Electromigration

With electromigration (EM) is understood to mean a material transport due to gradual movement of ions in a solid head which is caused by the electric current. Collisions of the electrons with the ions and to a lesser extent, the electric field exert a force on the ions, which is why they preferentially migrate during a diffusion step in a specific direction. By reducing the size of the structures, the practical importance of this effect increases.

4.1 Diffusion Mechanisms 4.1.1 Grain boundary diffusion
4.1.2 lattice diffusion
4.1.3 heterogeneous diffusion along interfaces
4.1.4 surface diffusion

4.2.1 Joule self heating
4.2.2 Thermal Stress

History of electromigration

The phenomenon of electromigration has been known for more than 100 years. Major technical importance was the issue from about 1965, when it was discovered that in the then-emerging integrated circuits ( ICs) used thin aluminum conductors are destroyed at high current densities. The theoretical basis to explain the electromigration set 1961/62 in two articles Huntington and Grone and Bosvieux and Friedel. A life prediction for damaged by electromigration conductor paths formulated in 1966, James R. Black, see blacksche equation. At that time, the interconnects were about 10 microns wide, while the width is only about 32 nm at today's highly integrated chips. In particular, through this continuous structure reducing wins this research area of increasing importance.

Practical implications of electromigration

Electric migration reduces the reliability of integrated circuits. At worst, they can be used for a total failure of one or more lines and thus lead to uselessness of the entire circuit. As the reliability of interconnects, not only in the fields of aerospace and the military, but also in civil applications, such as is the anti -lock braking system of cars, of great importance, this effect given high technological and economic significance.

With increasing miniaturization of high-and very large scale integrated circuits (VLSI / ULSI ) increases the probability of default by EM, because increases both the power density and the current density. Although it is possible by reducing feature sizes and operating voltages, the currents required to reduce, as smaller transistors have smaller gate capacitances, however, the currents are reduced to the same extent as the conductor cross-sections due to the increasing frequency. Therefore, the required current densities and thus electromigration phenomena take.

Instead of aluminum, in which electron migration at around 500 kA / cm ² occurs, some manufacturers use since about 2000 copper as wiring material. The advantages of copper are its better electrical conductivity (allows higher clock frequencies ) and its lower susceptibility to electromigration.

A deliberately induced electromigration finds application in ultra-pure ( > 99.99%) representation of the elements titanium, zirconium, hafnium, vanadium, among others The elements under high vacuum until just heated below its melting point and impurity ions are removed by electro-migration from the center, in which the element is now ultra pure present.

Basics

The material properties of the metal lines have a strong influence on the life. These properties mainly are the composition of the alloy, and the conductor cable dimensions as well as the line shape, the crystallographic orientation of the grains, and the properties of the passivation interfaces to other materials. The method used in the preparation of the layer deposition and heat treatment is also an effect on the service life.

Serious differences also result from the temporal profiles of the current: DC or AC various forms evoke different effects.

Forces ions in an electric field

The two forces acting on the ionized atoms in the conductor. The direct electrostatic force Fe is due to the electric field and is therefore in the direction of the electric field. The force from the momentum exchange with flowing charge carriers Fp points in the direction of the charge carrier flow. In metallic conductors Fp is caused by a so-called " electron wind ".

The resulting force Fres an excited ion in the electric field results

This one introduces an effective valence Z *. In it are both direct forces and the forces caused by the electrons with a high speed together. The elementary charge, q represents the product q · Z * so that the effective charge of the migrating ion dar. According ohmic law, the electric field E is the product of the current density j and ρ resistivity.

The force Fp is due to the shielding effect of electrons, usually the dominant force; the strength of the electrical field on the ions, however, is relatively small. Activated metal ions have a higher probability to fill a vacancy as other neighboring ions. As a result of these circumstances, to metal ions move to the anode, while vacancies move to the cathode. Compaction of vacancies results in small cavities ( voids ). This leads to open circuits by removing material. Short circuits between conducting paths through hill-shaped ( hillocks ) or filamentous structures ( whiskers ), caused by accumulation of ions to irregularities in the crystal.

Basic equations

Various experiments have shown that ions move in a constant field with a constant drift velocity. The linear dependence of the current of fast-moving electrons can be generally interpreted as a consequence of atomic diffusion, characterized by the self-diffusion coefficient D. In metals, free carriers arise with the charge Zion · q by ionizations in the metal lattice. In this product, Zion is the effective valence of the ion. By Nernst and Einstein is the mobility of ions ( ion mobility μion ) which can only be moved by an electric field, described as follows:

In the equation, k is the Boltzmann constant and T is the absolute temperature in Kelvin. Thus, the ions move with the average drift velocity of

Interpretation can be the equation by understanding FD = Zion · q · E as a force on an ion FD by the E field, which is matched by microscopic friction forces, while the average speed is.

Usually occurs the electrical resistance by collision of electrons with defects and lattice vibrations, called phonons. Through these collisions, a pulse is transmitted to the grating, which in turn results in that the thermal velocity of the electrons VE increases. The drift velocity resulting therefrom, can be written as ve = DFP / kT. Although the direct electrostatic force is different from the force by electrons at high speed, but they are the same microscopic forces that work against them and thus determine the self-diffusion and drift velocity. Therefore, one can combine the two effects and then receives for the drift velocity

Ion flux J is defined by the product of the particle density C and the average drift velocity.

