Theory Of Electromigration Research Articles

Comment on Lodder's “exact” electromigration theory

A. Lodder has presented a calculation of the driving force for motion in electromigration, characterized as “exact” and “conclusive.” This is a brief critique of Lodder's work, suggesting the omission of essential physical effects.

Fundamental questions in the theory of electromigration

Fundamental questions in the theory of electromigration

Mixtures of classical and quantum-mechanical particles and the ionic response in electromigration

The authors discuss the result of taking the classical limit on the ions of a metal while retaining a quantum-mechanical description of the electrons. One finds that when this limit is possible the ionic motion is determined by a classical Hamiltonian, but in general this gives rise to velocity-dependent forces. These forces are non-adiabatic in origin and the motion of the ions can be fully classical only if the non-adiabatic terms in the Hamiltonian are small enough for second-order terms to be negligible, although a quasiclassical description may still be possible if this condition is not fulfilled. The existence of the Hamiltonian is of fundamental importance to the theory of electromigration as it clarifies the origin of the driving forces and enables the authors to discuss the response of the ions to the driving forces in terms of the usual formulation. The formal solution of the linearised Liouville equation is obtained to first order and is discussed for the case where the driving forces are obtained to second order in the electron-ion scattering.

Electronic transport and ionic migration in molten Na-K and Na-Rb alloys

Abstract It is shown that the present theory of resistivity, thermopower, electromigration and thermal diffusion in liquid alloys implies that one can construct empirical potentials, i.e. provide full phase-shift specifications of the possible scattering potentials consistent with the experimental data. This is illustrated with calculations for Na-K and Na-Rb, comparing the resulting phase shifts with those obtained using modern scattering form factors, in particular those obtained from a Shukla-Taylor model potential and from norm-conserving pseudopotentials. It is observed that no single form factor is adequate for representing the transport data throughout the alloy regimes. Improvements required in the bare-ion pseudo-potentials are indicated, and future methods of approach are suggested.

Hall Voltage Induced by Hydrogen Diffusion in Palladium

A Hall-type voltage induced by the fast diffusion of hydrogen in a metal (palladium) in a strong magnetic field has been detected. The sign and the magnitude of this voltage imply that hydrogen in palladium acts as a particle of charge ${Z}_{\mathrm{H}}=1$. The presence of this effect is strong experimental evidence for the existence of the controversial direct-force term (i.e., the action of an electric field on the unscreened charge of an ion in a metal) in the theory of electromigration.

The role of bound states in electronic transport

A new polarisation denominator contribution is found to resolve the remaining formal difficulties of the inverse transport theory of Rousseau, Stoddart and March. The separation of the two contributions to the transport coefficient in numerator and denominator is then demonstrated to effect a partition of the role of bound and continuum states as non-ergodic and ergodic regions of the energy spectrum. In particular the theory provides a result independent of the assumed number of scattering (or conduction band) electrons, and provides a physical description of the renormalisation of the resistivity by polarisation behaviour as the metal-insulator transition is approached. Finally it is observed that the separation of the forces implicit in the derivation of the theory is equivalent to the separation of ldlectron wind” from the “direct field” force in electromigration theory.

Theory of electromigration in noble and transition metals

Theory of electromigration in noble and transition metals

The calculation of electromigration forces and resistivities for liquid binary alloys

The linear response theory of electromigration as proposed by Kumar and Sorbello (1975) and developed by Schaich (1976) is applied to a number of binary alloys. The authors have compared detailed model-potential calculations with experiment for the systems Pb-Bi, Sn-Pb, Na-K and Na-Rb. For the polyvalent systems the comparison is reasonably favourable but for the others the formulation in terms of model potentials appears to fail because the d wave scattering from K and Rb ions is not described correctly. In contrast, phase shift calculations appear to yield a correct semiquantitative description. The success of Ashcroft and Langreth in calculating the resistivity of Na-K using simple model potentials thus appears, at least in part, to be a consequence of the number of freely variable parameters in their theory, rather than of a correct description of the basic physics.

