Looking at the internal schematic of the TL431:
It looks to me like startup of the bandgap reference occurs as "REF" is brought up to some voltage slightly above 1.2V, causing the leftmost diode-connected transistor to turn on and drive current into the transistor with its base connected to 1k, which then bootstraps current into the bandgap gain-stage via the PNP mirror and defines the operating points of the rest of the circuit.
Two questions occur:
The datasheet gives "OFF" state current (Vk = 36, Vref = 0) as between
100 and 500uA - is this only comprised of leakage currents?Since the transistor connected to 1k is driven by a current, unless its beta is well-controlled I don't see how the current mirror current can be well-controlled. I think I understand the reasons for this, as when the '431 is in its "ON" state its supply current will be primarily the cathode current through the output stage, and IIRC bandgap performance is more dependent on matched scaling of emitter geometries than reference current. As you can buy them for 2 pennies I imagine they don't spend a lot of time worrying about it.
My question is that since the mirror current defines the gain stage current (transistor with 20p wrapped around it) I don't see how the open-loop gain can be well-controlled between devices. The TI datasheet at least gives it at 55dB @ 25C and 10mA Ika.