other works or may arise from the different exchangecorrelation energy functional applied. As far as experimental value is concerned, the only available one is for the Ta surface and that too is old. Experimental verification of the results for all the surfaces would be highly desirable.

1) Surface relaxations, surface energies, and work functions of the (001) surfaces of Niobium and Tantalum are determined at zero Kelvin from first principles using DFT with the GGA and LDA exchange-correlation functional. Results obtained with both the exchange correlations are in good agreement for all the surfaces considered. Surface energies and work functions all agree within 0.5 eV.

2) There is very good convergence with respect to the number of layers in the slab for all the properties in all the surfaces.

3) There is good overall agreement with the results of other ab-initio calculations and experimental results. This is a big boost for DFT methods of calculation which is increasingly becoming more and more popular and gaining wide spread acceptance.