The non-local nature of structure functions

Kolmogorov's two-thirds, ((Δv) 2) ∼ e 2/ 3r 2/ 3, and five-thirds, E ∼ e 2/ 3k -5/ 3, laws are formally equivalent in the limit of vanishing viscosity, v → 0. However, for most Reynolds numbers encountered in laboratory scale experiments, or numerical simulations, it is invariably easier to observe the five-thirds law. By creating artificial fields of isotropic turbulence composed of a random sea of Gaussian eddies whose size and energy distribution can be controlled, we show why this is the case. The energy of eddies of scale, s, is shown to vary as s 2/ 3, in accordance with Kolmogorov's 1941 law, and we vary the range of scales, γ = s max/s min, in any one realisation from γ = 25 to γ = 800. This is equivalent to varying the Reynolds number in an experiment from R λ = 60 to R λ = 600. While there is some evidence of a five-thirds law for g > 50 (R λ > 100), the two-thirds law only starts to become apparent when g approaches 200 (R λ ∼ 240). The reason for this discrepancy is that the second-order structure function is a poor filter, mixing information about energy and enstrophy, and from scales larger and smaller than r. In particular, in the inertial range, ((Δv) 2) takes the form of a mixed power-law, a 1+a 2r 2+a 3r 2/ 3, where a 2r 2 tracks the variation in enstrophy and a 3r 2/ 3 the variation in energy. These findings are shown to be consistent with experimental data where the polution of the r 2/ 3 law by the enstrophy contribution, a 2r 2, is clearly evident. We show that higherorder structure functions (of even order) suffer from a similar deficiency.

Nature of the electronic band gap in lanthanide oxides

Accurate electronic structures of the technologically important lanthanide/rare-earth sesquioxides (Ln2O3, with Ln=La, ⋯,Lu) and CeO2 have been calculated using hybrid density functionals HSE03, HSE06, and screened exchange (sX-LDA). We find that these density functional methods describe the strongly correlated Ln f electrons as well as the recent G0W0@LDA+U results, generally yielding the correct band gaps and trends across the Ln period. For HSE, the band gap between O 2p states and lanthanide 5d states is nearly independent of the lanthanide, while the minimum gap varies as filled or empty Ln 4f states come into this gap. sX-LDA predicts the unoccupied 4f levels at higher energies, which leads to a better agreement with experiments for Sm2O 3, Eu2O3, and Yb2O3. © 2013 American Physical Society.

Ni(Pt)-silicide contacts on CMOS devices: Impact of substrate nature and Pt concentration on the phase formation

Ni silicides used as contacts in source/drain and gate of advanced CMOS devices were analyzed by atom probe tomography (APT) at atomic scale. These measurements were performed on 45 nm nMOS after standard self-aligned silicide (salicide) process using Ni(5 at.% Pt) alloy. After the first annealing (RTA1), δ-Ni2Si was the only phase formed on gate and source/drain while, after the second annealing (RTA2), two different Ni silicides have been formed: NiSi on the gate and δ-Ni2Si on the source and drain. This difference between source/drain and gate regions in nMOS devices has been related to the Si substrate nature (poly or mono-crystalline) and to the size of the contact. In fact, NiSi seems to have difficulties to nucleate in the narrow source/drain contact on mono-crystalline Si. The results have been compared to analysis performed on 28 nm nMOS where the Pt concentration is higher (10 at.% Pt). In this case, θ-Ni2Si is the first phase to form after RTA1 and NiSi is then formed at the same time on source (or drain) and gate after RTA2. The absence of the formation of NiSi from δ-Ni 2Si/Si(1 0 0) interface compared to θ-Ni2Si/Si(1 0 0) interface could be related to the difference of the interface energies. The redistributions of As and Pt in different silicides and interfaces were measured and discussed. In particular, it has been evidenced that Pt redistributions obtained on both 45 and 28 nm MOS transistors correspond to respective Pt distributions measured on blanket wafers. © 2013 Elsevier B.V. All rights reserved.