# Where does -1 in BJT’s Ies equation come from?

I don’t know whether there is already a question and answer to this but I couldn’t find one yet. Regarding the following information from a text:

The equation for emitter reverse saturation current Ies shows that the Ies is directly caused by Vbe in non-linear way. But where does -1 in the parenthesis come from?

• Without the "-1", what would be the current with 0 applied voltage? Do you think that would be physically possible? – The Photon May 15 at 18:34
• No not possible. So is that the reason to zero the left side when Vbe is zero? – panic attack May 15 at 18:35
• More importantly, what would be the current if the $V_{be}$ were just slightly negative? What would that mean about the power consumption of the device? – The Photon May 15 at 18:37
• @ThePhoton Sadly I don’t have an answer to this one:( – panic attack May 15 at 18:39
• Try drawing the I-V curve of the device with the "-1" removed. What is the difference between quadrants I and III of an I-V graph vs quadrants II and IV? – The Photon May 15 at 18:46

The 1 comes from the rate of electron-hole pair generation in the junction; it is constant over voltage (although not over temperature -- I was in the industry for about 5 years before I realized that $$\I_{ss}\$$ is temperature dependent. I felt cheated that I was not told sooner).
The $$\e^\frac{V_{BE}}{V_T}\$$ part is from the rate of recombination of hole-electron pairs; it is exponential with voltage, and exactly matches electron-hole pair generation at $$\V_{BE} = 0\$$ (as one would hope it would).