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Fuqian Yang - One of the best experts on this subject based on the ideXlab platform.
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Analysis of the Lattice Diffusion-controlled growth of metallic whiskers
Journal of Physics D: Applied Physics, 2007Co-Authors: Fuqian YangAbstract:Whisker growth plays an important role in determining the performance and lifetime of micro/nano electronic devices. In this work, we analyse the contribution of Lattice Diffusion to the whisker growth in a bilayer structure. An analytical solution of the growth rate is obtained as a function of the average chemical stress and the whisker size. The growth rate is inversely proportional to the whisker size for the growth of a whisker over a semi-infinite crystal, while it is proportional to the thickness of the surface layer for larger ratio of the whisker size to the thickness of the surface layer. The analytical result provides us a rational basis to evaluate the growth behaviour of metallic whiskers and nanowires controlled by the Lattice Diffusion.
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Surface instability of an elastic conducting halfspace in an electric field: Lattice Diffusion
Journal of Physics D: Applied Physics, 2005Co-Authors: Fuqian YangAbstract:The surface evolution of an elastic conducting material subject to an infinitesimal surface perturbation and uniform loading in an electric field was evaluated with respect to Lattice Diffusion. A dispersion relation describing morphological evolution of the elastic material as a function of the electric field intensity was derived, and the time evolution of the surface perturbation was obtained. The critical spatial frequency of the infinitesimal surface perturbation, at which the growth rate of the perturbation is zero, increases with the increase of the electric field intensity and is independent of Young's modulus of the elastic halfspace. An electrical field enhances the surface growth of elastic conducting solids for atomic migration controlled by Lattice Diffusion, while tensile stress tends to smooth surface perturbations.
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Surface evolution of crystalline tubes—effect of Lattice Diffusion
Thin Solid Films, 2005Co-Authors: Fuqian Yang, Wei Song, Jun ZhangAbstract:The surface evolution of an annular tube has been established on the basis of Lattice Diffusion and linear stability analysis. Without surface disturbance, the annular tube shrinks to reduce the surface energy while the cross-sectional area of the tube remains constant. For an annular tube having infinitesimal thickness, the time dependence of the tube radius follows a linear law. When surface energy is significant, a new dispersion relation describing the morphological stability of crystalline tubes due to longitudinal surface perturbation has been formulated. A criterion has been obtained on the dependence of perturbation growth rate on perturbation frequency. The perturbation will grow when the perturbation frequency is less than the critical frequency, which is equal to the inverse of the inner surface radius. The surface instability leads to the formation of closed end of crystalline tubes.
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Surface evolution of crystalline tubes: effect of Lattice Diffusion
Thin Solid Films, 2004Co-Authors: Fuqian Yang, Wei Song, Jun ZhangAbstract:The surface evolution of an annular tube has been established on the basis of Lattice Diffusion and linear stability analysis. Without surface disturbance, the annular tube shrinks to reduce the surface energy while the cross-sectional area of the tube remains constant. For an annular tube having infinitesimal thickness, the time dependence of the tube radius follows a linear law. When surface energy is significant, a new dispersion relation describing the morphological stability of crystalline tubes due to longitudinal surface perturbation has been formulated. A criterion has been obtained on the dependence of perturbation growth rate on perturbation frequency. The perturbation will grow when the perturbation frequency is less than the critical frequency, which is equal to the inverse of the inner surface radius. The surface instability leads to the formation of closed end of crystalline tubes.
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On the interface instability of a cylindrical fiber embedded in a matrix
Scripta Materialia, 2003Co-Authors: Fuqian YangAbstract:The interface evolution of a fiber embedded in a matrix is investigated for separate interfacial axial and radial sinusoidal perturbations. A new dispersion equation is derived by considering Lattice Diffusion in both the fiber and the matrix.
Alain Portavoce - One of the best experts on this subject based on the ideXlab platform.
