# Why does the emitter current increase with an increase in collector to base voltage in the common base configuration of a BJT?

It is said that because of the Early effect that with an increase in collector to base voltage there is decrease in base width due to which $$\\alpha\$$ (the current gain) increases due to lesser recombination of holes and electron, so with increase in $$\\alpha\$$ emitter current should decrease according to this equation:

$$I_E=\frac{I_C}{\alpha} \, .$$

Also, the concentration gradient of minority charge carriers in the base region increases, due to which more majority charge carriers (of emitter region) come from emitter to base region and hence increase the emitter current.

Both of these effects are in contradiction to each other, so does it happen that the latter effect is greater than the former?

• Please include a circuit diagram with all circuit questions. Commented Dec 26, 2016 at 19:18
• Your present a false dichotomy. Base-width modulation due to $V_{BC}$ (aka Early Effect) is a latter modification to the Ebers-Moll model, but prior to the development of the Gummel-Poon model in 1970, which then included variation due to $V_{BE}$ (aka Late Effect.) Gummel-Poon (and its modifications, as well as the VBIC model and still more versions since) includes a more complete treatment of the physics. I'd recommend (relatively inexpensive) books such as Millman's 1979 edition of "Microelectronics" for a detailed walk-through.
– jonk
Commented Dec 27, 2016 at 5:59
• Both descriptions state a larger collector potential yields a larger collector current Commented Oct 1, 2018 at 2:33
• Possible duplicate of BJT gain.Width of base region vs collector current Commented Dec 21, 2018 at 6:11
• Kartik, There is no better paper to read than J. M. Early's "Effects of Space-Charge Layer Widening in Junction Transistors", 1952.
– jonk
Commented Dec 15, 2021 at 6:02

## 2 Answers

Not sure this will help you, but it helps me to understand that the metaphorical "bridge" that the collector current is crossing is both shorter in length (your first effect) and steeper (your second effect).

There are two different effects on collector current that happen when VCE is increased. Which one depends on whether the VBE is held constant, or the IB is held constant.

Base current is the sum of B -> E injection plus the recombination in the base.

If VBE is constant, then the injection from E -> B, and from B -> E at the BE junction remains constant as VC increases; but the base width does decrease, thus base current decreases and more of the injected emitter current reaches the collector. Emitter current remains constant. You can consider that 𝛼 increases.

If IB is constant, then the 'improvement' in collector current because of the reduction in recombination means there would be a reduction in base current. Since IB is constant, this is compensated by an increase in B-E current (injection), leading to a further increase in collector current ! Overall, the effective Early voltage with a constant base current drive appears lower than with a constant VBE. You can use this to distinguish between injection-limited and recombination-limited behaviour.

Note that in the constant IB case, 𝛼 also increases (because of the reduction in recombination). This is the same increase as in the constant VBE case. The further additional emitter and collector current is from the reduction in loss (recombination) of base current, making more available to induce carriers to flow from emitter to collector.