# Qustion about subthreshold voltage and driving capability

Recently,i read some paper,and some of paper said :

To reduce the power consumption of VLSI,Supply voltage has decreased to the subthreshold voltage,and the subthreshold circuits consume a very low power,but suffer from the speed degradation due to the low current-driving capability of transistors,and a low-threshold voltage transistor and a large size transistor can improve the driving capability.

My question is :

1.What is subthreshold voltage? i know the threshold voltage,are they the same?

2.What is subthreshold circuit?Can anyone give me an example?

3.Why can the low-threshold voltage transistor and a large size transistor improve the driving capability? especially the large size,can it know from some formula?

• I notice that you have asked 20 questions and received what looks like reasonable answers to several of them. You can (should is too strong a word) formally accept answers that appear to be the most useful to you. You can only formally accept one answer for one question so choose with care. – Andy aka Feb 1 '18 at 14:26
• Did you hear already about "translinear circuits" - invented by Barrie Gilbert? They work - as far as FETs are concerned - below the threshold voltages. – LvW Feb 1 '18 at 14:28
• @LvW You mean the translinear circuit is like the subthreshold circuit? – Shine Sun Feb 1 '18 at 14:31
• @LvW, they work in subthreshold because Barrie chooses to bias the transistors that way so that they have an exponential Id(Vgs) relation. Translinear circuits can also work in strong inversion mode but then Id(Vgs) has the familiar quadratic relation. – Bimpelrekkie Feb 1 '18 at 14:37
• Bimpelrekkie, yes I know. To work in this region it needs a corresponding biasing. That is obvious. – LvW Feb 1 '18 at 15:10

1) Have you read this article Wikipedia? Subthreshold region means using the MOSFET in weak inversion (as opposed to strong inversion as you'd normally use) by using a $V_{gs}$ slightly less than the value of the MOSFET's threshold voltage $V_t$.

Normally we say that a MOSFET will not conduct when $V_{gs} < V_t$ but that's not entirely true, it does conduct but only very small currents (compared to the currents when $V_{gs} > V_t$) can flow.

So yes, subthreshold is related to the MOSFET's threshold voltage

2) The circuits are often the same as we're used to but running at much less current. So for example an NMOS of W/L = 10um/1um with an Ids = 100 nA would be close to working in subthreshold or weak inversion. You could also use a more "normal current" like 10 uA flowing through a very wide MOSFET (like W = 1000um) which would then also be working in subthreshold or weak inversion mode.

It is the current density (Width of MOSFET / current through drain: W / Id) that actually matters. A low current density results in a low $V_{gs}$ value.

3) Yes a larger transistor (more precise: a wider transistor) can of course carry more current. But that making the transistor wider increases the gate capacitance so it will also require more current to drive it.

Regarding the formulas for subthreshold region: consult almost any book about CMOS circuit design.

In general subthreshold circuits are only needed when you need extremely low power consumption (a few uA or less) and you do not need a fast circuit. 1 MHz might already be quite fast for a subthreshold circuit.

In practice, in 25 years of designing CMOS circuits I have never deliberately designed a circuit to work in subthreshold. I did design very low power circuits and they might actually have transistors in them working in subthreshold or close to that. But when designing circuits I just make the currents how I want them and I do not bother with transistors being in subthreshold or not.

• sorry,but according to the formula in cutoff region:$I_d=I_{d0} e^{\frac{V_{gs}-V_{th}}{nV_T}}$,so if i want the high current density,the $V_{gs}-V_{th}$ value should be bigger,so the $V_{gs}$ should be higher,isn't it right? – Shine Sun Feb 2 '18 at 2:10
• I wrote: A low current density results in a low Vgs value. so then obviously for a higher current density you need a higher Vgs. – Bimpelrekkie Feb 2 '18 at 7:07
• sorry,my bad.and about the answer of 1 you said ,so the subthreshold voltage is actually the threshold voltage when the mos is in the cutoff region? – Shine Sun Feb 2 '18 at 7:10
• No, the threshold voltage is the threshold voltage, it does not change. There is no "subthreshold voltage". There is a subthreshold region, which has to do with the value of Vgs. You should read my answer more carefully, the information is there. – Bimpelrekkie Feb 2 '18 at 7:39

In the subthreshold region of MOSFETs, the gate to source voltage $V_{GS}$ controls the Drain to Source current $I_{DS}$ and is similar to the exponentially increasing current of a forward biased diode.

Just as in all diodes the capacitance reduces with reverse bias voltage and increases with conductance, MOSFETs also share this behavior when used (over threshold) as power switches. The size of chip and the gate charge increases as RdsOn reduces, so one Figure of Merit is the product Ciss*RdsOn. They are not on the datasheet since other factors like geometry, voltage rating affect this product in the choice of "a million" different MOSFETs.

Sub-threshold effects are used for many other applications but pertaining to this question there is a dynamic relationship between leakage current and capacitance. Ref on slope

As power switches, the Vgs threshold (Vgs(th) is at some rated curent like 0.5 mA was typically 4V with a wide margin and then the need for lower Vgs and lower RdsOn altered the geometry and construction of the FET length to width ratio to change the thresholds lower. Low Vgs(th) <1V are suitable for 3.3V logic level drive.

Still you need Vgs to go past Vgs(th) by 2.5~3x 250~300% to give a good low RdsOn rating. Since RC=T affects slew rate this affects the SMPS design speed on component selection. There is both a junction charge from gate to drain and gate to source.

One day I analyzed Digikey's TO-220 NFETs for RdsOn vs Q and this was the result. Recall Q = CV. I found the spreadsheet now , if anyone wants it.

Be careful with subthreshold circuits. You can badly degrade the jitter (phase noise) of logic signals, or XTAL oscillator output signals, using subthreshold designs. The slow edges, and the higher noise compared to squarelaw region, will cause problems.