Electron Scattering at Surfaces and Grain Boundaries in Rh Layers

Abstract

The resistivity size effect in Rh is investigated by quantifying electron scattering at surfaces and grain boundaries in polycrystalline Rh layers with thickness <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${d} =9$ </tex-math></inline-formula> –261 nm. Sputter deposition on SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Si(001) at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}_{s} =20$ </tex-math></inline-formula> , 350, and 350 °C followed by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> stepwise annealing to 750 °C yields three series of 111-textured Rh layers with increasing average lateral grain sizes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${D}$ </tex-math></inline-formula> . Electron backscatter diffraction (EBSD) maps show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${D}$ </tex-math></inline-formula> for annealed layers increases with layer thickness from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${D} =89$ </tex-math></inline-formula> to 134 nm, matching the surface morphological lateral correlation length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${{\xi }}=86$ </tex-math></inline-formula> –154 nm measured by atomic force microscopy (AFM). <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">In situ</i> transport measurements yield resistivity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${{\rho }}$ </tex-math></inline-formula> versus <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${d}$ </tex-math></inline-formula> data, which are described with a combined Fuchs–Sondheimer (FS) and Mayadas–Shatzkes (MS) model and indicate a Rh electron mean free path <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${{\lambda }} =9.5$ </tex-math></inline-formula> unboldmath± 0.8 nm and a reflection coefficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R} =0.41$ </tex-math></inline-formula> unboldmath± 0.05 for grain boundaries characterized by a rotation about the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\langle 111\rangle $ </tex-math></inline-formula> axis. As-deposited layers have considerably smaller grains, leading to a threefold and sixfold increase in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${{\rho }}$ </tex-math></inline-formula> above the bulk value for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${d} =10$ </tex-math></inline-formula> nm and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}_{s} =350$ </tex-math></inline-formula> and 20 °C, respectively. The overall results indicate a conductance benefit of Rh versus Cu for narrow interconnect lines and reveal the importance of Rh processing to achieve a large (>10 nm) grain size, which is essential to realize the conductivity advantage.