Reverse biased diode formula in Ebers-Moll model

As far as I understand in an PNP transistor the base voltage Vb is higher potential than the collector voltage. So since Vb>Vc the base collector junction is then reverse biased:

But in Ebers-Moll model one of the diode current is Icd as shown below:

And this Icd is formulated as follows:

Icd = Ics * (exp(Vcb/Vt) - 1)

But isn't such a formula for a diode valid only for forward biased diode?

• No, this formula is valid for reverse-biased diodes too. What you're seeing is the reverse leakage current of the diode; it's very small, but it's not zero. Commented Nov 13, 2018 at 1:20
• And that model will work correctly when the transistor is operated in reverse, with the collector and base interchanged. (I cannot remember the details, but TTL logic has one of the transistors running in reverse for one of the transitions, in a way that pulls current out of some node and speeds things up. Mind you, I'm remembering fragments of a lecture that I attended 35 years ago, so it is a bit foggy...). Commented Nov 13, 2018 at 2:00
• @TimWescott I'm interested. Perhaps if you see TTL AND, TTL inverter/NAND, and TTL output section it might trigger recollection. If I missed something important I'd want to improve those answers with what you recall.
– jonk
Commented Nov 13, 2018 at 6:34
• Here are the three equivalent 1st level Ebers-Moll models to examine. They are just three different ways of looking at the same thing. All equivalent.
– jonk
Commented Nov 13, 2018 at 6:36