Theory Of Electromigration Research Articles

Effects of Pulse Electric Field on the Clusters of Pb-Sn Molten Alloy

The authors investigate the effect of electric pulse field (EPF) on the grain size of Pb-Sn alloy and conclude the optimization parameter of EPF through the specialized experiment. Applying the electric dipole theory, the electro-migration theory and combining with the electrostatic force analysis, the author explain that the EPF can modify the liquid structure, can make the smaller cluster reorganized and growing up and at the same time can make the bigger cluster fission, then induce the cluster scale to the same and therefore improve the solidification structure from the theory point of view.

The effects of switching time and SrTiO3−xNy nanostructures on the operation of Al/SrTiO3−xNy/Al memristors

The nanostructure and switching properties of the Al/SrTiO3−xNy/Al memristors have been investigated. It was found that the formation of stacking faults defects in the perovskite structure during plasma nitridation facilitates resistivity switching in Al/SrTiO3−xNy/Al memristors. From thermal emission measurements we observed local heating of the Al/SrTiO3−xNy anode interface (285°C) during switching when the interface becomes rectified due to the formation of locally undoped region. A model for resistivity switching and parameters affecting the memristor operation is discussed considering the electromigration theory. The I–V curves are analyzed taking into account the tunnel barrier formations and an inhomogeneous Schottky barrier modification at the anode interface.

Electromigration Oscillations Occurring in Ternary Electrolyte Systems with Complex Eigenmobilities, as Predicted by Theory and Ascertained by Capillary Electrophoresis

Chemical oscillations are driven by a gradient of chemical potential and can only develop in systems where the substances are far from chemical equilibrium. We have discovered a new analogous type of oscillations in ternary electrolyte mixtures, which we call electromigration oscillations. They appear in liquid solutions of electrolytes and are associated with the electromigration movement of ions when conducting an electric current. These electromigration oscillations are driven by the electric potential gradient, while the system can be close to chemical equilibrium. The unequivocal criterion for the instability of the electrolyte solution and its ability to oscillate is the existence of complex system eigenmobilities. We show how to calculate the system eigenmobilities by utilizing the linear theory of electromigration and how to identify the complex system eigenmobilities to predict electromigration oscillations. To experimentally prove these electromigration oscillations, we employ a commercially available instrument for capillary electrophoresis. The oscillations start a certain period of time after switching on the driving electric current. The axial concentration profiles of the electrolytes in the capillary attain a nearly periodic pattern with a spatial period in the range of 1-4 mm, with almost constant amplitude. This periodic pattern moves in the electric field with mobility that is equal to the real part of the complex eigenmobility pair. We have found several ternary oscillating electrolytes composed of a base and two acids, of which at least one has higher valence than one in absolute value. All the systems have three system eigenmobilities: one is real and close to zero, and the two others form the complex conjugate pair, the real part of which is far from zero.

Fatigue mechanism of the ferroelectric perovskite thin films

Incorporating the vacancy electromigration theory into the switching-induced charge-injection mechanism into the local phase decomposition model has led to an analytical model for the dielectric fatigue behavior and the remnant polarization in perovskite structured ferroelectric thin films. The model has allowed us to reproduce the fatigue behavior in various ferroelectric thin films measured under different voltages, temperatures, and frequencies. We concluded the essential reason for electrical fatigue in ferroelectrics is the local phase separation induced directly or indirectly by other fatigue mechanisms proposed in previous papers.

