Vbe is changed externally. I can put a voltage source in the b-e terminals, and lock the voltage so the transistor cannot change it. Your equation above shows that vbarrier has to change to accomodate Vbe, because Vbi does not change at constant temperature once the transistor is manufactured.
Nodoby ever said you could't force vbe to equal an external value. That's a trival application of basic electronics, and proves nothing.
You cannot say Vbe does not change anything, it cancels some of the barrier voltage. Here is a quote from the textbook Semiconductor Circuit Analysis, by Phillip Cutler, p 19. I only deleted references to a diagram which shows a diode in series with a variable voltage power supply.
"At first I slowly increases, because because the applied voltage V has not sufficiently reduced the inherent potential barrier. As we increase V further, say to a few tenth of a volt, we find that I rapidly increases because V has finally become large enough to reducxt significantly the internal barrier potential and cause the recombination current to become quite large."
vbe is the junction voltage, and nothing more. It is made up of barrier voltage and contact voltage. vbe changes as barrier voltage is changed. To say a voltage changes itself makes no sense.
"For such a diode, the height of the potential barrier at the junction will be lowered by the applied forward voltage V. The equilibrium initially established between the forces tending to produce diffusion of majority carriers and the restraining influence of the potential-energy barrier at the junction will be disturbed."
So this text too, believes that Vbe cancels some of the barrier voltage.
Sedra and Smith says otherwise.
By the way, the reason S & S always talk about current is because they are analyzing the BJT with a current source. But it is still the Vbe that determines what the junction will be to support the current source.
It doesn't matter how the bjt is biased. The physics of the junction doesn't change.
Read my statement again. I said it opposes the energizing voltage. That is what a back voltage does.
I know what your statement said. I said a voltage can't change another voltage, and you've not proven otherwise. There is no "back voltage" in capacitors. There is only the voltage it is charged to.
Wrong twice. Look again at the quotes and especially the link. The link says the junction voltage is Vbi-Vbe, so Vbe is not the junction voltage.
No, I'm correct. The links doesn't prove otherwise. vbe is the junction voltage. If you want to prove that vbe is not the same as junction voltage, then you must show another voltage source. I don't think that equation appears in the link, as it would be quite impossible. When you cherry pick the potential equation, Φ = Φ1 - vbe, you conveniently neglect that Φ1 produces no voltage, as it only cancles contact potential, which results in ZERO voltage both at the junction and at the contacts with no external current supplied. So, the equation becomes Φ = ZERO - vbe =
-vbe, for any measurable voltage.
As I said before S & S analyze the BJT with a constant current source, but that does not change Vbe controlling the forward current.
And as I said, it doesn't change the junction physics. It's the same if the bias is voltage or current, vbe is changed by neutralized change in the junction. A voltage cannot change another voltage. This chapter by Sedra and Smith is the definitive explanation of how junction voltage, and thus current, is controlled in bjt's.
the equation for forward current should be Id-Is=I, which means diffusion current minus thermal current equals the forward current.
That's correct. But the important thing to keep in mind is the process that give rise to this current starts when charge is injected into the junction, that lowers the barrier voltage, and thus vbe. Also, the typo notwithstanding, thermal current is small, and not affected by input voltage or current, so the statement by Sedra and Smith that current through the junction is controlled by injected current is accurate.
The problem with some of these beginners texts is that the cartoons they show has vbe forced to some external voltage. That's OK for showing how bjt's work at a functional level, but does not show what is going in under the hood. And so, for example, when they show equations like the following:
Φ = Φ1 - va, which is technically correct, all they are showing is that is it
possible to force the junction voltage to be equal to an external voltage, per kirchoff's law. Unfortunately, however, to understand how vbe is changes, one needs junction physics theory such as in Sedra and Smith. One also needs to keep in mind basic laws of electronics physics. For example, the mesurement of potential between any two points includes voltage sources between those points. No voltage outside the measurement points can affect the measurement. One cannot show a single circuit where this principle is violated. Thus, although the junction voltage may be forced to be equal to an externally connected voltage ( which is never done in practice ) the external voltage can not change the junction voltage. It can only be changed by charge injected into the junction, per Sedra and Smith. And this, vbe is the same as junction voltage, as there are no other sources.
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