# Why four probe is used instead of two probe to find resistivity

Saurabh Kumar
9 years ago
Resistivity, Rho, is a particularly important semiconductor parameter because it can be related directly to the impurity content of a sample; The four point probe is the apparatus typically used to determine bulk resistivity.

The mobility of the carriers depends upon temperature, crystal defect density, and ALL impurities present. Hall Effect Measurements can determine the mobility of the carriers in a given sample to allow for more accurate dopant concentration measurements, but Hall measurements are usually destructive to the sample.

The four point probe contains four thin collinearly placed tungsten wires probes which are made to contact the sample under test. Current I is made to flow between the outer probes, and voltage V is measured between the two inner probes, ideally without drawing any current. If the sample is of semi-infinite volume and if the interprobe spacings are s1= s2 = s3 = s, then it can be shown that the resistivity of the semi-infinite volume is given by

Rhoo =(2 Pi s)V/I (1)

The subscription in the preceding equation indicates the measured value of the resistivity and is equal to the actual value, Rho, only if the sample is of semi-infinite volume. Practical samples, of course, are of finite size. Hence, in general, Rho != Rhoo. Correction factors for six different boundary configurations have been derived by Valdes.(1) These show that in general if l, the distance from any probe to the nearest boundary, is at least 5s, no correction is required. For the cases when the sample thickness is <= 5s, we can compute the true resistivity from

Rho = a 2 Pi s V/I = a Rhoo (2)

where a is the thickness correction factor which is plotted on page GT-2. From an examination of the plot we see that for values of t/s >= 5 the corresponding value of a is unity. Thus for samples whose thickness is at least 5 times the probe spacing, no correction factor is needed. Typical probe spacings are 25-60 mils and the wafers used in most cases are only 10-20 mils, so unfortunately we cannot ignore the correction factor. Looking again at the plot, however, we see that the curve is a straight line for values of t/s <= 0.5. Since it is a log-log plot the equation for the line must be of the form

a = K (t/s)^m (3)where K is the value of a at (t/s) = 1, and m is the slope.