Prediction and understanding system peaks in capillary zone electrophoresis

Introduction of a sample into the separation column (microchip channel) in capillary zone electrophoresis (microchip electrophoresis) will cause a disturbance in the originally uniform composition of the background electrolyte. The disturbance, a system zone, can move in some electrolyte systems along the separation channel and, on reaching the position of the detector, cause a system peak. As shown by the linear theory of electromigration based on linearized continuity equations formulated in matrix form, the mobility of the system zone--the system eigenmobility--can be obtained as the eigenvalue of the matrix. Progress in the theory of electromigration allows us to predict the existence and mobilities of the system zones, even in very complex electrolyte systems consisting of several multivalent weak electrolytes, or in micellar systems (systems with SDS micelles) used for protein sizing in microchips. The theory is implemented in PeakMaster software, which is available as freeware (www.natur.cuni.cz/gas). The linearized theory also predicts background electrolytes having no stationary injection zone (water zone, water gap, water dip, EO zone) or unstable electrolyte systems exhibiting oscillations and creating periodic structures. The oscillating systems have complex system eigenmobilities (eigenvalues of the matrix are complex). This paper reviews the theoretical background of the system peaks (system eigenpeaks) and gives practical hints for their prediction and for preparing background electrolytes not perturbed by the occurrence of system peaks and by excessive peak broadening.

Calculations of the screening of the charge of a proton migrating in a metal

The amount of screening of a proton in a metal, migrating under the influence of an applied electric field, is calculated using different theoretical formulations. First the lowest order screening expression derived by Sham (1975) is evaluated. In addition 'exact' expressions are evaluated which were derived according to different approaches. For a proton in a metal modeled as a jellium the screening appears to be 15 +/- 10 %, which is neither negligible not reconcilable with the controversial full-screening point of view of Bosvieux and Friedel (1962). In reconsidering the theory of electromigration, a new simplified linear-response expression for the driving force is shown to lead to essentially the same result as found by Sorbello (1985), who has used a rather complicated technique. The expressions allow for a reduction such that only the scattering phase shifts of the migrating impurity are required. Finally it is shown that the starting formula for the driving force of Bosvieux and Friedel leads exactly to the zero-temperature limit of well-established linear response descriptions, by which the sting of the controversy has been removed.

Real-time observation of liquid Indium unusual behavior inside silica nanotubes

Behavior of Indium embedded into amorphous silica nanotubes has been analyzed using a 300 kV field emission TEM. Under electron beam irradiation with a beam current density nearly 10 times that of normal TEM imaging conditions, a variety of unusual phenomena has been recorded: (i) melting, expansion and/or sudden shrinkage of encapsulated In-columns; (ii) liquid In squeezing out of fully sealed tubes, with the tube shape fully retained, accompanied by cyclic growth and ‘explosion’ of liquid In nanoballs on the tube periphery; (iii) ultrafast ‘birth’, ripening, coalescence and boiling of tiny In droplets inside and/or outside of tubular channels in areas where In was originally not present. The results are explained in the framework of electromigration theory.

System zones in capillary zone electrophoresis

When working with capillary zone electrophoresis (CZE), the analyst has to be aware that the separation system is not homogeneous anymore as soon as a sample is brought into the background electrolyte (BGE). Upon injection, the analyte creates a disturbance in the concentration of the BGE, and the system retains a kind of memory for this inhomogeneity, which is propagated with time and leads to so-called system zones (or system eigenzones) migrating in an electric field with a certain eigenmobility. If recordable by the detector, they appear in the electropherogram as system peaks (or system eigenpeaks). However, although their appearance can not be forecasted and explained easily, they are inherent for the separation system. The progress in the theory of electromigration (accompanied by development of computer software) allows to treat the phenomenon of system zones and system peaks now also in very complex BGE systems, consisting of several multivalent weak electrolytes, and at all pH ranges. It also allows to predict the existence of BGEs having no stationary injection zone (or water zone, EO zone, gap, dip). Our paper reviews the theoretical background of the origin of the system zones (system peaks, system eigenpeaks), discusses the validity of the Kohlrausch regulating function, and gives practical hints for preparing BGEs with good separation ability not deteriorated by the occurrence of system peaks and by excessive peak-broadening.

Eigenmobilities in background electrolytes for capillary zone electrophoresis: III. Linear theory of electromigration.