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Measurement of As diffusivity in Ni2Si thin films
Microelectronic Engineering, 2010Co-Authors: Ivan Blum, Alain Portavoce, Dominique Mangelinck, Rachid Daineche, Khalid Hoummada, János L. Lábár, V. Carron, Jean BernardiniAbstract:The Lattice and grain boundary Diffusion coefficients of As in 260nm-thick Ni"2Si films were measured. The Ni"2Si layers were prepared via the reaction between a Si layer deposited by low pressure chemical vapor deposition and a Ni layer deposited by magnetron sputtering on a Si substrate covered with a SiO"2 film. As was implanted in the silicide. Its concentration profiles were measured using secondary ion mass spectroscopy before and after annealing (550-700^oC). 2D finite element Diffusion simulations taking into account Lattice Diffusion and grain boundary (GB) Diffusion were performed based on the microstructure of the samples. They were found to fit accurately the measured profiles and allowed to measure the Diffusion coefficients for each temperature. Lattice Diffusion is characterized by a pre-exponential factor D^0v~1.5x10^-^1cm^2s^-^1 and an activation energy Qv~2.72eV. In the case of GB Diffusion P^[email protected]^0gb=9.0x10^-^3cm^3s^-^1 and the activation energy was found to be higher than for Lattice Diffusion with Qgb~3.07eV. Existing data concerning Diffusion in silicides and other materials is used to discuss these results. The Diffusion of As in Ni"2Si could be reduced due to impurity segregation in GBs.
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Dopant Diffusion in Si1-xGex Thin Films: Effect of Epitaxial Stress
Defect and Diffusion Forum, 2006Co-Authors: Alain Portavoce, Isabelle Berbezier, Antoine Ronda, J. S. Christensen, Patrick Gas, Andrej Yu. Kuznetsov, Bengt Gunnar SvenssonAbstract:We have investigated the Lattice Diffusion of B and Sb by means of molecular beam epitaxy in Si1−xGex (x
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Sb Lattice Diffusion in Si1-xGex/Si(001) heterostructures : Chemical and stress effects
Physical Review B, 2004Co-Authors: Alain Portavoce, P. Gas, Isabelle Berbezier, Antoine Ronda, J. S. Christensen, A. Yu. Kuznetsov, B. SvenssonAbstract:The Sb Diffusion coefficient in Si 1 - x Ge x /Si 1 - y Ge y (001) heterostructures grown by molecular beam epitaxy (MBE) was measured for temperatures ranging from 700 to 850 °C, Ge composition from 0 to 20 % and biaxial pressure from -0.8 (tension) to 1.4 GPa (compression). A quantitative separation of composition and biaxial stress effects is made. We show that the Sb Lattice Diffusion coefficient: (i) increases with Ge concentration in relaxed layers or at constant biaxial pressure and (ii) increases with compressive biaxial stress and decreases with tensile biaxial stress at constant Ge composition. The enhancement of Sb Lattice Diffusion in Si 1 - x Ge x layers in epitaxy on Si(001) is thus due to the cooperative effect of Ge composition and induced compressive biaxial stress. However, the first effect (composition) is predominant. The activation volume of Sb Diffusion in Si 1 - x Ge x layers is deduced from the variation of the Sb Diffusion coefficients with biaxial pressure. This volume is negative. The sign of the activation volume, its absolute value and its variation with temperature confirm the prediction of the thermodynamic model proposed by Aziz, namely, that under a biaxial stress the activation volume is reduced to the relaxation volume.
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Lattice Diffusion and surface segregation of B during growth of SiGe heterostructures by molecular beam epitaxy: effect of Ge concentration and biaxial stress.
Journal of Applied Physics, 2004Co-Authors: Alain Portavoce, P. Gas, Isabelle Berbezier, Antoine Ronda, J. S. Christensen, B. SvenssonAbstract:Si1-xGex/Si1-yGey/Si(100) heterostructures grown by Molecular Beam Epitaxy (MBE) were used in order to study B surface segregation during growth and B Lattice Diffusion. Ge concentration and stress effects were separated. Analysis of B segregation during growth shows that: i) for layers in epitaxy on (100)Si), B segregation decreases with increasing Ge concentration, i.e. with increased compressive stress, ii) for unstressed layers, B segregation increases with Ge concentration, iii) at constant Ge concentration, B segregation increases for layers in tension and decreases for layers in compression. The contrasting behaviors observed as a function of Ge concentration in compressively stressed and unstressed layers can be explained by an increase of the equilibrium segregation driving force induced by Ge additions and an increase of near-surface Diffusion in compressively stressed layers. Analysis of Lattice Diffusion shows that: i) in unstressed layers, B Lattice Diffusion coefficient decreases with increasing Ge concentration, ii) at constant Ge concentration, the Diffusion coefficient of B decreases with compressive biaxial stress and increases with tensile biaxial stress, iii) the volume of activation of B Diffusion ( ) is positive for biaxial stress while it is negative in the case of hydrostatic pressure. This confirms that under a biaxial stress the activation volume is reduced to the relaxation volume.
Pete G. Burnard - One of the best experts on this subject based on the ideXlab platform.
