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The four point probe measurement does not directly supply sample thickness, however, if one knows the bulk resistivity of the material and the sheet resistance (which the four point probe can measure), then the thickness can be calculated. For example, a customer mentioned that his tantalum film was supplied to him with a sheet resistance value of 8.0389 ohms-per-square, a film thickness of 2500 angstroms, and a bulk resistivity of 201.94 micro-ohms-cm. Normally you would not know all three of these, and so you could use a four point probe to determine the thickness if the bulk resistivity was supplied, or you could determine the bulk resistivity if the thickness was supplied. The relationship between these values is as follows: The thickness of the layer in centimeters times the sheet resistance value expressed as ohms-per-square is equal to the bulk resistivity in ohms-cm.Or, bulk resistivty (ohm-cm) divided by the sheet resistance (ohms-per-square) equals thickness in centimeters. For the tantalum, for which all three values were provided, i.e., film thickness, sheet resistance, and bulk resistivity, it would work out to: 0.000025 (thickness in cm) x 8.0389 (ohms-per-square value) = 0.0002009725 ohm-cm which equals 200.9725 micro-ohms-cm (which deviates less than 0.5% from the 201.94 micro-ohms-cm value supplied). To calculate the thickness of the layer using the supplied bulk resistivity value and the (measured) sheet resistance value, you would divide the bulk resistivity by the sheet resistance value. So, the 0.00020194 (201.94 micro-ohms-cm) / 8.0389 (ohms-per-square) = 2.5120352287004440906094117354364e-5 which is 0.00002512035228700 centimeters, or 2512.0352287 angstroms (which matches the expected 2500 angstroms). The following web pages might be helpful in making these calculations: http://onlineconversion.com/length_all.htm and http://www.csgnetwork.com/sntodeccalc.html |
| 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 |
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