Four-point surface resistance measurements at different temperatures
Sheet resistance measurements are a versatile tool for research and industry. Important examples are the electrical characterization of new materials, the monitoring of thin film processes and the determination of the homogeneity of semiconducting and conducting thin films. Traditionally, these measurements are carried out at room temperature. New applications such as solar cells or quantum technologies sometimes require significantly wider temperature ranges.
Using a combination of a cryogenic probe station and the M81-SSM (Synchronous Source Measurement System), our partner Lake Shore was able to demonstrate that measurements are possible in the fringe areas of modern applications.
One possible configuration for four-point sheet resistance measurements is the linear arrangement of four contacts with uniform distances between the measuring tips. If the measuring tips are small and the layer to be measured is thin compared to the substrate, the sheet resistance can be determined with
\(R_{SH} = {ρ\over t}={π\over ln (2)} {V\over l} \)
V is the voltage drop and I is the applied current through the external contacts. Complex contact structures are considered in [1].
A Lake Shore CRX-4K with a Multi-Contact Wedge (MCW) probe arm can be fitted with a suitable measuring tip to ensure that the measuring tips are at a fixed distance from each other (Fig. 1). This configuration has the advantage that several contact surfaces can be measured quickly with one measuring arm without the individual tips shifting against each other. Reliable and reproducible measurement results can therefore be provided.
A Lake Shore CRX-4K with a Multi-Contact Wedge (MCW) probe arm can be fitted with a suitable measuring tip to ensure that the measuring tips are at a fixed distance from each other (Fig. 1). This configuration has the advantage that several contact surfaces can be measured quickly with one measuring arm without the individual tips shifting against each other. Reliable and reproducible measurement results can therefore be provided.
The electrical measurements are carried out with Lake Shore’s M81-SSM. The current is applied to the outer contacts with the BCS-10 (Balanced Current Source) and the voltage drop at the two inner contacts is measured with the VM-10 (Voltage Measure). The BCS-10 module has an output for common mode rejection. This output is connected to input B of the VM-10 in order to reduce interference signals caused by earth currents or other interference in the measurement setup. For further details see [2].
Lake Shore's MeasureLINK™ software is used for logging, temperature monitoring and implementing a current reversal protocol to reduce thermoelectric effects.
The chosen example shows the measurement of the temperature-dependent sheet resistance of a 10 µm thick silver-platinum layer (Heraeus C4729). At room temperature, a value of 4.35 mΩ/□ (ohm per square) was determined for the sheet resistance, which is consistent with an expected sheet resistance of ≤ 5 mΩ/□.
These results show that this material exhibits a similar drop in sheet resistance at decreasing temperatures as moderately pure silver. Below 30 K, there is less of a drop due to the lower phonon contribution to electron scattering. In this example, the sheet resistance at 4 K is close to 100 µΩ/□. (Fig. 2)
Following this example we see that the combination of a Lake Shore Probe Station and M81-SSM is suitable for carrying out precise four-point surface measurements at different temperatures. Such a measurement setup can also be extended to other areas of application in the field of semiconductor thin-film characterization or the development of new materials.
Please contact us if you have any questions about the Lake Shore Probe Stations or the M81-SSM.
[1] Semiconductor Material and Device Characterization, Third Edition, D. K. Schroder, John Wiley & Sons, 2015
[2] "Minimizing the Effect of Common-Mode Noise Interference in Low-Temperature Applications," Lake Shore Cryotronics Application Note, J. R. Lindemuth and E. A. Codecido, 2022
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