What is the relation between reverse saturation current and leakage current in a BJT?

Question

I have been studying Studying Donald Neamen's Electronic Circuits 4th edition and Sedra Smith's Microelectronics 7th edition for quite some time now. I have been self studying. After searching extensively on Internet as well as trying to understand from the books, I have not been able to differentiate between two quantities in the context of BJT.

These two quantities are: $$I_{S}$$ $$and$$ $$I_{C B O}$$

According to Sedra Smith,

$$ I_{C B O}$$ is the collector base reverse current. Whereas $$ I_{S}=\frac{A_{E} q D_{n} n_{i}^{2}}{N_{A} W} $$

$$ i_{C}=I_{S} (e^{v_{B E} / V_{T}} -1) $$

$$I_{S}$$ is the saturation or scale current.

I have been wondering are these two quantities same or share some relation between them because I find the name for both these quantities being used inter-changeably at many places which is quite confusing and I believe they are not the same.

Also, I am confused which current is being referred to when on Internet I find the term "reverse saturation current". Searching on Internet the term "reverse saturation current" gives two kinds of sources: one referring it as $$I_{S}$$ and the other referring it as $$I_{C B O}$$ Another similar quantity is $$I_{C E O}$$.

According to another source (Balbir Kumar Electronic Devices and Circuits Second Edition), $$ I_{C}=-\alpha I_{F}+I_{C B O}\left(1-\mathrm{e}^{V_{CB} / V_{T}}\right) $$

This equation in the forward active region of npn BJT reduces to

$$ I_{C}=-\alpha I_{F}+I_{C B O} $$

References

[Sedra Smith Microelectronics Circuits]

[Donald Neamen Circuit Analysis and Design]

Answer 1

They are not equal, or even particularly related.

ICBO is a characteristic of the reverse biased C-B junction. Because the base part of the depletion region of this junction does not extend to the emitter region (in most BJTs), the junction leakage characteristic is just that of a 'simple' pn junction -- a function of the area and doping (mostly that of the collector doping).

If this junction was forward biased, ICBO would be the 'IS' term in its equation.

IS (as in the Sedra/Smith book notation) is the characteristic of the B-E junction, and depends on base and emitter doping. Because this junction is more heavily doped (because this gives higher beta to the BJT), this IS term is usually smaller than the corresponding C-B term (ICBO).

The total collector current consists of both terms -- the CBO leakage and the emitter current collected by BJT action from forward bias of the BE junction.

Note that therefore at very low VBE voltages, the base current might be negative -- because the ICBO current (which flows out the base in an NPN) exceeds the base component of the IS current. This is why a BJT will leak more current C-E when the base is open rather than shorted.

With base open, the ICBO current gets multiplied by the BJT beta (which may be significantly lower at such low current levels); the total current is then some beta*ICBO.

With base shorted to emitter, VBE is 0, and the IS term is multiplied by 1, making the total current ICBO + IS

With emitter open (and measuring leakage C-B), only ICBO is observed.