Electromigration

Electromigration is the transport of material caused by the gradual movement of the ions in a conductor due to the momentum transfer between conducting electrons and diffusing metal atoms. The effect is important in applications where high direct current densities are used, such as in microelectronics and related structures. As the structure size in electronics such as integrated circuits decreases, the practical significance of this effect increases.

History

The phenomenon of electromigration has been known for over 100 years, having been discovered by the French scientist Gerardin. The topic first became of practical interest during the late 1960s when packaged ICs first appeared. The earliest commercially available ICs failed in a mere three weeks of use from runaway electromigration, which led to a major industry effort to correct this problem. The first observation of electromigration in thin films was made by I. Blech. Research in this field was pioneered by a number of investigators throughout the fledgling semiconductor industry. One of the most important engineering studies was performed by Jim Black of Motorola, after whom Black's equation is named. At the time, the metal interconnects in ICs were still about 10 micrometres wide. Currently interconnects are only hundreds to tens of nanometers in width, making research in electromigration increasingly important.

Practical implications of electromigration

Electromigration decreases the reliability of integrated circuits. It can cause the eventual loss of connections or failure of a circuit. Reliability is critically important for space travel, military purposes, anti-lock braking systems, medical equipment like automated external defibrillators, and is even important for personal computers or home entertainment systems, so the reliability of chips is a major focus of research efforts.
Due to the difficulty of testing under real-world conditions, Black's equation is used to predict the life span of integrated circuits. To use Black's equation, the component is put through high-temperature operating life testing. The component's expected life span under real conditions is extrapolated from data gathered during this testing.
Although damage from electromigration ultimately results in the failure of the affected IC, the first symptoms are intermittent glitches, which are quite challenging to diagnose. As some interconnects fail before others, the circuit exhibits seemingly random errors, which may be indistinguishable from other failure mechanisms. In a laboratory setting, electromigration failure is readily imaged with an electron microscope, as interconnect erosion leaves telltale visual markers on the metal layers of the IC.
With increasing miniaturization, the probability of failure due to electromigration increases in VLSI and ULSI circuits because both the power density and the current density increase. Specifically, line widths will continue to decrease over time, as will wire cross-sectional areas. Currents are also reduced due to lower supply voltages and shrinking gate capacitances. However, as current reduction is constrained by increasing frequencies, the more marked decrease in cross-sectional areas will give rise to increased current densities in ICs going forward.
In advanced semiconductor manufacturing processes, copper has replaced aluminium as the interconnect material of choice. Despite its greater fragility in the fabrication process, copper is preferred for its superior conductivity. It is also intrinsically less susceptible to electromigration. However, electromigration continues to be an ever-present challenge to device fabrication, and therefore the EM research for copper interconnects is ongoing.
In modern consumer electronic devices, ICs rarely fail due to electromigration effects. This is because proper semiconductor design practices incorporate the effects of electromigration into the IC's layout. Nearly all IC design houses use automated EDA tools to check and correct electromigration problems at the transistor layout-level. When operated within the manufacturer's specified temperature and voltage range, a properly designed IC device is more likely to fail from other causes, such as cumulative damage from gamma-ray bombardment.
Nevertheless, there have been documented cases of product failures due to electromigration. In the late 1980s, one line of Western Digital's desktop drives suffered widespread, predictable failure after 12–18 months of field usage. Using forensic analysis of the returned bad units, engineers identified improper design-rules in a third-party supplier's IC controller. By replacing the bad component with that of a different supplier, WD corrected the flaw, but not before significant damage was done to the company's reputation.
Electromigration can be a cause of degradation in some power semiconductor devices such as low voltage power MOSFETs, in which the lateral current through the source contact metallisation can reach the critical current densities during overload conditions. The degradation of the aluminium layer causes an increase in on-state resistance, and can eventually lead to complete failure.

Fundamentals

The material properties of the metal interconnects have a strong influence on their life span. The characteristics are predominantly the composition of the metal alloy and the dimensions of the conductor. The shape of the conductor, the crystallographic orientation of the grains in the metal, procedures for the layer deposition, heat treatment or annealing, characteristics of the passivation, and the interface to other materials also affect the durability of the interconnects. There are also important differences with time dependent current: direct current or different alternating current waveforms cause different effects.

Forces on ions in an electrical field

Two forces affect ionized atoms in a conductor: 1) The direct electrostatic force F_e, as a result of the electric field, which has the same direction as the electric field, and 2) The force from the exchange of momentum with other charge carriers F_p, toward the flow of charge carriers, is in the opposite direction of the electric field. In metallic conductors F_p is caused by a so-called "electron wind" or "ion wind".
The resulting force F_res on an activated ion in the electrical field can be written as
where is the electric charge of the ions, and the valences corresponding to the electrostatic and wind force respectively, the so-called effective valence of the material, the current density, and the resistivity of the material.
Electromigration occurs when some of the momentum of a moving electron is transferred to a nearby activated ion. This causes the ion to move from its original position. Over time this force knocks a significant number of atoms far from their original positions. A break or gap can develop in the conducting material, preventing the flow of electricity. In narrow interconnect conductors, such as those linking transistors and other components in integrated circuits, this is known as a void or internal ''failure''. Electromigration can also cause the atoms of a conductor to pile up and drift toward other nearby conductors, creating an unintended electrical connection known as a hillock failure or whisker failure. Both of these situations can lead to a malfunction of the circuit.

Step bunching due to electromigration

Step bunching is a phenomenon in which a smooth surface forms 3D shapes that look like stair steps. Step bunching on DC-heated sublimating vicinal crystal surfaces of Si was observed by A. Latyshev et al. in 1989. Soon after, Stoyan Stoyanov advanced a model in which as the reason for step bunching is identified the biased diffusion of the adatoms. In 1998, Stoyanov and Tonchev extended Stoyanov's model by incorporating step-step repulsions and derived a scaling relation for the minimal step-step distance in a bunch under diffusion-limited sublimation, non-transparent steps, and step-down current conditions:
where is the number of steps in the bunch, and the proportionality coefficient has the dimension of length. This scaling law has been confirmed by numerous experimental studies. In 2018, Toktarbaiuly et al. reported electromigration-induced step bunching on vicinal W surfaces. Their study revealed that step bunching occurred for both step-up and step-down current directions at the same temperature, T = 1500°C, with distinct size-scaling exponents depending on the current direction.
More recently, Usov et al. demonstrated that electromigration-induced step bunching is not limited to silicon surfaces but can also occur on dielectric surfaces, such as sapphire. This study suggests that the fundamental mechanism of step bunching on W, Al₂O₃, and Si follows similar principles. Moreover, annealing W offcut in the direction with an up-step current produced a morphology where the bunch edges formed zigzag segments meeting at right angles.

Failure mechanisms

Diffusion mechanisms

In a homogeneous crystalline structure, because of the uniform lattice structure of the metal ions, there is hardly any momentum transfer between the conduction electrons and the metal ions. However, this symmetry does not exist at the grain boundaries and material interfaces, and so here momentum is transferred much more vigorously. Since the metal ions in these regions are bonded more weakly than in a regular crystal lattice, once the electron wind has reached a certain strength, atoms become separated from the grain boundaries and are transported in the direction of the current. This direction is also influenced by the grain boundary itself, because atoms tend to move along grain boundaries.
Diffusion processes caused by electromigration can be divided into grain boundary diffusion, bulk diffusion, and surface diffusion. In general, grain boundary diffusion is the major electromigration process in aluminum wires, whereas surface diffusion is dominant in copper interconnects.