Multiscale modeling of stress-mediated diffusion in silicon: <i>Ab initio</i> to continuum

Laudon, M.; Carlson, Neil N.; Masquelier, Michael P.; Daw, Murray S.; Windl, Wolfgang

doi:10.1063/1.1336158

Cited by 32 publications

(18 citation statements)

References 24 publications

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“…Because of anisotropic elasticity and/or the presence of defects in materials, such as dislocations, cracks, precipitates, and second-phase particles, this diffusion takes place in the presence of spatially non-uniform, and potentially very large, stresses. Diffusion under uniform stress has been well studied over the years but diffusion in stress fields that vary rapidly over the scale of diffusional hopping distances has been addressed to a much lesser degree [1,2]. Other atomistic studies that consider, for example, solute diffusion near a dislocation, use two-dimensional model crystals which lack the anisotropy that the transition state for diffusion in fcc material possesses [3,4].…”

Section: Introductionmentioning

confidence: 99%

Modelling diffusion in crystals under high internal stress gradients

Olmsted

Phillips

2004

Modelling Simul. Mater. Sci. Eng.

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Diffusion of vacancies and impurities in metals is important in many processes occurring in structural materials. This diffusion often takes place in the presence of spatially rapidly varying stresses. Diffusion under stress is frequently modelled by local approximations to the vacancy formation and diffusion activation enthalpies which are linear in the stress, in order to account for its dependence on the local stress state and its gradient. Here, more accurate local approximations to the vacancy formation and diffusion activation enthalpies, and the simulation methods needed to implement them, are introduced. The accuracy of both these approximations and the linear approximations are assessed via comparison to full atomistic studies for the problem of vacancies around a Lomer dislocation in Aluminium. Results show that the local and linear approximations for the vacancy formation enthalpy and diffusion activation enthalpy are accurate to within 0.05 eV outside a radius of about 13 Å (local) and 17 Å (linear) from the centre of the dislocation core or, more generally, for a strain gradient of roughly up to 6 × 10 6 m −1 and 3 × 10 6 m −1 , respectively. These results provide a basis for the development of multiscale models of diffusion under highly non-uniform stress.

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Section: Introductionmentioning

confidence: 99%

Modelling diffusion in crystals under high internal stress gradients

Olmsted

Phillips

2004

Modelling Simul. Mater. Sci. Eng.

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“…For the simple vacancy mechanism the anisotropy in the macroscopically-measured migration strain in (001) wafers should be zero due to crystal symmetry [7]. For boron diffusion by the interstitialcy mechanism in (001) wafers Daw and coworkers [11,12] predict that the migration strain anisotropy is zero, due to a detailed consideration of the effects of strain on the 768 migration paths of the Boron-selfinterstitial pair that are energetically degenerate in unstrained material. My own interpretation of their result is that zero migration strain anisotropy is a consequence of having a high enough symmetry that there is a sufficient degeneracy of diffusion pathways.…”

Section: Resultsmentioning

confidence: 99%

“…However, in certain cases, a measurement of the diffusivity under hydrostatic pressure and simple nonhydrostatic stress states can provide sufficient information to permit the prediction of behavior under arbitrary stress states [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Dopant diffusion under pressure and stress

Aziz

2003

International Conference on Simulation of Semiconductor Processes and Devices, 2003. SISPAD 2003.

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Abstract-The effects of stress on equilibrium point defect populations and on dopant diffusion in strained semiconductors are reviewed. The thermodynamic relationships presented permit the direct comparison of hydrostatic and biaxial stress experiments and of atomistic calculations of defect volumetrics for any proposed mechanism. Experiments on the effects of pressure and stress on the diffusivity of B and Sb are reviewed. The opposite effects of hydrostatic compression and of biaxial compression on the diffusivity are a consequence of the non-local nature of the point defect formation volume. Comparisons between these effects are made to determine quantitatively the anisotropy of the migration volume. The requirements to permit the prediction of the effect of an arbitrary stress state on diffusion in an arbitrary direction are discussed.

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“…Stresses have been proposed as a factor that may influence boron diffusion, albeit there is a controversy over whether they enhance or retard B diffusion. 16 Very large stresses are usually built up in the silicon area near the edge of thin gate layers due to lattice mismatch. In addition, extended defects such as dislocation loops may create a stress field around them.…”

Section: Fermi Level Shiftmentioning

confidence: 99%

Shouldering in B diffusion profiles in Si: Role of di-boron diffusion

Hwang

Goddard

2003

Applied Physics Letters

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The role of di-boron diffusion in evolution of B diffusion profiles has been investigated. We find that boron pair (B s -B i ) diffusion can become as important as boron-interstitial pair (B s -Si i ) diffusion when both boron concentration and annealing temperature are very high, leading to concentration-dependent B diffusion. Our simulated B diffusion profiles with dramatic shouldering are in excellent agreement with experimental ones reported by Schroer et al. ͓Appl Boron doping is an essential ingredient in the fabrication of silicon-based semiconductor devices. As gate dimensions shrink to nanometer scales ͑р100 nm͒, it becomes critical to gain precise control of doping profiles. Consequently, a great deal of effort is being devoted to understanding and controlling transient enhanced diffusion ͑TED͒ of boron during implantation and postimplantation annealing.While it is understood that a mobile boron-silicon interstitial pair (B-Si i ) plays an important role in B TED, 1,2 still little is known about underlying reasons for the enhancement ͑or the retardation͒ of B diffusion at high concentrations of boron (Ͼ10 18 cm Ϫ3 ) ͑or impurities, such as carbon or oxygen͒.We were particularly intrigued by the diffusion profiles ͑Fig. 1͒ determined by Schroer et al. 3 using secondary ion mass spectroscopy ͑SIMS͒. Their results show clearly a concentration-dependent behavior; that is, B diffusion is enhanced as the B concentration increases. They implanted boron at energies ϳ500 eV with a dose of 10 15 cm Ϫ2 into a p-type, epitaxially grown ͑epi͒ silicon layer on Si͑001͒. Then, the substrate was annealed at 1200°C. The concentrations of oxygen and carbon in the epi-Si layer are typically less than 10 15 cm Ϫ3 . Hence, impurities are likely to play an insignificant role in determining the doping profiles in these experiments. In addition, high temperature annealing at 1200°C results in fast dissolution of B clusters formed at the very early stages of annealing. Therefore, the density of immobile large boron clusters, if any, is too low to influence diffusion profile evolution. This suggests that only Si interstitials and mobile B species should be considered in explaining these experiments. In the absence of concentrationdependent and/or transient effects, single component diffusion should lead to a Gaussian distribution ͑once the diffusion profile is fully developed͒, but the experimental results 3 in Fig. 1 differ substantially from a simple Gaussian. B TED appears to be enhanced with increasing B concentration, leading to shouldering in the diffusion profiles. The shouldering behavior is consistent with a previous experimental observation 4 that shows B diffusion enhancement at high B concentration; that is, 10 B diffusion increased at the presence of high concentrations (Ϸ10 19 cm Ϫ3 ) of background boron 11 B. In fact, the concentration-dependent B diffusion has been explained by the variation of charged defect concentrations under extrinsic conditions ͑i.e., Fermi level shift effect, vide infra͒. 10 In this letter...

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Multiscale modeling of stress-mediated diffusion in silicon: Ab initio to continuum

Cited by 32 publications

References 24 publications

Modelling diffusion in crystals under high internal stress gradients

Modelling diffusion in crystals under high internal stress gradients

Dopant diffusion under pressure and stress

Shouldering in B diffusion profiles in Si: Role of di-boron diffusion

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