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Can the four-point probe be used to characterize dopant concentration in a film?
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The four-point probe method involves using four equally spaced probes to measure the electrical resistivity of a material. This technique minimizes the effects of contact resistance, allowing for more accurate measurements of the material's properties. Show more…
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In the lab, you wish to measure the conductivity of a thin film semiconducting sample. One method you use is what is known as a four-point probe, which is used to measure the resistivity. The basic setup of a four-point probe is shown below. During measurement, the four equally spaced probes are lowered to be in contact with the sample. A current is supplied through the outer probes and a voltage is measured across the inner probes. a) For a thin film sample, you have derived an expression for the resistance between points x1 and x2 to be R = (pi/ln2) * (V/I). Given that the differential resistance is dR = rho * (dx/A), derive an expression for the conductivity sigma. The cross-sectional area A = 2pi*xt for a sample of thickness t through which current flows is shown above on the right. b) You measure two films with the following doping characteristics. Calculate the electron and hole mobilities. Doping | sigma (ohm*m)^-1 | n (m^-3) | p (m^-3) Intrinsic | 8.9 x 10^4 | 8.7 x 10^23 | 8.7 x 10^23 Extrinsic (p-type) | 2.3 x 10^5 | 7.6 x 10^22 | 1.0 x 10^25
Another technique for determining the conductivity type of a semiconductor is called the hot probe method. It consists of two probes and an ammeter that indicates the direction of current. One probe is heated and the other is at room temperature. No voltage is applied, but a current will exist when the probes touch the semiconductor. Explain the operation of this hot probe technique and sketch a diagram indicating the direction of current for p- and n-type semiconductor samples.
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