Der Pauw Method Research Articles

Explicit resistance matrix for a Hall disk with multiple peripheral contacts: Application to a van der Pauw type method for extended contacts

A direct analytical method for determining the Resistance Matrix of a Hall disk with an arbitrary number of extended peripheral contacts has been developed. The method does not require the use of any conformal mappings. It works also in the case of large magnetic fields. The resulting explicit formulas involve the angular coordinates of the asymmetrical contacts ends, the sheet resistance, and the Hall angle θH as inputs. The formulas are obtained through the calculation of some definite integrals of analytical functions with integrable singularities at the end of the peripheral contacts. The method can be used for determining the sheet resistance and the Hall mobility of a circular plate with extended contacts on its boundary by utilizing two measurements similar to those used by van der Pauw's method for pointlike contacts.

On the van der Pauw's method applied to the measurement of low thermal conductivity materials.

The electrical van der Pauw's method has recently been extended to measure the thermal conductivity of different elements and compounds. This technique provides an easy way to determine the sample in-plane thermal conductivity by avoiding the influence of the thermal contact resistances. However, the reported calculated error values appear to be underestimated when dealing with the materials with low thermal conductivity (<5 W/Km) at room temperature. The causes of this underestimation are investigated in this communication and it has been found that they are due to the drastic influence of conduction heat losses through the thermo-resistance wires as well as the resulting modification of the sample temperature map. Both phenomena lead to experimental values of the sample thermal conductivity, which are systematically higher than the tabulated ones. The magnitude of this systematic error is ∼100% dealing with the samples of macroscopic dimensions, and low thermal conductivity indicated that the obtained accurate measurements can be quite challenging.

Tunable electrical properties of TaNx thin films grown by ionized physical vapor deposition

Tantalum nitride (TaNx) amorphous thin films with varying nitrogen content were grown on SiO2/Si using ionized physical vapor deposition. The composition of the films was examined by Rutherford back scattering spectrometry. The carrier density and the resistivity of TaNx films were measured by Hall effect and Van Der Pauw's method. TaNx thin films showed increased electrical resistivity and reduced carrier density as the amount of nitrogen was increased. By controlling the nitrogen content, the carrier density can be tuned within a large range of 1019–1022 cm−3 for 3 and 15 nm thick TaNx films. The metallicity of the films was confirmed using ultraviolet photoemission spectroscopy. For 3 nm thick TaNx films, carrier densities of ∼1021 cm−3 were obtained with the N2 flow rate in the range of 10–15 sccm. Such films have potential application in a quantum metal field effect transistor.

How to Extract the Sheet Resistance and Hall Mobility From Arbitrarily Shaped Planar Four-Terminal Devices With Extended Contacts

Van der Pauw's method enables the sheet resistance Rsq and the Hall mobility μH to be extracted from arbitrarily shaped simply connected planar samples with four peripheral pointlike contacts. This paper generalizes the method for devices with extended contacts. It is found that Rsq and μH can be extracted using only six resistance measurements in the absence of a magnetic field and a single magnetic sensitivity measurement. Conversely, if the μH of a simply connected planar conducting device with peripheral contacts is known, the magnetic sensitivity of the device can be predicted based on six resistance measurements in the absence of a magnetic field, without any further knowledge of the device geometry. The new method is applied to a variety of differently shaped diffused silicon n-wells with peripheral contacts. The extracted sheet resistance and Hall mobility values show excellent consistency and are in agreement with the fabrication specifications.

Van der Pauw method for measuring resistivity of a plane sample with distant boundaries

In the paper, we derive an algorithm which follows from the original van der Pauw's technique for measuring resistivity with the added advantage of allowing contacts to be positioned a distance away from the boundary. For a large sample area, we show that the resistivity calculated by our algorithm is equivalent to the resistivity calculated by the original van der Pauw's method. In practice, this configuration is easier to achieve and can eliminate errors associated with contacts that are not placed exactly at the edge.

