Study of Strain and Temperature Dependence of Metal Epitaxy

Metallic films are important in catalysis, magneto-optic storage media, and interconnects in microelectronics, and it is crucial to predict and control their morphologies. The evolution of a growing crystal is determined by the behavior of each individual atom, but technologically relevant structures have to be described on a time scale of the order of (at least) tenths of a second and on a length scale of nanometers. An adequate theory of growth should describe the atomistic level on very short time scales (femtoseconds), the formation of small islands (microseconds), as well as the evolution of mesoscopic and macroscopic structures (tenths of seconds). The development of efficient algorithms combined with the availability of cheaper and faster computers has turned density functional theory (DFT) into a reliable and feasible tool to study the microscopic aspects of growth phenomena (and many other complex processes in materials science, condensed matter physics, and chemistry). In this paper some DFT results for diffusion properties on metallic surfaces are presented. Particularly, we will discuss the current understanding of the influences of strain on the diffusion (energy barrier and prefactor) of a single adatom on a substrate. A DFT total energy calculation by its nature is primarily a static calculation. An accurate way to describe the spatial and temporal development of a growing crystal is given by kinetic Monte Carlo (KMC). We will describe the method and its combination with microscopic parameters obtained from ab initio calculations. It is shown that realistic ab initio kinetic Monte Carlo simulations are able to predict an evolving mesoscopic structure on the basis of microscopic details.Comment: 25 pages, 6 figures, In: ``Morphological Organisation during Epitaxial Growth and Removal'', Eds. Z. Zhang, M. Lagally. World Scientific, Singapore 1998. other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

First-principles studies of kinetics in epitaxial growth of III-V semiconductors

We demonstrate how first-principles calculations using density-functional theory (DFT) can be applied to gain insight into the molecular processes that rule the physics of materials processing. Specifically, we study the molecular beam epitaxy (MBE) of arsenic compound semiconductors. For homoepitaxy of GaAs on GaAs(001), a growth model is presented that builds on results of DFT calculations for molecular processes on the beta2-reconstructed GaAs(001) surface, including adsorption, desorption, surface diffusion and nucleation. Kinetic Monte Carlo simulations on the basis of the calculated energetics enable us to model MBE growth of GaAs from beams of Ga and As_2 in atomistic detail. The simulations show that island nucleation is controlled by the reaction of As_2 molecules with Ga adatoms on the surface. The analysis reveals that the scaling laws of standard nucleation theory for the island density as a function of growth temperature are not applicable to GaAs epitaxy. We also discuss heteroepitaxy of InAs on GaAs(001), and report first-principles DFT calculations for In diffusion on the strained GaAs substrate. In particular we address the effect of heteroepitaxial strain on the growth kinetics of coherently strained InAs islands. The strain field around an island is found to cause a slowing-down of material transport from the substrate towards the island and thus helps to achieve more homogeneous island sizes.Comment: 12 pages, 7 figures, REVTeX, Final version to appear in Appl. Phys. A (2002). Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Limit Theorems and Governing Equations for Levy Walks

The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the domain of beta-stable attraction, we prove functional limit theorems and derive governing pseudo-differential equations for the law of the walker's position. Both Levy Walk and its limit process are continuous and ballistic in the case beta in (0,1). In the case beta in (1,2), the scaling limit of the process is beta-stable and hence discontinuous. This case exhibits an interesting situation in which scaling exponent 1/beta on the process level is seemingly unrelated to the scaling exponent 3-beta of the second moment. For beta = 2, the scaling limit is Brownian motion

Structural stability, magnetic and electronic properties of Co2MnSi(001)/MgO heterostructures: A density functional theory study

A computational study of the epitaxial Co2MnSi(001)/MgO(001) interface relevant to tunneling magnetoresistive (TMR) devices is presented. Employing ab initio atomistic thermodynamics, we show that the Co- or MnSi-planes of bulk-terminated Co2MnSi form stable interfaces, while pure Si or pure Mn termination requires non-equilibrium conditions. Except for the pure Mn interface, the half-metallic property of bulk Co2MnSi is disrupted by interface bands. Even so, at homogeneous Mn or Co interfaces these bands contribute little to the minority-spin conductance through an MgO barrier, and hence such terminations could perform strongly in TMR devices.Comment: 4 pages, 3 fig

