Multiring Circular Transmission Line Model for Ultralow Contact Resistivity Extraction

Abstract

Accurate determination of contact resistivities ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\rho_{c}}$ </tex-math></inline-formula> ) below <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1 \times 10^{-8}\Omega \cdot \text {cm}^{2}$ </tex-math></inline-formula> is challenging. Among the frequently applied transmission line models (TLMs), circular TLM (CTLM) has a simple process flow, while refined TLM (RTLM) has a high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{c}$ </tex-math></inline-formula> accuracy at the expense of a more complex fabrication. In this letter, we will present a novel model—multiring CTLM (MR-CTLM) , which combines the advantages of a simple process and a high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{c}$ </tex-math></inline-formula> extraction resolution. We fabricated ultralow- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{c}$ </tex-math></inline-formula> Ti/n-Si contacts and demonstrated the capability of MR-CTLM to extract the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{c}$ </tex-math></inline-formula> as low as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6.2 \times 10^{-9}~\Omega \cdot {\rm cm}^{2}$ </tex-math></inline-formula> with high precision.