Van der Pauw method

The advantage of the van der Pauw technique is that it allows resistivity measurements avoiding problems due to the nonclassical bar- or bridge-shaped geometry of sample (Fig. 13.18). The technique was developed in order to measure the resistivity (and the sheet resistance) of thin and flat samples of semiconductors. 

Van der Pauw [30] showed that determination of the resistivity of samples of arbitrary shape requires (1) the contacts realized on the edge of the specimen, (2) the contact sufficiently small (point-like), (3) the sample with homogeneous thickness d, and (4) the sample without isolated holes (surface connected). Fulfilled conditions allow the van der Pauw theorem  

Using the van der Pauw method of conformal mapping with the contacts. A, B, C, and D placed successively along the periphery of a sample, the Hall coefficient is given by [57]  

Here / bd,ac is the potential difference Vac between contacts A and C per unit current between contacts B and A(/ bd,ac) i change in / bd,ac due to a magnetic field H applied perpendicular to the plane of the sample (Fig. 13.14). The van der Pauw technique has been successively applied to study the semiconducting properties of lithium intercalation compounds [58-61]. 

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Thus electrical conductivity is commonly measured in units of S/cm (0 cm ). Various experimental methods have been used to measure the electrical conductivity of conductive polymers, eg, 4-probe method. Van der Pauw method, etc, and are well documented in the Hterature. 

We investigated the transport properties of ZnO single erystals and PLD thin films by Hall measurements using the van der Pauw method. ... 

The electrical resistivity and the Hall coefficient were measured using Van der Pauw method at 77K and 300 K. Both of the properties were meassured along the plains perpendicular to the compacting direction during hot pressing. The sample size was 3mm X 4mm and 0.5 mm thick rectangular shape. 

The Seebeck coefficient were calculated from measurement of electromotive force with temperature difference of lOK. The electrical resistivity and Hall measurement were performed by van der Pauw method. The thermal conductivity were calculated from the thermal diffusivity, the specific heat and the density. The thermal diffusivity and the specific heat were measured by laser flash method and differential scanning calorimeter (DSC), respectively. 

The temperature dependence of Seebeck coefficient and electrical resistivity of the sintered Mn-Si element were measured simultaneously by the power factor measurement device 5. The temperature difference was kept at constant lOK in the temperature range up to HOOK. HaU coefficient and electrical resistivity were measured with van der Pauw method up to 500K. The each sample is spot-welded a 50 yU m platinum wire as the electrode. The current and magnetic field were 0.1 A and 0.356T respectively in the HaU measurement. In the measurement of electrical resistivity the current was 3mA... 

Characterization of Products Electrical Measurements. The van der Pauw method was used to measure the electrical resistivities. 

The room-temperature conductivities obtained for a number of PPy films appear in Table 12.3. We have applied both the linear four-probe and van der Pauw methods to the measurement of conductivity. The linear four-probe method has certain advantages the samples (narrow strips of film) are easily obtained and any anisotropy of the conductivity (within the film plane) can be investigated. The major source of error in conductivity measurements is the thickness measurement. The latter is conveniently done using a micrometer when the film thickness is greater than about 20 /zm. (Accurate thickness measurements of very thin films require the use of other techniques, such as electron microscopy.) It is advisable to make a number of conductivity measurements using specimens from different regions of a given film. 

Mglu204 thin films were prepared by the spray pyrolysis technique and H+, Li+ ions were implanted at room temperature. The acceleration energy was 1.5 MeV and the fluence range studied spanned from 10 to 10 ions cm . Some of the implanted films were annealed at 450°C for 5 h. Electrical conductivity measurements were carried out using a four-probe method and Hall measurements were performed by the Van der Pauw method under the magnetic field of 5000 Gauss (0.5 T). 

Effect of Li+ implantation and postannealing on Mgln204 films have been further characterized by measuring the carrier concentration and Hall mobility at room temperature by the Van der Pauw method. Obtained results are listed in Table 9.1. 

