Vacancy Condensation Research Articles

The origin of shallow etch pit defects in low dislocation density GaP crystals

The defect corresponding to shallow etch pits (S-pits) on GaP wafer has been revealed. It is a vacancy-type Frank dislocation loop which surrounds a stacking fault. It is proposed that this loop is formed by the condensation of excess gallium vacancies during cooling of the GaP crystal. The phosphorus precipitates on the dislocation loop result from the condensation of the emitted phosphorous interstitials accompanied by the growth of the loop. Stoichiometry control is necessary to suppress the formation of S-pit defects in low dislocation density compound semiconductor crystals.

Electromigration Voiding in Argon-Implanted Interconnects

AbstractElectromigration is a complex process consisting of the nucleation, growth, and movement of voids. While interconnect microstructure plays a major role in determining void nucleation time and location of void nucleation, recent studies have shown that this is not the only contributing factor. Thermodynamics and kinetics-based calculations by Flinn and Gleixner et al. have shown that electromigration void nucleation by vacancy condensation at both homogeneous and heterogeneous sites will not occur at a reasonable rate without a mechanism for reducing or altogether eliminating the energy barrier for nucleation. By implanting argon ions into the aluminum interconnect lines, we introduce an initial defect population (argon bubbles) of controlled size and location.Tests were performed in a high-voltage SEM (120 keV), which enables in-situ observation of the voiding process through the passivation layer. Images taken throughout the in-situ tests were analyzed to determine void nucleation times and locations. In the argon-implanted interconnects, ten of the 15 voids that nucleated were within implanted regions. Voids nucleated in the interior of the line within the implanted regions, as well as at the passivation/sidewall interface where voids are typically seen in conventional electromigration tests. In addition, voids in implanted regions nucleated much more quickly than those in unimplanted regions. These observations support the idea of argon bubbles reducing the nucleation barrier. TEM was used to analyze the microstructure of both control and implanted interconnect lines.

Crystallographic features and growth of creep cavities in a Ni–18Cr–18Fe alloy

The crystallographic nature and growth of creep cavities in a Ni–18Cr–18Fe alloy were examined as part of the study of behavior of nickel base superalloyys at high temperatures. Creep experiments were carried out at 973 K and 52 MPa, and grain boundary cavitation damage was examined in polished sections, as well as by scanning electron microfractography of surfaces exposed after hydrogen charging. Well developed cavities, whose development tended to favor one side of the grain boundary, were observed and identified with vacancy condensation on {111} planes. The preference is attributed to cavity nucleation in the grain in which the carbide-matrix interface is incoherent and vacancy condensation is energetically favored. A model for cavity growth patterned after crystal growth is suggested and discussed.

Highly faceted growth shape of microvoids in icosahedral Al-Mn-Pd

Faceted microholes in icosahedral Al-Mn-Pd quasicrystals form by condensation of thermal vacancies, typically during annealing in the temperature range above approximately 700oC. Prolonged annealing at temperatures between 750 and 830oC leads to the growth of large and highly faceted microholes through a classical Ostwald ripening process. The indexing of all facets of such a microhole is presented. The idealized morphology is found to correspond to an icosahedral polyhedron with 302 facets.

Synthesis and Electrical Properties of Dense Ce0.9Gd0.1O1.95 Ceramics

Uniform spherical powders of Ce0.9Gd0.1O1.95 with an average diameter of 250 nm were obtained at 700°C from a sol‐gel process of mixing nitrates and ethylene glycol. Broadening of the X‐ray peaks of the fluorite structure reveals a small crystallite size within the powders. Sintering in air of pressed pellets of the powders at 1585°C gives ceramics of 99% theoretical density with grain sizes 1‐10 µm and a cubic unit cell a= 5.422 ± 0.034 Å. The electrical conductivity σ=σo+σe has two components. In air or argon, the electronic component σe is negligible and the oxide‐ion conductivity σo is not described by a classical Arrhenius equation; a pronounced curvature at T similar/congruent T* has been observed in the Arrhenius plot of the bulk conductivity. The system could be modeled by a condensation of mobile oxygen vacancies into ordered clusters below a temperature T* similar/congruent 583 ± 45°C and a motional enthalpy ΔHm= 0.63 ± 0.01 eV for the vacancies. A measured trapping energy ΔHt(1 ‐ T/T*) has ΔHt= 0.19 ± 0.01 eV = 2.57 kT*. In a reducing atmosphere, σe exhibits a small‐polaron motional enthalpy ΔHp= 0.40 ± 0.08 eV for transfer of a 4 f electron from a Ce3+ to a Ce4+ ion and a ΔHp+ΔHpt= 0.51 ± 0.04 eV at T < T*.

