Four Point Probe Measurement Method

The four point method is also known as four point measurement. It is a method to measure the sheet resistance. The sheet resistance is the electrical resistance of a surface or a layer. It is defined by the resistivity of the layer divided by its thickness. The most common method for sheet resistance measurement is the four point probe method. This method uses a line of four probes with equal spacing arrayed in a line. A current flows between the two outer probes, resulting in a reduction of the voltage between the two inner probes. By measuring this voltage change, the sheet resistance can then be calculated.

Principle of the Four Point Probe Method

As described before, four-probe measurement works by contacting four equally-spaced probes to a conductive surface. Between probe 1 and 4 a current is applied. Then the voltage between probe 2 and 3 drops and is measured. With the known values for U and I, the sheet resistance can be calculated.

calculation sheet resistance.png
  • R is the sheet resistance
  • ΔU is the change in voltage between probe 2 and 3
  •  I is the current applied between the outer probes.

The unit Ω is the mathematically correct one, but to make a distinction to the bulk resistance the unit Ω/□ or also "ohm per square" is used.

If the thickness and sheet resistance of the measured material known, the resistivity can be calculated with:

Formel spezifischer Widerstand.png
  • ρ is the resistivity
  • d is the thickness of the material.

Four measuring probes with the same spacing are placed in a row on the surface, with a known current flowing between the two outer ones and the potential difference, i.e. the electrical voltage between these probes, being measured using the two inner probes. Since the method is based on the principle of four-wire measurement, it is largely independent of the contact resistance between the measuring tips and the surface (Thomson bridge principle). The closer the tips come to the edge of the sample, the more the measurement is distorted: the electric current lines cannot propagate freely, they must flow parallel to the edge of the sample.

 

4pp measurement.png

 

If adjacent measuring probes each have the same distance, the sheet resistance R is obtained from the measured voltage U and current I with:

Formel Flächenwiderstand.png

When the current is set to 4.53 mA, the resistivity is simply the voltage reading in mV.

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

  • The layer thickness must be much smaller than the distance between the probes. (typically 1 mm)
  • The total area of the layer must be (infinitely) large compared to the distance between the probes.
  • The substrate must be electrically insulating so that the current flows only through the layer. (In the case of semiconductor wafers, this condition is also fulfilled 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 deposited on the semiconductor, but in the process the layer can be damaged by the measuring tips.

A method to measure the resistance or sheet resistance without using a sensor array with equal distance is the van der Pauw Method.

More Precise Alternative to 4PP Measurement –
Eddy Current Measurement

technology_scheme_eddy_current_eng.png
  • Suitable for inline measurement
  • High quality mappings with up to 1 million measurement points per sample
  • No contamination or destruction of the surface, because of non-contact measurement
  • Able to characterize even hidden layers

Four Point Probe Measurement

Again, the sheet resistance is the result of dividing the resistivity (ρ) of a layer through the layers thickness (d).

formula sheet resistance rho and thickness.png

Four Point Probe Measurement of Thin Films

If the current flows through the contacts into the layer under investigation with a uniform resistivity, then the current spreads out in a circle. The current density can be given by:

current density.png

The current is induced at location r1 and drawn at location r4. This produces a typical dipole pattern. For the thin film approximation, the distance between the peaks must be much larger than the thickness of the thin film. Then the current density can be given by:

formula current density.png

The electric field is:

formula electric field.png

The measured voltage between r2 und r3 is:

measured voltage.png

The voltage is independend of the path:

measured voltage depending on direction.png

The voltage after integration is:

voltage after integration.png

with:

length.png

The resistivity is:

formula resistivity.png

If the thickness of the layer is unknown, then the resistance cannot be calculated. In this case, the sheet resistance can be given by:

formula sheet resistance 4pp.png

Four Point Probe Measurement of Bulk Resistivity

The is no difference in measuring the bulk resistivity and the sheet resistivity. The only difference: By using the layer thickness (d in cm) the resistivity is reported in cm-3. The following formula can only be used if the layer thickness is less than half of the probe spacing (d < l/2).

formula bulk resisitivity for layer thickness half the probe spacing.png

For layer thickness greater than half the probe spacing, the following formula can be used:

formula resistivity for thicker samples.png
  • l is the probe spacing.

Four Point Probe Measurement of Sheet Resistivity

Using the voltage and current readings from the probe:

formula sheet resistivity

With:

faktor.png

Two Point Probe Resistivity Measurement

Contact and propagation resistance are very high when using two-point probes. This means that the resistance of the sample cannot be isolated. This is the advantage of the four-point method. The contact and propagation resistances of the voltage probes are very low, which makes the measurement accuracy very high. This is because two wires are used, one to induce the current and the other to measure the drop in voltage.The be clear: a two point probe measures the combined resistivity of the sample, the contact resistance and the probe resistance whereas a four-point probe only measures the sample resistivity.

2pp vs 4pp resistivity

Four Point Probe Problems

Four point probe measurement have to handle with a few problems:

  • Due to the contact-based measurement, samples can be damaged
  • To get the best measurement results, the probe must be placed in the center of the sample
  • You always need a non-conductive layer under the layer to be measured
  • The measurement result always depends on the shape of the sample. There are different correction factors for different shapes. But not only the shape, but also the size and the thickness of the sample are important and need different correction factors

Four Point Probe vs Eddy Current Measurement Comparison

Is there a difference in sheet resistance measured with 4PP or Eddy Current?

