Electromigration

When an external electric field strength, E, in V.m , is applied to a semiconductor, it induces a drift of the electric charge carriers, denoted i (i.e., electrons and holes). At a low electric field the drift velocity of the charge carrier i is directly proportional to the electric field strength according to the following equation  

The proportional coefficient (sometimes denoted fi) is the intrinsic electric mobility of the charge carrier expressed in V m s We can express the overall flux of all the electric charge carriers through the semiconductor, /, in m fs , which is the summation of the flux of the holes and of the electrons  

Hence the overall electric current density vector j, in A.m , is the product of the overall flux by the elementary charge e, in C, and is expressed by the following equation  

The mobility of electrons and holes is affected by two main scattering mechanisms chemical impurities and lattice scattering. The mobility temperature dependence due to 

However, lattice defects also scatter electrons. This scattering is small and has only a shght temperature dependence. 

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Electrical Properties. Generally, deposited thin films have an electrical resistivity that is higher than that of the bulk material. This is often the result of the lower density and high surface-to-volume ratio in the film. In semiconductor films, the electron mobiHty and lifetime can be affected by the point defect concentration, which also affects electromigration. These effects are eliminated by depositing the film at low rates, high temperatures, and under very controUed conditions, such as are found in molecular beam epitaxy and vapor-phase epitaxy. 

Electrically assisted transdermal dmg deflvery, ie, electrotransport or iontophoresis, involves the three key transport processes of passive diffusion, electromigration, and electro osmosis. In passive diffusion, which plays a relatively small role in the transport of ionic compounds, the permeation rate of a compound is deterrnined by its diffusion coefficient and the concentration gradient. Electromigration is the transport of electrically charged ions in an electrical field, that is, the movement of anions and cations toward the anode and cathode, respectively. Electro osmosis is the volume flow of solvent through an electrically charged membrane or tissue in the presence of an appHed electrical field. As the solvent moves, it carries dissolved solutes. 

AES has also been applied to study preferential sputtering of TiSi forming for low-resistivity conductor films in ULSI devices [2.151], or the electromigration behavior of Au-Ag films on Si02 using AES, XPS and AEM [2.152]. 

B. D. Knowlton, J. J. Clement, C. V. Thompson. Simulation of the effects of grain structure and grain growth on electromigration and the reliability of interconnects. J Appl Phys 81 6012, 1997. 

It will be shown that a more elegant and more easily applicable solution of the problem is given by choosing another reference system. Both the dilute alloy and the unperturbed host can be described with respect to a common reference system, which consists of the unperturbed part of the alloy system and for obvious reasons is called void system. This void system allows for a single-site evaluation of the matrix element describing the wind force in electromigration and the t-matrix element required for the calculation of the residual resistivity due to a saddle-point defect. 

The paper is organized as follows. First the problem will be stated in a historical context. Subsequently, the matrix elements for electromigration and the residual... 

Figure 1 A dilute alloy system, showing a substitutional impurity, an interstitial impurity and an electromigration defect, and its reference system, the unperturbed host system. Some charge transfer effects are shown. Lattice distortion effects are omitted.

If the p labels refer to lattice sites j, this matrix reduces to 6(k) in the KKR matrix M(k) and Eq. (15) can be shown to reduce to Eq. (14). The evaluation of is hindered by the free-electron poles in the b matrices. This has formed a barrier for electronic structure calculations of interstitial impurities, but in some cases this problem was bypassed by using an extended lattice in which interstitial atoms occupy a lattice site. For the calculation of Dingle temperatures [1.3] and interstitial electromigration [14] the accuracy was just sufficient. Recently this accuracy problem has been solved [15, 16]. 

Figure 4 The wind valence in A1 along the migration path. The initial and saddle point positions are at the origin and at 0.5 respectively. The lower curve is for Cu, the upper curves are for self-electromigration. The dashed and the dotted curve show the influence of a Cu atom at positions 1 and 2 of Fig. 3 respectively, on the wind force in pure A1 (thick curve).

Defect configurations in dilute alloys, studied up to now in the framework of multiple scattering theory, are such that a one-to-one correspondence exists between the atoms in the alloy and the reference system, the latter system regularly being the unperturbed host system. This one-to-one correspondence does not apply to the defect studied in substitutional electromigration, in which a host atom or an impurity can move to a neighbouring vacancy. 

Electromigration of Ions movement of ions under an electric field. 

Supporting electrolytes are required in controlled-potential experiments to decrease the resistance of the solution, to eliminate electromigration effects, and to maintain a constant ionic strength (i.e., swamping out the effect of variable... 

The addition of a spillover proton to an adsorbed alkene to yield a secondary carbonium ion followed by abstraction of a proton from the C3 carbon would yield both isomers of 2-butene. The estimated faradaic efficiencies show that each electromigrated proton causes up to 28 molecules of butene to undergo isomerization. This catalytic step is for intermediate potentials much faster than the consumption of the proton by the electrochemical reduction of butene to butane. However, the reduction of butene to butane becomes significant at lower potentials, i.e., less than 0.1V, with a concomitant inhibition of the isomerization process, as manifest in Fig. 9.31 by the appearance of the maxima of the cis- and tram-butene formation rates. 

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