|
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 1964 National Bureau of Standards Technical Note 199, "Correction Factor Tables for Four-Point Probe Resistivity Measurements on Thin, Circular Semiconductor Samples", with each page available as an individual PDF file. The document provides extensive tables of geometrical correction factors.
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
|
1
|
National Bureau of Standards Technical Note 199 - "Correction Factor Tables for Four-Point Probe Resistivity Measurements on Thin, Circular Semiconductor Samples"
nbs.pdf 6.08 MEG PDF file which includes all 42 pages of the 1964 National Bureau of Standards Technical Note 199, "Correction Factor Tables for Four-Point Probe Resistivity Measurements on Thin, Circular Semiconductor Samples"
The individual pages range in size from 60K to 230K.
The individual pages:
nbs1.pdf NBS Document Cover Page
nbs2.pdf NBS Document Introduction Page I
nbs3.pdf NBS Document Introduction Page II
nbs4.pdf NBS Document Introduction Page III
nbs5.pdf NBS Document Introduction Page IV
nbs6.pdf NBS Document Introduction Page V
nbs7.pdf NBS Document References Page VI
nbs8.pdf NBS Document Geometry Page VII
nbs9.pdf NBS Document Tables, page 1
nbs10.pdf NBS Document Tables, page 2
nbs11.pdf NBS Document Tables, page 3
nbs12.pdf NBS Document Tables, page 4
nbs13.pdf NBS Document Tables, page 5
nbs14.pdf NBS Document Tables, page 6
nbs15.pdf NBS Document Tables, page 7
nbs16.pdf NBS Document Tables, page 8
nbs17.pdf NBS Document Tables, page 9
nbs18.pdf NBS Document Tables, page 10
nbs19.pdf NBS Document Tables, page 11
nbs20.pdf NBS Document Tables, page 12
nbs21.pdf NBS Document Tables, page 13
nbs22.pdf NBS Document Tables, page 14
nbs23.pdf NBS Document Tables, page 15
nbs24.pdf NBS Document Tables, page 16
nbs25.pdf NBS Document Tables, page 17
nbs26.pdf NBS Document Tables, page 18
nbs27.pdf NBS Document Tables, page 19
nbs28.pdf NBS Document Tables, page 20
nbs29.pdf NBS Document Tables, page 21
nbs30.pdf NBS Document Tables, page 22
nbs31.pdf NBS Document Tables, page 23
nbs32.pdf NBS Document Tables, page 24
nbs33.pdf NBS Document Tables, page 25
nbs34.pdf NBS Document Tables, page 26
nbs35.pdf NBS Document Tables, page 27
nbs36.pdf NBS Document Tables, page 28
nbs37.pdf NBS Document Tables, page 29
nbs38.pdf NBS Document Tables, page 30
nbs39.pdf NBS Document Tables, page 31
nbs40.pdf NBS Document Tables, page 32
nbs41.pdf NBS Document Tables, page 33
nbs42.pdf NBS Document Tables, page 34
Four-Point-Probes is a division of Bridge Technology. To request further information please call Bridge Technology at (480) 988-2256 or send e-mail to Larry Bridge at: sales@bridgetec.com
|
