Conductivity

Updated January 31, 2006

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This page discusses of the differences between five categories of materials according to their conductivities:

Insulators

Semi-insulators

Semiconductors

Conductors

Superconductors

This page also explains the concept of sheet resistance and conductivity.

The distinctions below are in common usage but may be seen as arbitrary since there is no industry standard that can be applied here (perhaps IEEE will someday come up with one). You can also check out our page on conducting materials.

Insulators

This category is VERY resistive (duh). Bulk resistivity is within the range of 10¹⁰ to 10²² ohm-centimeter to be considered an insulator. Any "good" dielectric material is an insulator. Insulators include glass, plastic, rubber, silicon dioxide, and silicon nitride
Insulating materials have tightly bound electrons (usually eight) in the outer shell that are happy to remain there even in the presence of high voltage electric fields.

Semi-Insulators

Semi-insulators have bulk resistivities between 10³ to 10¹⁰ ohm centimeters. Cut fresh from the boule, GaAs wafers are said to be semi-insulating.

Semiconductors:

Semiconductors have bulk resistivity in the range of 10^-4 ohm-cm (heavily doped) to 10³ ohm-cm (undoped, or intrinsic). That's seven orders of magnitude! Semiconducting elements include silicon and germanium, it is no coincidence they are both from group 4 of the period table. Semiconducting compounds include gallium arsenide, indium phosphide, and gallium nitride, from groups 3/5 or 2/6 of the period table.

Semiconductor materials have 4 electrons in their outer shell (it's half filled). When bonded together in a crystal lattice, atoms share electrons such that they each have eight electrons in the outer shell. Electrons are somewhat loosely bound so they can become carriers in the presence of an electric field.

Conductors:

To be considered a conductor, a material must have a bulk resistivity within the range of 10^-6 to 10^-4 ohm-cm. Conductor materials have loosely bound electrons (one or two) in the outer (valence) shell that can move easily under the influence of a voltage to form current. Conductors include elemental metals such as copper, gold, silver, aluminum. Heavily-doped semiconductors can also be considered conductors.

Superconductors:

What constitutes a superconductor? Not bulk resistivity of 10^-6 ohm-centimeters or less. Bulk resistivity of ZERO. We are talking perpetual motion here.

A superconductor is a material that loses all resistance to the flow of electric current when it is cooled below a certain temperature, called the critical temperature or transition temperature. Above this temperature, there is usually little or no indication that the material might be a superconductor. Below the critical temperature, not only does the superconductor suddenly achieve zero resistance, it gains other unusual magnetic and electrical properties.

H. Kamerlingh-Onnes discovered superconductivity in 1911. Learn more about him in our Microwave Hall of Fame.

Until recent years, superconductivity could only be achieved by cooling certain materials in liquid helium, a coolant that is expensive and difficult to handle but provides a temperature of 4 degrees Kelvin. The superconductors that require a liquid helium coolant are now called low temperature superconductors (LTSC).

In 1987, the discovery of materials that become superconducting at the temperature of liquid nitrogen (77°K or -196°C) made the science of superconductivity much more accessible to the unwashed masses including you and I. Since liquid nitrogen is an inexpensive and easily-handled coolant, experiments and demonstrations in superconductivity are now available to anyone with modest laboratory resources.

Superconductivity above the temperature of liquid nitrogen is called high temperature superconductivity (HTSC). "High temperature" may seem like a misrepresentation; to anyone who lives in the desert, -196°C seems pretty cold. Yttrium-barium-copper-oxide superconductor (YBCO) is a high-temperature superconductor.

The HTSC discovery renewed hope of discovering room-temperature superconductivity. So far, however, superconductivity remains in the realm of very low temperatures. Even without a room-temperature superconductor, rapid advances in superconductivity research are providing breakthroughs in microwave applications right now. The first application that will see the light of day is extremely high-performance RF filters (Q can be really high when you have no resistive losses). Superconductor Technologies Inc. is one vendor that you can talk to about this new market. These guys really get it... they even have a web page called "Superconductors 101!"

Sheet resistance and sheet conductivity

This concept is further explained on our page on resistor mathematics.

Bulk resistivity is a the property which is independent of frequency and geometry. In microwaves, often we are dealing with thin films of conductors, which have been applied at a controlled thickness. A more convenient property to deal with in this case is sheet resistance. The sheet resistance of a metal film is often expressed in ohms/square. What's a square? Exactly that. Who's on first? I Don't Know's on second.

Recall the equation for calculating resistance from bulk resistivity:

Remember, the resistance calculated this way does not account for skin depth effects. It is accurate if your conductor thickness is small compared to a skin depth.

If you consider the quantity L/A, it is unitless. It can be considered as a measure of how many squares of area your conductor or resistor has. For example, a thin-film resistor with length 30 mils and width 10 mils is three squares. A smaller resistor of 3 microns length and 1 microns width also has three squares (thanks Jack!) And if they both have the same thickness and bulk resistivity, they both have the same value in ohms. They will have far different power ratings, and the smaller resistor will have a higher usable frequency response. Be careful not to mix up length and width, a resistor with 10 microns length and 30 microns width measures 1/3 square, not three squares!

Sheet resistance, R_sh, is equal to bulk resistivity divided by thickness. It can be used to conveniently calculate resistance values from number of squares, as follows:

As in all engineering, you will need to keep units consistent in order to make the calculation correctly (if rho is in ohm centimeters, the thickness must also be in centimeters). One last thing to consider: sheet conductivity is the inverse of sheet resistivity. When is sheet conductivity useful? When you have more than one metal layer. The sheet conductivities of the layers can be added, because the conduction paths are in parallel.