In this article we will discuss about the measurement of conductivity using four probe method.
After a semiconductor material is grown, it is ofcourse vital to determine its usefulness for device fabrication. There are several properties which have a strong effect on the final characteristics of diodes and transistors made from single crystal of semiconducting material. Most important of these are the carrier type, conductivity of the crystal, lifetime of minority carriers and mobility of the carrier in the crystal.
In principle, the conductivity of semi-conductivity may be found by measuring the current drawn when a voltage is applied between the two contacts formed at the ends of a bar of the material. In practical, such a measurements is not straightforward because of the difficulty of making uniform ohmic contacts to the sample.
Further it is not always convenient to produce a specimen of known dimensions for a conductivity measurement. The four-point probe method eliminates the difficulties referred to it; it is used to measure, non-destructively and accurately, the conductivity of ingots or slices, both thick and thin, of semiconductor crystals.
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The probe head basically employs four springs loaded, equispaced needles which make contact with a plane lapped surface on the specimen as shown in Fig. 7.23. A stabilized current is passed through the outer pair of the probes, A and D, and voltage V, between the other two B and C is measured by a voltmeter which draws negligible current.
Let us firstly consider the sample discussions to be large compared with the probe spacing, d. We can the source current at A and the sink at D independently, using the superposition principle to find their combined effect later. Thus, the current density Jr at radius r from A, due to the current I entering at A is-
Jr = I/2πr2
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Since current only flows in the bottom half plane. We then use Ohm’s law to find the corresponding electric field Er, at r
Er = J/σ = I/2πσr2
Where σ is the conductivity of the material. By definition, the floating potential at some radius is then-
The potential difference between probes B and C due to the current source at A is then
If we now consider the current leaving at D separately, there exists a potential difference between B and C, which because of symmetry, is the same as that due to the current source above, given in above equation. By superposition, the total voltage measured between B and C is thus twice that for current source or sink alone or
V = I/2 πσ d
from which the conductivity is obtained.
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σ = I/2π d v
This equation is valid only for materials whose dimensions are large compared with the probe spacing d. If this is not the case, e.g., when measurements are made on thin slices or small dice of material, then a correction factor F, is introduced and conductivity is given by
σ = σ0F
where σ0 is the uncorrected value of σ. Factor F is a function of slice thickness, breadth, and width, normalized to the probe spacing.