Measurement of electromigration

Diffusion measurement

The first type of measurement is similar to the usual diffusion measurement except that the sample has to be shaped to allow the flow of current with a sufficient current density to produce a measurable amount of electromigration. The principle of this type of measurement is shown in Fig. 4.

Fig. 4. The isothermal isotope method: A, inert marker concentrations; B, concentration of matrix isotope. (From Huntington (1974)).

For bulk studies, the sample is usually made into a cylindrical form with liquid cooling of both ends. The element to be measured can be incorporated uniformly into the sample or inserted near the center of the sample. Upon passage of the current, the

composition distribution will change as a result of electromigration. [6] The concentration profiles of the tracer before and after electromigration are depicted in Fig. 4 by the curves A and B, respectively. The distance between the centroid of A and B divided by the annealing time gives the drift velocity, from which the DZ* can be determined. The spreading of curve B with respect to A determines D; the tracer diffusion is a random walk.

The difficulty of carrying out such an experiment is to maintain a uniform temperature over the entire sample, for otherwise a correction due to the effect of temperature gradient is required. [7]

The second type of measurement is called the 'vacancy flux' method which measures the change in the sample dimension as a result of the creation and annihilation of vacancies along the sample during the course of electromigration. The principle of this measurement is illustrated in Fig. 5. The early experiments simply measured the displacement of surface markers (scratches or indentations) separated by a uniform spacing along the length of a wire sample (Huntington and Grone 1961). Later, in a study of A1 (Penney 1964), it became apparent that the change in the dimension is not confined to being along the length of the sample only; there are also transverse dimensional changes. The latter was found to depend on the aspect ratio of the sample and should be included to account for the total vacancy flux. The simplicity of the measurement has made this method one of the principal techniques in electromigration studies and it has been applied to measure bulk

electromigration for a large number of pure elements. Results of these measurements are in general agreement, although not with the same accuracy, as those obtained from chemical analysis.[6]

Fig. 5 Vacancy flux method-schematic experiment: •electron, □vacancy. (From Huntington (1974))

Edge displacement technique (Drift velocity method)

The mass transport of electromigration in a thin metal film can be investigated directly using the drift velocity method [8-10]. The experiment is also called the “saddle movement experiment.” It was first presented by Blech in 1975 and as been widely adopted since then for the study of atomic drift velocity, the direction of the mass transport, and the activation energy, as well as other parameters.

A sample configuration for the drift velocity experiments is shown in Fig. 6.

Basically, a piece of metal track. For example, the metal film studied in the first drift velocity experiment [8] was Au while the metal track was Mo. A constant current is applied through the metal track, and most of the current is diverted into the highly conducting Au saddle in the overlapped region. As a result, the saddle experiences a continuous impulse from the electron wind force, in the direct from the cathode to the anode edge.

Fig. 6 Schematic of sample configuration for drift velocity measurements.

The mass in the saddle will therefore be transported in that direction, which is obtained from the effective movement of the saddle edge along the metal track. This average atomic drift velocity is given by

j

where ν is the drift velocity, J is the atomic flux, and ρ is the Resistivity of the film.

Equation (1.6) also can be rewritten as

)

Thus, measurement of drift velocity at various temperatures yields the value of activation energy. Equation (1.6) also indicates that measurement of the D⁰Z^* product is possible if the drift velocity is measured as a function of the current density [11].

A threshold current density exists for electromigration is found by I.A. Blech and is shown in Fig. 7 [9]. This current is approximately inversely proportional to stripe length.

The occurrence of the threshold is explained by opposing chemical gradients created by the atom pile-up and depletion at the stripe ends. The threshold is increased by decreasing the temperature or by enclosing the aluminum in silicon nitride. K. N. Tu et al proposed that in current crowding, the current-density gradient can exert a driving force strong enough to cause excess vacancies point defects to migrate from high to low current-density regions.

This leads to void formation in the latter [12].

Fig. 7 Average drift velocity of an aluminum stripe as a function of current density [7].

