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# Haldor Topsoe “Geometric Factors in Four Point Resistivity Measurement”

Question: What is the need for correction factors in four point probe measurements?

Answer: The geometry of the sample determines the correction factors that must be used, additionally the position of the probes on the sample and the spacings between the probes. The need for correction factors is caused by the proximity of a boundary which limits the possible current paths in the sample. The most basic sample would be semi-infinite in extent i.e., it extends to infinity in all directions below the plane in which the four probes are located. All other cases would restrict the current paths available, eg., an infinite plane sample of finite thickness requires a correction factor based on the thickness.

The table shown immediately below pertains to one of the most commonly needed correction factors, i.e., correction factors for measuring a “thin, circular slice”. After the table, you will find links to all of the pages from the 1966 (revised 1968) Haldor Topsoe book, “Geometric Factors in Four Point Resistivity Measurement”,with each page available as an individual PDF file. The book covers a wide range of correction factor topics.

Correction factors for measuring a thin circular slice, measured in the center

The following table pertains to sheet resistance measurements made in the center of a circular slice. d/s = diameter of sample divided by probe spacing (probe spacing being the distance between any two adjacent probes). For example, a 4mm diameter sample probed with a four point probe with 1mm tip spacing would have a correction factor of 0.6462. A 100mm wafer measured with a four point probe head that has 1mm tip spacing would have a correction factor of 0.9991. A result better than 0.1% can be obtained by measuring in the center of a circle with diameter greater than 100 x s., better than 1% is obtained with 40 x s.

d/s
Correction
3
0.5
3.448
0.5734
4
0.6462
5
0.7419
6.061
0.8089
7.5
0.8665
8.696
0.8972
10
0.9204
12.5
0.9475
15
0.9628
20
0.9788
28.57
0.9895
40
0.9945
100
0.9991
infinite
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Haldor Topsoe book, “Geometric Factors in Four Point Resistivity Measurement”

haldor.exe  11,088K   Self extracting file containing 64 individual PDF files that make up the Haldor Topsoe four point probe reference book, “Geometric Factors in Four Point Resistivity Measurement”

