Diffusion in Solids

Effect of near atmospheric pressure nitrogen plasma treatment on Pt/ZnO interface J. Appl. Phys. 112, 116104 (2012) Observation of boron diffusion in an annealed Ta/CoFeB/MgO magnetic tunnel junction with standing-wave hard x-ray photoemission B migration in Si and Ge matrices raised a vast attention because of its influence on the production of confined, highly p-doped regions, as required by the miniaturization trend. In this scenario, the diffusion of B atoms can take place under severe conditions, often concomitant, such as very large concentration gradients, non-equilibrium point defect density, amorphous-crystalline transition, extrinsic doping level, co-doping, B clusters formation and dissolution, ultra-short high-temperature annealing. In this paper, we review a large amount of experimental work and present our current understanding of the B diffusion mechanism, disentangling concomitant effects and describing the underlying physics. Whatever the matrix, B migration in amorphous (a-) or crystalline (c-) Si, or c-Ge is revealed to be an indirect process, activated by point defects of the hosting medium. In a-Si in the 450-650 C range, B diffusivity is 5 orders of magnitude higher than in c-Si, with a transient longer than the typical amorphous relaxation time. A quick B precipitation is also evidenced for concentrations larger than 2 Â 10 20 B/cm 3 . B migration in a-Si occurs with the creation of a metastable mobile B, jumping between adjacent sites, stimulated by dangling bonds of a-Si whose density is enhanced by B itself (larger B density causes higher B diffusivity). Similar activation energies for migration of B atoms (3.0 eV) and of dangling bonds (2.6 eV) have been extracted. In c-Si, B diffusion is largely affected by the Fermi level position, occurring through the interaction between the negatively charged substitutional B and a self-interstitial (I) in the neutral or doubly positively charged state, if under intrinsic or extrinsic (p-type doping) conditions, respectively. After charge exchanges, the migrating, uncharged BI pair is formed. Under high n-type doping conditions, B diffusion occurs also through the negatively charged BI pair, even if the migration is depressed by Coulomb pairing with n-type dopants. The interplay between B clustering and migration is also modeled, since B diffusion is greatly affected by precipitation. Small (below 1 nm) and relatively large (5-10 nm in size) BI clusters have been identified with different energy barriers for thermal dissolution (3.6 or 4.8 eV, respectively). In c-Ge, B motion is by far less evident than in c-Si, even if the migration mechanism is revealed to be similarly assisted by Is. If Is density is increased well above the equilibrium (as during ion irradiation), B diffusion occurs up to quite large extents and also at relatively low temperatures, disclosing the underlying mechanism. The lower B diffusivity and the larger activation barrier (4.65 eV, rather than 3.45 eV in c-Si) can be explained by the intrinsic shortage of Is in Ge and by their large formation energy. B diffusion can be strongly enhanced with a proper point defect engineering, as achieved with embedded GeO 2 nanoclusters, causing at 650 C a large Is supersaturation. These aspects of B diffusion are presented and discussed, modeling the key role of point defects in the two different matrices. V C 2013 American Institute of Physics. [http://dx.

The performance ofTi.3W.7 and Nb thin films as diffusion barriers for Au was investigated by Rutherford backscattering spectrometry (RBS) and Auger electron spectroscopy (AES). The films were sputter deposited in Ar:N2 (70:30 vol%) or pure Ar on amorphous Si02. They were annealed in air at temperatures ranging from 250·C up to 750·C for several hours. In-depth profiles revealed an onset of oxidation of the barriers at 520·C for Nb and 600·C for TiW. Barrier oxidation and extensive diffusion could be correlated. Distinct diffusion behavior as a function of temperature was established between TiW and Nb. A Nb multilayer structure was found to provide the best reliability as the barrier and as the adhesion layer.

