Turn on voltage of a bipolar transistor, Vbe/Ic

Annoyed by the inaccuracy of people saying, "It takes six tenths of a volt to turn a transistor on", I did a graph of a bipolar transistor (2N4250A) to see what happened. The graph shows an almost perfect straight line from 1na to 1 ma on a lin/log graph. (I quit at 1 ma to avoid heating the transistor up.) That is a current range of a million to one. I assume the line continues into the higher current ranges except for heat affecting the results and some of what is called, "bulk resistance". That is, there is some small amount of simple resistance in a bipolar transistor.

A well educated description is: ΔVbe = KT/Q Ln (I2/I1) where, under room temperature conditions, one can substitute .026 for KT/Q. This results in, "sixty millivolts ΔVbe for a tenfold change in collector current", and is called the Ebers-Moll equation. This simplified form is: ΔVbe = .026 Ln(I2/I1)

The graph of a real transistor shows an average of .06ΔVbe per ten x change in collector current in the range from 1 nanoamp to 1 microamp and an average of .07ΔVbe for 1 microamp to 1 milliamp. (Most real world applications use more current than anything in this range.) Caution: This result will not be exactly the same for every transistor or every range of current, and it explicitly changes with temperature.

The most interesting part, to me, is that the results go below a nanoamp for Ic while the slope of the ΔVbe line barely changes. The conclusion I come to is that there is no, "turn on" voltage for a bipolar transistor. It is always on to some degree, depending on the forward voltage from base to emitter.

If you graph this on a linear graph paper, the results will curve sharply upwards as the collector current goes up by powers of ten and the Vbe goes up linearly. The, "knee" of this curve will depend on how you choose the scale of the graph, thus, there is no definable place where the transistor, "turns on".

I had to attach the graph as a pdf because it takes over a megabyte to scan it well and there is an upload size limit on this site.
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