The individual pages:
Haldor Topsoe, Page 0, Haldor Topsoe cover page “Geometric Factors in Four Point Resistivity Measurement” 42K PDF
Haldor Topsoe, Page 1, “Introduction” (to Four-Point Probe Resistivity Measurements) 104K PDF
Haldor Topsoe, Page 2, “Introduction” (continued) 116K PDF
Haldor Topsoe, Page 3, “Introduction” (continued) 130K PDF
Haldor Topsoe, Page 4, “Introduction” (continued) 103K PDF
Haldor Topsoe, Page 5, “Introduction” (continued) 91K PDF
Haldor Topsoe, Page 6, “Introduction” (continued) 72K PDF
Haldor Topsoe, Page 7, “Introduction” (continued) 87K PDF
Haldor Topsoe, Page 8, “Introduction” (continued) 78K PDF
Haldor Topsoe, Page 9, “Introduction” (continued) 37K PDF
Haldor Topsoe, Page 10, “Quarter Infinite Volume, Probe Array Perpendicular to Edge” 88K PDF
Haldor Topsoe, Page 11, “Probe Array Parrallel to Edge” 54K PDF
Haldor Topsoe, Page 12, Graph – “Quarter Infinite Volume” 460K PDF
Haldor Topsoe, Page 13, “Infinite Plane Sample of Finite Thickness, Thick Sample”92K PDF
Haldor Topsoe, Page 14, Graph – “Infinite Plane Sample of Finite Thickness, Thick Sample” 474K PDF
Haldor Topsoe, Page 15, “Thin Sample” 75K PDF
Haldor Topsoe, Page 16, Graph – “Infinite Plane Sample of Finite Thickness, Thin Sample” 460K PDF
Haldor Topsoe, Page 17, “Semi-Infinite Plane Sample of Finite Thickness, Probe Array on the Edge” 59K PDF
Haldor Topsoe, Page 18, “Probe Array Perpendicular to Edge, Thick Sample” 66K PDF
Haldor Topsoe, Page 19, Graph – “Thick Semi-Infinite Plane Sample” 436K PDF
Haldor Topsoe, Page 20, “Probe Array Perpendicular to Edge, Thin Sample” 81K PDF
Haldor Topsoe, Page 21, “Probe Array Perpendicular to Edge, Thin Sample” (continued) 98K PDF
Haldor Topsoe, Page 22, Graph – “Thin Semi-Infinite Plane Sample” 377K PDF
Haldor Topsoe, Page 23, Graph – “Thin Semi-Infinite Plane Sample” (more) 430K PDF
Haldor Topsoe, Page 24, “Probe Array Parrallel to Edge, Thick Sample” 108K PDF
Haldor Topsoe, Page 25, Probe Array Parrallel to Edge, Thick Sample” (continued) 86K PDF
Haldor Topsoe, Page 26, Graph -“Thick Semi-Infinite Plane Sample” (more) 431K PDF
Haldor Topsoe, Page 27, “Probe Array Parallel to Edge, Thin Sample” 119K PDF
Haldor Topsoe, Page 28, “Probe Array Parallel to Edge, Thin Sample” (continued) 84K PDF
Haldor Topsoe, Page 29, Graph – “Thin Semi-Infinite Plane Sample” 415K PDF
Haldor Topsoe, Page 30, Graph – “Thin Semi-Infinite Plane Sample” 460K PDF
Haldor Topsoe, Page 31, “Bar of Rectangular Cross Section, Rectangular Cross Section” 137K PDF
Haldor Topsoe, Page 32, “Bar of Rectangular Cross Section, Rectangular Cross Section” (continued) 50K PDF
Haldor Topsoe, Page 33, “Infinite Bar of Rectangular Cross Section, Infinite Bar of Semi-Circular Cross Section” 141K PDF
Haldor Topsoe, Page 34, “Quadratic Cross Section” 85K PDF
Haldor Topsoe, Page 35, “Bar of Semi-Circular Cross Section” 100K PDF
Haldor Topsoe, Page 36, “Bar of Circular Cross Section” 97K PDF
Haldor Topsoe, Page 37, “Bar of Circular Cross Section” (continued) 142K PDF
Haldor Topsoe, Page 38, “Thin Circular Slice” 80K PDF
Haldor Topsoe, Page 39, Graph – “Thin Circular Slice” 384K PDF
Haldor Topsoe, Page 40, Graph – “Thin Circular Slice” 457K PDF
Haldor Topsoe, Page 41, “Probe Array on a Diameter” 83K PDF
Haldor Topsoe, Page 42, “Probe Array on a Diameter” (continued) 104K PDF
Haldor Topsoe, Page 43, Graph – “Thin Circular Slice” 487K PDF
Haldor Topsoe, Page 44, “Probe Array Perpendicular to a Diameter” 74K PDF
Haldor Topsoe, Page 45, “Probe Array Perpendicular to a Diameter” (continued) 111K PDF
Haldor Topsoe, Page 46, Graph – “Thin Circular Slice” 522K PDF
Haldor Topsoe, Page 47, “Probe Array Perpendicular to a Diameter at a Fixed Distance from the Periferi” 105K PDF
Haldor Topsoe, Page 48, “Probe Array Perpendicular to a Diameter at a Fixed Distance from the Periferi” (continued) 84K PDF
Haldor Topsoe, Page 49, Graph – “Thin Circular Slice” 389K PDF
Haldor Topsoe, Page 50, “Thin Circular Slice” (continued) 65K PDF
Haldor Topsoe, Page 51, “Thin Circular Slice” (continued) 90K PDF
Haldor Topsoe, Page 52, Graph – “Thin Circular Slice” 393K PDF
Haldor Topsoe, Page 53, “Thin Rectangular Slice” 78K PDF
Haldor Topsoe, Page 54, “Thin Rectangular Slice” (continued) 83K PDF
Haldor Topsoe, Page 55, Graph – “Thin Rectangular Slice” 401K PDF
Haldor Topsoe, Page 56, “Thin Rectangular Slice” (continued) 94K PDF
Haldor Topsoe, Page 57, Graph – “Thin Rectangular Slice” (continued) 439K PDF
Haldor Topsoe, Page 58, “Narrow Rectangular Slice” (continued) 113K PDF
Haldor Topsoe, Page 59, Graph – “Thin and Narrow Rectangular Slice” (continued) 498K PDF
Haldor Topsoe, Page 60, “General Considerations of Finite Slices” 128K PDF
Haldor Topsoe, Page 61, “General Considerations of Finite Slices” (continued) 148K PDF
Haldor Topsoe, Page 62, “General Considerations of Finite Slices” (continued) 139K PDF
Haldor Topsoe, Page 63, “References” 89K PDF

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