Electrical conductivity of gelcast alumina sintered under inert atmosphere

Electrically conductive alumina ceramic has been successfully fabricated by sintering of dried gelcast alumina in an inert atmosphere. The process was developed similar to the conventional gelcasting method except for varying the amount of monomer in the premix solution. The sintering treatment was carried out in argon gas from 1100 °C to 1700 °C. Van der Pauw's method was used to measure the electrical resistivity. The results showed that increasing monomer addition and sintering treatment were significantly affecting in lowering electrical resistance. Using the lowest monomer addition and increased sintering treatment, the measured electrical resistivities were in the range from 1.94 Ω-cm to 0.37 Ω-cm. The material exhibited ohmic behavior and rendered two regimes of Arrhenius profile in the plot of electrical conductivity against increasing temperature from 20 °C to 600 °C. All conduction processes were governed by the presence of carbon that caused the alumina grains in polygonal morphology typical of densification. Furthermore, physical tests were conducted to describe the electrical conduction behavior of the material.

Sheet Resistance Determination Using Symmetric Structures With Contacts of Finite Size

This paper proposes an extension of van der Pauw's celebrated method for the extraction of the sheet resistance R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sq</sub> of planar homogeneously conducting samples with four point-like contacts to symmetric samples with contacts of finite length. Using the method, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sq</sub> can be extracted, e.g., from symmetric integrated Hall plates and stress sensors, without having to resort to dedicated van der Pauw structures. First, the analog of van der Pauw's formula for arbitrarily shaped samples with four extended contacts separated by point-like insulations is derived. Based on this and van der Pauw's original result, an interpolation formula applicable to symmetric samples with contacts of arbitrary length is constructed. The new formalism was successfully put to the test using ten widely differing CMOS sensor structures, with contacts covering between 10.1% and 91.3% of the device periphery. The extracted R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sq</sub> values lie within the range specified by the CMOS foundry used for the fabrication of the samples and show a relative standard deviation of 1.04%.

Electrically conductive gelcast porous alumina sintered under argon atmosphere

Electrically conducting porous ceramics have gained a recent surge of interest in the development of high performance radiant heaters for the oxidation of noxious emissions, and others. This paper describes a simple and direct approach for introducing an electrical conductive phase into insulating porous alumina by gelcasting of mechanically foamed slurry, followed by inert sintering. The amount of monomer in the mechanically foamed slurry was varied with sintering in argon atmosphere. The electrical resistivity was measured using the van der Pauw's method. Results showed increasing monomer additions significantly affecting the lowering of electrical resistance, which measured at about 1.15 Ω-cm to 0.32 Ω-cm. The increase in temperature of the sample over increasing current as well as under microwave supported that this material is a potential porous heater in the oxidation of hazardous emissions, and absorber for electromagnetic waves. Further tests were conducted such as X-ray diffraction, TGA, and I– V plot that were used to describe the electrical conductive behavior of the material.

Dopant behaviour and damage annealing in silicon implanted with 1 keV arsenic

The level of activation in ultra-shallow As doped Si as a function of the anneal condition has been investigated with spreading resistance profiling (SRP), four point probe (FPP) and Van der Pauw (VDP) methods. Double alignment medium energy ion scattering (MEIS) and low energy secondary ion mass spectrometry (SIMS) have been used to assess the damage annealing and dopant behaviour in the near surface regions. An inactive dopant solid solution was formed in Si following re-growth of the amorphous layer. When annealing in an oxidising ambient, although a high fraction of the implanted dose remains trapped in the oxide layer, a higher level of electrical activation is observed than compared to the non-oxidising anneal. Evidence of dopant out diffusion is observed during high temperature annealing in a non-oxidising gas ambient. The processes that occur during the anneal in the near surface regions of the sample have been discussed and related to the level of dopant activation achieved.

On measurement of the hall coefficient of anisotropic semiconductor single crystals and films

An equation for the Hall electromotive force of anisotropic single crystals is derived on the basis of the solution to the associated boundary problem of electrodynamics. The equation coincides with that used in measuring the Hall electromotive force of isotropic materials by van der Pauw's method. The results are tested experimentally on anisotropicZnAs 2 specimens.

