Author Topic: Resistivity Measurements of Conductors and Semiconductors of Different Geometric  (Read 2694 times)

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Author : Amir J. Majid
International Journal of Scientific & Engineering Research Volume 2, Issue 10, October-2011
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Abstractó The resistivity of conductive and semi-conductive materials, are determined using an algorithmic computation approach of Van der Pauw technique. Different geometrical shapes, such as bulk, surface, bars, wafers, are used are implemented. The four-point method has been extended to multi-point measurement of surface and volume geometrical shapes, with consequently rearranging the equations derived in Van der Pauw technique. It is proposed that the multi-point measurements derivations can be applied using a multiplexer (MUX) and a de-multiplexer (de-MUX) digital circuits, and further on, embedded microprocessors and microcontrollers.

Index Termsó resistivity, Van der Pauw, conductors, semiconductors, shapes, geometries, equation derivations, digital, MUX, de-MUX

To measure the resistivity of low resistance materials such as contacts, foils, bars rods and superconductors, very sensitive voltmeter with a current source or a micro-ohmmeter are required. The measurement is subject to additional erroneous sources including lead resistance, non-ohmic contacts, thermoelectric EMFs and device heating.
Semiconductors, on the other hand, have high resistance and can induce significant noise sources such as Johnson noise. It must also be noted that high resistance measurements are subject to a loading errors from the meter input impedance, as well as the impedance of the connecting cable. This requires extra efforts to reduce errors such as the use of very high input resistance meters as well as guarding cables and wires used.
Other noise sources are magnetic fields and ground loops arising from leakage currents due to insulated materials in the circuit measurement. In order to measure voltages from high-resistance sources accurately, the insulation leakage resistance of the test fixtures, test leads, and measuring voltmeter must be several orders of magnitude higher than the Thevenin equivalent resistance of the circuit under test, depending on the accuracy and resolution required. This is due to the shunting effects of insulators, which makes detecting inferior insulation in test-ups difficult.
Temperature and humidity effects on noise and insulation can also generate erroneous measurements. High temperature can increase Johnson voltage noise, whereas high humidity can degrade the function of insulation

2    Resistivity Measurements
2.1 The Four-Point Method
Due to the limitations of a typical two-wire method in which a test current is forced through the test leads and the resistance being measured, and the voltage drop across sample resistance is measured; the 4-wire (Kelvin) connection method [1], [2], [3], [4], is generally preferred, as depicted in Fig. 1. It can be seen that some small current may flow through the sense leads, but generally can be ignored for smaller length leads. The resistivity is calculated as follows:

ρ=k V∕I                  (1)   
where V = the measured voltage,    I  =  the source current and  k =  sample material and shape constants.

2.2 Van der Pauw Technique
Van der Pauw technique [5], [6], implements the four-wire method to reduce thermoelectric EMFs effect. It is particularly useful for measuring very small samples because the dimensions of the sample and the spacing of the contacts are unimportant. This technique uses four isolated contacts on the boundary of a flat, arbitrary shaped sample. A total of eight measurements, are made around the sample, [7], as illustrated in Fig. 2.

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