Thermocatalytic decomposition (TCD) of methane is a promising method to produce hydrogen. A series of experiments was conducted to study the apparent kinetic, catalyst deactivation and effect of mass diffusion for methane TCD to produce hydrogen using palm-shell carbon based activated carbon (ACPS) as a catalyst in a fixed bed reactor. The experiment was carried out under atmospheric pressure at 775e850 C, and different methane residence times calculated based on changing the ACPS weight at a constant methane flow rate or changing the methane flow rate at a constant ACPS weight. A reaction order as found substantially differs from that found in literature. A deactivation order of 0.5 and deactivation energy of 177 KJ mol À1 is obtained and the results fitted well with a simple developed model. Mass diffusion transfers are accounted for by calculating change of Weisz modulus with time on-stream using different weights of ACPS or different flow rates of methane. The result showed that Weisz modulus decrease with time and it is attributed to the deposition of carbon produced from methane decomposition. Surface properties measurements of the virgin and deactivated ACPSs indicated that methane decomposition occurs mainly within AC micropores.

The evolution of the high-frequency vibrational energy density of slender heterogeneous structures such as Timoshenko beams or thick shells is depicted by transport equations or radiative transfer equations (RTEs) in the presence of random heterogeneities. A diffusive regime arises when their correlation lengths are comparable to the wavelength, among other possible situations, and waves are multiply scattered. The purpose of this paper is to expound how diffusion approximations of the RTEs for elastic structures can be derived and to discuss the relevance of the vibrational conductivity analogy invoked in the structural acoustics literature. Its main contribution is the consideration of a heterogeneous background medium with varying parameters and the effects of polarization of elastic waves. The paper also outlines some of the remarkable features of the diffusive regime: depolarization of waves,energy equipartition, and asymptotic Fick’s law.

We have calculated the diffusivity of aluminium in periclase, MgO, under pressures relevant to deep planetary interiors from first principles. We reconcile differences between experimental migration enthalpies and those obtained with previous theoretical studies by finding a lower energy saddle point for the aluminium atom migration. Previous studies did not recognise a bifurcation at the saddle point. We also explain differences between experimental and theoretical binding enthalpies of an aluminium with a magnesium vacancy. We find that binding enthalpies continuously increase with decreasing aluminium concentrations, such that the difference between experimental and theoretical binding energies can be attributed to differing concentrations. We also find that binding energies increase with pressure as the permittivity decreases. Aluminium therefore not only causes extrinsic vacancy formation but also binds some of them, effectively removing them for magnesium diffusion. We discuss the implications for how other 3? ions affect diffusion in oxides and silicates.

"The sintering behavior of the interface between Al :Si(l%) alloy and polycrystalline Si (poly-Si) was studied as a function of the poly-Si implantation dose by combining RBS, SEM, TEM and X-ray microanalysis. Two different N-dopants were used: arsenic and phosphorus. The dopants were implanted in the poly-Si layer and thermal annealing was used to obtain dopant segregation towards the poly-Si interfacea.
After sir&ring, two main effects were detected: (1) Al-Si eutectic phase precipitates and Si crystallites are formed at the interface. (2) The density of precipitates is a function of the implantation dose. For doses above 1 x lOI5 at./cm2. segregated arsenic and phosphorus are found to completely inhibit this precipitation process, provided that the segregation peak of the dopant profile is preserved before metallization.
Several conclusions can be drawn: for surface concentrations higher than 8~10’~ at./cm3, arsenic and phosphorus inhibit the precipitation of the Al-Si eutectic phase, and thus inhibit interactions between the films at the interface. Moreover, argon gas, usedfor sputtering deposition of aluminum, segregated at the poly-Si/Al: Si(l%) interface and may also inhibit the metal-semiconductor interdiffusion.""

NOTE: As the first and principal author of this journal article, I need to add a comment about  the atomistic model I proposed in Fig.2 of this paper, to  explain the anomalously fast diffusion of metals in semiconductors at low temperatures. I expanded on it in my PhD thesis, but is not quite stated in the present paper:

So why would  metal atoms like Au and Si so easily go in solution and diffuse in Si, SiO2, glass, etc...?

It turns out this phenomenon has been observed for decades. It was first reported in the articles cited in this paper by Kobayahsi and Hiraki,  back in 1979 and 1982 , for in situ deposition of metallic layers on silicon (100) in ultra-high-vacuum.
They also measured by X-ray Photoelectron Spectroscopy (XPS) how electronic bonding changes as one deposits metals atom-by-atom, in increasingly thicker layers of atomic clusters, just as is done nowadays in nano-wires and quantum dots.