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Argon storage and Diffusion in Earth’s upper mantle
Geochimica et Cosmochimica Acta, 2019Co-Authors: Rémi Delon, Mohamed Ali Bouhifd, Pete G. Burnard, Sylvie Demouchy, Yves Marrocchi, Patrick Cordier, Ahmed AddadAbstract:In this study, fine-grained polycrystalline olivine was doped with argon at static high pressure (0.30 ± 0.01 GPa) and high temperature (1050 ± 25 °C) conditions during 24 h in a Paterson press, and analysed using a step-heating extraction protocol coupled with noble gas mass spectrometry to investigate argon storage and diffusivity in Earth’s upper mantle. Our results show that a single Diffusion mechanism controlled argon Diffusion in our samples during the step heating experiments. Effective Ar Diffusion in olivine has a low activation energy, implying that argon diffusivity is governed by both grain boundary and Lattice Diffusion. Mean values of Lattice Diffusion parameters obtained from our results and by reprocessing literature data are Ea = 166 ± 44 kJ mol−1 and D0 = 10−7.04 ± 1.13 m2·s−1, and grain boundary Diffusion parameters determined from our data are Ea = 22 ± 5 kJ·mol−1 and D0 = 10−12.87 ± 0.3 m2·s−1. Isotopic diffusivity ratios were constant and close to the values determined by Graham’s law in the C-regime (i.e., bulk Diffusion dominated by grain boundary Diffusion) and A-regime (i.e., bulk Diffusion controlled by grain boundary and Lattice Diffusion in proportion to the segregation of Ar between those sites), but varied in the B-regime (i.e., bulk Diffusion controlled by both grain boundary and Lattice Diffusion in a complex manner), implying a higher isotopic fractionation in the kinetic B-regime. Extrapolation to typical mantle grain sizes implies that around 22% of the argon in the upper mantle can be stored at grain boundaries and that effective Diffusion is mostly in the A-regime, suggesting a low isotopic fractionation and diffusivities faster than Lattice diffusivities alone. The consideration of grain boundaries as a potential Ar storage site can modify equilibrium during partial melting and significantly enrich a liquid in Ar during fluid percolation. The grain size dependence of Ar storage and diffusivity highlights the underestimated role of grain boundaries in the upper mantle, especially in zones of reduced grain size (via dynamic recrystallization) possibly followed by fluid percolation and/or partial melting, such as in subduction zones or below oceanic ridges
E. B. Watson - One of the best experts on this subject based on the ideXlab platform.
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Lattice Diffusion and solubility of argon in forsterite enstatite quartz and corundum
Chemical Geology, 2008Co-Authors: J B Thomas, D J Cherniak, E. B. WatsonAbstract:Abstract Argon diffusivities and solubilities in single, gem-quality crystals of forsterite, enstatite, quartz and corundum were determined from experiments conducted between 0.5 and ~ 6000 bars Ar pressure and temperatures from 425 °C to 1200 °C. Polished single-crystal slabs and specimens with natural facets were placed in open containers and exposed to an argon atmosphere either in a pressure vessel or in a gas-flow tube furnace at near-atmospheric pressure. Argon atoms from the pressure medium diffused into the crystals to produce near-surface concentration gradients, which were directly profiled using Rutherford backscattering spectrometry. The following Arrhenius relations were obtained for Ar Diffusion: F o r s t e r i t e : D A r = 7.2 × 10 - 20 exp ( - 42 k J m o l - 1 / R T ) m 2 s - 1 E n s t a t i t e : D A r = 1.3 × 10 - 20 exp ( - 32 k J m o l - 1 / R T ) m 2 s - 1 Q u a r t z : D A r = 3.1 × 10 - 19 exp ( - 43 k J m o l - 1 / R T ) m 2 s - 1 C o r u n d u m : D A r = 1.2 × 10 - 20 exp ( - 33 k J m o l - 1 / R T ) m 2 s - 1 The reported activation energies probably represent apparent activation energies that are a combination of the effects of Lattice Diffusion of Ar atoms with trapping in point-defect vacancies. There are no discernible differences in Ar Diffusion in different crystallographic directions, and diffusivities do not vary as a function of the intrinsic oxygen fugacity of the experimental vessels. In addition to diffusivities, the uptake gradients also yielded Lattice solubilities of argon, as represented by the concentrations at the mineral surfaces. There are small differences between the solubilities of forsterite, quartz and corundum, but all solubilities are high at ~ 2000 ppm (by mass). The Ar solubilities for the iron-bearing minerals enstatite and San Carlos olivine are much higher than for the other minerals. The mean value for enstatite is 30–60% higher than the iron-free minerals, owing, perhaps, to incorporation of Ar in point defects that are more abundant in enstatite due to oxidation of minor FeO. Argon solubilities are independent of Ar pressure at PAr > ~ 1 bar, but slightly lower at PAr ≈ 0.5–1 bar. This behavior suggests that all sites capable of accommodating Ar atoms are filled at Ar pressures of ~ 1 bar. In all cases, Ar appears to be compatible in the minerals investigated, although the degree of compatibility will depend upon assumptions concerning the minimum Ar fugacity required to fully populate the available vacancies. A series of validation experiments and surface-sensitive analyses were conducted to confirm that the near-surface regions of crystals used in the experiments were crystalline, unreacted and free of structural damage that could potentially influence Diffusion and solubility results.
