Not true. The collector current is an expotential function of the base - emitter voltage. The charge in the base - emitter region is proportional to the Vbe. If the charge is excessive, the transistor is in saturation. If not, it is in the active region.
Certainly Ic = hFE * Ib is a very useful relationship, Ib is required to maintain the b - e charge.
Len
The most useful relationship is as follows:
Ic = alpha*Ie.
This is the relation we use to bias a bjt. Placing a voltage source across the b-e junction is never done. The device would be thermally unstable. The saturation current Ies in the Ebers Moll equation has a positive temperature coefficient.
Ie = Ies*exp((Vbe/Vt)-1).
Ies increases greatly with temperature. If constant voltage of 0.65V is connected b-e, a current is established per E-M. But temperature must increase due to power dissipation. Then, Ies increases, further increasing Ie, etc. Thermal runaway takes place.
Also, connecting a voltage source across b-e results in unpredictable emitter/collector current even not considering thermal runaway, since Ies varies widely with temp and speciman.
This is why we never "voltage-control" a bjt, nor an LED, nor any forward p-n junction.
To bias the b-e junction, Ib and Vbe are both needed. A constant voltage source, or a constant current source will provide both. With constant current drive, thermal stability is achieved. As temp increases, Ies goes up but Vbe goes down, resulting in a stable operating point. Vb = Vt*ln((Ie/Ies)+1).
We can control either the base current or the emitter current. If we establish Ib, then Ic = beta*Ib. This is thermally stable but suffers from "beta dependency". Ic can vary with beta which changes with temp, bias level, and speciman.
But if we control Ie, then Ib = alpha*Ie. Alpha is generally 0.98 to 0.998, or 0.99 plus/minus 0.01. This method is thermally stable and precise and predictable.
The bjt is usually controlled with emitter current, not Vbe, and usually not Ib. When used as a switch, Ib is often controlled. The device is overdriven in the base resulting in a forced beta smaller than the device minimum beta. This results in predictable operation.
Have I helped? BR.
Claude