# Interpreting range of conductivity diagram

I have found the following diagram (unfortunately in german) about the range of conductivity of conductors (Leiter), semiconductors (Halbleiter) and insulators (Isolatoren).

How should one interpret the ranges of conductivity for a specific material?

Is it correct that for the semiconductors the range is because of the temperature dependence of conductivity? However the conductors are also temperature dependent (positive temperature coefficient) and should therefore also occupy a range.

Is it correct, that the ranges for the insulators is just because for example hard rubber is not an element and can have many different chemical implementations? Or is the conductivity of Insulators temperature dependent too?

So it would be nice, if someone could clarify those points, add a bit background and give me some orders of magnitude and perhaps references for this.

Because its in german I add some translations:

• The axis to the right is the specific electrical resistance.
• Fester Körper: solid
• Eisen: iron
• Bernstein: Amber
• Glimmer: mica
• Hartgummi: hard rubber
• Kupferoxid: Copper oxide
• Quecksilber: Mercury
• Silizium: Silicon
• Silber: Silver
• Selen: Selenium
• Germanium: Germanium
• Glas, Keramik: Glass and ceramics
• Quarz: Quartz
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Conductors, semi-conductors and insulators are generally distinguished by their different mechanisms of conduction.

In metallic conductors there are electrons that are not bound to any particular atom and are relatively mobile. This means they move easily when a voltage is applied, and hence the metal conducts well. See http://en.wikipedia.org/wiki/Metal#Electrical for an introduction and follow the links therein for more details.

Semi conductors do not have the free electrons that metals have. However the distance between the lowest occupied electron band and the lowest empty electron band is quite small, and at room temperature a significant number of electrons are thermally excited into the empty band, and these electrons can conduct. Because this is a thermal excitation the conductivity is usually highly temperature dependant, and because only a few electrons are involved the conductivity is a lot less than metals. Again Wikipedia has an excellent article on this, see http://en.wikipedia.org/wiki/Semiconductor.

Note that pure (intrinsic) semiconductors often have impurities added to change their electrical properties. This is known as doping and is an essential part of maing integrated circuits. See http://en.wikipedia.org/wiki/Doping_(semiconductor) for more info.

In insulators the gap between the highest full and lowest empty eletron band is large compared to room temperature so there are no free electrons available to conduct electricity, though all insulators conduct a bit. For info see, yes it's Wikipedia again, http://en.wikipedia.org/wiki/Insulator_(electricity).

I've mention electron bands several times. See http://en.wikipedia.org/wiki/Band_structure for what I mean by this. Basically they're the solid state equivalent of molecular orbitals. Full bands don't conduct because the electrons have no free energy states to move into, so they are immobile. Electrons in part filled bands are mobile so materials with such bands will conduct.

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Thanks for the long explanation, but this doesn't really answer my questions. So it would be nice if you could tie it more explicitly to my questions in my original post. –  martin Mar 18 '12 at 19:32
I can't comment on the diagram because I haven't read the paper it came from. The conductivity of semiconductors is affected by even low levels of impurities, so the range may indicate silicon of a range of different purities. Metals are must less affected by impurities, which is presumably why no range is shown. For insulators conduction tends to be mainly due to impurities or defects, and of course for natural materials like mica the composition can be variable. –  John Rennie Mar 19 '12 at 11:01

John Rennie is correct with the different mechanisms of conduction, to the range part of your question I want to add that it depends on other things than the material.

The part of your question about the ranges is more connected to the difference of a real material and it's ideal description. Electricial resistivity is heavily influenced by impurities and defects in materials, this leads to large resistance ranges for a single substance. In metals you can get residual resistivity ratios (so $\rho$ at room temperature vs. $\rho$ at low T) between 10 and 10000 just depending on the treatment of the material.

For semiconductors it largely depends on doping and purity. If you test a very clean piece of silicon it will behave like an isolator (especially at lower temperatures). With a high doping level you can get the resistivity almost to a metallic level.

For insulating materials such as ceramics you can still have conduction via tunneling between defect sites.

So the main reason for the large ranges are impurities, defects and dopings of otherwise ideal materials.

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When you say, that residual resistivity ratios are between 10 and 10000 for metals, does that mean, that the posted image is not correct, because there for example iron is displayed by a dot? –  martin Mar 18 '12 at 20:05
@martin: The image is not wrong for what it is trying to show. There is definitely not a single value for iron and a range for Germanium. The usual range for iron is just smaller, that's why they choose a dot. The residual resitivity ratios tell you something about the temperature dependence, so they are a guideline for the purity of the material. At room temperature the resistivity is more determined by scattering of electrons with phonons and other electrons than by scattering at defects. –  Alexander Mar 19 '12 at 12:08