As one, then two, then three, then four monolayers of metallic atoms are deposited on CLEAN Si, the electronic bonding of the metals to the silicon surface first mimicks that
of Si(100). This is  WHY metals such as Al and Au  CAN be grown epitaxially on Si despite the lattice mismatch between close-packed metals and the open lattice structure of semiconductors like Si and GaAS.  So both Aluminum and Gold can bond as an ordered sheet of atoms on the surface.  The first ordered hetero-epitaxial metal layer skips one silicon atomic row about every 4 or 5 rows. This enables for the metal atoms align themselves in a commensurate manner with the cubic symmetry of the Si(100) surface atoms.

When about the fifth monolayer is deposited, electronic delocalization start occurring as they is now a longer range metallic environment in the film, atoms in the core of the film can be now surrounded by 1st, 2nd and 3rd neighbors metallic films, and start screening the effect of the Silicon.
Remember now how many atoms are in cluster/dot or what nano-wires cross-sections because the size of the clusters matters to determine the electronic bonding inside the metallic nano-cluster and at the nano-cluster/silicon or GaAs interface.

Around 4-5 monolayers of thickness, Kobayashi measured that, the energy of the XPS emission of electrons from Au changes, and that the energy of electrons emitted from the Au layer becomes closer to that from an electron emitted from an metallically bonded atoms as opposed to a more covalent bond.

Once a metallic layer reaches a thickness where the sea of electrons from metallic bonds take over, the electronic bond start to exhibit a true metallic character. Electronic become delocalized and free to move, and their "atoms" shrink to their ionic core. The effect is especially dramatic with Gold, with Z= 79, thus 79 electrons, of which the majority are outer shell electrons as opposed to inner shell electrons.

My PhD thesis [reference 13] was metal-semiconductor interdiffusion at low temperatures. I proposed in it his model, published here in short form, and shown in Fig.2. Fig.2. describes in a cartoon-form abut my then very poor scientific English gives far from a clear explanation.

Low-energy (< 1 keV) ions are used in a variety of thin-film techniques. When low-energy ions are used during growth, the atomic mobility is athermally enhanced. This can lead to a significant lowering of the temperature necessary to induce epitaxial growth and chemical reactions. Athermal enhancement of atomic mobility in semiconductors can be described below the temperature for plastic deformation (T = 540-degrees-C in Si) by classifying the mechanisms involved into three categories according to their respective timescale: collisions, elastic recombination, and thermal diffusion. A quantitative model can then be derived to predict the conditions of temperature, dose rate, and energy to obtain thin film growth, and oxidation in techniques such as ion beam deposition (IBD), and ion beam oxidation (IBO). Using computer simulations, the dynamics of defect generation and redistribution, and the resulting thin-film growth rate can be investigated. Energies below 200 eV are found not only to minimize damage and sputtering, but also create defect distributions that favor surface recombination and hence growth. This elucidates the mechanism of thin-film formation with high atomic density, oxidation with a sharp inteface with the substrate and epitaxial growth, and experimental findings on the energy dependence of IBD and IBO.

We are investigating the use of low energy ions (< 1 keV) in low temperature thin film growth techniques, ion beam deposition (IBD) and combined ion and molecular deposition (CIMD). In IBD, a thin film is directly grown from a low energy ion beam as the only source of material, while in CIMD, low temperature growth of thin films is achieved by depositing materials simultaneously from a low energy ion beam and one or several molecular beams. A simple model of the IBD process has been developed and accounts for atomic collisions and thermal diffusion during thin film growth. Computer simulation of IBD of Si on Si have been conducted as a function of ion energy to support more quantitatively this physical description of IBD. The results show that the IBD growth mechanism is mediated by the fast diffusing interstitials and establish a low energy limit to achieve epitaxial growth by IBD that depends on the point defect diffusivities. The defect generation has to be confined in the subsurface region in order to favor interstitial recombination with the surface, leading to net thin film growth, and vacancy annihilation to prevent amorphization. The effect of point defect diffusivities on the IBD growth process is also investigated. It is found that a model including fast moving interstitials can account for various experimental observations specific to IBD.