There is no difference in sheet resistance measured with 4PP or Eddy Current. Both testing methods measure the sheet resistance as a physical property. This property is independent from its measurement method.

What is the advantage of non-contact sheet resistance measurement over common four-point-probe devices?

SURAGUS non-contact measurement solutions allow accurate measurement without impacts due to inhomogeneous contact quality, without damaging any sensitive surfaces or inducing artifacts due to contacting. Furthermore, it allows the accurate measurement of inaccessibly buried or encapsulated layers.

Applying SURAGUS non-contact technology, there is no wear of needles / tips, which typically causes high replacement costs in common 4-point-probe mapping systems. A further significant advantage is the short measurement time: SURAGUS TF Series devices take only a few milliseconds for each measurement and no time for con­tacting the sample is needed.

This also allows to measure inline during production or “on the fly” in mapping systems. In result, the SURAGUS sheet resistance mapping systems measure thousands of positions in a couple of seconds. No interpolation between measurements points - as typical in 4-point-probe mapping systems – is required. In result defects and non-uniform areas are not missed.

Non-contact Eddy Current Testing

Four Point Probe Measurement / 4PP

Contact-free

Contact

Higher repeatability as 4PP

Homogeneous contact quality reduces measurement quality

Measurement range from 0.1 mOhm/□ to 100 kOhm/□

Measurement range from 1 mOhm/□ - 10 kOhm/□

„real-time“ – up to 1,000 Measurements per second /  „on the fly“

Relative long measurement time mainly due to contact establishment (couple seconds)

Imaging and inline solutions with thousands of measurements
e.g. 10,000 Measurement in a pitch of 1 mm on a 4 inch sample within 200 seconds. 

Imaging solution and inline solutions with small number of measurement points. Interpolation is required

No costs for wearing

Wearing costs (especially relevant for mapping and inline solutions)

No contamination due to contact

Danger of contamination (especially for semiconductor, OLED industry)

No physical impact to sensitive films

Danger of layer damage through physical impact

Measurement of conductive multilayer systems.
Layer separation by parallel resistance formula.

Measurement of accessible top layers only

Characterization of hidden and encapsulated films

No measurement of encapsulated films

Applied for 30 years

Applied for 70 years

Calibration by manufacturer or by user

Calibration by manufacturer or by user

Does roughness affect the measurement quality?

No, other than for contacting measurement technologies, roughness of the layer does not affect the quality or accuracy of the SURAGUS non-contact measurement. SURAGUS non-contact devices are commonly applied with good results for measuring rough or sensitive layers.

Is the system applicable to multilayer systems?

SURAGUS EddyCus TF series devices measure through the complete stack of all layers. Multiple conductive films in one stack electrically behave as parallel resistors and can be separated accordingly using standard formulas. Hence, multiple conductive layers can be separated by measuring after each coating step.

What is the measurement pitch / measuring point distance for inline or mapping solutions?

Inline measurements and mapping systems use a lateral measuring point distance of 250 microns to 10 mm (400 mil) depending on the application. The standard distance for property imaging is 1 mm.

What is the spot size of a system?

The sensitivity of the measurement system is highest in the center of the sensor and decreases towards the outside and then no longer contributes to the characterization. The high sensitive zone (HSZ) of sheet resistance measuring systems ranges from 5 to 25 mm depending on the setup. Some systems with 100 mm HSZ were realized for wide coverage in the past as well. This HSZ diameter is primarily defined by the distance to the sample and some sensor characteristics. Smaller distances and sheet resistances enable smaller measurement spot sizes.

Structure and defect monitoring systems utilize a HSZ from 0.5 to 5 mm. Additionally, differential sensors with very high sensitivities are used for the detection of local defects and variations.

What is the spatial resolution?

The spatial resolution is determined by the contrast of the measuring effect, the measurement point distance and the spot size. For example, a wafer mapping can be obtained using a distance (gap) of 2 mm. The high sensitive zone (HSZ) then has a diameter of about 5 mm. Sheet resistance fluctuations of 4% can be measured when affecting about 25% of the 5 mm HSZ. Defects that cause a higher contrast can be detected when affecting smaller areas. For instance, cracks with only a few microns width can be easily detected as the contrast and measurement effect is very high. 

Do I need to change several sensors to cover a large measurement range?

The measurement range of one sensor covers 6 decades of sheet resistance. The required measurement range requested by the application is set during manufacturing of the device. There is no need for sensor changes or system adjustments.

Do I have to consider an "edge effect"?

The eddy current-based measurement relies on an induced electric current in conductive layers. The currents have a high current density below the sensor that diminishes with increasing distance to the sensor. This effect is also known from 4PP systems, which use the similar physics and cope with the same effect. Typically, there is a correction formula deepening on the distance to the edge in the user manual of 4PP and Eddy Current systems so the user can correct those measurements by multiplying a factor.

SURAGUS mapping devices provide an integrated and automated correction of this “edge effect” for many pre-configured sample sizes and allow an accurate measurement at any position of the sample.

Do vibrations of the sample have an influence on the measurement?

Depending on the measuring range and the measuring gap different vibrations can be tolerated. The standard tolerance is ± 1 mm. A low sheet resistance and large measuring gap allow tolerating large variances of up to ± 5 mm. For the measurement of curved substrates sensors are used with integrated ultrasonic sensors, the measured values are compensated according to the position in the measuring gap and position-independent accurate measurement values can be determined.

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