![bipolar transistor bipolar transistor](https://alltopnotch.co.uk/wp-content/uploads/imported/5/10-x-BC557-PNP-Bipolar-General-Purpose-Transistor-BC557B-TO-92-361958864575-2-162x300.jpg)
Electric fields (hence potential energies and band diagrams) and current densities can be deduced from charge configurations and evolution. Personally, I see the above hidden linearity in an inherently nonlinear device as a reflection of the fact that what matters is charge: how much is there, where is it and how does it move. If you really want to find a fundamental equation that sums up the inner working of the transistor you should look at the continuity equation, a là Bob Widlar. The answer is that there is indeed linearity, but it is in the concentration of carriers. Here the battery symbols represent the positive convention for the voltages (that can assume negative valuesīut the transistor is an inherently nonlinear device (its V-I characteristics are exponentials and logarithms), so you should ask yourself this question: how is it possible to construct a model using the superposition of effects? The complete transport model (here shown for a PNP transistor) is the superposition of the excitation of the base and collector junction separately. The transport model is basically considering the working of a transistor as a superposition of the effects of currents flowing in the device when only one junction at the time is excited. If you really are in search for an explanation that is closer to the physics of the device, I suggest you take a look at the concentration of carriers.
![bipolar transistor bipolar transistor](https://gbsg.ch/wp-content/uploads/2022/07/Calibre-Market-Research-and-forecast-6-11-750x470.jpg)
Hence, current control or voltage control are equivalent way to explain the transistor's working. My point is that that voltage across the base-emitter junction is also associated with a current injected into the base - no delay at all, they are concomitant.
![bipolar transistor bipolar transistor](https://cdn.shopify.com/s/files/1/0215/6458/products/3599-00_2048x.jpg)
This is not denying causality: when I force a voltage between base and emitter I am causing - presumably a few nano or picoseconds later - a current to flow in the collector. Some people will say the transistor is a current controlled device (because, you know, \$I_c = \beta I_b\$ or \$I_c = \alpha I_e\$), some people will say it is definitely a voltage controlled device (because of the \$I_C = f(V_\$ (and viceversa). Unfortunately, when the current control interpretation of the BJT is brought up we must face what appears to be the engineering version of the chicken and egg conundrum. (And maybe it will look more natural if you consider a PNP and look at holes, because the main flow of carriers is in the same sense as the conventional currents in the outside circuit.) TL DR Yes, you are basically correct in your intuition. So that is the amplification caused in collector current due to the change we wanted in base current. So what have we achieved? We got what we wanted in base current but as a result we also ended up getting 198 electrons flowing per second in collector current. To do that we need to increase the emitter current so that it emits 200 electrons per second. Now suppose we want the base current to be increased so that it carries 2 electrons per second. Suppose firstly the emitter was emitting 100 electrons in one second and the base current is contributed by one electron and hence the collector current is contributed by 99 electrons. Now we will deal with fractions so what is amplification? Amplification is the change in collector current with respect to change in base current. The phrase "a small fraction of electrons" is very important. Most of the electrons will flow to the collector region and contribute to the collector current. The emitter base region is forward biased, so electrons from emitter will flow in the direction of the base but since the the base region is lightly doped and is very thin only a very small fraction of electrons will recombine into the P region or contribute in the base current. Suppose we take an NPN as the transistor in our case. I faced a lot of problems in understanding BJT.