# The ideality factor of Silicon and Germanium

Hi,

I am currently taking a course on electronics and not quite sure of what ideality factor really means...what does ideality factor indicates actually?

And the crucial part is what is the ideality factor of Silicon and Germanium? I've googled and found no relevant results are given other that strings of unknown equations.

By the way, is ideality factor denoted by the symbol η ?

Thanks for lending your hand to this electronic amateur. Related Electrical Engineering News on Phys.org
rbj
take a look at

http://en.wikipedia.org/wiki/Diode#Shockley_diode_equation

in the equation:

$$I=I_\mathrm{S} \left( e^{V_\mathrm{D}/(n\ V_\mathrm{T})}-1 \right)$$

the voltage $n\ V_\mathrm{T}$ defines when the exponential function is going to really take off, so it defines where the "corner" of the "elbow" of the junction's volt-amp characteristic.

$$V_\mathrm{T} = \frac{k_\mathrm{B}T}{e}$$

is the same for Si or Ge. wp says "The ideality factor $n$ typically varies from 1 to 2 (though can in some cases be higher), depending on the fabrication process and semiconductor material and in many cases is assumed to be approximately equal to 1 (thus the notation $n$ is omitted)."

i believe that $n$ is lower (closer to 1) for germanium and higher for silicon. this means that it takes a little more voltage to turn on a silicon diode (about 0.6v or 0.7v) and make it conduct than it takes to turn on a germanium diode (about 0.3v).

when i was a kid, i built a crystal radio where the headphones were powered solely by the radio transmitter which was 30 to 60 km away. all it was, was a simpled tuned circuit with a variable cap and a wound coil with a tap and a diode as a rectifier and headphones. and a long-wire antenna that has an "aperture" and scoops a measurable amount of power out of the sky. but you can imagine it was microwatts and, with 600 ohm headphones, it would be maybe hundreds of millivolts. the lower that gate threshold, the more energy that gets to the headphones.

so which kind of material was used for the rectifier diode, Si or Ge?

if you don't know, look up 1N34 .

Thanks...Actually the main thing that i want to know is the η or n or whatever value of Silicon and Germanium. My lecturer told my class to find the numerical constant depending on the material of the diode, η. Does my lecturer meant ideality factor? Or anything else?

rbj
as best as i can tell, this factor is 1 for germanium and around 2 for silicon. is your assignment to derive it from the atomic structure of these two elements? both are Group IV which is why they are semiconductors. they both have the same number of valence electrons in the outer shell, which is 4 (and has 4 missing electrons, too). i suppose that since germanium has an additional shell than does silicon, that is why its easier to get it to conduct in a PN junction (germanium is a little more metallic than is silicon) which makes its corner voltage less which means that $n$ is less. but i do not know how to derive that factor from the atomic structure. it was just listed in a table when i took solid-state physics.

:tongue2: actually it is for my exam... My lecturer leak out a question saying that η for Silicon and Germanium must be memorised. He didn't teach this in lecture, that's the reason why I seems a bit blur. Anyway, thanks!

Anyone else can give me the ideality factor, η for Silicon and Germanium?

rbj
here is a link http://webphysics.davidson.edu/alumni/jocowan/exp1doc.htm to a paper someone did somewhere where they empirically extracted the ideality factor from the V-I curves of various germanium and silicon diodes.

unlike what i would think is true, they have results where the ideality factor is larger for Ge than for Si. i find that hard to believe because i know that Ge diodes have a lower turn-on voltage than Si diodes.

