On the MOSFET Threshold Voltage Extraction by Transconductance and Transconductance-to-Current Ratio Change Methods: Part I—Effect of Gate-Voltage-Dependent Mobility

This paper presents a study of the effect of the gate-voltage-dependent mobility on the threshold voltage extraction in long-channel MOSFETs by the transconductance change method and recently proposed transconductance-to-current ratio change method, using analytical modeling and experimental data obtained on advanced silicon-on-insulator (SOI) FinFETs and ultrathin-body SOI MOSFETs with ultrathin high- gate dielectrics. It is shown that, at vanishingly small drain voltage and constant mobility, both methods yield the same values, coinciding with the position of the maximum of the second derivative of the inversion carrier density in respect to the gate voltage. However, such is not the case anymore when considering gate-voltage dependence of mobility around threshold. Analytical expressions for the errors in the values obtained by both methods due to mobility variation around threshold are obtained. Based on analytical modeling and experimental data, it is demonstrated that, for the same mobility variation, the resulting error on the extraction caused by the gate-voltage-dependent mobility is much smaller for the transconductance-to-current ratio change method than for the transconductance change method.