We present first-principle calculations on absolute diffusion rates of high- and low-spin ferrous iron in ferro-periclase. The diffusivity of high- and low-spin iron depends on the physical conditions (pressure and temperature), iron concentration and the value of the chosen Hubbard U. We also find that low-spin iron swaps back to high-spin during migration. Our results show that throughout the Earth's lower mantle, iron diffuses at a faster rate than magnesium (up to an order of magnitude). Thus, the effect of the spin transition only has a small impact on the rheology of periclase in the Earth's mantle. Using reasonable vacancy concentrations, we find that ferro-periclase is much weaker than MgSiO3-perovskite throughout the mantle. We conclude, therefore, that ferro-periclase controls the viscosity of the mantle in regions where it becomes interconnected, such as regions of high strain around slabs or near plumes. At very high pressures, such as in Super-Earths, low-spin iron diffusion is expected to become much slower than magnesium, eventually making ferro-periclase more viscous than pure periclase.► The spin-transition of Fe2+ in ferro-periclase has a weak effect on diffusion. ► The rheology of ferro-periclase is therefore weakly affcted by the spin-transition ► Iron diffuses slightly faster than magnesium throughout the Earth's lower mantle.

""ABSTRACT
Three important effects of low energy direct Ion Beam Deposition (IBD) are the athermal incorporation of material into a substrate, the enhancement of atomic mobility in the subsurface, and the modification of growth kinetics it creates. All lead to a significant lowering of the temperature necessary to induce epitaxial growth and chemical reactions. The fundamental understanding and new applications of low temperature kinetics induced by low energy ions in thin film growth and surface processing of semiconductors are reviewed. It is shown that the mechanism of IBD growth can be understood and computed quantitatively using a simple model including ion induced defect generation and sputtering, elastic recombination, thermal diffusion, chemical reactivity, and desorption. The energy, temperature and dose dependence of growth rate, epitaxy, and chemical reaction during IBD is found to be controlled by the net recombination rate of interstitials at the surface in the case of epitaxy and unreacted films, and by the balance between ion beam decomposition and phase formation induced by ion beam generated defects in the case of compound thin films. Recent systematic experiments on the formation of oxides and nitrides on Si, Ge/Si(100), heteroepitaxial SixGe1−x/Si(100) and GaAs(lOO) illustrate applications of this mechanism using IBD in the form of Ion Beam Nitridation (IBN), Ion Beam Oxidation (IBO) and Combined Ion and Molecular beam Deposition (CIMD). It is shown that these techniques enable (1) the formation of conventional phases in conditions never used before, (2) the control and creation of properties via new degrees of freedom such as ion energy and lowered substrate temperatures, and (3) the formation of new metastable heterostructures that cannot be grown by pure thermal means.""

The possible use of wood ash as an adsorbent of nickel sulphate from dilute solutions and the effect of operating parameters were investigated in this study. The rate constants of adsorption were determined at different concentrations and temperatures. The applicability of the first-order reversible equation and an empirical kinetic model were tested to understand the kinetics of nickel sulphate removal at different concentrations. Pore diffusion was found as the rate-controlling step. The Langmuir and Freundlich isotherms were applied to find out the adsorption parameters. The activation energy of adsorption was −11.54 kJ mol−1. The value of the enthalpy change was ΔH=−10.35 kcal mol−1.

The performance of Ti0.3W0.7 and Nb thin films as diffusion barriers for Au was investigated by Rutherford Backscattering Spectrometry (RBS) and Auger Electron Spectroscopy(AES). The films were sputter deposited in Ar:N2 (70:30 vol%) or pure Ar on amorphous SiO2. They were annealed in air at temperatures ranging from 250 °C up to 750 °C for several hours. In‐depth profiles revealed an onset of oxidation of the barriers at 520 °C for Nb and about 600 °C for TiW. Barrier oxidation and extensive diffusion could be correlated. Distinct diffusion behavior as a function of temperature was established between TiW and Nb. A Nb multilayer structure was found to provide the best reliability as the barrier and as the adhesion layer.