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The ideality factor, n, relates to recombination sites in the space charge region. A diode that's free of recombination defects will have an ideality factor of 1. As the number of defects go up (i.e. doping with gold), the diodes ideality factor tends towards 2.
This value has no relevance to the type of material used. What is important, and intrinsic to the material, is it's bandgap energy. This is the energy required to jump from the valence to conduction bands. It's 1.11ev for silicon and .67ev for germanium.

rbj
This value has no relevance to the type of material used. What is important, and intrinsic to the material, is it's bandgap energy. This is the energy required to jump from the valence to conduction bands. It's 1.11ev for silicon and .67ev for germanium.
now doesn't that energy gap difference affect the turn-on voltage for the diode? and if the V-I equation is:

$$i = I_0 \left( e^{v/(n\ V_\mathrm{T})} - 1 \right)$$

now isn't the voltage $n\ V_\mathrm{T}$ directly proportional to the turn-on voltage of the diode? it seems to me that the two would have to be related.

dlgoff
Gold Member
I've been following this thread trying to understand this "ideality factor". I did a Google Scholar search on semiconductor ideality factor and this one was at the top of the list.

Abstract

A new and simple-to-use method to obtain homogeneous Schottky barrier heights from effective barrier heights and ideality factors that are determined from current-voltage (I-V) characteristics of metal-semiconductor contacts is presented. This approach is justified by a theory of metal-semiconductor interfaces with laterally inhomogeneous distributions of barrier heights. Effective barrier heights and ideality factors were determined from I-V characteristics of Si and GaN Schottky contacts and a linear reduction of the effective barrier heights with increasing ideality factors was always observed. These findings are explained by numerical simulations of inhomogeneous Schottky contacts which are based on theoretical results by Tung [Phys. Rev. B 45, 13509 (1992)]. The homogeneous barrier heights of metal-semiconductor contacts are obtained by a linear extrapolation of the effective barrier heights to nif ≅ 1.01, the value of the ideality factor characteristic for image-force lowering of Schottky barriers only. © 1997 American Vacuum Society.
"ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4969230" [Broken]

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The ideality factor is not primarily related with the semiconductor.

It has very much to do with the shape of the junction, which is almost never flat (except in a few photodetectors or Solar cells); a cylindrical junction differs from 1 even in simple theory.

It results strongly from the doping profile, that is, doping doesn't change abruptly from full-N to full-P within the thickness of the depleted zone - far less so as the zone gets thinner in direct polarisation, which is the case when the ideality factor plays.

Diodes tend to have a factor seriously above 1. When one needs a component that works like a simple diode, especially with this factor near 1, he has to use a transistor, with base and collector tied together. This is important if measuring the temperature through a junction voltage, or if building a bandgap voltage reference.

rbj
i would expect it would have something to do with the doping profile. am a little surprized that it's affected by the concentric cylindrical junction shape vs. flat.

but what i am still stuck with from my old experience from 40 years ago is that Ge diodes always had a significant smaller turn-on voltage (about 0.3 v) than did Si diodes (about 0.6v or 0.7v). now as i look at this V-I equation:

$$i \ = \ I_0 \left( e^{v/(n \ V_\mathrm{T})} - 1 \right)$$

i can't help but infer that the turn-on voltage is directly proportional to $n\ V_\mathrm{T}$. and since $V_\mathrm{T}=\frac{k_\mathrm{B}T}{e}$ is the same for every junction, isn't the only think that can move this diode breakpoint voltage is $n$?

"Ideality factors between 1.0 and 2.0 are normally
attributed to the competition between the carrier driftdiffusion
process and the Sah–Noyce–Shockley generationrecombination
process.9 Ideality factors exceeding 2.0
have been suggested to originate from the trap-assisted
tunneling4–7 and carrier leakage.7 However, no quantitative
attempts have been reported to connect these two mechanisms
to the abnormally high ideality factors found experimentally
in GaN-based LEDs."

The origin of the high diode-ideality factors in GaInN/GaN multiple
quantum well light-emitting diodes
Di Zhu,1 Jiuru Xu,1 Ahmed N. Noemaun,1 Jong Kyu Kim,1 E. Fred Schubert,1,a
Mary H. Crawford,2 and Daniel D. Koleske2
1Department of Physics, Applied Physics, and Astronomy, Future Chips Constellation
and Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute,
Troy, New York 12180, USA
2Sandia National Laboratories, Albuquerque, New Mexico 87185, USA

Classically, it's recombination. As to Germanium and silicon having different forward voltages, they also have vastly different leakage currents.