Electromigration

thumb|Electromigration (red arrow) is due to the momentum transfer from the electrons moving in a wire

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 (ICs) decreases, the practical significance of this effect increases.

History

The phenomenon of electromigration has been known for over 100 years, having been discovered by obscure French scientist under the name of 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

Top visualization of electromigration under scanning electron microscope of a nanoconstriction (60 nm width) on silicon oxide substrate.|thumb

thumb|right|[[scanning electron microscope|SEM image of a failure caused by electromigration in a copper interconnect. The passivation has been removed by reactive ion etching and hydrofluoric acid.]]

Electromigration decreases the reliability of integrated circuits (ICs). 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 (ICs) 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 (HTOL) testing. The component's expected life span under real conditions is extrapolated from data gathered during this testing. 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.

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 (EM) continues to be an ever-present challenge to device fabrication, and therefore the EM research for copper interconnects is ongoing (though a relatively new field).

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 (open circuit). 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 (short circuit). 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(111) 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 <math> N </math> 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(110) 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. (2020) demonstrated that electromigration-induced step bunching is not limited to silicon surfaces but can also occur on dielectric surfaces, such as sapphire (Al₂O₃(0001)). This study suggests that the fundamental mechanism of step bunching on W(110), Al₂O₃(0001), and Si(111) follows similar principles. Moreover, annealing W(110) offcut in the [001] 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.

:<math>\text{MTTF} = \frac{A}{J^n} \exp{\left(\frac{E_\text{a{k T}\right)}</math>.

Here <math>A</math> is a constant based on the cross-sectional area of the interconnect, <math>J</math> is the current density, <math>E_\text{a}</math> is the activation energy (e.g. 0.7 eV for grain boundary diffusion in aluminum), <math>k</math> is the Boltzmann constant, <math>T</math> is the temperature in kelvins, and <math>n</math> a scaling factor (usually set to 2 according to Black).

Pure copper wires can withstand approximately five times more current density than aluminum wires while maintaining similar reliability requirements. This is mainly due to the higher electromigration activation energy levels of copper, caused by its superior electrical and thermal conductivity as well as its higher melting point. Further improvements can be achieved by alloying copper with about 1% palladium which inhibits diffusion of copper atoms along grain boundaries in the same way as the addition of copper to aluminium interconnect.

Bamboo structure and metal slotting

A wider wire results in smaller current density and, hence, less likelihood of electromigration. Also, the metal grain size has influence; the smaller grains, the more grain boundaries and the higher likelihood of electromigration effects. However, if one reduces wire width to below the average grain size of the wire material, grain boundaries become "crosswise", more or less perpendicular to the length of the wire. The resulting structure resembles the joints in a stalk of bamboo. With such a structure, the resistance to electromigration increases, despite an increase in current density. This apparent contradiction is caused by the perpendicular position of the grain boundaries; the boundary diffusion factor is excluded, and material transport is correspondingly reduced.

However, the maximum wire width possible for a bamboo structure is usually too narrow for signal lines of large-magnitude currents in analog circuits or for power supply lines. In these circumstances, slotted wires are often used, whereby rectangular holes are carved in the wires. Here, the widths of the individual metal structures in between the slots lie within the area of a bamboo structure, while the resulting total width of all the metal structures meets power requirements. which need to be solved for three-dimensional geometrical domains representing segments of an interconnect structure. Such a mathematical model forms the basis for simulation of electromigration in modern technology computer aided design (TCAD) tools. Use of TCAD tools for detailed investigations of electromigration induced interconnect degradation is gaining importance. Results of TCAD studies in combination with reliability tests lead to modification of design rules improving the interconnect resistance to electromigration.

Constraint programming

Constraint programming can be used to produce a layout of a chip's power grid while satisfying multiple requirements including predicted electromigration. Another of these constraints is IR drop noise, which is the load-dependent voltage drop caused by the wire's electrical resistance.

Prediction tools

A 2020 study describes a neural network-based supervised learning approach. Using current density, interconnect length, interconnect temperature as input, the machine learning model predicts the mean time to failure of the design due to EM.

Healing

In as early as the 1990s it was noted that electromigration failure takes much longer to develop under alternating current (AC) than under direct current (DC). This suggests that a backward current can induce metal ions to move in the backward direction and partially "heal" electromigration. Although it has been consistently shown that such "healing" is never complete, it does provide a large amount of recovery between 70% and 90% in the bidirectional pulse case. A 2016 work further shows the significant contribution of healing in the unidirectional case, suggesting that more aggressive power-saving methods that turn off parts of a chip (e.g. deeper C states) can also reduce electromigration. Further more, this passive healing is faster and more complete under a higher temperature. It is possible to prolong the lifespan of a wire by periodically subjecting it to a reverse current, but applying it for too long would also break the wire by causing too much electromigration in the other direction.

Electromigrated nanogaps

Electromigrated nanogaps are gaps formed in metallic bridges formed by the process of electromigration. A nanosized contact formed by electromigration acts like a waveguide for electrons. The nanocontact essentially acts like a one-dimensional wire with a conductance of <math>G = 2\,e^2\!/h</math>. The current in a wire is the velocity of the electrons multiplied by the charge and number per unit length, <math>\,I = veN/L\ </math> or <math>\ G=veN/LV</math>. This gives a conductance of <math>G=ve^2\!N/LE</math>. In nanoscale bridges the conductance falls in discrete steps of multiples of the quantum conductance <math>G = 2\,e^2\!/h</math>.

Electromigrated nanogaps have been proposed for use as electrodes in molecular scale electronics and as quantum tunneling sensors. Researchers have used feedback controlled electromigration to investigate the magnetoresistance of a quantum spin valve.

Reference standards

EIA/JEDEC Standard EIA/JESD61: Isothermal Electromigration Test Procedure.
EIA/JEDEC Standard EIA/JESD63: Standard method for calculating the electromigration model parameters for current density and temperature.
Fundamentals of electromigration, Chapter 2 In: Fundamentals of Electromigration-Aware Integrated Circuit Design, Springer (2025)

References

External links

[http://www.csl.mete.metu.edu.tr/Electromigration/emig.htm] What is Electromigration?, Computer Simulation Laboratory, Middle East Technical University.
[http://www.eetimes.com/design/eda-design/4017969/Electromigration-for-Designers-An-Introduction-for-the-Non-Specialist] Electromigration for Designers: An Introduction for the Non-Specialist, J.R. Lloyd, EETimes.
Semiconductor electromigration in-depth at DWPG.Com
Modeling of electromigration process with void formation at UniPro R&D site
DoITPoMS Teaching and Learning Package- "Electromigration"