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Ohms per Square What?

by: Steve Fowler

 

The answer is: "It does not Matter." Square anything!

This term has been used for years by many who deal in electrical measurements but it is still not clearly understood.  ASTM D-254 test method is used to measure the surface resistivity of materials. The units of measurement are Ohms per Square. Even though the ESD Associations Test Method S11.11 uses resistance measured in Ohms, the resistivity of many materials is still required for characterization and contract requirements. Most people do not ask what it means for fear of showing their ignorance. Let 's try to clear it up a bit.

Ohms per square is the unit of an electrical measurement of surface resistivity across any given square area of a material. It is the measurement of the opposition to the movement of electrons across an area of a material's surface and normalized to a unit square. This measurement is intended to be a basic material parameter and not dependent on absolute area, length or thickness. Unlike resistance, resistivity is not exactly a point-to-point measurement. It is a measurement where the electrons can take multiple paths across a uniform surface. However, the electrons are considered to generally flow only on the surface.

The measurement of resistance is not the same as resistivity. Resistance is the opposition to electron flow across or through a material, and is measured from point-to-point . It is not normalized. This measurement is very dependent on size, length, cross-section, etc.

The above figure shows the measurement of a material with the same dimensions on all sides. It is a square area of the material.  It can be 1 inch or 1 mile on a side.  When electrodes are attached as shown, and the Ohm meter measures 1 Ohm, we can state that this material has a surface resisitivty of 1 Ohm per square.

If two squares of the material (the same size as above) are laid end to end and electrodes attached as shown below, the resistance is the addition of these two squares or 2 Ohms.  This measurement is of two resisters in series.

 

Or if two of these squares are stacked as shown below, the resistance is that of two resisters in parallel or 1/2 Ohm.

 

Now if we combine these two examples we have four squares of the materials in an arrangement of two parallel resisters in series.  Or the resulting four resisters which now form a square again read 1 Ohm on the Ohm meter.

 

If we take the examples to a higher level where we have 16 squares of the material arranged as shown below,  the result is again 1 Ohm.  It is again in this example a square.  If the first example is 1 square inch then this example is 4 square inches and the results are the same - 1 Ohm.

 

So you see that it really doen't matter.  A square inch or a square mile of a material with a surface resistivity of 1 Ohm per square will read just 1 Ohm on an Ohm meter.

Strange isn't it?

 

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