Conductivities of polycrystalline pressed pellets were determined by van der Pauw method at the University of Nancy (France). 

The sheet conductivities of the PPy-PEO composite nanofiber mats were in the order of 10" S/cm calculated from the four-probe measurement data. Conductivities of electrospun nanofibers measured by using the four-probe method were about 10" S/cm. PPy was coated on PS nanofiber mats, and the conductivities of the PS-Cl-PPy and PS-TS-PPy fiber mats were found to be 2 x 10" S/ cm and 5 x 10 S/cm, respectively. It was demonstrated that the conductivity of the porous fiber mat could be influenced by the amount (PPy/PS ratio), doping, and crystallinity (polymer chain packing) of PPy in the fibers, the void volume, and the connectivity between fibers in the mat. When the PS template of the PS-TS-PPy fiber mat was removed by THF treatment and the electrical conductivity of the remaining material (TS-PPy) was measured, the conductivity increased to 0.13 S/cm by using the four-probe Van der Pauw method. ... 

The resistivity of the films and Hall mobility of the carriers were measured using the four-contact Van der Pauw method. 

Figure 20. Doped olivines of stoichiometry Lii xMxFeP04 show electrical conductivity at room temperature that is a factor of ca. 10 greater than in undoped LiFeP04, and absolute values > 10 S cm" over the temperature range -20 °C to +150 °C of interest for battery applications. Results are for polyciystals fired at 700-850 °C and measured by two-point d.c. and four-point van der Pauw methods. Inset shows expanded plot for series of dense, single-phase samples fired at 800 °C, showing lower activation energy of the doped compositions. [122]...

The electrical resistivity p, carrier concentration n, and mobility p, of CVD wafers measured by the van der Pauw method are shown in Table 3. The carrier concentration decreases with increasing silicon content for the n-type specimens (samples 1 and 3) and increases for the p-type materials (samples 2 and 4). The silicon atoms act as acceptors and are incorporated at the phosphorus sites in BP. Results of measurements of the lattice constants by the Bond method are shown in Table 4 they were obtained after calibration, using the thermal expansion coefficient (49). The conduction types of the BP wafers were determined using excess boron or phosphorus and were found to be either p- or n-type (50). The excess phosphorus atoms occupy the boron sites in the BP lattice in the -type material and vice versa for the p-type material (44). The ionic radii of boron and phosphorus in BP are expected to be 0.88 and 1.10 A, respectively. The lattice shrinks in the p-type materials (sample 4), whereas it expands in the n-type materials (sample 3). The difference in the ionic radii of phosphor and silicon is not so large and no appreciable effect of Si on the lattice constant could be detected. 

Fig. 6.24 (a) Arrhenius plot of the electrical conductivity of V60]3 and Li cV60i3 in the composition range 0 < x < 6. Measurements were carried out on pellets using the van der Pauw method, (b) FTIR absorption spectra of VgOj3 and Li3 2VsOi3... 

Chwang R, Smith BJ, Crowell CR (1974) Contact size effects on the van der Pauw method for resistivity and Hall coefficient measurement. Solid State Electron 17 1217-1227... 

Ramadan AA, Gould RD, Ashour A (1994) On the Van der Pauw method of resistivity measurements. Thin Solid Films 239 272-275... 

Levy M, Sarachik MP (1989) Measurement of the Hall coefficient using van der Pauw method without magnetic field reversal. Rev Sci Instrum 60 1342... 

When samples have irregular shapes but are flat and uniform in thickness their conductivity can be measured by a modified four-electrode method, the van der Pauw technique, where small, point-like electrodes are placed arbitrarily at the periphery of the samples. Two measurements are performed with commuted current and voltage connections, and for calculation of the conductivity value, a correction factor, numerically calculated and published by van der Pauw, is needed. Another modification of the four-probe method, the Montgomery method, is similar to the van der Pauw method but is applied to anisotropic materials. This method allows the determination of the anisotropy ratio of investigated materials. 

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