© 1984 American Vacuum Society
Received 15 September 1983 Accepted 31 October 1983
"

In this work the Si self-interstitial-carbon interaction has been experimentally investigated and modeled. The interactions between self-interstitials, produced by 20-keV silicon implantation, and substitutional carbon in silicon have been studied using a Si 1Ϫy C y layer grown by molecular beam epitaxy ͑MBE͒ and interposed between the near-surface self-interstitial source and a deeper B spike used as a marker for the Si-interstitial concentration. The C atoms, all incorporated in substitutional sites and with a C-dose range of 7ϫ10 12 -4 ϫ10 14 atoms/cm 2 , trap the self-interstitials in such a manner that the Si 1Ϫy C y layer behaves as a filtering membrane for the interstitials flowing towards the bulk and, consequently, strongly reduces the boron-enhanced diffusion. This trapping ability is related to the total C dose in the Si 1Ϫy C y membrane. Substitutional carbon atoms interacting with self-interstitials are shown to trap Si interstitials, to be removed from their substitutional sites, and to precipitate into the C-rich region. After precipitation, C atoms are not able to further trap injected self-interstitials, and the interstitials generated in the surface region can freely pass through the C-rich region and produce B-enhanced diffusion. The atomistic mechanism leading to Si-interstitial trapping has been investigated by developing a simulation code describing the migration of injected interstitials. The simulation takes into account the surface recombination, the interstitial diffusion in our MBE-grown material, and C traps. Since the model calculates the amount of interstitials that actually react with C atoms, by a comparison with the experimental data it is possible to derive quantitative indications of the trapping mechanism. It is shown that one Si interstitial is able to deactivate about two C traps by means of interstitial trapping and C clustering reactions. The reaction causing trapping and deactivation is tentatively described.

In this work the Si self-interstitial-carbon interaction has been experimentally investigated and modeled. The interactions between self-interstitials, produced by 20-keV silicon implantation, and substitutional carbon in silicon have been studied using a Si 1Ϫy C y layer grown by molecular beam epitaxy ͑MBE͒ and interposed between the near-surface self-interstitial source and a deeper B spike used as a marker for the Si-interstitial concentration. The C atoms, all incorporated in substitutional sites and with a C-dose range of 7ϫ10 12 -4 ϫ10 14 atoms/cm 2 , trap the self-interstitials in such a manner that the Si 1Ϫy C y layer behaves as a filtering membrane for the interstitials flowing towards the bulk and, consequently, strongly reduces the boron-enhanced diffusion. This trapping ability is related to the total C dose in the Si 1Ϫy C y membrane. Substitutional carbon atoms interacting with self-interstitials are shown to trap Si interstitials, to be removed from their substitutional sites, and to precipitate into the C-rich region. After precipitation, C atoms are not able to further trap injected self-interstitials, and the interstitials generated in the surface region can freely pass through the C-rich region and produce B-enhanced diffusion. The atomistic mechanism leading to Si-interstitial trapping has been investigated by developing a simulation code describing the migration of injected interstitials. The simulation takes into account the surface recombination, the interstitial diffusion in our MBE-grown material, and C traps. Since the model calculates the amount of interstitials that actually react with C atoms, by a comparison with the experimental data it is possible to derive quantitative indications of the trapping mechanism. It is shown that one Si interstitial is able to deactivate about two C traps by means of interstitial trapping and C clustering reactions. The reaction causing trapping and deactivation is tentatively described.

We have elucidated the mechanism for B migration in the amorphous (a-) Si network. B diffusivity in a-Si is much higher than in crystalline Si; it is transient and increases with B concentration up to 2 10 20 B=cm 3 . At higher density, B atoms in a-Si quickly precipitate. B diffusion is indirect, mediated by dangling bonds (DB) present in a-Si. The density of DB is enhanced by B accommodation in the a-Si network and decreases because of a-Si relaxation. Accurate data simulations allow one to extract the DB diffusivity, whose activation energy is 2.6 eV. Implications of these results are discussed.

The effect of pressure on ionic diffusion in orthorhombic MgSiO3 perovskite has been investigated using density functional theory. An intensive investigation of possible silicon pathways revealed new positions of the saddle-points and an enthalpy of migration at 26.2 GPa of 4.7 eV that is in fair agreement with the experimental values of about 3.5 eV at 25 GPa. This is much lower than found in previous studies (~9 eV) and removes the need to explain silicon diffusion by a complicated process involving coupled oxygen vacancies, as has been previously proposed. Our migration enthalpies for oxygen and magnesium are in excellent agreement with experiments. We find that oxygen diffusion occurs via a chain of several inequivalent jumps along the octahedron edges, and that magnesium occurs via two inequivalent [110] jumps and one [001] jump. We also present activation volumes for all three species at 25 and 135 GPa.

