Random telegraph noise (RTN) has attracted much attention, as it becomes higher for smaller devices. Early works focused on RTN in linear drain current, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}_{\textit{D},\text{LIN}}$</tex-math> </inline-formula> , and there is only limited information on RTN in saturation current, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}_{\textit{D},\text{SAT}}$</tex-math> </inline-formula> . As transistors can operate in either linear or saturation modes, lack of RTN model in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}_{\textit{D},\text{SAT}}$</tex-math> </inline-formula> prevents modeling RTN for real circuit operation. Moreover, circuit simulation requires both driving current and 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">$\textit{V}_{\text{TH}}$</tex-math> </inline-formula> . A common practice of early works is to evaluate the RTN in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{V}_{\text{TH}}$</tex-math> </inline-formula> by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \textit{V}_{\text{TH}}= \Delta \textit{I}_{\textit{D},\text{LIN}}$</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">$\textit{g}_{\textit{m}}$</tex-math> </inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{g}_{\textit{m}}$</tex-math> </inline-formula> is the transconductance. It has been reported that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \textit{V}_{\text{TH}}$</tex-math> </inline-formula> evaluated in this way significantly overestimates the real <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \textit{V}_{\text{TH}}$</tex-math> </inline-formula> , but there is little data for establishing the cumulative distribution function (CDF) of the real <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \textit{V}_{\text{TH}}$</tex-math> </inline-formula> . An open question is whether <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \textit{V}_{\text{TH}}$</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">$\Delta \textit{I}_{\textit{D},\text{LIN}}$</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">$\textit{I}_{\textit{D},\text{LIN}}$</tex-math> </inline-formula> follow the same CDF. The objectives of this work are threefold: to provide statistical test data for RTN in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}_{\textit{D},\text{SAT}}$</tex-math> </inline-formula> ; to measure the RTN in real <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \textit{V}_{\text{TH}}$</tex-math> </inline-formula> by pulse <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}_{\textit{D}}$</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">$\textit{V}_{\textit{G}}$</tex-math> </inline-formula> ; and, for the first time, to apply the integral methodology for developing the CDF per trap for all four key parameters needed by circuit simulation— <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \textit{I}_{\textit{D},\text{LIN}}$</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">$\textit{I}_{\textit{D},\text{LIN}}$</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">$\Delta \textit{I}_{\textit{D},\text{SAT}}$</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">$\textit{I}_{\textit{D},\text{SAT}}$</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">$\Delta \textit{V}_{\text{TH,\text{LIN}}}$</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">$\Delta \textit{V}_{\text{TH,\text{SAT}}}$</tex-math> </inline-formula> . It is found that the log-normal CDF is the best for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \textit{I}_{\textit{D},\text{LIN}}$</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">$\textit{I}_{\textit{D},\text{LIN}}$</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">$\Delta \textit{I}_{\textit{D},\text{SAT}}$</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">$\textit{I}_{\textit{D},\text{SAT}}$</tex-math> </inline-formula> , while the general extreme value CDF is the best for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \textit{V}_{\text{TH,\text{LIN}}}$</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">$\Delta \textit{V}_{\text{TH,\text{SAT}}}$</tex-math> </inline-formula> . Both <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \textit{I}_{\textit{D},\text{SAT}}$</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">$\textit{I}_{\textit{D},\text{SAT}}$</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">$\Delta \textit{V}_{\text{TH,\text{SAT}}}$</tex-math> </inline-formula> are higher than their linear counterparts and separate modeling is required. Finally, the applicability of integral methodology in predicting the long term <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \textit{I}_{\textit{D},\text{LIN}}$</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">$\textit{I}_{\textit{D},\text{LIN}}$</tex-math> </inline-formula> is demonstrated.
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