Failure Mechanisms in Beam Lead Semiconductors

Hybrid microcircuits (HMC's) designed for the Energy Research and Development Administration (ERDA) by Sandia Laboratory in Albuquerque, NM, are manufactured by the Kansas City, MO, Division of the Bendix Corporation employing beam lead devices (BLD's) as active components. The HMC's consist of sputtered tantalum-nitride (Ta <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> N) resistors and evaporated chromium-gold (Cr-Au) conductors on alumina substrates with applique components and thermocompression bonded ribbons, lead frames, fine wires, and beam lead devices. During recent testing of HMC's for a new program, failures of the BLD's resulted in unacceptable yields and increased rework. These BLD failures showed up primarily as increased leakage failures, intermittent failures that repeated on a random basis, and in worst cases, as direct device shorts. An investigation of the problem showed that cracks often appear on the edge of the silicon and on the silicon nitride lip that overhangs the edge of the beam. These cracks appear at various phases of the processing, but primarily during BLD bonding. High temperature reverse bias (HTRB) tests of diodes and transistors combined with analysis of the devices that failed during these tests indicated that gold in the cracks was a primary cause of failures. The gold in the cracks is the result of gold "relocation" or migration from the gold beams on the semiconductor. The gold was detected by energy dispersive X-ray analysis (EDAX) and electron-beam induced-current methods. Gold was observed on the silicon cracks above the beams and in silicon nitride cracks on either side of the beams. Gold resistive leakage paths of this type have been observed only in devices such as p-n-p transistors and p+ silicon substrate zener diodes, where one of the gold beams is more than 1.42 V positive with respect to the body of the silicon chip. This indicates that the gold leakage paths are formed by electromigration of gold from the beam to the silicon chip. Results of HTRB tests on n-p diffused zener diodes,1 p-n diffused zener diodes, and n-p-n transistors are consistent with the gold electromigration theory. Several conditions are theoretically required for gold e!ectromigration of this type: the gold beam must be positive with respect to the silicon chip by more than some minimum voltage (the gold-gold electrolytic potential is 1.42 V); there must be a crack in the silicon nitride, or at the intersection of the beam and a chip, or a crack in the silicon above the beam; and an electrolyte such as moisture-containing halogen ions must be present in the crack. Vacuum baking of HMC's after cleaning and just before electrical testing, the elimination of water as a cleaning agent, and the elimination of trichloroethylene at final assembly cleaning have solved the leakage problem caused by gold electromigrafion in the devices.

Electromigration in aluminium thin films under pulsed-current conditions

Despite extensive investigation of electromigration in aluminium interconnections, the available data are sufficient to apply to tracks carrying pulsed currents in operational conditions. A theory of electromigration that considers the growth of microscopic voids in a track has been developed for the case of electromigration under pulsed-current conditions. The resulting model has been confirmed by a limited number of experimental results. Failure of tracks stressed with a.c. was observed to be due to mechanisms other than electromigration.

Electro-migration in a two-band metal and in Hall field; Application to an electron-hole drop

The Das-Peierls semi-classical model for a theory of electro-migration in metals is extended to a two-band system of electron and hole carriers. It is shown how the “effective charge” on the electro-migrating ion can be obtained from electro-migration experiments in Hall field. An experiment of this type is proposed to determine the charge on an electron-hole drop recently observed in some semi-conductors.

Residual resistivity dipoles

Current flow past lattice defects in metals is associated with a localized conduction band polarization. This has become generally recognized in electromigration theory, but there is disagreement about the details of the polarization pattern. Discussions by others have emphasized polarization terms which are first order in the perturbation potential. This paper analyzes the polarization terms which are proportional to scattering probabilities and thus related to the increase in resistivity. These are second order, or higher, in the scattering potential. A simple physical picture is used to estimate the size of this dipole moment associated with the residual resistivity. A quantum mechanical discussion is given for the one-dimensional case. The conditions under which the polarization can be expected to be linear in the scattering cross-section is discussed.

Separation of Isotopes by Electromigration Theory of Steady‐State Enrichment at the Low Concentration Range

The general differential equation for isotope separation by countercurrent electromigration is derived, normalized for the general case independent of properties of any particular liquid system, and solved for steady‐state enrichment of an isotope of low abundance. Two primary process parameters are defined, the reduced reflux ratio, p, and reduced number of plates, v, in terms of which the process is specified. The ranges within which the reflux ratio and number of plates may vary are determined. Minimum pv is established as a criterion for preferred operation and a general solution is derived to comply with this criterion. The general solutions of the differential equations provide easy application of the results for any system of any particular properties

The effect of electrical migration on the chronopotentiometric transition time

Sand's theory of electro-migration in chronopotentiometry has been re-derived and extended. The theory, although approximate, satisfactorily describes the enhancement of cathodic transition times. The behaviour of thallous sulfate in the presence of little or no supporting electrolyte agrees well with that predicted by the equation iτ 1 2 / AC = ( nπ 1 2 FD 11 1 2 /2(I— T 1)). The enhancement of the cupric ion transition time for the reduction of cupric sulfate in the presence of little or no supporting electrolyte is less than predicted by this equation. As expected, the transition time for the reduction of benzoquinone is little affected by the concentration of supporting electrolyte.