The general expression for subthreshold slope (swing) is S= (d(log10Ids)/dVgs)-1. Or from the above plot, at very low Vgs, take the derivative of log values of Ids with respect to Vgs and then invert the resulted value. I do not know whether from author's permission or by some numerical software, you can extract the values of Ids in the log plot and then values of Vgs. After that at very low Vgs values, do the point to point derivative ( y2-y1/x2-x1) for few sample points and take the average. Slope will be inverse of the average. From the plot it is evident, the log plot itself is highly non-linear even at low Vgs. So any slope extracted here will be heavily dependent on gate bias voltage.

Sincerely,

Dr. Nabil Shovon Ashraf

Assistant Professor

Department of ECE

North South University

Dhaka, Bangladesh.

Adding to Dr. Nabil,

A very simple method is that you draw the best straight line fit the to smallest bias values where the subthreshold current is ruling. Extend this line for any number of current decades as you can. One decade is a 10 fold multiplier such as  1 picoampere and 10 picoamperes.  Read the corresponding voltage difference say dV. The required slope as per definition= dV/ the number of current decades.

Best wishes

Dear Dr. Nabil,

Is subthreshold slope equal to subthreshold swing? if no, so the above formula is for slope or swing?

-1 is power?

for low Vgs it seems that the plot is nearly linear , why you tell highly non-linear?

Dear Dr. Zekry,

the threshold voltage is -0.6 V that Log(Id) is 10^-15 (1fA) in this voltage ,

Is it true that I tell the subthreshold swing is the required increase in Vgs voltage for a factor of 10 increase in drain current? in the other hand the voltage difference to increase drain current from 10^-16 (A) to 10^-15 (A)

I plot Log(Id) vs Vgs for spread range, and calculate the slope of graph below threshold voltage (from -0.5V to -0.64V for one decade increase in Id current) with ruler tools that is showed in attached file, slope is -7.1 and Inv.slope is -0.141, which one is subthreshold swing? 

Subthreshold slope is the direct derivative of log of current with respect to gate voltage. Subthreshold swing is inverse of that. That is why you show the exponent -1 on the derivative. When I saw the plot, generally log plot of Id with respect to Vgs is nearly straight at low Vgs essentially defining the subthreshold region. Your plot of the device has a parabolic bend and at low Vgs the curve is not straight to define a constant subthreshold slope just like MOSFET. The way I told you to make a few slope calculations and then invert it to get swing should be OK but with a certain degree of deviation. I hope you understand both mine and Professor Dr. Zekry's responses. We both understand from our responses to guide you to at least calculate an accurate subthreshold swing. It is up to you to read carefully what our message and guideline are.

Sincerely,

Dr. Nabil Shovon Ashraf.

Actually I did not look into the plot upclose as the Vgs is negative signalling it is either JFET or depletion mode FET. In fact after looking into the plot, it became clear the two curves merge to linearity between Vgs = -1 V and Vgs = -1.3 V. So apply the procedure I outlined in my previous two responses and take the swing or inverse of swing (slope of the curve) at the closest vicinity of Vgs (i.e., -1 V and -1.2 V with may be three point-to-point derivative averaged). I am sorry for any loss of clarity if you felt from the previous responses as I did not look close whether Vgs values are positive or negative.

Sincerely,

Dr. Nabil Shovon Ashraf

Assistant Professor

Department of ECE

North South University

Dhaka, Bangladesh.

I came back again in case you did not figure out by this time what the subthreshold swing for your plot. As I have hinted in very last email of mine that the linear region is between -1 V and say -1.125 V. At these two Vgs values Id value is roughly 4.8x10^-12 A and 1.4 x 10^-11 A. log10(4.8x10^-12) = -11.319 and log10(1.4 x 10^-11)=-10.854. Then slope m = (-10.854+11.319)/(-1+1.125) = 3.72. Subthreshold swing is roughly 1/3.72 = 0.269 or 269 mV/decade. Check your actual answer. It should close to this value.                                                                                  

Sincerely,

Dr. Nabil Shovon Ashraf

Assistant Professor

Department of ECE

North South University

Dhaka, Bangladesh.

Dear Reza, your answer on my post is very correct. The correct inverse slope which is the incremental voltage change per decade is as per  your readings is -0.14 V per decade which is about 5.6Vt, with Vt the thermal voltage at room temperature.

Best wishes

Dear Dr. Nabil, thanks for your valuable responses.

I read all of your comments and tips, During this time I did the simulation again and export the data of Id-Vgs graph in csv format (excel).

Beacuse of the threshold voltage is -0.6V, I select two point less than that, to calculate the subthreshold slope. from the exported data I have these points value:

(Vgs1=-0.6   Id1=-1.28E-14 ) and (Vgs2=-0.55    Id2=-5.36E-15  ) and (Vgs3=-0.5  Id3=-2.12E-15 )  

so the slope is  m=(-14.67+14.27)/(-0.5+0.55)=-8 and Subthreshold swing is

125 mV/dec, Is it correct?

the authers of related paper told the TFETs due to their built-in tunneling barrier, show a SS below 60 mV/dec, but the simulation result is in conflict with it, How is the justify of this result?

Best Regards

Dear Dr. Zekry, thanks for your valuable responses.

Now it is clear that the SS is more than 100 mV/dec, but based on the introduction of the above IEEE paper that I have refferenced and as respects that the simulation result is for it,

the SS for TFET due to their built-in tunneling barrier is below 60 mV/dec, How is the justify of this result?

Best Regards

Dear Reza, what is the SS value given by the authors? What is the value of the threshold voltage? One has to be sure that the device works in the deep sub threshold region not in the mixed mode of operation between the weak inversion and strong inversion. Are these results experimental or simulated results? If they experimental it may be that the fabrication tolerances may reduce the tunneling effect.

Could you attach the paper?

Best wishes

My response of a reasonable estimate of subthreshold swing in previous email was based on the first plot you attached where the Vgs extension was up to -1 V and I took the values in the linear region and the method is correct. However after reading the IEEE paper, I find the figure 7 should be used for subthreshold swing calculation. In this figure 7, for 1 decade of current increase from 10^-15 A to 10^-14 A, the Vgs is roughly -1.1 to -1.14 or -1.15 V as the curve is very steep. The inflection point they reported is -1.3 V which is what I find from the figure 7. As per the values I approximately reported here from figure 7 of the paper, my calculation gives swing less than 60 mV/decade. There are some anomalies between figure 5 and 7 if you would like to use them for precise SS (subthreshold swing).

Sincerely,

Dr. Nabil Shovon Ashraf

Assistant Professor

Department of ECE

North South University

Dhaka, Bangladesh.

can anyone calculate ON/OFF ratio of attached curve approximately.