B diffusion in crystalline Ge is investigated by proton irradiation in thin layers with B delta doping under different fluences ͑1 ϫ 10 15 -10ϫ 10 15 H + / cm 2 ͒, fluxes ͑6 ϫ 10 11 -35ϫ 10 11 H + / cm 2 s͒, and temperatures of the implanted target ͑from −196 to 550°C͒, both during and after irradiation. B migration is enhanced by several orders of magnitude with respect to equilibrium. Moreover, B diffusion is shown to occur through a point-defect-mediated mechanism, compatible with a kick-out process. The diffusion mechanism is discussed. These results are a key point for a full comprehension of the B diffusion in Ge.

Realistic, complex industrial structures exhibit typical transport and diffusive behaviour in the high-frequency range of vibration, as demonstrated by the experiments described in [1] among others. Whereas their dynamics are physically well represented by global standing waves (the eigenmodes) in the low-frequency range, this approach fails dramatically as the frequency increases, because of the multiple interactions of waves with material heterogeneities, and reflections from the boundaries and at the interfaces between structural components with different stiffnesses (stiffeners on plates and shells, bulkheads, stringers ...). Predictive methods for high-frequency vibrations are required in the automotive and aerospace industries for applications to noise control, acoustic comfort and discretion, or pyrotechnic shock simulation for example. Statistical Energy Analysis (SEA [2]) is the most popular method among mechanical engineers to deal with such problems. It is based on some rigorous arguments developped in the late 1950s, but also on several phenomenological assumptions which can hardly be satisfied exactly. Derivation of a vibrational conductivity analogy (VCA) for high-frequency structural dynamics has attracted several researchers in the early 1990s [3], but this model is based on heuristic, unproven arguments as well. On the basis of (rigorous) mathematical arguments, it can be shown that the evolution of the high-frequency vibrational energy density of visco-elastic media is depicted by Liouville transport equations [4], or radiative transfer equations in the presence of random heterogeneities [5]. These results generalize the well-known method of geometrical optics. The transport regime is obtained under the assumptions that (i) wavelengths are SHORT with respect to the macroscopic features of the medium (the high-frequency range), (ii) they are comparable to the correlation lengths of random heterogeneities, and (iii) fluctuations of the latter are small and rather isotropic.
Radiative transfer equations are costly to solve numerically. However they can be approximated by diffusion equations in a rather systematic way for long propagation distances with respect to the scattering mean free path, which is the mean distance travelled by an energy ray before its direction is significantly altered by scattering on the heterogeneities. This paper deals with diffusion approximations of the stochastic Liouville equations and the radiative transfer equations. Heat conduction-like diffusion equations are directly derived from the latter in the limit of a large ratio of the typical propagation distance to the scattering mean free paths. Fokker-Planck diffusion equations are derived from the former when the correlation length of the heterogeneities is small with respect to the medium size, but still large with respect to the wavelength. Some numerical simulations for a random Mindlin plate are presented to illustrate the approach. These results are used to discuss the relevance of the Vibrational Conductivity Analogy invoked in the structural acoustics literature.

In this study, sorption and diffusion of carbon dioxide (CO2) in wood-fiber/polystyrene composites were investigated. The effects of gas pressure and fiber content on the solubility and diffusion coefficients were evaluated. A statistical analysis indicated that pressure is more important than fiber content in determining the solubility and diffusivity of CO2. An increase in saturation pressure causes an increase in the solubility and diffusion coefficients, whereas inclusion of the fibers decreases both of these properties. Models were developed to predict the uptake and diffusion coefficients of CO2 in the composite samples as functions of pressure and fiber content. A theoretical model based on Henry's law and the Langmuir equation compared favorably to the experimental data for CO2 solubility. This dual mode model also described both the transient sorption and desorption data, but only if the concentration-dependent value of diffusivity was treated as a history-dependent parameter.
(citation # 20)

B diffusion in crystalline Ge is investigated by proton irradiation in thin layers with B delta doping under different fluences ͑1 ϫ 10 15 -10ϫ 10 15 H + / cm 2 ͒, fluxes ͑6 ϫ 10 11 -35ϫ 10 11 H + / cm 2 s͒, and temperatures of the implanted target ͑from −196 to 550°C͒, both during and after irradiation. B migration is enhanced by several orders of magnitude with respect to equilibrium. Moreover, B diffusion is shown to occur through a point-defect-mediated mechanism, compatible with a kick-out process. The diffusion mechanism is discussed. These results are a key point for a full comprehension of the B diffusion in Ge.

