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44I am referring to Millman's Integrated electronics and there I came across and equation $$ \begin{equation} (I_c) = -\alpha(I_E)+I_{Co}(1-\exp^{V_C/V_T}) -->eqn(5.6) \end{equation} $$ where $$ I_{Co}(1-\exp^{V_C/V_T}) $$ represents shows reverse saturation current . Can any one explain me how this equation came . Also is not reverse saturation current independent of applied voltage then why is there $$V_c$$ there in equation ?

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Ico is the reverse saturation current when in CB mode the emitter is assumed open hence the,there is a reverse bias between base and collector,and it is dependent on the value of applied voltage.
Hence the BJT acts like a p-n juction and the equation seriously satisfies with the Shockley diode equation .

So the current will decrease as Vc increase (Vc is positive pnp case and Vc is negative in case of npn), hence increase in Vc will result increase Ico which is also intuitively correct as the reverse current will increase as the reverse voltage will go up.

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Ico wil have to be replaced by the current in a PN diode(that consisting of the base and collector regions).this current is given by voltage ampere relationship I=Io(1−expVc/Vt) Replacing Io by -Ico & V by Vc
we get I=Ico(expVc/Vt-1)_____________________________________________eq.1 (where Vc represents the voltage drop across collector base junction Jccfrom the pside to n side)
as (Ic)=α(IE)+Ico {changeing Ico to Ico(expVc/Vt-1) from eq.1} we get Ic=α(IE)-Ico(expVc/Vt-1) or Ic=α(IE)+**Ico(1-expVc/Vt)
where α is fraction of total current Ie which constitues Ihc carrier current here holes

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