A. La Magna

Accelerated Monte Carlo algorithms for defect diffusion and clustering

Abstract We present a hierarchy of accelerate Monte Carlo (MC) algorithms which can be used to investigate the kinetic evolution of systems consisting of interacting defects or impurities in a solid matrix. Local models are used to approximate the interactions among particles and a specific application of the algorithms to the study of vacancy agglomeration is presented. It is shown that an extension of the Ising model, including an effective second neighbour interaction, gives a vacancy clusters energetics in good agreement with some recent quantum mechanical calculations. The accelerate algorithms implemented allow to speed up the calculations avoiding the bottlenecks which occur when the standard Metropolis algorithm is applied. These bottlenecks are due to the huge amount of rejected transition attempts and to the rapid fluctuations between quasi-degenerate configurations. We demonstrate the equivalence between the results obtained using standard and accelerated algorithms. Moreover we discuss in detail the gain in terms of CPU time when the algorithms are applied to two different vacancy interaction models. In the case of a simple Ising model (SIM) an optimised code ∼105 times faster than the standard Metropolis can be implemented; on the other hand, when the extended interaction is considered, the gain reduces to ∼103. Therefore the gain in speed, achievable with accelerate codes, is strongly dependent on the kinetic features of the interaction models. Indeed a relevant consequence of the second neighbor interaction is the migration of the aggregates which boosts the agglomeration process. This faster agglomeration reduces the effects of bottlenecks during the ripening process thus reducing the difference in efficiency between accelerated and conventional codes.

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.

A multi-scale atomistic study of the interstitials agglomeration in crystalline Si

Abstract Interstitial (I) clustering in Si has been investigated using a hierarchy of atomistic approaches: the tight binding molecular dynamics (TBMD), the molecular dynamics (MD) based on environment dependent interatomic potentials (EDIP) and a lattice kinetics Monte Carlo (LKMC) code. The model implemented in the LKMC code reproduces the energetic derived by means of MD calculations. The modalities of elementary kinetic steps have been tested using EDIP. Kinetics, simulated by LKMC, shows a peculiar evolution pathway characterized by quite well defined phases. The nucleation phase is dominated by clusters containing few interstitials in a over coordination state. In dependence on thermodynamic constrain, droplets form which store Is in more adjacent compact clusters. Droplets formation favors Is organization in 〈1 1 0〉 elongated chain. A qualitative comparison of simulation results with experimental data on post-implanted Si characterization is reported.

Activation of ion implanted Si for backside processing by ultra-fast laser thermal annealing: Energy homogeneity and micro-scale sheet resistance

High dopant activation LTA process Over 70% activation rate Shallow Box-shaped profiles (high diffusivity of B in liquid) High temperatures only near the surface, sub-microsecondtimescale Excellent within shot activation uniformity Scan steps down to 5 μm with MicroRSP-M150 tool RSstandard deviation below 1% Overlap parameter optimization is possible 2.5% better RSin overlap region (multi shot process) Effective overlap size smaller than optical size 2 possible solutions Low cost: Overlap optimization High end: Full Die Exposure optics

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.

Ultra-Low Energy Boron Implants in Crystalline Silicon: Atomic Transport Properties and Electrical Activation

We investigated the atomic transport properties and electrical activation of boron in crystalline epitaxial silicon after ultra-low energy ion implantation (0.25–1 keV) and rapid thermal annealing (750–1100 °C). A wide range of implant doses was investigated (3×10 12 -1×10 5 /cm 2 ). A fast Transient Enhanced Diffusion (TED) pulse is observed involving the tail of the implanted Boron, the profile displacement being dependent on the implant dose. The excess of interstitials able to promote enhanced diffusion of implanted boron occurs, provided the implant dose is high enough to generate a significant total number of point defects. The Boron diffusion following the fast initial TED pulse can be described by the equilibrium diffusion equations. The electrical activation of ultra-shallow implants is hard to achieve, due to the high concentration of dopant and point defects confined in a very shallow layer that significantly contributes to the formation of clusters and complex defects. Provided a correct combination of annealing temperatures and times for these ultra-shallow implants is chosen, however, a sheet resistance 500 Δ/square with a junction depth below 0.1μm can be obtained, which has a noteworthy technological relevance for the future generations of semiconductor devices.

Indium in silicon: a study on diffusion and electrical activation.

In this work we investigate the diffusion and the electrical activation of In atoms implanted in silicon with different energies, in the range 80-360 keV, after rapid thermal processing. Our investigation shows a clear dependence of In out-diffusion and electrical activation on the implant depth, being the electrically active fraction higher with increasing the implant energy for a fixed dose. The data are explained considering the balance between the local In concentration and the C background inside the silicon substrate and the formation of C-In complexes, which play a role in the enhanced electrical activation due to the shallower level they introduce into the Si band gap (E v +0.111 eV), with respect to the rather deep level (E v +0.156 eV) of In alone. In and C co-implantation has also been studied within this work, in order to confirm the key role of C in the increase of the electrical activation. A large increase of the electrical activation has been detected in the co-implanted samples, up to a factor of about 8 after annealing at 900°C. However, C precipitation occurs at 1100°C, with dramatic effects on the carrier concentration.

Point-Defect Migration in Crystalline Si: Impurity Content, Surface and Stress Effects

The results of several recent experiments aimed at assessing the room temperature migration properties of interstitials (D) and vacancies (V) in ion implanted crystalline Si are reviewed. We show that combining the results of ex-situ techniques (deep level transient spectroscopy and spreading resistance profilometry) and in-situ leakage current measurements new and interesting information can be achieved. It has been found that at room temperature I and V, generated by an ion beam, undergo fast long range migration (with diffusivities higher than 10 −1 cm 2 /sec) which is interrupted by trapping at impurities (C, O) or dopant atoms and by recombination at surface. Analysis of two-dimensional migration of point defects injected through a photolithographically defined mask shows that a strong I recombination (characterized by a coefficient of 30 μm −1 ) occurs at the sample surface. Moreover, we have found that the strain field induced by an oxide or a nitride mask significantly affects defect migration and produces a strong anisotropy of the defect diffusivity tensor. Finally, using in-situ leakage current measuremens, performed both during and just after ion irradiation, the time scale of point defect evolution at room temperature has been determined and defect diffusivities evaluated. The implications of these results on our current understanding of defect and diffusion phenomena in Si are discussed.

Damage evolution in implanted silicon by pulsed excimer laser annealing

The evolution of the implantation damage during a Pulsed Laser thermal annealing process is investigated by means of an accurate modeling which could stimulates focused experimental analyses. The model is based on the simulation of the detailed kinetic of the defect system in the extremely far-from-equilibrium conditions caused by the laser irradiation in the non-melting, melting and partial melting regimes. It considers defect (interstitials Is and vacancies Vs) clustering and annihilation in presence of fast varying temperature, high thermal gradients and phase transition. Simulations allow a characterization of the residual damage (in terms of total residual defects density and cluster size distribution) as a function of the process conditions (i.e. laser fluence). The thermal budget supplied to the system in the submelting regime is not sufficient to drive a consistent defect evolution and the total defects density is slightly reduced with respect the initialization (i.e. the post-implants conditions, where B and P implantations have been considered: Boron 40 keV, 3e14 cm−2 and Phosphorus 350 keV, 1e14 cm−2). Residual damage after melting processes is considerably reduced when compared to the as implant case. In this cases a relevant portion of the I type defect resides in clusters (small and large) while for the simulated cases clustering does not take place for V type defects.