MEASUREMENT OF SHEET RESISTANCE FOR MICROA- REAS BY USING A MODIFIED VAN DER PAUW'S METHOD

The sheet resistance of square microareas with an area of 100 × 100μm2 can be determined by using a modified Van der Pauw's method. In this method, the tip positions of the four probes are controlled respectivly at the four corners out side the inner tangential circle of square microareas by direct inspection using a microscope with a magnification of 8 × 10. The measurement results are independent of wanderings of probes and it is not necessary to determine the precise positions of probes in order to make corrections for the boundary effect. These conclusions are proved in this paper by using FEM and have been confirmed by the determination of sheet resistance of gold microbumps.

Electrical properties of boron-doped polycrystalline diamond films

Boron-doped (B-doped) polycrystalline diamond films (PDFs) were synthesized by thermal filament chemical vapour deposition, and the Hall effect, together with the resistivity of samples with different dosages, was measured by Van der Pauw's method. The Hall mobility and the hole concentration in the samples were also calculated. The experimental results show that B-doped PDFs are p-type semiconductors in which the resistivity has decreased by 11 orders of magnitude compared with the intrinsic samples (from 10 9 Ω cm to 10 −2 Ω cm). The activation energy of the B-doped PDFs was reduced through 0.307 eV (for lightly doped PDFs) to 0.075 eV (for heavily doped PDFs). However, the Hall mobility of the samples was only about 7 cm 2V −1s −1 and was almost independent of the impurity concentration. A preliminary discussion of the experimental results is also given in this paper.

The Determination of the Deformation Potential Constant of the Conduction Band in InSb by the Electron Mobility in the Intrinsic Range

The electron Hall mobility in InSb has been measured at 200∼430 K by van der Pauw's method. The experimental data were compared with theoretical values calculated by an iteration technique with a variable parameter |El|. In the calculations, the temperature dependence of m* was estimated from the experimental data of Eg(T) and m*(0) on the basis of Ravich's theory, and the value of κs was taken to be 16.8 instead of κs∼17.5. The comparison between the theoretical and experimental values of µH led to the value of |El|=33 eV, which is more than two times larger than that obtained in a previous work.

Electrical Characterization of Sige Thin Films

ABSTRACTAn apparatus for measuring electrical resistivity and Hall coefficient on both thin films and bulk material over a temperature range of 300K to 1300K has been built. A unique alumina fixture, with four molybdenum probes, allows arbitrarily shaped samples, up to 2.5 cm diameter, to be measured using van der Pauw's method. The system is fully automated and is constructed with commercially available components. Measurements of the electrical properties of doped and undoped Si-Ge thin films, grown by liquid phase epitaxy reported here, are to illustrate the capabilities of the apparatus.

Synthesis and electrical conductivities of charge-transfer complexes of bis(vinylenedithio)tetrathiafulvalene and its methyl derivatives with strong acceptors

Charge-transfer complexes of bis(vinylenedithio)tetrathiafulvalene (VT), bis(methylvinylenedithio)tetrathiafulvalene (DMVT) or bis(dimethylvinylenedithio)t tetrathiafulvalene (TMVT) with several strong acceptors, such as TCNQ, F 4TCNQ, DDQ, TCNE, Bu 4NBr 3 and I 2, were synthesized by leaving the mixed solution of a donor and an acceptor to stand at ambient temperature. Not only the usual 1:1 (donor:acceptor) complexes but also 2:1, 1:2, 3:1, 3:2 and 5:2 ones were obtained. Unfortunately, a single crystal of good quality was not obtained. The electrical conductivities of the compressed pellet samples were measured by van der Pauw's method. Most of them showed high conductivities of 10 0–10 −1 S cm −1 at room temperature. However, the TCNQ complexes were insulators. The electrical conductivities could be explained on the basis of the i.r. spectra of the complexes and the redox potentials of the donor and acceptor molecules.

