Dear Brajesh,

By definition the transfer characteristics of a transistor is its drain current IDS a function of its VGS for certain  VDS or the load line for the dynamic transfer characteristics.

This characteristics is divided into three ranges, the off range where IDS= ION and the intermediate range where the transistor acts as an amplifier.

So, accordingly it is clear that the current level can be used to judge the state of the transistor as defined previously.

So i would choose the second expression of yours for the judgement of the conduction state of the transistor provided the you may use EQUAL OR larger than IDON OR EQUAL OR SMALLER THAT IDOFF.

wish you success

On-Off Ratio = Id max/ Id min 

Thank you very much Abdelhalim Sir and Rohit Sir.

But most of paper on Graphene nanoribbon TFET as switch preferred [ION, IOFF]= IDS[VGS, VGS-VDS] notation.

What are the ON and OFF  current definition in fabricated Si and III-V compound TFET ?

Dear Brajesh,

The transfer characteristics of conventional FETs are independent on VDS in the saturation region till the onset of pinch off region where the tranistor enters in the linear region. The transfer characteristics will depend o both VGS and VDS.

Since in the binary switching operation one has to define the off point and the on point then one has to give both VGS and VDS in every point since both  contribute to the current of every point.

Like wise in the advanced short channel transistor there is no saturation and the drain current is also a strong function to VDS in addition to VDS.

This my interpretation to the switching conditions given by you.

best wishes

Thank you very much Abdelhalim sir for kind response. It has clarified my doubt.

For agiven VDS ;  transfer characteristic  (Vgs Vs ID) for the threshold level of gate voltage corresponding  logarithmic scale of drain current  (log ID) is called  - ION  and the least level of gate voltage when  minimum or only leakage conduction through the channel is available the corresponding drain current  logarithmic scale (log ID) is called-   I OFF