Thermal migration (TM), sometimes referred to as thermomigration, is a phenomenon driven by temperature gradients within metal wires. In this process, high temperatures lead to increased atomic movement, as atoms in warmer regions gain energy and become more mobile.
As shown in the Figure, Atoms in hotter places are more likely to dislocate than those in colder areas because of this temperature-related activation. As a result, more atoms move from hotter regions to cooler ones, causing net diffusion or mass movement in the direction of the negative temperature gradient.
The primary reasons for the emergence of temperature gradients in metal wires are as follows:
Joule Heating
High electric currents passing through a wire can generate heat through Joule heating. This localized heating within the wire can create temperature variations.
External Heating
Nearby high-performance transistors or other heat sources can externally heat the wire, contributing to temperature gradients.
External Cooling
Conversely, external cooling mechanisms, such as through-silicon vias (TSV) connected to a heat sink, can cool the wire. This cooling effect can be significant when combined with low thermal conduction properties of the wire and its surrounding materials, especially in cases involving narrow wires embedded in thermally insulating dielectrics.
Interestingly, thermal migration also plays a role in thermal transport, as heat is coupled to the transported atoms. This means that thermal migration directly affects its own driving force, which is a departure from electromigration (EM), where the current density is influenced indirectly by increased resistance in certain scenarios.
In summary, thermal migration in metal wires is a consequence of temperature gradients induced by various factors, including current-induced heating, external sources of heat, and cooling mechanisms. Understanding and managing this phenomenon is essential in the design and reliability assessment of electronic circuits and devices.