In my understanding, in an NPN junction for example, an increase in the emitter-collector voltage should widen the depletion layer in the base-collector junction therefore increasing the electric field in that region. This should normally speed up any electrons that reach that region toward the collector and the negative terminal of the battery. This should logically increase the current since current is the number of charges (Coulombs) per second.
The only explanation I managed to find is that the number of free electrons in the emitter region is limited and therefore the number of charges per second can't increase because there simply are not enough charges. Unfortunately, this seems very counter-intuitive to me because in that case we should be facing the exact same problem when we increase the the emitter-base voltage.
Someone stated that the electrons in the emitter region are shielded by the base but the explanation he gave wasn't related to any kind of shielding at all and I don't understand what that shielding could be.
Why doesn't the current in a BJT transistor increase with an increase in emitter-collector voltage?