The Resistivity Size Effect in Epitaxial Nb(001) and Nb(011) Layers

• Published in: IEEE transactions on electron devices Vol. 66; no. 8; pp. 3473 - 3478
• Main Authors: Milosevic, Erik, Kerdsongpanya, Sit, McGahay, Mary E., Wang, Baiwei, Gall, Daniel
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Alternative metals; back end of line (BEOL); Conductivity; Electrical resistivity; Epitaxial growth; interconnects; Lower bounds; mean free path; middle of line (MOL); niobium; Oxidation resistance; Predictions; resistivity scaling; Rough surfaces; Roughening; Sapphire; Scattering; Size effects; Substrates; Surface resistance; Surface roughness; surface scattering; Temperature measurement; Thickness
• ISSN: 0018-9383; 1557-9646
• DOI: 10.1109/TED.2019.2924312

Epitaxial Nb(011) and Nb(001) layers are sputter deposited onto <inline-formula> <tex-math notation="LaTeX">{a} </tex-math></inline-formula>-plane and <inline-formula> <tex-math notation="LaTeX">{r} </tex-math></inline-formula>-plane sapphire substrates, respectively, and their resistivity <inline-formula> <tex-math notation="LaTeX">\rho </tex-math></inline-formula> measured in situ , ex situ , and at 77 K as a function of layer thickness <inline-formula> <tex-math notation="LaTeX">{d}= 4 </tex-math></inline-formula>-400 nm. The resistivity increase with decreasing <inline-formula> <tex-math notation="LaTeX">{d} </tex-math></inline-formula> is independent of layer orientation and is described with the model by Fuchs and Sondheimer (FS), providing a value for the bulk electron mean free path <inline-formula> <tex-math notation="LaTeX">\lambda = {20} \pm {2} </tex-math></inline-formula> nm at room temperature. Exposure to air causes a 1.5-nm-thick surface oxide and an increase in <inline-formula> <tex-math notation="LaTeX">\rho </tex-math></inline-formula> by up to 74%, suggesting a decrease in the surface scattering specularity from <inline-formula> <tex-math notation="LaTeX">{p}_{{{1}}}= {0.9} \pm {0.1} </tex-math></inline-formula> at the Nb-vacuum interface to completely diffuse scattering (<inline-formula> <tex-math notation="LaTeX">{p}_{{{1}}}= {0} </tex-math></inline-formula>) at the oxidized Nb surface. Alternatively, this increase in resistance can be attributed to roughening during surface oxidation while retaining completely diffuse scattering, yielding a lower bound for the room-temperature <inline-formula> <tex-math notation="LaTeX">\lambda </tex-math></inline-formula> of 9.0±0.4 nm. The product of the bulk resistivity <inline-formula> <tex-math notation="LaTeX">\rho _{o} </tex-math></inline-formula> times <inline-formula> <tex-math notation="LaTeX">\lambda </tex-math></inline-formula> is temperature-independent and, depending on either choosing the roughness or the specularity interpretation, <inline-formula> <tex-math notation="LaTeX">\rho _{o}\,\,\lambda = {14}\times {10}^{{-{16}}} </tex-math></inline-formula> or <inline-formula> <tex-math notation="LaTeX">{30} \times {10}^{{-{16}}}\,\,\Omega \text{m}^{{{2}}} </tex-math></inline-formula>, respectively. These values are 3.9 and 8.5 times larger than <inline-formula> <tex-math notation="LaTeX">\rho _{o}~\lambda </tex-math></inline-formula> from a previous theoretical prediction, indicating a dramatic break down of the classical FS model for Nb and indicating that the resistivity size effect in Nb is considerably larger than predicted earlier. They are also larger than for W, Ru, and Co, making Nb not promising for high-conductivity narrow interconnect lines.