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Oxygen self-Diffusion ''fast-paths'' in titanite single crystals and a general method for deconvolving self-Diffusion profiles with ''tails''
Geochimica et Cosmochimica Acta, 2007Co-Authors: Xiaoyu Zhang, E. B. Watson, Daniele J. CherniakAbstract:Like most other minerals, titanite rarely if ever forms perfect crystals. In addition to the point defects that might affect Lattice Diffusion, there may be extended line- or planar defects along which fast Diffusion could occur. During the course of an experimental study of oxygen Lattice Diffusion in titanite, we found that almost all of the 18 O uptake profiles produced in natural titanite crystals departed from the complementary error function solution expected for simple Lattice Diffusion with a constant surface concentration. Instead, they exhibited ‘‘tails’’ extending deeper into the samples than expected for simple Lattice Diffusion. The purpose of this contribution is to report on these features—described as ‘‘fast-paths’’ for oxygen Diffusion—and outline a method for coping with them in extracting information from Diffusion profiles. For both dry and hydrothermal experiments in which the ‘‘fast paths’’ are observed, 18 O was used as the diffusant. In dry experiments, the source material was 18 O-enriched SiO2 powder, while 18 O-enriched water was used for the hydrothermal experiments. Diffusive uptake profiles of 18 O were measured in all cases by nuclear reaction analysis (NRA) using the 18 O (p,a) 15 N reaction [see Zhang X. Y., Cherniak D. J., and Watson E. B. (2006) Oxygen Diffusion in titanite: Lattice and fast-path Diffusion in single crystals. Chem. Geol. 235 105–123]. In our experiments, different sizes of ‘‘tails’’ (with varying 18 O concentrations) were observed. Theoretically, under the same temperature and pressure conditions, the sizes of tails should be affected by two factors: the Diffusion duration and the defect density. For the same experiment duration, the higher the defect density, the larger the ‘‘tail’’; for the same defect densities, the longer the Diffusion duration, the larger the ‘‘tail.’’ The Diffusion ‘‘tails’’ could be a result of either planar defects or one-dimensional ‘‘pipe’’ Diffusion. AFM imaging of HF etched titanite surfaces confirmed that the etched features might be caused by either parallel planar defects or parallel pipe defects, but could not differentiate between these possibilities. Through theoretical calculations simulating the tailed Diffusion profiles using reasonable assumptions of Lattice diffusivities and fast-path diffusivities, and comparing these with tail features measured in our samples, it can be concluded that the ‘‘tails’’ observed in our experiments are caused by planar defects rather than pipe defects. A new method was developed for separating the ‘‘fast-path’’ contribution from the overall composite Diffusion profile consisting of both ‘‘fast-path’’ and Lattice Diffusion. Through this process, the Lattice Diffusion coefficient could be determined, which is required to analyze the tail. The oxygen Diffusion rates in the fast-paths were obtained by traditional graphical analysis methods, using the Whipple–Le Claire equation (for 2-D defects) assuming that the width of the fast-path is 1 nm. Two Arrhenius relations were obtained for the fast-path Diffusion phenomenon, one for experiments under dry conditions, and the other for hydrothermal conditions: Ddry ¼ 4:03 � 10 � 2 ðm 2 =sÞ expð� 313 � 22 Þð kJ=molÞ=RT Dwet ¼ 3:48 � 10 � 7 ðm 2 =sÞ expð� 219 � 39 Þð kJ=molÞ=RT
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Oxygen Diffusion in titanite: Lattice Diffusion and fast-path Diffusion in single crystals
Chemical Geology, 2006Co-Authors: X.y. Zhang, Daniele J. Cherniak, E. B. WatsonAbstract:Oxygen Diffusion in natural and synthetic single-crystal titanite was characterized under both dry and water-present conditions. For the dry experiments, pre-polished titanite samples were packed in 18 O-enriched quartz powder inside Ag–Pd capsules, along with a fayalite–magnetite–quartz(FMQ) bufferassemblagemaintainedphysicallyseparatebyAg–Pdstrips.ThesealedAg–Pdcapsules were themselvessealedinsideevacuatedsilicaglasstubesandrunat700–1050°Candatmosphericpressurefordurationsrangingfrom1hto several weeks. The hydrothermal experiments were conducted by encapsulating polished