Ultra-low $p_{c}$ Extraction for Recessed and Non-Recessed Contacts: Generalized Transmission Line Model

A universal transmission line model (TLM) is developed to provide an accurate extraction of specific contact resistivity $\rho_{c}$ for both recessed and non-recessed contacts. This new model eliminates the need for the assumption that semiconductor sheet resistance under the contact $R_{shc}$ is equal to that $\mathrm{in}$ the contact gap region $R_{sh}$ which has been used for decades and expands the application of TLM-based methods for alloyed contacts for the first time. The model was verified experimentally by applying it to directly extract $\rho_{c}, R_{shc}$, and metal sheet resistance $R_{m}$ of alloyed p+-GeSn contact. The change of $R_{shc}$ due to alloying or recess-etching is well captured and ultra-low $\rho_{c}$ values of $1.0\times 10^{-9}\Omega-\mathrm{cm}^{2}$ are extracted. In contrast, conventional TLM-based methods lead to a large variation $\mathrm{in}\rho_{c}$ extraction and miscalculate $\rho_{c}$ by neglecting the deviation of $R_{shc}$ from $R_{sh}$.