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# Sheet Resistance Measurements of Thin Films

Sheet resistance (or surface resistivity) is an important property of many materials, quantifying the ability for charge to travel along uniform thin films. For example, this property is critical in the creation of high-efficiency perovskite photovoltaic devices, where low sheet resistance materials are needed to extract charge. Furthermore, resistivity (and hence conductivity) can be determined from the measurement of the sheet resistance, enabling electrical characterisation of a material.

## Introduction

The most common technique used for measuring sheet resistance is the four-probe method. This technique involves using four equally-spaced, co-linear probes (known as a four-point probe) to make electrical contact with the material. Most four-point probes available commercially use sharp needles as probes. These can scratch or pierce delicate materials often used in thin film electronic devices. This can make it difficult to take accurate sheet resistance measurements, and result in the thin film becoming unusable.

The Ossila Four-Point Probe System (shown in Figure 1) was designed to overcome these issues. This system utilises spring-loaded probes with rounded tips that apply a constant 60 grams of force whilst in contact. Additionally, contact is made using a precision vertical translation stage that is operated with a micrometre to allow for soft, controlled contact with the sample.

This application note gives an overview of the four-probe method and explains how the sheet resistance of delicate thin films can be measured using the Ossila Four-Point Probe System.

## The Four-Probe Method

The four-probe method works by contacting four equally-spaced, co-linear probes to the material. This is known as a four-point probe, and a schematic is shown in Figure 2.

A DC current is applied between the outer two probes (1 and 4) and a voltage drop is measured between the inner two probes (2 and 3). The sheet resistance can then be calculated using the following equation:

Here, Rs is the sheet resistance, ΔV is the change in voltage measured between the inner probes, and I is the current applied between the outer probes. The sheet resistance is expressed with the units Ω/sq, or “ohms per square”, to differentiate it from bulk resistance.

In addition to the factor of π/ln(2), a geometric correction factor is often required. The correction factor is based upon the size and shape of the sample, as well as the positioning of the probes, and accounts for the limitation of current pathways through it. Further information (including correction factor tables and equations) can be found in our sheet resistance theory guide. However, it should be noted that the most accurate measurements are taken from the centre of the sample.

If the thickness of the measured material is known, then the sheet resistance can be used to calculate its resistivity:

Here, ρ is the resistivity, and t is the thickness of the material.

This technique is also known as the Kelvin technique, a method of eliminating wire and contact resistances from a resistance measurement. Figure 3 shows the circuit resistances of a four-point probe measurement. Figure 3: Equivalent circuit diagram of a four-point probe, showing the wire resistances (RW), contact resistances (RC), and sample resistances (RS). The green arrows represent current flow.

As no current flows through the inner two probes, the wire resistances of RW2 and RW3 and the contact resistances of RC2 and RC3 do not affect the voltage measured at the voltmeter. This means that the measured decrease in voltage (ΔV) between the inner two probes arises entirely from RS2. Therefore, ΔV can be used along with the applied current in the sheet resistance equation to calculate the value of RS2 (i.e. the sheet resistance).

## Soft Contact

The Ossila Four-Point Probe System reduces the potential of damaging delicate thin films via three features. Firstly, the probes used to make contact have rounded tips (unlike other probes which are sharp needles). These rounded tips have a radius of 0.24 mm and give the probes a larger contact surface area than a needle would, therefore spreading out the downward force being applied to the sample. Secondly, the probes are mounted on springs, enabling them to retract into the probe head when making contact with the sample. This ensures that a uniform force of 60 grams is applied. A schematic of the probes is shown in Figure 4. Figure 4: Schematic diagram of the probes used by the Four-Point Probe System.

Finally, the sample is positioned beneath of the probes on a precision vertical translation stage. This stage is controlled using a micrometre, which allows the user to slowly and carefully raise the sample to meet the probes. Figure 5: The Four-Point Probe System in contact with a silver nanowire thin film on a PET substrate.

## Performing a Measurement

Taking a measurement with the Four-Point Probe System is simple, as it has a built-in source-measure unit included in the system. After plugging the system into the power and PC, start the Ossila Sheet Resistance Lite software, and follow these steps:

This guide is intended for those who have used the Four-Point Probe System previously and need a reminder on the steps involved in a measurement.

1. Install the software and drivers on the USB drive provided.
2. Connect the system to the power supply.
1. Allow the system to warm up for 30 minutes before performing a measurement.
3. Connect the system to your computer
4. Place the sample on the stage, centred beneath the probes.
1. For rectangular samples, align the long edge parallel to the line of probes.
5. Use the micrometer to raise the sample until it makes contact with the probes.
1. To ensure good, ohmic contact between the sample and probes, complete at least one full turn of the micrometer after the probes first contact the sample.
6. Start the Ossila Sheet Resistance Lite software.
7. Set the sample geometry in the software.
8. Click the on button.
1. The program will calculate the appropriate geometric correction factor for the sample.
2. The system applies a current between the outer probes, starting at the highest current range and working downwards until a stable current is achieved.
3. Once a stable current has been achieved, the current between the outer probes and voltage between the inner probes is measured and used to calculate the sheet resistance.
4. The sheet resistance is displayed in the program.
5. If the sample's thickness is provided, the resistivity and conductivity will also be calculated and displayed.
9. The measurement continues until the off button is clicked.
1. Data can be saved at any point whilst the measurement is running by clicking the save icon.

Below is an example measurement of a thin film of silver nanowires on a PET substrate. This could be used as an electrode layer in a thin-film photovoltaic device or LED. Figure 6: Example sheet resistance measurement of a silver nanowire thin film. The average sheet resistance is 340 Ω/square.

## Conclusions

The Ossila Four-Point Probe System is an excellent tool for performing the four-probe method to measure the sheet resistance of thin films that are prone to being easily damaged. Soft contact can be made by using probes which have rounded tips to spread out the contact force, mounting them on springs that apply a uniform force when making contact, and using a micrometre-controlled vertical translation stage to make contact. This significantly reduces the possibility of damaging delicate thin films, even those with thicknesses in the range of nanometres.