A mathematical model of capillary zone electrophoresis (CZE) based on the conception of eigenmobilities, which are the eigenvalues of a matrix M tied to the linearized governing equations is presented. The model considers CZE systems, where constituents, either analytes or components of the background electrolyte (BGE), are weak electrolytes--acids, bases, or ampholytes. There is no restriction on the number of components nor on the valence of the constituents nor on pH of the BGE. An electrophoretic system with N constituents has N eigenmobilities. In most BGEs one or two eigenmobilities are very close to zero so their corresponding eigenzones move very slowly. However, there are BGEs where no eigenmobility is close to zero. The mathematical model further provides: the transfer ratio, the molar conductivity detection response, and the relative velocity slope. This allows the assessment of the indirect detection, conductivity detection and peak broadening (distortion) due to electromigration dispersion. Also, we present a spectral decomposition of the matrix M to matrices allowing the assessment of the amplitudes of system eigenpeaks (system peaks). Our model predicted the existence of BGEs having no stationary injection zone (or water zone, gap, peak, dip). A common practice of using the injection zone as a marker of the electroosmotic flow must fail in such electrolytes.

Ab initiocalculation of electromigration effects at polyvacancy clusters in aluminum

The process of the drift of atoms due to an applied voltage, called electromigration, is studied both in materials science and in fundamental physics. The development of voids at the cathode side of an aluminum film and the growth of hillocks at the anode, 1 which is due to self-electromigration, shorten the lifetime of an integrated circuit. This process is commonly attributed to migration along grain boundaries. In the electronic industry a great deal of effort is made in slowing down this process. 2 In the present paper we report about a microscopic study of electromigration in polyvacancy clusters. For a certain cluster shape the results obtained can be considered as a first step in the direction of a microscopic description of electromigration along a grain boundary. In the theory of electromigration one concentrates on the calculation of the driving force, 3‐7 which is commonly written as a sum of two components, a direct force Fdirect and a wind force Fwind . The direct force is due to a net charge of the migrating atom, while the wind force is due to scattering of the current-carrying electrons off the atom. Both forces are proportional to the electric field and can be characterized by a valence,

Theory of surface electromigration on heterogeneous metal surfaces

We report a calculation of the magnitude of the wind force for the self-electromigration of adatoms on heterogeneous metal surfaces. Using a layer-KKR method we computed the wind valence of adatoms within small monolayer islands and voids on Cu(100). We show that the electromigration driving force felt by an adatom is significantly altered by the scattering of carriers among neighboring atoms within the island. Using the results of these calculations as input to kinetic Monte-Carlo simulations, we explore how this inhomogeneity of the wind force is manifest in the driven surface diffusion of Cu islands on a current-carrying Cu(100) substrate.

Effects of electric current on solid state phase transformations in metals

The influence of an electric current on the following solid state transformations in metals are considered: (1) intermetallic compound formation and growth in diffusion couples, (2) precipitation, (3) crystallization of amorphous alloys and (4) recrystallization and grain growth of cold worked metals. The formation and growth of intermetallic compounds were in qualitative accord with electromigration theory. Regarding precipitation, an electric current can either enhance or retard the precipitation rate, depending on the alloy, the current density and its frequency. Important factors appear to be the effect of current on the quenched-in vacancies and the presence of an internal stress. Both a continuous d.c. current and high current density electropulsing enhanced the crystallization rate of amorphous alloys. The effects are greater than can be explained by simple electromigration theory and suggest the cooperative motion of a larger number of atoms. Electropulsing enhanced the recrystallization rate of cold worked metals, but retarded subsequent grain growth. Enhancement of the recrystallization rate resulted mainly from an increase in the pre-exponential factor of the Arrhenius rate equation, which is considered to refer to the nucleation rate. Retardation of subsequent grain growth resulted from a lower residual dislocation density within the newly-formed grains.

On the lifetime of the parallel vibrational motion of adsorbates on metallic surfaces

We point out that the relationship between the adatom-induced surface resistivity, ϱ s, and the lifetime of the parallel vibrational motion of adatoms, τ, recently derived by Persson can be recast to read as F f J f = n e el f ϱ s n a , where F f , J f , n e, l f, and n a are the damping force on the adatom, the apparent current density in the metal seen from the adatom, the electron density in the metal, the film thickness, and the 2-dimensional density of adatoms, respectively. This has essentially the same form as the relationship between ϱ s and the indirect (“electron-wind”) force F w on the adatom located in a current density J w , i.e., F w J w = n e el f ϱ s n a , which has been known for a long time in the theory of electromigration. Using a first-principles linear response approach, we show that both the equations hold true if the substrate is translationally invariant in the plane (flat jellium model). We derive a simple expression of the surface resistivity, ϱ s, which can be evaluated from the scattering amplitudes of one-electron wave functions at the Fermi energy alone.