Ionic transport in Tl 2ZrF 6 and related compounds

Due to the large polarizability of the Tℓ + ion, the peculiar role played by this cation as mobile species in fluorides or as cation with a large size associated to the fluorine ion in fluoride ion conductors has been emphasized by several studies carried out in our laboratory on single phases issued from the TℓF-ZrF 4 system, namely TℓZrF 5 and Tℓ 3ZrF 7. During the study of the ionic transport properties of various phases of this system, a.c. ionic conductivity measurements performed on sintered polycrystalline samples using the complex impedance method revealed good performances for compositions between 66.6 and 62.5 moles per cent of TℓF. The electronic insulator character of these materials was proved by d.c. conductivity measurements using the Van der Pauw's method. In order to specify the ionic transport mechanism the crystal structure of the Tℓ 2ZrF 6 phase has been determined from single X-ray diffraction data and will be reported. The possibility for this phase to exhibit a non stoichiometric domain will be discussed. Pulsed NMR techniques has been applied to the study of both 19F and 205Tℓ nuclei motion. Thermal and frequency dependences of nuclear spin-lattice relaxation times will be reported. Correlations between structural, electrical and NMR studies will be presented and discussed while comparison with other fluorides of monovalent elements will bring out the role of the thallium.

Electrical conductivity, structure and hall effect measurements of InSe films

Stoichiometric InSe films were prepared by discrete evaporation using spectrally pure (99.999%) InSe powder in a residual pressure of about 4×10 −6 Torr. The thickness of the films was varied from 500 to 3000 Å. The elctrical conductivity of the films was measured by Van der Pauw's method. The as-deposited films had an amorphous structure as observed with an electron microscope. Thermal annealing was carried out through a number of annealing cycles and a transformation to a crystalline state during the process was evidenced by the electron micrographs. Conductivity measurements were made on the amorphous films from the transition temperature to liquid air temperature and the activation energies were calculated from the variation in conductivity with temperature. The density of states at the Fermi level was also calculated at low temperatures. Hall effect measurements were made on the annealed films and the Hall mobility μ H, the Hall coefficient R H and the carrier concentration n were evaluated.

A comment on "An extension and application of the Thompson-Lampard theorem"

This letter proves that the conductivity measuring technique presented by Rehman-Murti can be directly derived from the Van Der Pauw's method by a simple transformation of the current field. Hence, conclusions obtained for one method can be transposed to the other one. It is also proved that the Rehman-Murti structure can also be applied to Hall mobility measurements.

Applicability of the Method of VAN DER PAUW to Samples with Two‐dimensional Defects

AbstractThe influence of cleavage steps and low angle boundaries on the results of conductivity and Hall measurements by Van der Pauw's method are investigated and some criterions for evidence of sample inhomogeneities by the assumption of symmetrical sample shape and contact arrangement formulated. Hall voltage is less influenced by cleavage steps, so that the determination of carrier concentration is nearly correct also in strongly disturbed samples. Conductivity and carrier mobility measurements in the usus usual calculation procedure will lead to considerable errors. By one pair of contacts only for conductivity as well as for Hall measurements, the influences of inhomogeneities cannot be distinguished from volume effects of the sample.

Resistivity measurement of thin doped semiconductor layers by means of four point-contacts arbitrarily spaced on a circumference of arbitrary radius

The resistivity of a thin doped semiconductor layer or wafer measured in the vicinity of four point contacts placed on the semiconductor surface is shown to be independent of the relative distance between the contacts, provided the contacts are located on a circumference, and the distance to the boundary of the surface will not fall short of the greatest actual spacing between contacts. This method combines the advantage of the four probe resistivity measurement originally proposed by Valdés, that is the determination of ρ in a restricted layer region, with the advantage of arbitrary spacing of the probes, which characterizes van der Pauw's method. Experiments are in agreement with results obtained by the measuring methods of Valdés and van der Pauw.