M. Jaraiz

PHYSICAL MECHANISMS OF TRANSIENT ENHANCED DOPANT DIFFUSION IN ION-IMPLANTED SILICON

Implanted B and P dopants in Si exhibit transient enhanced diffusion (TED) during annealing which arises from the excess interstitials generated by the implant. In order to study the mechanisms of TED, transmission electron microscopy measurements of implantation damage were combined with B diffusion experiments using doping marker structures grown by molecular-beam epitaxy (MBE). Damage from nonamorphizing Si implants at doses ranging from 5×1012 to 1×1014/cm2 evolves into a distribution of {311} interstitial agglomerates during the initial annealing stages at 670–815 °C. The excess interstitial concentration contained in these defects roughly equals the implanted ion dose, an observation that is corroborated by atomistic Monte Carlo simulations of implantation and annealing processes. The injection of interstitials from the damage region involves the dissolution of {311} defects during Ostwald ripening with an activation energy of 3.8±0.2 eV. The excess interstitials drive substitutional B into electric...

B diffusion and clustering in ion implanted Si: The role of B cluster precursors

A comprehensive model for B implantation, diffusion and clustering is presented. The model, implemented in a Monte Carlo atomistic simulator, successfully explains and predicts the behavior of B under a wide variety of implantation and annealing conditions by invoking the formation of immobile precursors of B clusters, prior to the onset of transient enhanced diffusion. The model also includes the usual mechanisms of Si self-interstitial diffusion and B kick-out. The immobile B cluster precursors, such as BI2 (a B atom with two Si self-interstitials) form during implantation or in the very early stages of the annealing, when the Si interstitial supersaturation is very high. They then act as nucleation centers for the formation of B-rich clusters during annealing. The B-rich clusters constitute the electrically inactive B component, so that the clustering process greatly affects both junction depth and doping level in high-dose implants.

Atomistic calculations of ion implantation in Si: Point defect and transient enhanced diffusion phenomena

A new atomistic approach to Si device process simulation is presented. It is based on a Monte Carlo diffusion code coupled to a binary collision program. Besides diffusion, the simulation includes recombination of vacancies and interstitials, clustering and re‐emission from the clusters, and trapping of interstitials. We discuss the simulation of a typical room‐temperature implant at 40 keV, 5×1013 cm−2 Si into (001)Si, followed by a high temperature (815 °C) anneal. The damage evolves into an excess of interstitials in the form of extended defects and with a total number close to the implanted dose. This result explains the success of the ‘‘+1’’ model, used to simulate transient diffusion of dopants after ion implantation. It is also in agreement with recent transmission electron microscopy observations of the number of interstitials stored in (311) defects.

B cluster formation and dissolution in Si: A scenario based on atomistic modeling

A comprehensive model of the nucleation, growth, and dissolution of B clusters in Si is presented. We analyze the activation of B in implanted Si on the basis of detailed interactions between B and defects in Si. In the model, the nucleation of B clusters requires a high interstitial supersaturation, which occurs in the damaged region during implantation and at the early stages of the postimplant anneal. B clusters grow by adding interstitial B to preexisting B clusters, resulting in B complexes with a high interstitial content. As the annealing proceeds and the Si interstitial supersaturation decreases, the B clusters emit Si interstitials, leaving small stable B complexes with low interstitial content. The total dissolution of B clusters involves thermally generated Si interstitials, and it is only achieved at very high temperatures or long anneal times.

Simulation of cluster evaporation and transient enhanced diffusion in silicon

The evaporation of {311} self‐interstitial clusters has recently been linked to the phenomenon of transient enhanced diffusion in silicon. A theory of cluster evaporation is described, based on first‐order kinetic equations. It is shown to give a good account of the data over a range of temperatures. The theory simultaneously explains several of the unexpected features of transient enhanced diffusion, including the apparently steady level of the enhancement during its duration, and the dependence of the duration on implant energy and dose. The binding energy used to match the theory to data is in good agreement with molecular dynamics calculations of cluster stability in silicon.