Microscopic theory of electromigration on semiconductor surfaces.

Electromigration has a dramatic effect on the morphology of semiconductor surfaces, inducing, for example, step bunching instabilities. To explain these phenomena from a microscopic point of view, we study self-diffusion on Si(111) through first principles calculations, and propose a mechanism for diffusion bias induced by external electric fields. A competing, wind-force effect arises from enhanced surface electron density, due to incomplete melting. The competition leads to two transitions in surface kinetics with increasing temperature, in agreement with experimental observations.

Theory of surface electromigration on metals: application to self-electromigration on Cu(111)

We present a calculation of the force, due to electron scattering, acting upon an adatom at the surface of a current-carrying metal, i.e., the so-called “wind” force in surface electromigration. The force is calculated from the Feynman-Hellmann theorem in which the electron scattering states are computed with full multiple scattering corrections by a layer-KKR method. In contrast to previous jellium models, this approach allows the proper treatment of electron scattering by both the surface barrier and the substrate and its effect upon the current-carrying states at the surface. The electron scattering force is computed for the self-electromigration of Cu adatoms on Cu(111). At room temperature, the effective valence of the adatom is found to be ≈ −21. We conclude that surface electromigration of Cu on Cu(111) is dominated by the electron scattering force and that any direct force originating from charge transfer to the adatom is likely to be unimportant in this case. The implications of the computed value of the wind force for the mass transport at a current-carrying metal surface are discussed.

On the theory of steady-state electromigration in thin films

Steady-state electromigration along grain boundaries in a monatomic polycrystalline thin film has been analyzed in a two-dimensional model by balancing the (applied) electric and (induced) stress driving forces to achieve a zero flux divergence. The continuity of chemical potential requires a unique stress normal to each of the three boundaries terminating at a given triple point. These stresses and the steady-state fluxes are determined by a set of linear equations subject to boundary conditions at the intersection of grain boundaries with the film edge (edge points). When the normal stress is assumed zero at all edge points, the stress typically attains maxima and minima at triple points, whereas, when the flux is assumed zero at all edge points, the stress typically builds up monotonically in the field direction.

Clarification of the direct-force controversy in electromigration theory

A new derivation for the driving force on an impurity in the electron-impurity model system is given which results in an exact cancellation of the direct force for the electron-impurity system unambiguously, in accordance with an independent derivation by others in the past. However, the conclusion becomes much different if electron-phonon interaction is accounted for. Then the screening of the direct force appears to be much less effective. Since at the temperatures, at which electromigration experiments on dilute interstitial alloys are done, the electron-phonon interaction is predominant, the direct force valence is expected to lie in practice closer to the bare ion valency than to the completely screened value of zero. The theory predicts a resistivity-dependent direct force in contrast with the constant value used in the past.

On Sorbello's corrections to the new electromigration theory

Sorbello's criticism of a recently obtained exact result for the driving force on an impurity in the electron-impurity model system is shown to be untenable.

Corrections to Lodder's “exact” electromigration theory

Lodder's so-called “exact” result in electromigration theory is shown to be based on a number of approximations and on a subtle error in the evaluation of a response function. In consequence, his theory, like that of Bosvieux and Friedel, leads to the perfect screening of the direct force and to an unphysical result for the local transport field. A corrected evaluation of the response function is given in the weak-scattering limit, and is found to lead to an unscreened direct force.

Analysis of Landauer's comment on “Exact linear-response result for the driving force in electromigration”

It is elucidated that the degree of consensus concerning electromigration theory, referred to by Landauer, was founded on weak grounds. Further, his counter example to the new exact result is shown to be not valid. Finally, it is made clear that a conclusive result for the driving force can be derived only from a theory of electromigration which describes the local situation at an impurity exactly. In this respect a momentum-balance consideration, describing a bulk situation and leading to a force per impurity, necessarily fails.