Van der Pauw method

van der PauwVan der Pauw constant
The van der Pauw Method is a technique commonly used to measure the resistivity and the Hall coefficient of a sample.wikipedia
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Hall effect

Hall coefficientHall-effectCorbino effect
The van der Pauw Method is a technique commonly used to measure the resistivity and the Hall coefficient of a sample.
The sample inhomogeneity might result in spurious sign of the Hall effect, even in ideal van der Pauw configuration of electrodes.

Electrical resistivity and conductivity

electrical conductivityresistivityconductivity
The van der Pauw Method is a technique commonly used to measure the resistivity and the Hall coefficient of a sample.

Electrode

electrodescathodemicroelectrode
Its power lies in its ability to accurately measure the properties of a sample of any arbitrary shape, as long as the sample is approximately two-dimensional (i.e. it is much thinner than it is wide), solid (no holes), and the electrodes are placed on its perimeter.

Perimeter

Perimeter lengthperimeter of the polygon
Its power lies in its ability to accurately measure the properties of a sample of any arbitrary shape, as long as the sample is approximately two-dimensional (i.e. it is much thinner than it is wide), solid (no holes), and the electrodes are placed on its perimeter.

Four-terminal sensing

Kelvin sensingKelvin connectionfour terminal measurement
The van der Pauw method employs a four-point probe placed around the perimeter of the sample, in contrast to the linear four point probe: this allows the van der Pauw method to provide an average resistivity of the sample, whereas a linear array provides the resistivity in the sensing direction.

Homogeneity and heterogeneity

heterogeneoushomogeneousheterogeneity
3. The sample must be homogeneous and isotropic

Isotropy

isotropicisotropicallyanisotropic
3. The sample must be homogeneous and isotropic

Order of magnitude

orders of magnitudeorderon the order of
5. The area of contact of any individual contact should be at least an order of magnitude smaller than the area of the entire sample.

Thermoelectric effect

thermoelectricPeltier effectSeebeck effect
In addition to this, any leads from the contacts should be constructed from the same batch of wire to minimise thermoelectric effects.

Electric current

currentelectrical currentcurrents
The velocity the electrons are traveling at is (see electric current):

Ohm's law

ohmicOhmohmic losses
From these two values, a resistance (for this example, R_{12,34}) can be found using Ohm's law:

Reciprocity (electromagnetism)

reciprocalreciprocityreciprocity theorem
The reciprocity theorem tells us that

Iterative method

iterativeiterative methodsiterative algorithm
In most other scenarios, an iterative method is used to solve the van der Pauw formula numerically for R S.

Nested intervals

nested intervals theoremnested interval modelnested sequence of closed intervals
Instead, nested intervals converge slowly but steadily.

Magnetic field

magnetic fieldsmagneticmagnetic flux density
When a charged particle—such as an electron—is placed in a magnetic field, it experiences a Lorentz force proportional to the strength of the field and the velocity at which it is traveling through it.

Coulomb

CPicoCoulomBExacoulomb
:where q is the charge on the particle in coulombs, v the velocity it is traveling at (centimeters per second), and B the strength of the magnetic field (Wb/cm²).