How To Test Resistivity Of Semiconductor By Four Probe Method

How To Test Resistivity Of Semiconductor By Four Probe Method

Do you know how to test the resistivity of semiconductors by using the four-point probe method? Would you like to learn which qualities of a semiconductor material affect its electrical properties like resistivity and why resistivity measurement is important in the first place? Have you heard about the special test equipment used by the semiconductor industry to carry out such measurements with great precision?

Keep reading to find out how the four-point probe method is used, and how the measurement of resistivity is done on semiconductor wafers using a parameter analyzer device. You’ll also learn why this method of measurement is so important to the research and development of new semiconductors, and their manufacture to meet the growing demands of the future.  

The Resistivity Of Semiconductors

Electrical resistivity is the characteristic of a material that determines how much it can resist the flow of an electric current. The lower the resistivity, the better it can allow a current to flow within it. Resistivity measurements are given in ohm-meter (Ω⋅m) as per the International System of Units and are represented by the Greek letter ρ (pronounced rho). The resistivity and conductivity of semiconductor material are explained by the band theory. 

This theory describes how the electrons of a solid material are distributed among energy levels or bands. For a solid material to conduct an electric current, it requires charge carriers that have mobility, such as electrons in its conduction band. A metal naturally has free electrons in its conduction band, allowing them to behave as charge carriers. This enables a metal to conduct an electric current when a voltage is applied. 

In a semiconductor, the electrons in its valence band can be excited to jump into the conduction band by acquiring some energy. This creates free electrons in the conduction band and positive charge carriers called holes left over from the vacated electrons in the valance band. Now there are free charge carriers to conduct a current if a voltage is applied. 

Why The Four-Point Probe Resistivity Measurements Are Needed

The four-point probe method is what is used by the industry to measure the resistivity of semiconductor material for a variety of reasons. This includes research and development of new materials and quality control of semiconductor wafers during the manufacturing process. 

Research And Development Into New Semiconductor Materials

Research And Development Into New Semiconductor Materials | INQUIVIX TECHNOLOGIES
A four-point probe testing station

Different semiconductors will exhibit unique resistivity levels. The number of charge carriers per volume of material (charge carrier density) can also be increased in semiconductors through a process called ‘doping’. This adds extra electrons into the conduction band, changing the conductivity and resistivity of the material. Furthermore, doping can also affect the series resistance and capacitance of a semiconductor device. 

Scientists and engineers in the industry are always adjusting doping concentrations of materials and experimenting with new manufacturing processes. Their intention is to improve production yield, reduce defects, and produce a final product that has superior performance. This is a necessity due to the growing demand worldwide for faster and more reliable microprocessors and electronic components. Since doping affects resistivity, which in turn affects the conductivity of a material, it becomes vital for researchers to have an accurate method to test their latest innovations. 

Quality Control In Semiconductor Manufacturing

Quality Control In Semiconductor Manufacturing | INQIVIX TECHNOLOGIES
A semiconductor wafer being tested with probes

Semiconductor wafers are produced at fabrication plants on a massive scale. They also need to be tested at various stages of production for quality control before any faulty wafers or packaged integrated circuits are sent off to customers further down the supply chain. This testing of wafers and other circuit components is performed by machines called automated test equipment (ATEs).

ATEs have sophisticated control systems to manipulate the test samples. They can also insert the inner and outer probes with great precision to make contact with the sample. Afterward, they can measure voltage, current, resistivity, and many other types of properties of the sample to ensure it’s performing up to specifications. This allows manufacturers to identify defects, and supply their customers with only the best products. Sometimes faulty products do end up with a consumer, and semiconductor failure analysis is done to understand what went wrong.  

How The Four-Point Probe Method Is Used For Resistivity Measurements

The industry standard way of measuring the resistivity of a wafer is to utilize what is known as the ‘four-point probe’ method, also called the ‘Kelvin measurement method’. It is named after the famous physicist Lord William Thomson Kelvin who developed it back in 1876. As the name suggests, this method utilizes four probes. Two probes for measuring voltage, and two probes to measure the source current. 

