Subthreshold slope

The subthreshold slope is a feature of a MOSFET's current–voltage characteristic.

In the subthreshold region, the drain current behaviour—though being controlled by the gate terminal—is similar to the exponentially decreasing current of a forward biased diode. Therefore, a plot of drain current versus gate voltage with drain, source, and bulk voltages fixed will exhibit approximately log-linear behaviour in this MOSFET operating regime. Its slope is the subthreshold slope.

The subthreshold slope is also the reciprocal value of the subthreshold swing S_s-th which is usually given as:^[1]

${\displaystyle S_{s-th}=\ln(10){kT \over q}\left(1+{C_{d} \over C_{ox}}\right)}$

${\displaystyle C_{d}}$ = depletion layer capacitance

${\displaystyle C_{ox}}$ = gate-oxide capacitance

${\displaystyle {kT \over q}}$ = thermal voltage

The minimum subthreshold swing of a conventional device can be found by letting ${\displaystyle \textstyle {C_{d}}\rightarrow 0}$ and/or ${\displaystyle \textstyle {C_{ox}}\rightarrow \infty }$, which yield ${\displaystyle S_{s-th,\min }=\ln(10){kT \over q}}$(known as thermionic limit) and 60 mV/dec at room temperature (300 K). A typical experimental subthreshold swing for a scaled MOSFET at room temperature is ~70 mV/dec, slightly degraded due to short-channel MOSFET parasitics.^[2]

A dec (decade) corresponds to a 10 times increase of the drain current I_D.

A device characterized by steep subthreshold slope exhibits a faster transition between off (low current) and on (high current) states.

References

1. Physics of Semiconductor Devices, S. M. Sze. New York: Wiley, 3rd ed., with Kwok K. Ng, 2007, chapter 6.2.4, p. 315, ISBN 978-0-471-14323-9.
2. Auth, C.; Allen, C.; Blattner, A.; Bergstrom, D.; Brazier, M.; Bost, M.; Buehler, M.; Chikarmane, V.; Ghani, T.; Glassman, T.; Grover, R.; Han, W.; Hanken, D.; Hattendorf, M.; Hentges, P.; Heussner, R.; Hicks, J.; Ingerly, D.; Jain, P.; Jaloviar, S.; James, R.; Jones, D.; Jopling, J.; Joshi, S.; Kenyon, C.; Liu, H.; McFadden, R.; McIntyre, B.; Neirynck, J.; Parker, C. (2012). "A 22nm high performance and low-power CMOS technology featuring fully-depleted tri-gate transistors, self-aligned contacts and high density MIM capacitors". 2012 Symposium on VLSI Technology (VLSIT). p. 131. doi:10.1109/VLSIT.2012.6242496. ISBN 978-1-4673-0847-2. S2CID 23675687.

External links

• Optimization of Ultra-Low-Power CMOS Transistors; Michael Stockinger, 2000