A simulation technique for anisotropic size effect on electrical resistivity manifesting in single-crystalline metallic interconnects

December 24, 2024

It is well known that electrical resistivity in poly-crystalline metallic interconnects increases with downsizing their critical dimension^[1]. Additionally, an anisotropic property manifests itself by single-crystallization, where the increase of electrical resistivity due to downsizing depends on crystallographic orientation^[2]. We have successfully developed a numerical simulation technique to predict the anisotropic size effect on electrical resistivity in the single-crystalline nanoscale metallic interconnects^[3].

Figure 1 shows a schematic of our simulation method. Underlying mechanism of the anisotropic size effect is attributed to anisotropic property of Fermi velocity distribution^[2]. Therefore, we calculated the anisotropic Fermi velocity distribution by density functional theory and implemented it to our particle-based transport simulator for metallic materials. As a result, we have successfully reproduced an anisotropic size effect in electrical resistivity in bcc-W interconnects^[2] as shown in Figure 2.

In addition, it takes about 10 min to obtain electrical resistivity for a specified wire structure on a typical workstation, and our simulation method can be applicable for other metallic materials such as Cu. By utilizing our simulation program, we will investigate anisotropic size effect in electrical resistivity in other single-crystalline metallic materials.