How The Four Probes Eliminate Measurement Errors

There is another method that utilizes just two probes. However, with this method, the resistance of each probe starts to influence the measurements, creating errors in the calculation when materials with very low resistivity are being tested. The use of four probes is what eliminates the errors in measurements that can arise due to the probe resistance, as well as the spreading resistance under each probe. It also reduces errors due to the contact resistance between the semiconductor and each metal probe. 

The four-point probe method can be performed in two different ways. The first is the collinear four-probe technique, and the other is the van der Pauw method.  

The Collinear Four-Point Probe Measurement 

The Collinear Four-Point Probe Measurement  | INQUIVIX TECHNOLOGIES
How the Collinear Four Point Probe measurement is done

This four-point probe technique involves bringing four equally spaced probes that are carefully brought into contact with the sample that is to be measured. As shown in the diagram below, the two outer probes supply a DC current, while the two inner probes are used to measure the voltage drop between their respective contact points across the surface of the sample. This means that a DC current supply and a highly sensitive voltmeter are needed for the measuring. 

The Resistivity Calculation In The Four Point Collinear Probe Technique

The Resistivity Calculation In The Four Point Collinear Probe Technique | INQUIVIX TECHNOLOGIES
The formula used for the resistivity calculation

The geometric factors related to the semiconductor sample, the source currents supplied at the two outer probes, and the resulting voltages measured between the inner probes are what allow us to calculate the resistivity. The volume resistivity can be calculated as shown by the formula below. 

‘ρ’ is the volume resistivity in Ω-cm, ‘V’ is the voltage drop across the inner probes in Volts, ‘I’ is the source current supplied at the outer probes in Amperes, ‘t’ is the sample thickness (wafer thickness) in centimeters, and ‘k’ is the correlation factor. This factor is determined by two ratios. Firstly, the ratio of the probe to wafer diameter, and secondly, the wafer thickness to probe spacing.

Sheet Resistance

In some cases, the sample is so thin that the surface resistivity or sheet resistance measurement is taken instead. This is done for measuring things like coatings and thin films where the sample thickness is negligible compared to the wafer thickness.       

The Van Der Pauw Technique

The Van Der Pauw Technique | INQUIVIX TECHNOLOGIES
Measuring configurations for the van der Pauw technique. 

In the van der Pauw technique, the current is supplied and voltage is measured by the four probes. However, instead of placing them linearly along the length of the sample as we saw before in the collinear technique, the van der Pauw way is to place them around the perimeter of the sample. 

This allows us to get an average resistivity for the entire sample and is very effective for measuring small samples where the probe spacing is not very important. Basically, the sample is so small that it doesn’t matter how far apart the probes are spaced. A total of eight measurements are taken in the van der Pauw technique to calculate the average resistivity as shown by the diagram below.  

The Equipment Used For The Four Point Probe Resistivity Measurement 

A parameter analyzer capable of measuring the resistivity of semiconductors using the four-point probe method.  

In the lab, whether you’re using the collinear four-point probe technique or van der Pauw, the equipment used for measuring the voltage while supplying the source current is called a ‘parameter analyzer’. The earliest of these commercially available devices was developed back in 1955 by the Tektronix company. 

These first models were a step up from the classic oscilloscopes, and many of them are still in use today due to their relative simplicity of operation. The latest ones offer touchscreen displays, and data-export features, and can be connected to computers that can automatically perform van der Pauw calculations from different configurations.

Want To Learn More About Semiconductors?

To learn more about parameter analyzers, the unique properties of semiconductors, and semiconductor manufacturing, visit Inquivix Technologies!


How To Measure The Resistivity Of A Semiconductor Material?

The resistivity of semiconductor materials is measured using the four-point probe method which is performed via a parameter analyzer. A current is supplied through the outer probes, while the inner probes measure the voltage across the points of contact in the collinear technique of using the four-point probe method.

Why Measuring The Resistivity Of A Semiconductor Is Important?

New semiconductor materials with various doping concentrations and new manufacturing processes are introduced all the time to produce semiconductor wafers. The electrical properties of these new wafers need to be tested to ensure their performance is up to specifications. One of the ways this is done is by measuring the resistivity of the semiconductor wafer sample.  

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