Analytical expressions for correction factors for noise measurements with a four-point probe

L.K.J. Vandamme, G. Leroy

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The linear four-point probe method is useful to measure the resistivity, by passing a current I14 through the outer probes and by measuring the voltage V23 between the inner probes. The contacts are on a line and denoted by 1, 2, 3, 4, respectively. The sheet resistance for thin layers with thickness t is Rsh = ¿/t (O). The sheet resistance is measured as Rsh = (V23/I14). C23 where the correction factor is C23 = p/ln2 = 4.53 for t smaller than s, the distance between probe points. In order to characterize the 1/f noise of a film with a four-point probe we need noise correction factors for the calculation of the conductance noise from the voltage noise between the pair of points, where the current is not passed through. Our calculations of the noise correction factors are based on the general theory for conductance noise investigations with four arbitrarily shaped and placed electrodes. Analytical expressions for noise correction factors Fij and fij are derived and compared with experimental results for the three cases. The subscripts of F and f denote the voltage sensor contacts. The following cases are investigated: 1) I14 and V23, 2) I13 and V24 and 3) I12 and V34. The subscripts in I and V denote the current driver contacts and voltage sensor contacts, respectively. From the calculations and experimental results it follows that: i) case1 (I14 and V23) is the best choice in order to suppress a non-intentional noise contribution from the interface between probe tip and layer, ii) the reciprocity relation is applicable to voltage noise due to conductance fluctuations. The voltage noise SV23 that is observed by passing a constant current I14 through the pair of probes 1, 4 is equal to the voltage noise SV14 if we pass the same current through the contacts 2, 3. The four-point probe method with the noise correction factors can be recommended to investigate e.g., the conductance noise of conductive polymer layers even with an insulating top layer and without the preparation of rectangular samples with perfect noise-free line contacts. The four-point probe can punch an insulating top layer and allows the measurement of sheet resistance and noise. Several tests show that the noise contributions from the interface between probe tip and layer are negligible. The ratio of the conductance (1/f) noise, Cus, normalized for frequency and area and the sheet resistance gives an indication of the degree of percolation in composite conductive layers.
Original languageEnglish
Pages (from-to)L161-L178
JournalFluctuation and Noise Letters
Issue number2
Publication statusPublished - 2006

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