Stability Constraints Define the Minimum Subthreshold Swing of a Negative Capacitance Field-Effect Transistor

Abstract

The current-voltage characteristics of a classical field-effect transistor (FET) is dictated by thermal injection of charge carriers over a gate-controlled energy barrier. It is well known that the subthreshold swing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\((S)\) </tex-math></inline-formula> associated with these transistors cannot be reduced below the Boltzmann limit of 60 mV/decade, which in turn defines the lower limit of power dissipation. Therefore, a number of groups have recently proposed to use negative capacitance (NC) gate insulators in FETs to reduce <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(S\) </tex-math></inline-formula> below the Boltzmann limit. The ferroelectric-FET (FE-FET) and suspended-gate FET (SG-FET) are two examples. It is now well accepted that NC-FETs can lower <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(S\) </tex-math></inline-formula> , but given a specific device architecture, the question of whether there is a lower limit of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(S\) </tex-math></inline-formula> (and if so, the conditions that define the limit) has not been answered. In this paper, we: 1) demonstrate that the fundamental constraints of stability and hysteresis-free operation dictate that there is a lower limit of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(S\) </tex-math></inline-formula> associated with each NC-FET technology; 2) provide a general algorithm to calculate the minimum subthreshold swing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\((S_{\rm min})\) </tex-math></inline-formula> ; and 3) illustrate the concept using SG-FET and FE-FET for two different channel configurations, namely, a bulk FET and an FET with constant channel capacitance. Our results broaden the understanding of field-effect action in NC-FETs and should inform research on these devices.