The problem that I'm having is that I don't understand why current flows from collector to emitter if the P-N junction from base to collector is forward biased.
When a PN junction is forward biased, there is a constant flow of carriers (of each type) across the junction in each direction. The net flow of current depends upon the magnitudes of these flows.
The flows result from two processes. Diffusion and Drift. Like one gas diffusing within another, the random thermal motion of carriers causes them to diffuse from an area area of high concentration to an area of low concentration.
However, diffusion will often lead to an imbalance in net charge density. As a result of this imbalance of net charge density, strong electric fields are created. These strong electric fields exert forces on the carriers giving them a tendency to drift.
In an equilibrium situation, the diffusion current in one direction is balanced by the drift current in the opposite direction. However, if equilibrium is upset, there will be net current flowing in one direction or the other. Note that this works equally well in both directions. If some factor increases drift current more than diffusion current, the net current will flow one way. If instead some factor increases diffusion current more than drift current, the net current will flow the other way. A PN junction does not intrinsically prevent current from flowing in one direction or the other. Rather, factors such as applied voltage and carrier concentrations on each side of a junction will affect the balance between drift and diffusion currents, and thus the net current flow.
An NPN transistor with a forward biased base-emitter junction, will have a high concentration of electrons in the base. The high concentration of electrons in the base is higher than the concentration of electrons in the collector, even though the base is P-type, and the collector is N-type. (This is true provided electrons are free to exit the collector via the collector terminal). This high concentration of electrons in the base upsets any equilibrium that might have existed between the drift and diffusion currents across the base-collector junction. The result is a net flow of electrons from the base into the collector, despite the fact that in a saturated NPN bjt, the base is at a more positive potential than the collector. The positive potential of the base will encourage some electrons to flow in the opposite direction, i.e. from collector to base. But because the majority are going from base to collector, rather than from collector to base, the net electron flow is from base to collector.
Or, in terms of conventional current, the net current flows from collector to base.
As a side note, it will be easier to understand how a BJT works from the point of view of the movement of carriers, rather than the direction of conventional current. In an NPN transistor, the carriers of most interest are electrons, and they flow from the emitter terminal into the emitter, across the base-emitter junction into the base. A small percentage of them then leave the base through the base terminal and out of the device, while the majority cross the base-collector junction, into the collector, on to the collector terminal, and out of the device. The conventional current flows the other way, but thinking in terms of the conventional current doesn't really give insight into how a BJT works internally.