{111} Planar Faults in a Quenced and Annealed NiAl-0.3Hf Single Crystal Alloy

Abstract Quenched-in vacancies, vacancy agglomeration and solute-vacancy association can play a significant role in affecting the mechanical behavior of an alloy. It is well known that B2- NiAl can retain a high supersaturation of thermal vacancies which has been shown to manifest itself as dislocation loops, voids, or spiral dislocations. Dislocation climb loops formed in NiAl have been observed to emanate from impurity particles as concentric {100} loops which are prismatic in nature1. Impurity particles have also been shown to be responsible for nucleating faceted voids. However, addition of alloying elements can alter this mode of vacancy condensation and depending upon the degree of interaction between alloying element and vacancies, a completely different defect structure can result. In a recent study, addition of Boron to Fe-35 mol. % Al has been shown to produce complex {100} planar faults having both APB and stacking fault character, whereas Cr, Pd and W produced APBs on {111} planes.

On S(Al2CuMg) precipitation in an Al[sbnd]Cu[sbnd]Mg alloy containing small additions of beryllium

The effect of a small addition of Be on S(Al2CuMg) precipitation in an AlCuMg alloy was investigated. Alloys of nominal weight composition Al0.1Be, Al2.5Cu1.2Mg and Al2.5Cu1.2Mg0.1Be were cast, homogenized, rolled, solution heat treated, quenched, naturally aged and artificially aged for various times at temperatures ranging from 160 to 300°C. The microstructures and the age hardening behavior were characterized and the results for these alloys were compared with the available data in the literature on the similarly treated pure Al and ternary AlCuMg alloy. It is shown that Be additions to both pure Al and the AlCuMg alloy inhibit vacancy condensation during quenching, whilst encouraging extensive dislocation loop formation during subsequent natural aging. Upon artificial aging, the dislocation loop structures in the quenched binary alloy are replaced by a uniform distribution of very small, spherical and stable Be precipitates throughout the microstructure. In the similarly treated Be modified AlCuMg alloy, the dislocation loop structures provide sites for heterogeneous nucleation of the S phase. Be precipitates, which occur in the binary alloy, also form in the artificially aged AlCuMgBe alloy and are found to provide additional sites for heterogeneous nucleation of the S phase. This resulted in refinement of the S precipitate distribution.

Ductile fracture by vacancy condensation in f.c.c. single crystals

We explore the feasibility of vacancy condensation as the void-nucleating mechanism underlying ductile fracture by void growth and coalescence in single crystals at room temperature. Vacancies are presumed to be primarily generated by the dragging of intersection jogs. The equations governing the rate of growth of voids by vacancy condensation are derived. These equations are used to follow the evolution of vacancy concentrations and void sizes in the Wang and Anderson [ Acta metall. 39, 779 (1991)] [1] ⩞9 test. We find that, when pipe diffusions are taken into account, the time required for the nucleation of a macroscopic void in the near-tip region is of the order of one minute, which is well within the time-scale of quasistatic fracture tests.

Transmission electron microscopic observation of thermally introduced planar faults in Fe-35 mol.% Al alloys

Abstract Thermally introduced planar faults are investigated both in an Fe-35 mol.%Al binary alloy and in B, Cr, Pd and W added ternary alloys using transmission electron microscopy. Air cooling of the alloys from 1273 K followed by annealing at 698 K for 120 h introduces two types of planar faults. One type is the antiphase boundary (APB), which is observed in all of the alloys. The other is the complex planar fault having both APB and stacking fault characters, which is observed in only the B-added alloy. The formation of the APBs is envisaged from a collapse of the lattice owing to vacancy condensation on triple layers of {111} planes. The size, distribution and planarity of the APBs are affected by ternary element addition.

