Why is the Collector current of a BJT transistor independent of the Collector Base voltage?

Question

Ignoring the modulation of the effective base width, why is the collector current independent of the reverse bias voltage across the Base-Collector P-N junction? On one hand, it is easy to see that KCL must be obeyed, so the Emitter current flowing into the base must exist through the collector; but how is that "obeyed" given the large electric field the carriers roll down when they reach the Base-Collector junction. Surely the electric field in the depletion region accelerates the carriers which by the Drift current equation: , increases the current as E can be very large?

Answer 1

You seem to think that because the depletion area is large for the base collector junction that there must be a large field there. That is the opposite of how it works. The voltage difference between the emitter, base, and collector is dropped exclusively in the depletion region. Thus the larger the depletion region, the more spread out the field is and so the less strong the field is. In fact, back injection is one of the reasons for hetero junction transistors. In the non depletion regions, diffusion is the dominant mechanism. Thus by creating a large electric field that essentially acts like a reverse flow barrier, the BJT forces diffusion to occur. The reason the current flows from C->E (NPN) or E->C (PNP) is because the BJT uses different doping levels to create depletion widths for different purposes. The reverse biased C-B depletion region, being large, is dropped almost exclusively on the collector's side. That means there's very little length for diffusion. That small length means that the Collector becomes an excellent source of minority carriers for the base compared to the emitter, whose large electric field is almost insurmountable. When those minority carriers cross, they drive diffusion in the base. Once the base provides that minority carrier to the emitter, it can't get it back, so it must get another one from the collector.

In essence the collector current is dependent only on the amount that flows out of the emitter, not on the field, which is designed to drop almost entirely over the collector.

Please leave a comment on this if you don't understand, because I needed about 10 pictures to get this down in college.

Edit: The BJT picture to rule them all!

Answer 2

Why is the Collector current of a BJT transistor independent of the Collector Base voltage?

One can perhaps gain some insight into this question by considering why the reverse leakage current of a diode is highly independent of the diode's reverse bias (until breakdown occurs).

The answer, in both cases is that to minority carriers, a reverse biased PN junction might be compared to a waterfall. When water reaches the edge of a waterfall, it falls over, and how far down it has to fall does not affect how much water will fall over the edge. Likewise, when a minority carrier reaches a reverse biased PN junction, the electric field is favorable for that minority carrier to be swept across the junction. The total voltage drop across the junction is like the height of the waterfall. Once the minority carriers reach the junction, they are swept across, and how much of a potential difference there is from one side of the junction to the other does not matter, as long as the electric field is in the right direction.

In a reverse biased diode, (below breakdown) there are few minority carriers. And so the reverse leakage current is small. In a transistor in the forward active mode there are many minority carriers in the base. These minority carriers get there because the emitter base junction is forward biased, and so a good portion of the many majority carriers in the emitter cross the emitter-base junction. Once they arrive at the base, these carriers change names, and become minority carriers. Because the base has much less doping than the emitter, these minority carriers have an extended lifetime before they recombine. Some of them do recombine, but many more reach the base-collector junction before they have a chance to recombine in the base. The ones that "reach the edge", "fall over the waterfall". As a result, the collector current is largely controlled by the minority carrier concentration in the base, and is controlled very little by the base-collector voltage. The minority carrier concentration in the base, in turn is largely controlled by the base-emitter voltage. That, in a nutshell is an intuitive explanation for why the collector current in a BJT in forward active mode is largely independent of the base-collector voltage.