The geometric resistivity correction factor for several geometrical samples

Serdar Yilmaz

doi:10.1088/1674-4926/36/8/082001

J. Semicond. > 2015, Volume 36 > Issue 8 > 082001, doi: 10.1088/1674-4926/36/8/082001

SEMICONDUCTOR PHYSICS

The geometric resistivity correction factor for several geometrical samples

Serdar Yilmaz^{1, 2}

+ Author Affiliations

Corresponding author: Serdar Yilmaz, E-mail: syilmaz@mersin.edu.tr

Abstract: This paper reviews the geometric resistivity correction factor of the 4-point probe DC electrical conductivity measurement method using several geometrical samples. During the review of the literature, only the articles that include the effect of geometry on resistivity calculation were considered. Combinations of equations used for various geometries were also given. Mathematical equations were given in the text without details. Expressions for the most commonly used geometries were presented in a table for easy reference.

Key words: semiconductor, four point probe, conductivity measurement, resistivity correction factor

References

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Fig. 1. The measurement with random four probes on surface.

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Fig. 2. Measurement set-up with four in-line array probes.

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Fig. 3. Electrical current on the conductive layer.

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Fig. 5. $Y$ point away from single polar X point.

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Fig. 6. The $Y$ point that $r_{1}$ and $r_{2}$ distance from electrical dipole.

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Fig. 7. The two different points away from current dipole with $r$ distance.

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Fig. 4. The sample with $t$ thickness.

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Fig. 8. $B$ reference point on the sample with semi-infinite extensions and $t$ thickness.

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Fig. 9. Randomly selected the $B$ point that is $r$ distance from current dipole $A$ and $C$ point.

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Fig. 10. Randomly selected two points (1 and 2) that are $r$ distance from current dipole 1 and 4 point.

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Fig. 11. Infinitesimal thin and circular surface.

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Fig. 12. Thin circular sample with $t$ thickness.

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Fig. 13. Placements of probes on circular sample.

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Fig. 14. Rectangular prism sample with $t$ thickness and probes with $R$ radius.

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Fig. 15. Cylindrical sample with $R$ radius.

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Table 1. $t$ and $s$ relations commonly used for an infinite extent.

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Table 2. $F_{1}(t/s)$ factor values versus $t/s$ ratio.

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Table 3. The effect of the thickness.

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Table 4. Computed $F_{2}$ values for different $d/s$ ratios.

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Table 5. The Geometric Factor equations for the commonly used geometries.

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Received: 07 January 2015 Revised: Online: Published: 01 August 2015

This paper reviews the geometric resistivity correction factor of the 4-point probe DC electrical conductivity measurement method using several geometrical samples. During the review of the literature, only the articles that include the effect of geometry on resistivity calculation were considered. Combinations of equations used for various geometries were also given. Mathematical equations were given in the text without details. Expressions for the most commonly used geometries were presented in a table for easy reference.

The geometric resistivity correction factor for several geometrical samples

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