Resistometric measurement

The resistance of a metal interconnect in integrated circuits is sensitive both to its microstructural and geometrical parameters. When electromigration creates voids, cracks, or hillocks within a metal line, the line microstructure and geometry are distorted and the line resistance changes. This techniques is suitable for study of the early stage of

electromigration, where the conditions of uniform current density and temperature have not been disturbed significantly. Under the assumption of the early stage of electromigration, that is, the dimensions of the maximum voids are much less than the line width-it is

straightforward to show that the line resistance of a thin film conductor has the following Where R⁰ is the line resistance at a reference temperature, C is a constant depending on the film geometry, the grain boundary structure, and the grain size, t is the time that the conductor has been stressed, Ea is activation energy, k is Boltzmann’s constant, and T the absolute temperature. As indicated by Eq. 1.8, at a fixed current density j resistance measurements at different temperatures provide information on the value of the activation energy Ea, and the measurements at different current density levels determine the value of the exponent n. [6]

J.Y. Choi, S.S. Lee and Y.C. Joo reported that electromigration characteristics of eutectic SnPb solder which using thin stripe-type test structures in which the temperature and the current density were varied from 80 to 100℃ and from 4.6 to 8.7 10⁴ A/cm². They assumed that the electromigration-induced drift of the solder materials is the main cause of the initial resistance change; it can be assumed that the normalized rate of change in resistance is proportional to the electromigration-induced flux shown in eq. (1.7).

Rewritten the equation, as

const

The activation energy of electromigration can be obtained by plotting ln(T．nomalized rate) vs 1/T, as seen in Fig. 8. The calculated activation energy is 0.77 eV.[13]

Fig. 8 Calculation of activation energy for electromigration of eutectic SnPb solder from initial rate for change[13]

Mean Time to Failure

In 1969, Black provided the following equation to analyze failure in Al interconnects caused by electromigration.[14]

) 1 exp(

kT Ea A j

MTTF = _n ………(1.10)

The derivation of equation was based on an estimate of the rate of forming voids across an Al interconnect. The most interesting feature of the equation is the dependence of MTTF on square power of current density, i.e., n=2. In essence, Black assumed that the rate of mass transport in electromigration is proportional to electron momentum and number of electrons per unit area per unit time. Both of them are proportional linearly to current density, hence the square power dependence. In MTTF equation, whether the exponent n is 1, 2 or a large number has been controversial, especially when the effect of

joule heating is taken into account. However, assuming that mass flux divergence is required for failure, the nucleation and growth of a void requires vacancy super-saturation, Shatzkes and Lloyd have proposed a model by solving the time-dependence diffusion equation and obtained a solution for MTTF in which the square power dependence on current density is also obtained.[15] However, whether Black’s equation can be applied to MTTF in Cu interconnects and flip chip solder joints deserves a careful examination.

Electromigration of eutectic SnPb flip chip solder joints and their

mean-time-to-failure have been studied in the temperature range of 100 to 140 °C with current densities of 1.9 to 2.75 ×10⁴ A/cm² by W. J. Choi, E. C. C. Yeh, and K. N. Tu. In these joints, the under-bump-metallization (UBM) on the chip side is a multilayer thin film of Al/Ni(V)/Cu, and the metallic bond-pad on the substrate side is a very thick, electroless Ni layer covered with 30 nm of Au. When stressed at the higher current densities, the MTTF was found to decrease much faster than what is expected from the published Black’s equation. When the measured MTTF is plotted against temperature (T+∆T) which Joule heating was considered as shown in Figs. 9(a) and 9(b), the calculated

activation energy Q is found to be 0.5 and 0.8 eV for the eutectic SnPb solder and eutectic SnAgCu solder, respectively.[16]

Fig. 9. Plots of MTTF against 1/k(T+∆T), where ∆T is the temperature increase due to Joule heating: (a) eutectic Sn Pb solder joints, and (b) eutectic SnAgCu solder joints.[16]