A Novel Method to Extract Channel Mobility and Parasitic Resistance of 2-D Material MOSFETs

A novel technique, called Fermi-Dirac (FD)-function method, is proposed for extracting channel mobility (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu _{\text {CH}}$ </tex-math></inline-formula>) and parasitic resistance (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{P}$ </tex-math></inline-formula>) of 2-D material (2DM) MOSFETs. The functional form of this method is formalized using three (two) parameters for describing the gate bias-dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu _{\text {CH}}$ </tex-math></inline-formula> (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{P}$ </tex-math></inline-formula>) of a back gate (BG) and top gate (TG) 2-D MOSFET. The method is successfully demonstrated by uniquely extracting these parameters from an antimony (Sb) contacted MoS<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> BG-MOSFET experimental data. Also demonstrated our FD-function method on palladium (Pd) contacted WSe<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> top-gated BG-MOSFET experiments. The extraction accuracy is tested against experiment calibrated TCAD simulations with widely different <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu _{\text {CH}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{P}$ </tex-math></inline-formula>. These tests show <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu _{\text {CH}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{P}$ </tex-math></inline-formula> extraction errors within ±10% and ±8%, respectively. Thus, the proposed FD-function method is highly accurate enables fast extraction and can be easily incorporated in the routine industrial wafer acceptance testing (WAT).