Dear Igor,

welcome,

If you please read carefully the references which i gave in my first comment, you will get a satisfactory answer for sure. The physical and technological parameters

needed to calculate the reverse saturation current are discussed in full details and i measured and calculated them many times.

All waht do you need now is to master the pn junction diode theory.

In case of asymmetrical pn junction we have low doped side which is the n-side with doping Nd and we have the emitter side with high doping which is = Na.

As hinted above Na and Nd are in two different sides og the p-n junction.

So, in the case of unsymmetrical p-n junction the diode reverse saturation current is dominated by the reverse saturation current inth lower doped side.

That is

I0= I0n+I0p with

I0n is the electron current in the p-side and I0p is the hole current in the n-side.

It is so here that

I0p>>I0n

and

I0= I0p to a good degree of approximation.

Also for the width of the depletion region in asymmetrical diode

W= Wn+wp the extension of the scr in the n and p sides respectively.

If Na in the p-side >>> the Nd in the n-side, then

W=Wn

Best wishes

Looks like I found one suitable source. Edmond et al, 1988, "Electrical properties of ion‐implanted p‐n junction diodes in β-SiC". Nitrogen-doped 3C-SiC, Nd = nn0 = 4e18 cm-3, Na = pp0 = 1e17 cm-3, T = 300, 373, 473, 573, 673 K.

However, I still need papers on other materials (Si, 4H-SiC, 6H-SiC) and more papers on 3C-SiC (with different values of Na and Nd).

Dear Igor Ivanov

At first the Shockley diode equation is not correct but just interprets the ALMOST exponential I-V characteristics in forward direction of idealized abrupt P-N junctions. You should therefore consider an ideality factor, which depends on material type, temperature and injection level. In revere bias, this relation is very crude and should be also corrected to interpret many phenomena in real P-N junctions, such as the thermal generation, hot carrier thermal diffusion and breakdown. However, there exist so many methods for the extraction of parameters of real semiconductor devices, including SiC devices of different allotropes such as 3C-SiC.

Chapter Parameters Extraction of Semiconductor Devices

Dear Igor,

Hope you are well!

What you want to carry out here is done in the literature along the development history of the semiconductor devices. The Shockley theory of the p-n junction diode is valid under the idealized conditions when only the recombination-diffusion current dominates the current conduction in the diode. As the colleague Hamza said , it is valid at low injection condition and neglected recombination at the surface of the diode and in its space charge region.

You can locate this current range by plotting the log I versus V. Under this condition the relation will be a straight line with the slope resulting in a nonideality factor n of the diode is equal to 1.

The other comment is that the diodes are constructed such that they their p-n junction is unsymmetrical with the emitter layer doping is much higher than the base layer. The Heavily doped emitter layer plays a minor role in determining the reverse saturation current since the reverse saturation current is inversely proportional to the doping concentration current in that layer.

So mostly its current is neglected.

I my self verified this equation many times by measuring all its parameters.

I want that you review my old papers and you see that i verified this equation and worked out its validity condition.

As a example please follow the papers: https://www.researchgate.net/publication/232710923_A_Zekry_and_G_El-Dllal_effect_of_MS_contact_on_the_electrical_behavior_of_solar_cells_Journal_of_solid-state_Electronics_Vol31_No1_1988

Article A distributed SPICE-model of a solar cell

Article M. Abdelnaby, A. Zekry, F. Elakkad and H. F. Ragaie, “ Depen...

I would like also that you follow the fundamentals book:

Book Electronic Devices

Even the advanced junctions follow an equation like that of the Shockley equation.

Best wishes

Dear Muhammad Hamza El-Saba and Abdelhalim abdelnaby Zekry ,

thanks so much for your answers! I partially read your papers. Unfortunately, it did not help to solve my problem completely.

1) According to the literature, in the case of Nd > Nd. Such approximation will significantly affect the values of μp and τp (and therefore J0).

2) I followed your recommendations and added generation current density component [1]

q * ni * W / τg

to my reverse current density equation. The calculated current values have become much more adequate. However, there is the same problem: the depletion width W is a function of both Nd and Na.

How can one solve such a problem? What doping value should be used to calculate the values of μ, τ and W in the case of an asymmetric p-n junction for which Nd is known, but Na is unknown? For example, in [4] Nd = 6...7 * 1015 cm-3, but the value of Na is not specified.

[1] Ruff et al, 1994, "SiC devices: physics and numerical simulation"

[2] Hatakeyama et al, 2013, "Physical models for SiC and their application to device simulations of SiC insulated-gate bipolar transistors"

[3] Stefanakis and Zekentes, 2014, "TCAD models of the temperature and doping dependence of the bandgap and low field carrier mobility in 4H-SiC"

[4] Shenoy and Baliga, 1995, "Planar, ion implanted, high voltage 6H-SiC P-N junction diodes"

Please look at the book

Microelectronics

by

Grabel

from

Northeastern university

Na and Nd are doping concentrations. They are not constants, they are something you adjust when you make the material. Generally, if Na and Nd are not known you can still use the diode equation but then js becomes a fitting parameter. And you can then put fitted js into equation to see if it corresponds to reasonable values of Na or Nd.

As Mikhail says, you don't need to know Na in the n-region, because the n side is doped only with donors. There you only need Nd.

It is thrue that in the real device there exists also a small quantity of acceptors in the n-region. Thus, in fact one measures Nd - Na there. However in the calculations one uses the obtained result as Nd.

Thanks a lot, dear colleagues!

My main problem was in incorrect usage of Na and Nd. Special thanks to Mikhail Skorikov for clarification.