Matthias Strobel

Coarsening mechanisms in surface morphological evolution

Based on a temperature-dependent, quantitative scanning tunneling microscopy analysis for the homoepitaxial growth and erosion of Pt(111), several possible atomic-scale mechanisms for the coarsening of mounds and pits are discussed: (i) noise-assisted coarsening, (ii) coalescence coarsening, (iii) step-edge diffusion present only during deposition or erosion, (iv) step-edge diffusion present even in the absence of growth or erosion, and (v) step-atom attachment. For Pt(111), mechanism (iv) is found to be decisive for coarsening. It is argued that for many low-index surfaces this coarsening mechanism is likely to be operative. Instead of a surface diffusion current driven by changes in surface curvature frequently assumed in phenomenological theories of coarsening, it appears that, even at high temperatures, coarsening is driven only by differences in curvature along contours of constant height.

Can core/shell nanocrystals be formed by sequential ion implantation? Predictions from kinetic lattice Monte Carlo simulations

Abstract High-dose ion implantation has proven to be a powerful technique to form a large variety of nanocrystals in the near surface layer of substrates. However, core/shell nanocrystals, which possess some unique physical properties, have been synthesized up to now only by colloid chemistry. A kinetic 3D lattice Monte Carlo (KLMC) model is used for the study of the diffusion, precipitation and interaction kinetics of the sequentially implanted atom types X and Y in a chemically neutral matrix. Applying a simplified model of collisional mixing, the coating behavior of previously nucleated precipitates of atom type X by atoms of type Y has been simulated.

EVOLUTION OF NANOCLUSTER ENSEMBLES : COMPUTER SIMULATION OF DIFFUSION AND REACTION CONTROLLED OSTWALD RIPENING

Abstract The Ion Beam Synthesis (IBS) of nanoclusters can be controlled by the flux and the fluence of ions as well as by the implantation and/or annealing temperature. The evolution of the precipitates, mainly described by their particle radius distribution (PRD), the number of remaining particles and the critical radius, depends on these parameters. However, the evolution is expected to behave different for systems like SiO2 and CoSi2 clusters in Si, because they are characterized by quite different ratios of diffusion to reaction constants. Here we present a unified model of Ostwald ripening of nanoclusters, which describes the pure diffusion and reaction controlled limits as well as all intermediate, mixed processes. Expressing the exact solution of the adiabatic diffusion equation by multipole moments we derive the governing equation for the evolution of an ensemble of nanoclusters in the leading monopole approximation. Whereas in the diffusion controlled regime we have the well known infinite range 1 r interaction among the nanoclusters, 1 r 2 interactions come into play in the reaction limited regime. Computer simulations for ensembles of several thousands of nanoclusters demonstrate the evolution for typical cases.

A combination of atomic and continuum models describing the evolution of nanoclusters

Ion beam synthesis is a promising technique to form nanoclusters. However, the synthesis of an ensemble of nanoclusters having a specific size and depth distribution requires a comprehensive understanding of the physical processes. We present two models, a discrete and a continuous one, where each is suited to study special stages of ion implantation and annealing. On the atomic scale our kinetic 3D lattice Monte-Carlo (MC) model is used to study nucleation and growth of nanoclusters. On the mesoscopic scale, rate-equations are used to describe their coarsening. By a combination of both methods the use of data from the MC simulation provides for the first time realistic initial conditions for the rate-equation approach to Ostwald ripening. As an application, the combined atomic-scale and continuum simulation tools are used to study the evolution and self-organization of nanoclusters.

A kinetic lattice Monte-Carlo approach to the evolution of boron in silicon

Abstract A kinetic 3D lattice Monte-Carlo (MC) model is introduced, which allows to describe the evolution of boron-rich silicon, especially the formation of boron-interstitial clusters of various structures and compositions. Using a refined bcc lattice with lattice constant abcc=aSi/4 a large variety of defect configurations can be mapped essentially without geometrical distortions. The energetics of defects can be specified by means of a set of energy parameters. Boron diffusion is implemented via an interstitial-assisted mechanism. First results of interstitial-mediated boron clustering are presented. The future capabilities to study the kinetics of BnIm cluster formation are outlined.

Computer simulation of precipitate coarsening: A unified treatment of diffusion and reaction controlled Ostwald Ripening

Abstract In Ion Beam Synthesis of nanoclusters the postimplantation annealing step causes major redistribution of the implanted impurity atoms by Ostwald Ripening (OR). The diffusion-reaction equations describing OR are highly nonlinear. Therefore, analytical studies are restricted to special cases like the asymptotic behavior, the diffusion or reaction controlled limit, low cluster concentration, etc. An alternative to analytical studies of OR is the numerical integration of the diffusion-reaction equations. Using this method we take into account the diffusion and reaction control of OR, i.e. we present for the first time a unified treatment for the whole range of and in between the diffusion and reaction controlled limits. Based on a local mean field theory, our model starts with a multipole expansion of the concentration field, which satisfies the stationary diffusion equation. Using appropriate boundary conditions on the precipitates we derive self-consistently the governing equations for the evolutio...

Atomic scale computer aided design for novel semiconductor devices

Abstract Conventional simulation tools for microelectronic technological processes will be soon obsolete since the scaling-down of semiconductor devices requires atomic scale design. In this context only the concurrent use of different complementary methodologies can satisfy the demands of accurate and efficient modelling. We have applied a series of approaches to a noteworthy case: the B-type doping of Si. The choice of appropriate methodology depends on the peculiar problem we must address. Statics and migration mechanism are studied by quantum mechanical calculation. These calculations validate semiempirical approaches based on atomic particle–particle potential which are applied to the system evolution simulation. These last methodologies are useful when the kinetic evolution occurring during the processes is characterized by rearrangements in different structural identities. Moreover, using these simulations, we can set the parameters ruling the complex dissolution rates in the models which can be applied to the large system simulation.

Atomistic simulations and the requirements of process simulator for novel semiconductor devices

Abstract The successful scaling down of novel semiconductor devices requires that corresponding simulation tools should reach atomic resolution, while satisfying the need of the industrial users in term of efficiency. In this context, we show the potential of multi-scale methodologies based on interconnected approaches ranging from quantum mechanical calculations to Monte Carlo (MC) methods for system kinetics. We prove that one key element for a successful matching of different theoretical methods is the use of low level approaches, not only for parameter extraction, but also for the direct derivation of effective interaction models implemented in MC codes. The matching procedure requires on lattice MC model settlement. This gives an added value to the developed stochastic code: it is able to simulate in detail the evolution of nano-structures (impurity aggregates, impurity–defects complex, extended defects) concurring to the overall material modification during processing. The predictivity of this approach is related to the accurate modeling of atomic level phenomena (e.g. diffusion, cluster formation/dissolution, structural transitions) spanning many orders of magnitude in time. We will report examples of the method application to the simulation of different defective Si system.

Interstitial Cluster Evolution and Transient Phenomena in Si-crystal

The evolution of Interstitial (I) type defects in Si and its influence on out of equilibrium I super-saturation level is investigated. Two approaches complementary to Quantum Mechanics Calculations (QMC) are applied: the Kinetic Lattice Monte Carlo (KLMC) and the Non-Lattice Kinetic Monte Carlo (NKMC). Our simulations show that the behaviour of I-super-saturation during a far from equilibrium stage is strongly affected by the correspondent aggregate structural evolution. Therefore, even if KLMC and NKMC are based on the same energetics derived by QMC, they give a different prediction of the super-saturation behaviour.