Four point method

This article relates to the measurement of the electrical resistance of surfaces or thin layers. The measurement of other (not areal) electrical resistances with four connections is dealt with under four-wire measurement .

The four-point method , also called four-point measurement or four-point measurement , is a method to determine the sheet resistance , i.e. the electrical resistance of a surface or thin layer.

description

Arrangement of the measuring tips

Four measuring tips are placed in a row on the surface, with a known current flowing through the two outer ones and the potential difference , i.e. the electrical voltage between these tips, being measured with the two inner ones . Since the method on the principle of four-wire measurement is based, it is largely independent of the contact resistance between the probe tips and the surface (principle Kelvin Bridge ). The closer the tips come to the edge of the sample, the more the measurement is falsified: the electric streamlines cannot spread freely, they have to flow parallel to the edge of the sample.

If neighboring measuring tips have the same distance, the sheet resistance is obtained from the measured voltage and the current using: ${\displaystyle R_{\Box }}$ ${\displaystyle U}$ ${\displaystyle I}$

${\displaystyle R_{\Box }={\frac {\pi }{\ln {2}}}{\frac {U}{I}}=4{,}532{\frac {U}{I}}}$.

However, this formula only applies in the ideal case of a very thin (compared to the tip distance), infinitely extended surface with homogeneous resistance behavior.

This measurement method is tied to various requirements:

• The layer thickness must be much smaller than the distance between the tips. (typically 1 mm)
• The total area of ​​the layer must be (infinitely) large compared to the distance between the tips.
• The base must be electrically insulating so that the current only flows through the layer. (In the case of semiconductor wafers, this condition is also met if the layer and the substrate are doped in opposite directions, since the boundary layer then serves as an insulator.)

Four-point measurements are used, for example, in semiconductor technology to determine the sheet resistance of a layer applied to the semiconductor, but the layer can be damaged by the measuring tips.

To calculate the specific resistance of the layer material from the sheet resistance , multiply it by the layer thickness : ${\displaystyle R_{\Box }}$ ${\displaystyle \rho }$ ${\displaystyle d}$

${\displaystyle \rho ={d}\cdot {R_{\Box }}}$

This equation only applies if it is a square sample with the condition (the length is equal to the width of the layer or sample to be measured). ${\displaystyle l=b}$ ${\displaystyle l}$ ${\displaystyle b}$

The Van der Pauw measuring method was developed to determine the specific resistance of a layer or its sheet resistance with any arrangement of the measuring contacts .

application

The four-point method is the standard measurement method for determining electrical conductivity in the semiconductor industry ( semiconductor technology , photovoltaics , etc.).

Web links

• Declaration on the ICR Jena website