In input characteristics of a common base transistor input current Ie increases with increase in output voltage Vcb. I know the answer is something to do with early effect, "the answer says that because of early effect the number of recombination at the base decreases and thus the input current increases."I want to know why decrease in number of recombinations at base increases the input current.
When Vcb increases, CB junction width increases, while EB junction width decreases. The result of this is -> less recombination of electrons and holes at EB junction. It means more electrons can now flow between B and E. Which implies that emitter current, Ie increases. Now we know in CB configuration: $$I_C = \alpha I_E$$
Hence Ic increases.
As Vcb increases, the collector-base depletion region gets wider; part of this increase comes from collector and part from base, which narrows the base region available for recombination of base-current with emitter-current.
Less recombination in the base causes higher emitter efficiency ---- more Ie becomes Ic.