The growth of thin nitride films of Si, MBE-grown Ge and Si(x)Ge(1-x) alloys on Si by low energy ion beam nitridation (IBN) has been investigated both theoretically and experimentally. This paper focuses on the modeling of the kinetics of IBN thin film growth. The model is based on our recent experimental results and includes the present understanding of atomic collisions at low energy and the thermal diffusivity and chemical reactivity of point defects generated by 1BN. Three variables relevant to ion beam nitridation (IBN), ion energy, ion dose, and substrate temperature, are studied for their effect on the growth of nitride films and their resulting properties. These variables are shown to constitute attractive processing parameters to control nitride properties in a way that cannot be achieved thermally. The proposed model takes into account the range and range straggling of the ions, physical sputtering, desorption, chemical reaction and enhanced mobility of point defects created in the collision cascade. Based on this model, the film thickness and stoichiometry at any stage of IBN can be computed using finite differences calculation methods. Analytical expressions can also be derived for the two limiting cases of "low dose" or initial stage, and "high dose" which corresponds to growth saturation at steady state. Such modeling is shown to be useful in determining the chemical processes which govern the reactive growth of IBN nitride thin films. IBN is shown for instance to be a reaction of order greater than one. Diffusivity and reactivity are found to be competitive during IBN, quite the opposite of ion beam oxidation (IBO), where reactivity dominates over diffusivity.

We use radiative transfer equations to describe the high-frequency vibrations of randomly heterogeneous plates. The diffusive regime is depicted both numerically and analytically from this model. Numerical simulations are based on the Monte-Carlo method, whereas the analytical model is obtained by an asymptotic analysis. The objectives are to improve the understanding of high-frequency vibrations of complex industrial structures.

Fluorine-19 NMR was used to study the structure and mobility of the perfluorosulfonate ionomer Nafion (Dupont trademark) in the presence of dimethyl methylphosphonate (DMMP). Fluorine-19 resonances arising from the ionomeric side chain narrowed rapidly with increasing DMMP content while the resonances arising from the perfluoroethylene backbone units remained broad. The plasticization of the side chains indicates that the DMMP is primarily associated with this structural unit which forms its own nanophase in Nafion. To further characterize the morphological structure, fluorine-19 spin diffusion experiments between the side chain and backbone resonances were performed. At low DMMP content, swelling of the pendant group domain is observed while at higher concentrations an unusual change in the spin diffusion indicates the development of a new morphology consisting of larger domains associated with the pendant group plus DMMP. To augment information on this system, proton pulse field gradient experiments were performed as a function of concentration and temperature to obtain DMMP self-diffusion constants. In the same concentration range where morphological change occurred, there was a rapid rise in translational mobility of the DMMP. This reflects the influence of the new larger domains which allow longer range motion of DMMP with fewer obstructions from the backbone domains which are relatively impermeable to DMMP. A fraction of the smaller domains originally present in dry Nafion remain even at high levels of DMMP, indicating an inability of all of the Nafion to undergo the morphological transition to the larger domains.