If, now, the last two equations in one another, we obtain with the help of Ohm's law for the flow of ions and the self-diffusion coefficient D

, According to the continuity equation, the time change of the particle density is the negative divergence of the ion current. With the last equation we obtain now

Under DC conditions, we obtain the continuity equation divj = 0 Thus, the second term vanishes on the right side.

The diffusion coefficient D depends negative exponentially on the activation energy EA and the reciprocal of the temperature T.

Now if one uses the last equation in the antepenultimate equation, it can be seen that the ion flux is of T -dependent.

EA is the activation energy in electron volts. These considerations are the basis for the blacksche equation.

The temperature dependence of the black 's equation is known as activated or arrheniussches behavior. The activation energy EA indicates significantly, which is the main cause of failure. These findings are now back in the design process to the appropriate circuits, so that the reliability of the lines will be improved by changing the conductor geometry of the conductor cross section or thickness of the passivation layers. For subsequent generations of chips, these findings may also lead to the use of new, for the electromigration less susceptible material combinations.

Causes of failure

Diffusion mechanisms

A possible cause of failure is the diffusion of ions as a result of EM. This can be done by grain boundary diffusion, lattice diffusion and diffusion along heterogeneous interfaces or free surfaces.

Grain boundary diffusion

Due to the low activation energy of the grain boundary diffusion of one of the most important mechanisms of the above diffusion mechanisms. Mass flow through a homogeneous region as a result of EM takes place without the formation of " voids" or " hillocks ". The divergence of the ion flux, see equation is zero. However, inhomogeneities occur in the material, so the divergence of the ion flux is non-zero, and there are macroscopic defects. The proportion of the ion flux on the basis of EM at the grain boundaries will now be described by:

To this equation is the ratio of the effective grain boundary width δ for mass transport to the average grain size d The ratio also results from the area of all grain boundaries, and the total area of the conductor. A crucial role for differences in ion flux are points where three grain boundaries are to each other, see figure to the right.

Since the mass flow along grain boundaries in such a " triple point " is equal to the mass flow from the frontier zone out occurs divergence. Therefore, arise " voids" and " hillocks " preferred at such boundaries. In the figure on the right is removed for the angle of and material and attached to material.

Attempts to counteract this effect by placing the grain structures at the metal deposition and the annealing in the magnitude of the track width. This so-called " bamboo structure " minimizes the effect of the grain boundary diffusion - in the bamboo structures outweighs the lattice diffusion. During the grain boundary diffusion advances miniaturization increasingly so in the background. Results of Black show that nearly doubled the activation energy in traces, where the grain sizes are about half as large as the wire widths in comparison to finely crystalline traces. Here, the process for metal deposition has remained the same.

Lattice diffusion

The activation energy for EM within the metal lattice is very high. This is firstly due to the high binding energy of the atoms in the lattice, on the other hand by the lack of defects.

A significant impact in this case has the crystallographic orientation of the atoms in the lattice: EM lifetime of (111) from a chemical vapor deposition ( Sheet Chemical Vapour Deposition, CVD ) discrete copper is 4-fold greater than that of the (200) CVD copper.

Diffusion along heterogeneous interfaces

Because of voids between the metal and passivation layer or barrier, and dangling bonds of the metal atoms, it is to interface diffusion. This is due to poor adhesion of the two layers together. The activation energy is, therefore, dependent on the materials conductor and passivation or barrier. Voids at the interface favor mass transport and dangling bonds of the metal atoms to reduce the activation energy.

Surface diffusion

A major difference was found between passivated and unpassivated interconnects. The activation energy has risen by almost 50 %, after you had the großkristalligen strip conductors provided with a silicon oxide passivation. The passivated surface diffusion is suppressed.

Is the average velocity of the atoms on the surface, caused by a constant electric force F

Where Ds is the surface diffusion coefficient. The mass transport at the surface consists mainly of diffusion and electromigration. The proportion, the adsorption and desorption yields is negligible.

Surface diffusion depends on the orientation of the atoms in the crystal. The activation energy is in a (111) orientation is substantially less than in a (001 ) or ( 011).

Deff Effective diffusion coefficient is derived from the sum of the individual constants of the four diffusion mechanisms.

The indices G, K, I and O stand for lattice, grain boundary, interface and surface diffusion.

Thermal effects

Joule self heating

The high current density causes self Joule heating which causes a temperature increase in the test patterns. Such an increase in temperature makes the interpretation of the data difficult, since it leads to a displacement of the predetermined conditions.

The mass transport is caused not only by EM, but also by thermal migration, which further accelerates this. Reason for the self- heating is caused by the power dissipation P = I2 · R. It was = 1.106 A/cm2 reported increases of 5-10 ° C for single lines at J. Particularly strong utilizes the Joule self- heating noticeable when several parallel lines are tested side by side. In such arrangements, temperature increases can occur up to 200 ° C, the pipes have to be measured individually.

In the following, the physical relations of the self heating are described: The metal temperature is given by

In this equation, Tm is the temperature of the metal, Tref is the reference temperature of a chip and the temperature rise which is caused by the current flow. Under thermal steady-state conditions, the temperature is described by self- heating by the following equation

This Ieff the effective value of the current conductor resistance R, T is the period, and the thermal impedance between conductor and substrate. In addition, it is assumed that the current frequency is much greater than the inverse of the thermal time constant. This in turn means that the metal temperature hardly fluctuates.

Thermal stresses

Another cause of failure may be the occurrence of mechanical stresses due to thermal mismatch between metallic conductors and the substrate surface. This phenomenon is also called " stress- migration" or " stress- voiding ". Stress migration is directly related to the EM.