Van der Pauw method

The van der Pauw method of measurement used to determine the electrical surface resistivity and Hall coefficient of thin, homogeneous layers of any desired shape. In the semiconductor industry, measurements of resistivity and Hall coefficient play a major role, as can be determined, the carrier concentration and mobility of these two variables.

Measurement of the resistivity and the sheet resistance

The Messtruktur consists of an arbitrarily shaped area without holes, which is contacted on its edge on 4 points (AD). In this structure, the resistance is

Measured by A and B, a current is impressed between the contacts and the voltage dropping between the contacts C and D of voltage is measured. Similarly, the resistor according to a cyclic permutation of the contacts is measured.

With methods of conformal mapping showed Van der Pauw, that can be calculated from these two resistances of the resistive layer and in that this calculation does not have the specific shape of the structure is received, the position of the contacts. It results in the following dependence:

With = specific resistance and = layer thickness.

If both the layer thickness and the resistance RAB, CD and RBC, DA are known, an equation with the desired unknowns. For an arbitrarily shaped structure, the resistivity, however, can not be expressed by a closed formula. Therefore we determined iteratively by either of intervals or approximately by the following formula:

The correction factor f is taken from the adjacent picture. For more precise measurements using a test pattern having at least one axis of symmetry and whose contacts are also arranged in accordance with this symmetry. It is then and for the resistivity results in the formula

This allows to

Summarized.

The method is exact only for ideal point contacts. When choosing a suitable form of Messtruktur the influence of the contact size is in practice negligible. In the semiconductor manufacturing structures are used in the form of a clover leaf or a cross, to determine the specific surface resistance of thin films, such as polysilicon or diffusion areas.

The sheet resistance of the layer is obtained by dividing the obtained resistivity by the layer thickness:

Measurement of the Hall coefficient

For the measurement of the Hall coefficient, the same conditions as for coating thickness measurement apply. In contrast, the current is injected through the contacts A and C, and the resistance measured. Subsequently, a homogeneous magnetic field is applied perpendicular to the disk Β. Because of changes to the value of Δ.

The Hall coefficient is given by:

The magnetic Β causes the carrier Q a Lorentz force perpendicular to the current lines and perpendicular to the magnetic field effect.

The current density can be expressed by. A transformation after and then inserting results in a field strength of:

Is proportional to and Β.

Is the proportionality constant and the Hall coefficient. As is known, can now be the concentration of charge carriers in the test pattern to determine.