Are you refering to cut-in voltage? In that case, the tangent to the curve at higher bias(>>3 KT/q, < 0.7 V) is extended to intercept the x axis. The x-intercept is the cut-in voltage.
Is there any specific point where tangent need to be drawn or any point for the range you have mentioned (>>3 KT/q, < 0.7 V) , i will be able to get cut-in voltage correctly.
This answer may come late. To determine the cut in voltage of the pn-diode you make a linear plot of the I-V curve in the current range of interest.
Then, it appears as broken line with two pieces; one horizontal pieca and one inclined piece with the twp pieces are the best linear fit to the real I-V curve. The intersection point of the two pieces will be the cut-in point.
So, it is practical to find different values of the cut in voltage depending on the fitted current range. So, one has to give the cut in voltage with its valid current range.
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