Electrical Resitivity, (also known as specific electrical resistance or volume resistivity) is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electrical charge.†
Resistivity, or the four-point probe, has been widely used for studying semi-conductor materials, and the relationship between the probe geometry, voltage drop, and sample resistivity has been established for many common cases. Although the relationship cannot be solved in closed form for a sample of arbitrary geometry, two important cases lead to very simple solutions.
In view of the figure above, we see the following: current through the sample, the voltage detected across the inner probes, the distance between the probes, and the thickness of the sample. For samples of length and width several times the overall probe spacing, the resistivity is:
(1) ρ = Vt/I 1n2 = 4.53Vt/I for sheets with t < 0.5s, and
(2) ρ = 2πs V/I = 6.28sV/I for sheets with t > 3s
The sample resistivity ρ is in units of µΩcm (micro-ohms cm).
Note that for thin sheets, ρ is determined independent of the probe spacing. For thick sheets, the determination is independent of thickness. An important implication of Equation 2 is that the resistivity can be determined for massive samples (e.g., ingots, bars, large weldments) provided only that there is one surface available for probe placement and that the overall sample size is large compared to the probe spacing.
There have been analyses of several cases where the probe dimensions and where the solutions are considerably more complex than Equations 1 and 2. It is possible to use their results to determine the resistivity in these intermediate cases. However, it has been our experience that for most cases of practical interest it is possible to choose a probe spacing that allows the use of either Equation 1 or 2.‡