An Analysis Of Void Nucleation In Passivated Interconnect Lines Due To Vacancy Condensation And Interface Contamination

AbstractNucleation of voids due to vacancy condensation in passivated aluminum lines is analyzed within the context of classical nucleation theory. A discussion of sources of hydrostatic tensile stress in such lines provides a reasonable upper limit of 2 GPa. The void nucleation rate is then calculated at various sites within the line. Results suggest that nucleation rates are far too low to account for observed rates of voiding. Void nucleation at a flaw at the line/passivation interface is then considered as an alternative nucleation mechanism. Such flaws may be created by contaminants introduced during fabrication of the line. In this case, nucleation is feasible at greatly reduced stresses, well within the observed values. Furthermore, a simple model of void growth indicates that a fast atomic transport path, such as a grain boundary, must intersect the void for an appreciable growth rate. These results suggest that void nucleation in aluminum interconnect lines occurs at flaws at the sidewall of the line and that stress-induced and electromigration-induced voiding can be controlled by eliminating interfacial contamination.

An Analysis of Void Nucleation In Passivated Interconnect Lines Due to Vacancy Condensation and Interface Contamination

AbstractNucleation of voids due to vacancy condensation in passivated aluminum lines is analyzed within the context of classical nucleation theory. A discussion of sources of hydrostatic tensile stress in such lines provides a reasonable upper limit of 2 GPa. The void nucleation rate is then calculated at various sites within the line. Results suggest that nucleation rates are far too low to account for observed rates of voiding. Void nucleation at a flaw at the line/passivation interface is then considered as an alternative nucleation mechanism. Such flaws may be created by contaminants introduced during fabrication of the line. In this case, nucleation is feasible at greatly reduced stresses, well within the observed values. Furthermore, a simple model of void growth indicates that a fast atomic transport path, such as a grain boundary, must intersect the void for an appreciable growth rate. These results suggest that void nucleation in aluminum interconnect lines occurs at flaws at the sidewall of the line and that stress-induced and electromigration-induced voiding can be controlled by eliminating interfacial contamination.

Structure of stacking fault pyramids in silicon‐on‐insulator material

Using transmission electron microscopy (TEM), we have analyzed stacking fault pyramids found in multiple implant silicon‐on‐insulator material. From a comparison of computer simulations with weak‐beam TEM images, and from the constraints imposed by crystallography, we have found that the Burgers vectors of the pyramidal stair‐rod dislocations are edge dislocations with the Burgers vector 1/3〈100〉. We have also determined that the stacking faults in these pyramids are intrinsic, and therefore probably formed through vacancy condensation.

Passivity Breakdown on Solid Versus Liquid Gallium

Pits are found to nucleate on solid gallium in buffered chloride solutions, and we propose that the pits nucleate from blisters that form beneath the passive film on the metal substrate. The proposed association of pitting with blister formation is accounted for by the point defect model for the growth and breakdown of passive films, and has been tested by comparing the behaviors of solid and liquid gallium upon anodic polarization in chloride‐containing environments. This study shows that liquid gallium resists passivity breakdown much more readily than does the solid, which we attribute to the inhibition of cation vacancy condensation, in liquid substrate, and hence to the formation of blister precursors at the metal/film interface. Thus, solid gallium is added to the growing list of metals and alloys that apparently suffer passivity breakdown via a vacancy condensate precursor.

Self-repair of monolayers with vacancy damage.

Lennard-Jones monolayers are shown by molecular dynamics simulation to exhibit a self-healing behavior which involves a rapid condensation of vacancies into dislocation dipoles. An associated collapse of the shear modulus similar to the Kosterlitz-Thouless dipole dissociation occurs for high vacancy concentrations. By contrast monolayers having nearest neighbor piecewise linear interactions are found to cavitate by agglomeration of vacancies into clusters.

On the Formation of Voids in Anodic Oxide Films on Aluminum

A mechanism is proposed for the formation of voids at triple points between grains in the anodic oxide formed on aluminum and for the growth of porous films. The proposed mechanism involves the condensation of cation and/or metal vacancies below regions in the barrier film (triple points) that are characterized by high cation vacancy diffusivity, due to the high degree of lattice disorder. Vacancy condensation causes local decohesion of the barrier layer from the substrate, thereby inhibiting the growth of the layer into the metal in these regions. The lower film growth rate, relative to the surrounding areas, accounts for the observation that the voids subtend protrusions of the metal into the film. Periodic detachment of the voids, followed by nucleation and growth of new voids at the apex of the protrusions, accounts for decoration of the barrier layer with voids as well as for the formation of the hexagonal array of pores, when aluminum is anodized in some electrolytes.