Density Functional Theory of Epitaxial Growth of Metals

This chapter starts with a summary of the atomistic processes that occur during epitaxy. We then introduce density functional theory (DFT) and describe its implementation into state-of-the-art computations of complex processes in condensed matter physics and materials science. In particular we discuss how DFT can be used to calculate parameters of microscopic processes such as adsorption and surface diffusion, and how they can be used to study the macroscopic time and length scales of realistic growth conditions. This meso- and macroscopic regime is described by the ab initio kinetic Monte Carlo approach. We discuss several specific theoretical studies that highlight the importance of the different diffusion mechanisms at step edges, the role of surfactants, and the influence of surface stress. The presented results are for specific materials (namely silver and aluminum), but they are explained in simple physical pictures suggesting that they also hold for other systems.Comment: 55 pages, 20 figures, to be published "Growth of Ultrathin Epitaxial Layers", The Chemical Physics of Soild Surfaces, Vol. 8, Eds D. A. King and D. P. Woodruff (Elsevier Science, Amsterdam, 1997

Effect of the cluster size in modeling the H_2 desorption and dissociative adsorption on Si(001)

Three different clusters, Si_9H_12, Si_15H_16, and Si_21H_20, are used in density-functional theory calculations in conjunction with ab initio pseudopotentials to study how the energetics of H_2 dissociativ e adsorption on and associative desorption from Si(001) depends on the cluster size. The results are compared to five-layer slab calculations using the same pseudopotentials and high qu ality plane-wave basis set. Several exchange-correlation functionals are employed. Our analysis suggests that the smaller clusters generally overestimate the activation barriers and reaction energy. The Si_21H_20 cluster, however, is found to predict reaction energetics, with E_{a}^{des}=56 +- 3 kcal/mol (2.4 +- 0.1 eV), reasonably close (though still different) to that obtained from the slab calculations. Differences in the calculated activation energies are discussed in relation to the efficiency of clusters to describe the properties of the clean Si(001)-2x1 surface.Comment: 10 pages, 6 figures, submitted to J. Chem. Phy

First-principles statistical mechanics study of the stability of a sub-nanometer thin surface oxide in reactive environments: CO oxidation at Pd(100)

We employ a multiscale modeling approach to study the surface structure and composition of a Pd(100) model catalyst in reactive environments. Under gas phase conditions representative of technological CO oxidation (~1 atm, 300-600 K) we find the system on the verge of either stabilizing sub-nanometer thin oxide structures or CO adlayers at the surface. Under steady-state operation this suggests the presence or continuous formation and reduction of oxidic patches at the surface, which could be key to understand the observable catalytic function.Comment: 4 pages including 2 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

First-principles, atomistic thermodynamics for oxidation catalysis

Present knowledge of the function of materials is largely based on studies (experimental and theoretical) that are performed at low temperatures and ultra-low pressures. However, the majority of everyday applications, like e.g. catalysis, operate at atmospheric pressures and temperatures at or higher than 300 K. Here we employ ab initio, atomistic thermodynamics to construct a phase diagram of surface structures in the (T,p)-space from ultra-high vacuum to technically-relevant pressures and temperatures. We emphasize the value of such phase diagrams as well as the importance of the reaction kinetics that may be crucial e.g. close to phase boundaries.Comment: 4 pages including 2 figure files. Submitted to Phys. Rev. Lett. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Density-functional theory study of half-metallic heterostructures: interstitial Mn in Si

Using density-functional theory within the generalized gradient approximation, we show that Si-based heterostructures with 1/4 layer $\delta$-doping of {\em interstitial} Mn (Mn$_{\mathrm int}$) are half-metallic. For Mn$_{\mathrm int}$ concentrations of 1/2 or 1 layer, the states induced in the band gap of $\delta$-doped heterostructures still display high spin polarization, about 85% and 60%, respectively. The proposed heterostructures are more stable than previously assumed $\delta$-layers of {\em substitutional} Mn. Contrary to wide-spread belief, the present study demonstrates that {\em interstitial} Mn can be utilized to tune the magnetic properties of Si, and thus provides a new clue for Si-based spintronics materials.Comment: 5 pages, 4 figures, PRL accepte