titanite crystals with 18 O enriched water and running at 700–900 °Cand 10–160MPa instandard cold-sealpressurevessels for durationsof1day toseveral weeks. Diffusive uptake profiles of 18 O were measured in all cases by nuclear reaction analysis (NRA) using the 18 O( p,α) 15 N reaction. For the experiments on natural crystals, under both dry and hydrothermal conditions, two mechanisms could be recognized as responsible for oxygen Diffusion. The Diffusion profiles showed two segments: a steep one close to the initial surface attributed to self Diffusion in the titanite Lattice; and a “tail” reaching deep into the sample attributable to Diffusion in a “fast path” such as planar defects or pipes. For the experiments on synthetic crystals, Lattice Diffusion only is apparent in crystals with euhedral morphology, while both mechanisms operate in crystals lacking euhedral morphology. For the dry experiments, the following Arrhenius relation was obtained:
B. Svensson - One of the best experts on this subject based on the ideXlab platform.
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Sb Lattice Diffusion in Si1-xGex/Si(001) heterostructures : Chemical and stress effects
Physical Review B, 2004Co-Authors: Alain Portavoce, P. Gas, Isabelle Berbezier, Antoine Ronda, J. S. Christensen, A. Yu. Kuznetsov, B. SvenssonAbstract:The Sb Diffusion coefficient in Si 1 - x Ge x /Si 1 - y Ge y (001) heterostructures grown by molecular beam epitaxy (MBE) was measured for temperatures ranging from 700 to 850 °C, Ge composition from 0 to 20 % and biaxial pressure from -0.8 (tension) to 1.4 GPa (compression). A quantitative separation of composition and biaxial stress effects is made. We show that the Sb Lattice Diffusion coefficient: (i) increases with Ge concentration in relaxed layers or at constant biaxial pressure and (ii) increases with compressive biaxial stress and decreases with tensile biaxial stress at constant Ge composition. The enhancement of Sb Lattice Diffusion in Si 1 - x Ge x layers in epitaxy on Si(001) is thus due to the cooperative effect of Ge composition and induced compressive biaxial stress. However, the first effect (composition) is predominant. The activation volume of Sb Diffusion in Si 1 - x Ge x layers is deduced from the variation of the Sb Diffusion coefficients with biaxial pressure. This volume is negative. The sign of the activation volume, its absolute value and its variation with temperature confirm the prediction of the thermodynamic model proposed by Aziz, namely, that under a biaxial stress the activation volume is reduced to the relaxation volume.
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Lattice Diffusion and surface segregation of B during growth of SiGe heterostructures by molecular beam epitaxy: effect of Ge concentration and biaxial stress.
Journal of Applied Physics, 2004Co-Authors: Alain Portavoce, P. Gas, Isabelle Berbezier, Antoine Ronda, J. S. Christensen, B. SvenssonAbstract:Si1-xGex/Si1-yGey/Si(100) heterostructures grown by Molecular Beam Epitaxy (MBE) were used in order to study B surface segregation during growth and B Lattice Diffusion. Ge concentration and stress effects were separated. Analysis of B segregation during growth shows that: i) for layers in epitaxy on (100)Si), B segregation decreases with increasing Ge concentration, i.e. with increased compressive stress, ii) for unstressed layers, B segregation increases with Ge concentration, iii) at constant Ge concentration, B segregation increases for layers in tension and decreases for layers in compression. The contrasting behaviors observed as a function of Ge concentration in compressively stressed and unstressed layers can be explained by an increase of the equilibrium segregation driving force induced by Ge additions and an increase of near-surface Diffusion in compressively stressed layers. Analysis of Lattice Diffusion shows that: i) in unstressed layers, B Lattice Diffusion coefficient decreases with increasing Ge concentration, ii) at constant Ge concentration, the Diffusion coefficient of B decreases with compressive biaxial stress and increases with tensile biaxial stress, iii) the volume of activation of B Diffusion ( ) is positive for biaxial stress while it is negative in the case of hydrostatic pressure. This confirms that under a biaxial stress the activation volume is reduced to the relaxation volume.