Effect of aluminum and titanium additions to Fe-21%Cr-32%Ni on the oxidation behavior in an impure helium atmosphere at high temperatures

The effects of aluminum and titanium additions on the oxidation and carburization behavior of Fe-21%Cr-32%Ni in an HTGR-simulated impure helium environment at high temperatures were studied. Intragranular and intergranular oxidation were the principal forms of degradation, with the effect of aluminum being major and that of titanium relatively minor. As the aluminum content in the alloy increased, the mode of degradation changed from both uniform intragranular and intergranular oxidation, to one involving only uniform intragranular oxidation. This transition in the degradation mode was explained by the volume changes in the alloy resulting from a combination of both a volume increase due to internal-oxide precipitation and shrinkage due to the condensation of vacancies formed as a result of selective removal of alloying elements to the external scale. Intergranular oxidation was observed only when the resultant volume change was due to shrinkage. When the resultant volume change was positive, only uniform intragranular oxidation occurred and at the same time, extensive carburization was observed probably due to the deterioration of the surface scale caused by the deformation of the alloy substrate. A small amount of titanium, ca. 0.4%, appeared to modify the phenomena caused by aluminum additions, e.g., causing increased intergranular penetration for the 0.4% Al alloy and internal-to-external transition for the 2.1% Al alloy. External scale formation without any internal oxidation was observed for alloys containing more than 1.9% Al at 973 and 1023 K and for an alloy containing 2.1% Al and 0.4% Ti at 1073 and 1123 K. In these cases, carburization was almost completely eliminated.

Effect of the proximity of the external surface on the growth characteristics of inert gas bubbles

Experimental evidence is discussed in order to show that the proximity of an external surface has a strong effect on the growth of inert gas bubbles. This effect can be explained as follows: while bubbles act as sinks, the external surface provides a copious source for vacancies. These observations suggest the possibility of the growth of inert gas bubbles through spontaneous vacancy condensation.

Phase transformation and microstructure in (Mg,Ti)-PSZ

Phase transformation and microstructure in Mg-PSZ (8 mol% MgO), sintered (1600°C, 6 h) with 0 to 15 mol% additions of TiO2 (designated as 0T to 15T specimens), were studied by X-ray diffraction and electron microscopy. According to the room-temperature X-ray lattice parameter, the saturation of TiO2 in the cubic (c-) zirconia was reached at a total TiO2 addition of ca. 6 mol% at 1600°C, whereas the solubility limit in tetragonal (t-) zirconia was not reached in the composition range studied. The amount of t-zirconia increases with increasing TiO2 content at 1600°C, as indicated by the monoclinic (m-) zirconia content in the furnace-cooled specimens. Regardless of the modification of the lattice misfit strain by TiO2 dissolution, the precipitates of t-phase in the c-matrix remain lenticular with {1 0 0} habit plane. Loops, due probably to condensation of the structural vacancies, were found in the m-phase of 9T, but not in 1T and 6T specimens.

On the structure of faulted interfaces in aluminium nitride ceramics

Abstract An unusual two-dimensional structure in hot-pressed wurtzite A1N, composed of a mixture of both curved and flat elements, is analysed by weak-beam and high-resolution electron microscopy. It is demonstrated that the structure, in its elementary form, is a ‘dome’-like faulted defect. This defect is characterized by a Frank-type dislocation loop containing a metal-vacancy-induced stacking fault in the basal plane with displacement Rp = (1/3) [1100] + 0·15[0001] and a curved faulted interface with displacement vector Rc = (1/3)[1100] + (1/2)[0001]. The elementary dome is found always pointing in the same direction, reflecting the lack of symmetry in the tetrahedral unit structure of A1N with respect to the basal plane. Condensation of supersaturated metal vacancies on both interfaces, combined with the segregation of impurities, mainly oxygen, only on the planar interface, is considered to be the driving force for the nucleation and growth of the structure.

Model for nonprotective oxidation of Al-Mg alloys

The oxidation of Al-5Mg alloy has been studied at 550°C in dry air. Morphological details of the MgO layers which develop on this alloy during hightemperature oxidation have been studied by scanning electron microscopy (SEM). A localized detachment of the protective, adherent MgO layer was found, which is caused by voids formed by vacancy condensation at the metal-oxide interface. The source of these vacancies was the outward diffusion of Mg through the oxide layer. Continuing growth of these voids was responsible for cracking of oxide ridges and nodules, as well as the growth of new MgO having a “cauliflower” morphology. A model describing the process of the outward diffusion is given.