Carbon in silicon: Modeling of diffusion and clustering mechanisms

Carbon often appears in Si in concentrations above its solubility. In this article, we propose a comprehensive model that, taking diffusion and clustering into account, is able to reproduce a variety of experimental results. Simulations have been performed by implementing this model in a Monte-Carlo atomistic simulator. The initial path for clustering included in the model is consistent with experimental observations regarding the formation and dissolution of substitutional C–interstitial C pairs (Cs–Ci). In addition, carbon diffusion profiles at 850 and 900 °C in carbon-doping superlattice structures are well reproduced. Finally, under conditions of thermal generation of intrinsic point defects, the weak temperature dependence of the Si interstitial undersaturation and the vacancy supersaturation in carbon-rich regions also agree with experimental measurements.

Diffusion and interactions of point defects in silicon: molecular dynamics simulations

Abstract We have simulated the motion and clustering of vacancies and interstitials in silicon using molecular dynamics methods. The diffusion coefficients of isolated defects were calculated from atomic displacements in simulations performed over a wide range of temperatures. The results give an apparent migration energy barrier of E(M)V=0.43 eV for vacancies and E(M)1=0.9 eV for interstitials. The diffusion coefficients are between 10−6 and 10−5 cm2/s at 800°C, and are in approximate agreement with recent first-principles calculations, although they are many orders of magnitude larger than the most direct experimental measurements. Simulations with high concentrations of defects show that like defects aggregate into stable clusters, and that individual defects are bound to these clusters with energies in the range of 0.6–2.3 eV. Defect clusters have mobilities which can differ substantially from those of the individual defects. The di-interstitial has a dramatically smaller diffusion barrier, E(M)21 ≈ 0.2 eV, whereas the tri-interstitial has a mobility which is so small that it is difficult to measure accurately by molecular dynamics simulations. We discuss some of the implications of these simulations for diffusion under silicon device-processing conditions.

Atomistic modeling of point and extended defects in crystalline materials

Atomistic process modeling, a kinetic Monte Carlo simulation technique, has the interest of being both conceptually simple and extremely powerful. Instead of reaction equations it is based on the definition of the interactions between individual atoms and defects. Those interactions can be derived either directly from molecular dynamics or first principles calculations, or from experiments. The limit to its use is set by the size dimensions it can handle, but the level of performance achieved by even workstations and PCs, together with the design of efficient simulation schemes, has revealed it as a good candidate for building the next generation of process simulators, as an extension of existing continuum modeling codes into the deep submicron size regime. Over the last few years it has provided a unique insight into the atomistic mechanisms of defect formation and dopant diffusion during ion implantation and annealing in silicon. Object-oriented programming can be very helpful in cutting software development time, but care has to be taken not to degrade performance in the critical inner calculation loops. We discuss these techniques and results with the help of a fast object-oriented atomistic simulator recently developed.

Activation and deactivation of implanted B in Si

The temporal evolution of the electrically active B fraction has been measured experimentally on B implanted Si, and calculated using atomistic simulation. An implant of 40 keV, 2×1014 cm−2 B was examined during a postimplant anneal at 800 °C. The results show a low B activation (∼25%) for short anneal times (⩽10 s) that slowly increases with time (up to 40% at 1000 s), in agreement with the model proposed by Pelaz et al. [Appl. Phys. Lett. 74, 3657 (1999)]. Based on the results, we conclude that B clustering occurs in the presence of a high interstitial concentration, in the very early stages of the anneal. For this reason, B clustering is not avoided by a short or low-temperature anneal. The total dissolution of B clusters involves thermally generated Si interstitials, and therefore, requires long- or high-temperature anneals.

Modeling of the ion mass effect on transient enhanced diffusion: Deviation from the “+1” model

The influence of ion mass on transient enhanced diffusion (TED) and defect evolution after ion implantation in Si has been studied by atomistic simulation and compared with experiments. We have analyzed the TED induced by B, P, and As implants with equal range and energy: TED increases with ion mass for equal range implants, and species of different mass but equal energy cause approximately the same amount of TED. Heavier ions produce a larger redistribution of the Si atoms in the crystal, leading to a larger excess of interstitials deeper in the bulk and an excess of vacancies closer to the surface. For high-mass ions more interstitials escape recombination with vacancies, are stored in clusters, and then contribute to TED. TED can be described in terms of an effective “+n” or “plus factor” that increases with the implanted ion mass.