From what I've studied and read, it doesn't really clear my concept as to why the collector current increases exponentially, more specifically Beta times the base current, when increased.
From my understanding, upon providing a positive voltage at the emitter with respect to the base the base-emitter junction is forward biased, so a large number of electrons flow into the base, where some recombine, giving rise to one component of the base current. On the other hand, the majority carriers (holes) in the base, drift to the emitter region, contributing to the second component of the base current.
So if anything, increasing the base current would imply more recombination and more drifting of holes from base to emitter region, how does that, in any way, affect the collector current?
This is what I got from youtube videos:
For an NPN transistor:
In an NPN transistor, increasing the base current (consisting of electrons) does not directly cause more electrons to be injected from the emitter into the base region. Instead, it affects the operation of the transistor in the following way:
The base current flows through the base-emitter junction, which is forward-biased. This biasing arrangement allows the base-emitter junction to act as a diode, permitting current flow.
As the base current increases, it establishes a higher level of electron concentration in the base region compared to the equilibrium concentration.
This higher electron concentration in the base narrows the depletion region around the base-emitter junction.
The narrower depletion region reduces the resistance for electron injection from the emitter into the base region.
Consequently, more electrons are injected from the emitter into the base region, forming the emitter current.
The injected electrons combine with the available holes in the base region, which are the majority carriers in the base.
Some of the injected electrons recombine with holes, and the remaining electrons that did not recombine constitute the base current.