# What is a typical diode's ideality factor?

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?

• 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. " researchgate.net/publication/… Commented Apr 18, 2018 at 13:02
• 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). Commented Apr 18, 2018 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. Commented Oct 29, 2020 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 Commented Oct 30, 2020 at 2:03

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:

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.

• $y = mx + c\$, so $y = ln(I)\$, $m = \frac{1}{n} \frac{e}{kT}\$, $x = V\$, and $c = ln(I_0)$. Commented Jun 30, 2022 at 8:02
• 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. Commented Jun 30, 2022 at 8:18