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Some background, for anyone unfamiliar: The Shockley diode equation is

$$ I_D = I_S·\left(e^{\frac{V_D}{n·V_T}}-1\right) $$

with the quantity \$n\$ called the ideality factor, a number between 1 and 2. Ideal diodes have an ideality factor of 1, while real diodes do not. (And, to my understanding, the ideality factor of real diodes can depend strongly on temperature and diode current.)

My question is this: What is a typical ideality factor for commercially-available pn diodes at room temperature? In what range can one expect the ideality factor to be? Will it be different for Schottky diodes?

The impression I got from my semiconductor devices class is that it's close to 2 for low currents, shifts nearer to 1 for moderate currents, and goes back to 2 at very high currents; is this correct? Are there more precise numbers available anywhere?

Kuba hasn't forgotten Monica
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Hearth
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  • It depends on the efficacy of the diode to photo stimulation and dark current, temperature . ..." some types of solar cells shows an ideality factor greater than 2 and even may be as high as five. " https://www.researchgate.net/publication/232710742_M._Abdelnaby_A._Zekry_F._Elakkad_and_H._F._Ragaie__Dependence_of_dark_current_on_zine_concentration_in_Znx_Cd1-x_SZn_Te_hetero__junctions_Solar_Energy_Materials_and_Solar_Cells_29_%281993%29 – Tony Stewart EE75 Apr 18 '18 at 13:02
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    All the SPICE models have this in them, and they vary quite a bit depending on device; that is the reason that a diode connected transistor is most commonly used in semiconductor temperature sensors (because the base - emitter diode ideality is quite close to 1 - the 2N3904 is a favourite here). – Peter Smith Apr 18 '18 at 15:22
  • @TonyStewartSunnyskyguyEE75 To complement your statement, I have recently measured an ordinary UV-A 405nm LED to have ideality factor about 6.1 in the 1μA-10mA regime, and about twice so in the nA regime. – dominecf Oct 29 '20 at 18:56
  • You can simulate the physics of an custom LED in Falstad’s site with ideality factors Rs and Vf to test and verify – Tony Stewart EE75 Oct 30 '20 at 02:03

2 Answers2

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I am currently taking a semiconductor class and we recently did an experiment to measure the ideality factor for two different diodes, one of germanium and one of silicon composition. The experiment found the silicon diode to have an ideality factor of 1 and the germanium to have a factor of 1.4. According to my professor the ideality factor is indicative of the type of charge carrier recombination that is occurring inside of the diode based on the following chart.

Recombination Type n Description
SRH, band to band (low level injection) 1 Recombination limited by minority carrier.
SRH, band to band (high level injection) 2 Recombination limited by both carrier types.
Auger 2/3 Two majority and one minority carriers required for recombination.
Depletion region (junction) 2 Two carriers limit recombination

In order to calculate n, I measured and graphed the I-V (V being the voltage across the diode not the applied voltage) characteristics of the diodes and found the slope as such:The IV characteristics of a silicon diode in a logarithmic scale

Then knowing this relationship where e is the charge of an electron, T is temperature and K is the Boltzman constant and \$I_{0}\$ is the inverse saturation current

$$ \ln I = \ln I_{0} + \frac{1}{n} \left( \frac{eV}{kT} \right). $$

I find the slope of the graph to be

$$ m = \frac{1}{n} \frac{e}{kT}. $$

Solving for n yields a 1.

I think that answers 3 out of 5 of your questions.

I hope all of that helped!

RussellH
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Kevin
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  • I imagine which type of charge carrier recombination is happening depends on things like temperature and current density, too, no? – Hearth May 24 '18 at 18:37
  • \$y = mx + c\ \$, so \$y = ln(I)\ \$, \$m = \frac{1}{n} \frac{e}{kT}\ \$, \$x = V\ \$, and \$c = ln(I_0)\$. – Unknown123 Jun 30 '22 at 08:02
  • So after simple linear regression, let \$r\$ be the sample correlation coefficient. It will be equal to \$m\$, which is the slope of the graph. Easy to automate. – Unknown123 Jun 30 '22 at 08:18
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https://www.youtube.com/watch?v=BC1E13CKf8g

You can watch this video. An ideal diode has the ideality factor of 0. Forward bias, the current --> infinity. Reverse bias, the current --> 0. This diode does not exist in real life. And due to the recombination property of the Si and Ge, all the diode made by these two materials have the ideality factor between 1 and 2. The diode having ideality factor <1 does not exist either.

Robert Zhang
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