In this work the Si self-interstitial-carbon interaction has been experimentally investigated and modeled. The interactions between self-interstitials, produced by 20-keV silicon implantation, and substitutional carbon in silicon have been studied using a Si 1Ϫy C y layer grown by molecular beam epitaxy ͑MBE͒ and interposed between the near-surface self-interstitial source and a deeper B spike used as a marker for the Si-interstitial concentration. The C atoms, all incorporated in substitutional sites and with a C-dose range of 7ϫ10 12 -4 ϫ10 14 atoms/cm 2 , trap the self-interstitials in such a manner that the Si 1Ϫy C y layer behaves as a filtering membrane for the interstitials flowing towards the bulk and, consequently, strongly reduces the boron-enhanced diffusion. This trapping ability is related to the total C dose in the Si 1Ϫy C y membrane. Substitutional carbon atoms interacting with self-interstitials are shown to trap Si interstitials, to be removed from their substitutional sites, and to precipitate into the C-rich region. After precipitation, C atoms are not able to further trap injected self-interstitials, and the interstitials generated in the surface region can freely pass through the C-rich region and produce B-enhanced diffusion. The atomistic mechanism leading to Si-interstitial trapping has been investigated by developing a simulation code describing the migration of injected interstitials. The simulation takes into account the surface recombination, the interstitial diffusion in our MBE-grown material, and C traps. Since the model calculates the amount of interstitials that actually react with C atoms, by a comparison with the experimental data it is possible to derive quantitative indications of the trapping mechanism. It is shown that one Si interstitial is able to deactivate about two C traps by means of interstitial trapping and C clustering reactions. The reaction causing trapping and deactivation is tentatively described.

The effect of O implantation in crystalline Ge on the density of native point defects has been investigated through transmission electron microscopy and B diffusion experiments. Annealing at 650 • C following O implants produces a band of defects (∼5-10 nm), compatible with GeO 2 nanoclusters (NCs). A clear shape transformation from elongated to spherical forms occurs within 2 h, concomitant with a transient enhanced diffusion of B. A large injection of self-interstitials from GeO 2 NCs, giving a vacancy undersaturation, and a long-range migration of self-interstitials are evidenced and discussed.

B diffusion in crystalline Ge is investigated by proton irradiation in thin layers with B delta doping under different fluences ͑1 ϫ 10 15 -10ϫ 10 15 H + / cm 2 ͒, fluxes ͑6 ϫ 10 11 -35ϫ 10 11 H + / cm 2 s͒, and temperatures of the implanted target ͑from −196 to 550°C͒, both during and after irradiation. B migration is enhanced by several orders of magnitude with respect to equilibrium. Moreover, B diffusion is shown to occur through a point-defect-mediated mechanism, compatible with a kick-out process. The diffusion mechanism is discussed. These results are a key point for a full comprehension of the B diffusion in Ge.

The effect of O implantation in crystalline Ge on the density of native point defects has been investigated through transmission electron microscopy and B diffusion experiments. Annealing at 650 • C following O implants produces a band of defects (∼5-10 nm), compatible with GeO 2 nanoclusters (NCs). A clear shape transformation from elongated to spherical forms occurs within 2 h, concomitant with a transient enhanced diffusion of B. A large injection of self-interstitials from GeO 2 NCs, giving a vacancy undersaturation, and a long-range migration of self-interstitials are evidenced and discussed.

Proton and sodium-23 spectra are reported on acid and sodium neutralized forms of the perfluorosulfonate ionomer (Nafion), respectively. This local structural view is compared with pulse field gradient diffusion measurements of water, methanol and dimethyl methylphosphonate (DMMP) in several Nafion films. Both the proton and sodium-23 spectra indicate that the counter ions are primarily in clusters or aggregates with no evidence for isolated ions. The proton resonance from the sulfonic acid group reflects hydrogen bonding but these protons rapidly exchange with sorbed water. There is also evidence for small amounts of water not in contact with the ionic clusters. Pulse field gradient diffusion measurements of water show little evidence of tortuous diffusion though a tortuous pathway might be expected for diffusion through domains of ionic clusters. A cast film shows greater evidence of a tortuous pathway than commercially prepared Nafion sheets though the level of tortuosity is still low. Methanol diffusion shows more tortuosity in both commercial films and cast films with the most tortuosity in a cast film containing fumed silica nanoparticles. Even greater tortuosity is observed for DMMP. The greatest tortuoisty is observed for DMMP in cast films with nanoparticles and this is an improvement in terms of potential applications of Nafion in chemical protection. Though the high-resolution proton spectra show only modest differences between commercial film, cast film and nanocomposite film, more significant structural changes on a larger length scale are detected in the pulse field gradient NMR experiments. Cast films may display more tortuous diffusion because of better-organized domains of ionic groups, backbone units and side chains even though this is not clearly indicated by focusing on the structure of the ionic cluster itself.