How is reverse saturation current of a BJT measured empirically?
Ies in this case is Is: Reverse Saturation Current. When they measure it, they just take several different current readings for several different Base Emitter voltages. They also do this at a "constant" temperature, or they use a cold junction reference to actively measure the temperature. Solve for the unknown. (Note: "Ies" = emitter saturation current, and this is a first order approximation) You could put the base-emitter into reverse bias, but you'd need to be very careful to not destroy the device as Vebo is generally around 5V or less! Where as the first technique has much more tolerance for not destroying your BJT that you might want to use.

Edit: A more precise answer due to some ambiguity of the question.





Where


ic = collector current
ib = base current
ie = emitter current
βF = forward common-emitter current gain
βR = reverse common-emitter current gain
Is = reverse saturation current
Vbe = base-emitter voltage
Vbc = base-collector voltage
Vt = thermal voltage


Solve for as many of these as you feel like to find Is.