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this question seems to be basic, while reading about early effect, that is base width modulation , one of it's consequence was written there is : "there would be a less chance of recombination in the newly formed "narrowed" base".

my question is why the chance is less? my guess is : because now the CB depletion region is more close to the emitter, so most of the electrons pumped by the emitter would feel a larger force applied by the depletion region on them so they won't get much chance to recombine and will be pushed towards collector, but if the depletion region is far enough from the emitter then many of the electron will not efficiently "feel" the force of the depletion region and will get bore and recombine and flow out through the base. Is this even close to correct?

also one more question is, since now the base is narrowed and there would be less chance of recombination, so most of the emitter pumped electrons will go to the collector, so does it mean the base current will reduce?

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    \$\begingroup\$ The way I remember it, the base-collector is reversed biased as the base-emitter is forward bias. \$\endgroup\$ Apr 22, 2021 at 14:25

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It's better to go back to the original papers to understand something well. In this case, "Effects of Space-Charge Layer Widening in Junction Transistors," by J. M. Early, 1952, from the Proceedings of the I.R.E.

Here's the first diagram from that paper (illustrating an NPN BJT):

enter image description here

While Shockley\$^1\$, in 1949, and then Shockley, Sparks, and Teal\$^2\$, in 1951, showed that an increase in the potential across a barrier would increase the barrier thickness, they also assumed that such changes in collector- and emitter-barrier thicknesses would not affect base-layer thickness. The assumption turned out to be false, so Early\$^3\$ addressed it by realizing that an increase in the barrier thickness, \$x_m\$ in the above diagram, would spread in both directions and therefore reduce the thickness of \$w\$ in the above diagram.

This decrease in \$w\$ has two important effects.

  1. On average, a carrier diffuses across the narrower base layer, \$w\$, in less time so this decreases recombination of injected minority carriers in the base layer. And of course, this increases \$\beta\$, which is just the fraction of emitted minority carriers that reach the collector compared to those that are recombined in the base layer while traveling to the collector.
  2. The narrower base layer also decreases the impedance seen by the minority carrier current injected by the emitter. (That impedance includes both resistivity as well as the effect due to the base layer thickness.) The net result of lowering of impedance is that there is an increase in the proportion of emitter current carried by electrons (NPN), which is an increase in the ratio of electron emitter current to total emitter current. This impacts \$\beta+1\$ (which obviously affects \$\beta\$.)

Perhaps the key insight here, one that wasn't reached earlier than 1952 (as Schockley et. al. failed to recognize it in their earlier paper) is that increases in \$x_m\$ spreads in both directions and that the dual principal impacts each tend to increase \$\beta\$.

The reality for an active mode NPN is that the depletion region at the BE junction shrinks (Late Effect that wasn't accounted for until the Gummel Poon model, as Early's paper wrote: ".. it is very thin and may be neglected .."), while the depletion region at the BC junction widens (Early Effect.) Keep in mind that the base itself is made quite thin and is lightly doped.

\$^1\$ W. Shockley, "The theory of p-n junctions in semiconductors and p-n junction transistors," Bell Sys. Tech. Jour., vol. 28, p. 435; July, 1949.

\$^2\$ W. Shockley, M. Sparks, G. K. Teal, "The p-n junction transistors," Phys. Rev., vol. 83, p. 151; July, 1951.

\$^3\$ J. M. Early, "Effects of Space-Charge Layer Widening in Junction Transistors," Proc. of the I.R.E., vol. 40, p. 1401-1406, November, 1952

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The chance is less because electrons "flight time" in the p region is short.

The base transit time is of minority carriers (electrons) in the base, at low current injection densities, is:

Tn = Wb ^ 2 / Dn

Where Wb is the base thickness and Dn is the electron diffusion constant.

Source (equation 5.22): https://www.sciencedirect.com/topics/engineering/base-transit-time

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Question: "Since now the base is narrowed and there would be less chance of recombination, so most of the emitter pumped electrons will go to the collector, so does it mean the base current will reduce?"

Yes - for constant Vbe the emitter current Ie will be constant and because of Ie=Ic+Ib the base current will reduce for rising Ic. Nevertheless, very often the output characteristics Ic=f(Vce) are given for Ib=const.

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