Characterizing and Modeling RTN Under Real Circuit Bias Conditions

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> <tex-math notation="LaTeX">${I}_{D,\text {LIN}}$ </tex-math></inline-formula>, and there is only limited information on RTN in saturation current, <inline-formula> <tex-math notation="LaTeX">${I}_{D,\text {SAT}}$ </tex-math></inline-formula>. As transistors can operate in either linear or saturation modes, lack of RTN model in <inline-formula> <tex-math notation="LaTeX">${I}_{D,\text {SAT}}$ </tex-math></inline-formula> prevents modeling RTN for real circuit operation. Moreover, circuit simulation requires both driving current and threshold voltage, <inline-formula> <tex-math notation="LaTeX">${V}_{\text {TH}}$ </tex-math></inline-formula>. A common practice of early works is to evaluate the RTN in <inline-formula> <tex-math notation="LaTeX">${V}_{\text {TH}}$ </tex-math></inline-formula> by <inline-formula> <tex-math notation="LaTeX">$\Delta {V}_{\text {TH}}= \Delta {I}_{D,\text {LIN}}/{g}_{m}$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">${g}_{m}$ </tex-math></inline-formula> is the transconductance. It has been reported that the <inline-formula> <tex-math notation="LaTeX">$\Delta {V}_{\text {TH}}$ </tex-math></inline-formula> evaluated in this way significantly overestimates the real <inline-formula> <tex-math notation="LaTeX">$\Delta {V}_{\text {TH}}$ </tex-math></inline-formula>, but there is little data for establishing the cumulative distribution function (CDF) of the real <inline-formula> <tex-math notation="LaTeX">$\Delta {V}_{\text {TH}}$ </tex-math></inline-formula>. An open question is whether <inline-formula> <tex-math notation="LaTeX">$\Delta {V}_{\text {TH}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\Delta {I}_{D,\text {LIN}}/{I}_{D,\text {LIN}}$ </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> <tex-math notation="LaTeX">${I}_{D,\text {SAT}}$ </tex-math></inline-formula>; to measure the RTN in real <inline-formula> <tex-math notation="LaTeX">$\Delta {V}_{\text {TH}}$ </tex-math></inline-formula> by pulse <inline-formula> <tex-math notation="LaTeX">${I}_{D}$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">${V}_{G}$ </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> <tex-math notation="LaTeX">$\Delta {I}_{D,\text {LIN}}/{I}_{D,\text {LIN}}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\Delta {I}_{D,\text {SAT}}/{I}_{D,\text {SAT}}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\Delta {V}_{\text {TH, LIN}}$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$\Delta {V}_{\text {TH, SAT}}$ </tex-math></inline-formula>. It is found that the log-normal CDF is the best for <inline-formula> <tex-math notation="LaTeX">$\Delta {I}_{D,\text {LIN}}/{I}_{D,\text {LIN}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\Delta {I}_{D,\text {SAT}}/{I}_{D,\text {SAT}}$ </tex-math></inline-formula>, while the general extreme value CDF is the best for <inline-formula> <tex-math notation="LaTeX">$\Delta {V}_{\text {TH, LIN}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\Delta {V}_{\text {TH, SAT}}$ </tex-math></inline-formula>. Both <inline-formula> <tex-math notation="LaTeX">$\Delta {I}_{D,\text {SAT}}/{I}_{D,\text {SAT}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\Delta {V}_{\text {TH, SAT}}$ </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> <tex-math notation="LaTeX">$\Delta {I}_{D,\text {LIN}}/{I}_{D,\text {LIN}}$ </tex-math></inline-formula> is demonstrated.