How to measure the On/Off current ratio in TFETs and MOSFETs
The drain current of TFET in the off-state is very low, in the picoamperes or even femtoamperes range. To measure currents that low is a challenge. To tackle this challenge in practical measurements, a parameter &quot;subthreshold swing&quot; is extracted from TFET's output characteristics, rather than directly measured.
The drain current in the subthreshold region (a weak inversion in MOSFET) has basically an exponential dependence on overdrive voltage: ~exp(q·(v_GS - V_thresh)/nKT), for the source tied to bulk, and ~exp(q·(κ·(V_G - V_thresh) - V_S)/nKT), for the source not tied to bulk. In a log-linear plot, the drain current in subthreshold region is linear with a slope that is called the &quot;subthreshold slope (SS)&quot;. The MOSFET physics posits and proves that this subthreshold swing (reciprocal SS, [subthreshold swing] = 1/[subthreshold slope]) cannot be less than ca. 60 mV/decade.
For BTBT TFET, a subthreshold region can be coarsely defined as the region where the conduction band of the intrinsic region is still not aligned with the valence band of the P region. Although the TFET physics and device models differ from MOSFET's, there is also an approximately linear region in the drain current-vs-gate voltage log-linear plot for TFET device.
There is a number of methods to extract the threshold voltage (and, with a certain precision, the subthreshold swing) parameters from MOSFET output characteristics. See, for example, https://www-elec.inaoep.mx/seminario2013/ortiz_SNDA13.pdf and http://compass.formfactor.com/2018/wp-content/uploads/sites/8/COMPASS2018-Cheng-Comparative-Vt-Techniques.pdf . Some of these methods (not all, because of an ambiguity in threshold voltage definitions for TFET) can be applied to TFET subthreshold swing parameter extraction, see https://www.sciencedirect.com/science/article/abs/pii/S0038110113003675 and https://www.researchgate.net/publication/337610522_Effects_of_Back-Gate_Bias_on_Subthreshold_Swing_of_Tunnel_Field-Effect_Transistor.
I think the answer to your first question (&quot;Can we measure the On/Off current ratio from transfer and output characteristic curves?&quot;) is: yes, we can extract the source-drain leakage current component I_off from output characteristics, but only indirectly, with data processing using computations and, to some extent, device model data (there is also the gate-oxide leakage-current component). In the on state (I_on), the drain current is in the microamperes range and can be read directly from output characteristics.
The ratio I_on/I_off improves reliability (noise immunity) of low-power devices and so it is the figure of merit. These currents are also autonomous 'figures of merits': a low I_off decreases stand-by power consumption, a high I_on increases fan-out capability of logic gates.
For the importance of the I_on/I_off figure of merit, search 'steep-slope transistors', 'steep-slope designs'. You will find many references, for example, https://rlpvlsi.ece.virginia.edu/sites/rlpvlsi.virginia.edu/files/MWCAS_2017_Final_IEEE_Submitted.pdf and https://core.ac.uk/download/pdf/208847741.pdf , each of which discusses advantages of high I_on/I_off ratio in a multifaceted way.
ADDENDUM
However exacting the task of their measurement is, subpicoampere currents are routinely measured in research and industry. The SE policy discourages commercial product advertisement and even recommendations on product use, but, having no vested interest in Tektronix, Inc., I venture into mentioning Tektronix's Low Level Measurements Handbook. Notice FIGURE 4-21: IDS vs. VGS for an Enhancement Mode MOSFET
Also, it is not extraordinary for competent engineers to develop femtoampere designs of their own, see https://www.edn.com/design-femtoampere-circuits-with-low-leakage-part-3-low-current-design-techniques/ and https://www.edn.com/achieve-femtoampere-leakage-in-surface-mount-op-amp-layouts/ .