$g_{m}/I_{\rm d}$ Method for Threshold Voltage Extraction Applicable in Advanced MOSFETs With Nonlinear Behavior Above Threshold

Abstract

A method is proposed for determining the threshold voltage in a MOSFET, based on the derivative of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gm</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> ratio with respect to the gate voltage, which theoretically originates from the unified charge-control model similar to the capacitance-derivative method. This yields threshold voltages significantly less affected by gate-voltage-dependent mobility and series resistance than linear-extrapolation techniques. Moreover, it is more physically adequate in the case of advanced MOSFETs with ultrathin dielectrics, thin SOI body, or double gate operation, featuring a gradual transition from the exponential to linear charge control. The robustness of the method is experimentally verified on FinFETs with different lengths.