Author Topic: An Innovative Method of Measuring Semiconductors Resistivity Using Van der Pauw  (Read 1906 times)

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Author : Amir J. Majid
International Journal of Scientific & Engineering Research Volume 2, Issue 10, October-2011
ISSN 2229-5518
Download Full Paper : PDF

Abstractó Van der Pauw technique for measuring semiconductors resistivity is adopted to remove contacts and isolation effects on high resistance materials. An innovative digital method is proposed using, analog-to-digital (ADC) and digital-to-analog (DAC) circuits to reduce voltage coefficient, temperature coefficient and geometrical errors. With the aid of an N-bit timer and N-bit ADC and DAC, a set of 2N values of different values of current sources are applied and consequent voltage measurements are used in the calculation of resistivity. Consequently, a more accurate average is obtained with less voltage coefficient and temperature effects. This can be implemented by the use of embedded computers and microcontrollers.

Index Termsó resistivity, measurement, Van der Pauw, semiconductors, contacts, voltage coefficient, microcontrollers

1. Introduction
Semiconductors have high resistivity in the mega-ohm range and special methods are required to avoid contact and isolation resistances, leakage currents as well as voltage, temperature and bandwidth effects. The four-point method and Van der Pauw techniques are normally used for the resistivity measurement to avoid most of these erroneous effects. A more innovative method is needed, in which not analog measurement, but rather digital arrangement is used with the aid of embedded microcomputers.

   Semiconductor Resistivity
Certain conductor materials, such as silicon, may have high resistivity. Several factors can complicate measuring the resistivity of these materials, including problems in making good contact with the material. Special probes have been designed for making resistivity measurements on semiconductor wafers and bars. These probes typically use
a hard metal such as tungsten, which is ground to a sharp point . Contact resistance is a very high in these cases, thus  either a four-point probe or four isolated probes should be used. While two contacts supply a constant current, the other two contacts are used to measure the voltage drop across a portion of the sample, as depicted in Fig. 1. The resistivity can be calculated by applying geometrical factors in the computation of sample resistance.
These measurements may seem straightforward, but certain precaution should be observed, such as good shielding of the contacts and electrical leads is in order to avoid any diode action pickups.

Four-Point Resistivity Method
The four-point collinear probe resistivity measurement technique, [1], [2], [3], [4] involves bringing four equally spaced probes in contact with the material of unknown resistance, such as a semiconductor wafer. The probe array is placed in the center of the material as shown in Fig. 2. A known current source is passed through the two outside probes and the voltage is sensed at the two inside probes. The resistivity ρ is then calculated as:

ρ = (π/ln2) t k V/ I              (1)

where:   V =  the measured voltage (volts)
   I  =  the source current (amps)
   t  =  the wafer thickness (cm)
k =  a correction factor depending on the ratio of the probe to wafer diameter and on the ration of wafer thickness to probe separation.

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