Temperature-Dependent Threshold Voltage Extraction of FinFETs Using Noise Measurements

Abstract

In this article, a temperature-dependent threshold voltage extraction method based on noise measurement is proposed. This method induces a mathematical solution for acquiring channel temperatures ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> ) of transistors in the saturation region to extract threshold voltages. In order to gain accurate channel temperature, a small-signal equivalent circuit model was established to determine transconductance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$g_{m}$ </tex-math></inline-formula> ). Then, the extracted transconductance and measured noise power spectral density (NPSD) were used to obtain channel temperatures. On this basis, the temperature-dependent threshold voltage ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm {th}}$ </tex-math></inline-formula> ) was derived. To validate the reliability of this method, a four-Fin six-finger N-FinFET and a four-Fin eight-finger N-FinFET were fabricated using the 14-nm bulk FinFET technology. In this study, the scattering parameters were obtained from 0.2 to 40.2 GHz. Also, the NPSDs were measured from 1 to 500 Hz, while gate voltage and drain voltage were set as 0.3, 0.49, and 0.75 V. Besides, the transistor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{\mathrm {ds}}$ </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">$V_{\mathrm {ds}}$ </tex-math></inline-formula> characteristics was also investigated when drain–source bias voltage changed from 0.05 to 0.9 V. Compared with the measurement results, the calculation results of drain–source current model using temperature-dependent threshold voltage achieved higher accuracy. Also, the root mean square errors (RMSEs) were less than 0.60% for four-Fin six-finger N-FinFET and less than 0.51% for four-Fin eight-finger N-FinFET. Therefore, the proposed extraction method can be applied to accurately predict transistor temperature-dependent threshold voltage.