# Why should the subthreshold swing value be small?

I am given to understand from the link below that a small value of subthreshold swing in MOSFETs implies that there is a better on-off current ratio. But, a small subthreshold swing would imply a large subthreshold slope and hence, at sub threshold values of Vgs, there'll be a larger value of current than for a smaller subthreshold slope. It should follow that the static power dissipation will be higher. Isn't this an undesired characteristic? Also, why is a better on-off current ratio desirable and how does one justify that a higher subthreshold swing value leads to an improved on-off current ratio?

The source of my information: http://www.iue.tuwien.ac.at/phd/stockinger/node13.html#e:sts

• "large subthreshold slope and hence, at sub threshold values of Vgs, there'll be a larger value of current than otherwise" <- Why? If a line has positive slope, and you go further left on the graph, the y-value goes down. If the slope increases, you go down even more. The y-value in this case would be current. – horta Sep 10 '17 at 16:30
• Old pacemakers use lots of subthreshold FETs. – analogsystemsrf Sep 10 '17 at 16:36
• My choice of words there was probably poor. I have edited the description to hopefully convey what I mean. I meant to say that for a higher value of subthreshold slope, the current changes more per unit change in Vgs. And this is exactly what we don't want because an ideal MOSFET has no variation of Id(=0) with respect to Vgs in the subthreshold region. I really hope I'm not making a silly, mathematical error. – Amogh Sep 11 '17 at 11:06
• @Amogh I guess it depends on what you mean by "ideal mosfet" but unless you mean some kind of not-real-at-all step function model, the current changes in the subthreshold region and has a minimum subthreshold swing around 60 V/dec at room temp. – Matt Sep 11 '17 at 12:59
• That should be 60 mV/dec – Matt Sep 11 '17 at 13:04

You want a very small subthreshold swing S, i.e. you want that for a decade variation in the drain current a very small Vgs variation is required.

In conventional (i.e. non tunnel-based) FETs, S has the lower limit set to 60mV/dec (at room temperature, 300 K), because it is a diffusion limited process. This is achieved with an infinite Cox (gate oxide) capacitance (i.e. never), or with a double-gate MOSFET.

This will result a large Ion/Ioff ratio.

You want an infinite (i.e. as large as possible) Ion/Ioff, because:

• Speed requirements (in logic) or current carrying capability (in power MOSFETs) determine the minimum Ion. The larger Ion/Ioff, the smaller the static power dissipation due to off-state leakage.

• DC level requirements. Consider an inverter: you can approximate it as a series of two resistors. One resistor will have a high value (because its MOSFET is in the Off state), the other will have a lower value (because its MOSFET is in the on state). The larger Ion/Ioff, the larger the ration between these two equivalent resistors, the better the output level.

• "You want a very small subthreshold swing S, i.e. you want that for a decade variation in the drain current a very small Vgs variation is required." Doesn't this indicate a deviation from the characteristics of the ideal MOSFET where there is 0 Id for Vgs<Vt? – Amogh Sep 11 '17 at 12:04
• You are seeing this phenomenon going from 0... up to Vth, and maybe this is the source of your confusion. Let's see on the opposite direction! At Vgs > Vth you want your MOSFET on. At, let's say, 300mV below Vth you would like that the drain current were as small as possible. If S is 300mV/dec (very bad mosfet), the current will be just 10 times smaller than that at Vgs=Vt. If S = 60mV/dec (best mosfet you can hope), the current will be just 1/10^5 the value at Vgs=Vt. The smaller S, the better the Off-state current. – next-hack Sep 11 '17 at 13:01
• Interesting! Shifting the reference puts everything in a different perspective! However, consider a nMOS transistor A with Id at Vgs = Vt as X nA and another MOS transistor B with Id at Vgs = Vt as X+x nA. To me, A is the better transistor. Now say B had a smaller subthreshold swing; would B still be considered the better transistor? – Amogh Sep 11 '17 at 15:45
• I'm confused: if at Vgs = Vt, the transistor B has a larger current and also a smaler subthreshold swing, of course it's better. Perhaps I'm missing something? – next-hack Sep 11 '17 at 16:40
• Let's talk about technology/process, and not the finished transistor. Let's fix the channel Width/Length aspect ratio (W/L=Z). There are processes that allows for high current but bad subthreshold slopes (given the same W/L). These would be very useful, say for power applications, or maybe RF. There are other that feature smaller currents but better swing. These might be useful for low power or digital or analog. What changes with the subthreshold swing is the Ion/Ioff ratio, once Vdd is defined. The question is: can you live with a small Ion/Ioff? Some applications can, other cannot. – next-hack Sep 11 '17 at 16:45

I am given to understand from the link below that a small value of subthreshold swing in MOSFETs implies that there is a better on-off current ratio.

Whether or not a better (smaller) subthreshold swing implies a better (higher) on-off current ratio is going to depend on your definition of off-state current. People publishing papers, trying to brag about their amazing on-off current ratio will take the off state current to be the smallest current they can ever measure from their device. In this case, the subthreshold swing does not affect the on-off current ratio.

Perhaps a more useful off state current would be at some value of $V_g$ where you will be operating the device. In this case, an improved subthreshold swing will reduce the current, assuming all other parameters remain constant.

But, a small subthreshold swing would imply a large subthreshold slope

Correct.

and hence, at sub threshold values of Vgs, there'll be a larger value of current than otherwise.

Incorrect. A higher subthreshold slope means there will be a smaller value of current, for all $V_g<V_T$ (until you reach the leakage floor) than otherwise, if all other parameters are constant.

Also, why is a better on-off current ratio desirable

A better on-off current ratio is desirable since, for a given required on-state current, your off-state leakage current will be reduced. In an IC with millions of transistors, every little bit of leakage current adds up and can become significant. This is one of the major limiting factors in modern processor power supply requirements.

and how does one justify that a higher subthreshold swing value leads to an improved on-off current ratio?

This again depends on your definiton of off-state current as outlined above. This is only true if you define off-state current to be at a particular value of $V_g$.