Non-Contact Sheet Resistance Instrumentation


Principle of Operations

In its most ubiquitous application, eddy current technology is used as a nondestructive testing (NDT) method to find cracks in conductive materials and structures, such as air frames. However, one of the more complex applications of this technology is to determine the sheet resistance of conductive materials.

The essential element of an eddy current meter is an inductor, to which an alternating current (AC) is applied. This current creates a magnetic field. When this field is introduced to a conductive material, it induces eddy currents in the material. The characteristics of the material being tested create a unique set of results that can be used to deduce the sheet resistance of the material.

Only the magnetic field interacts with the material being evaluated. This field is relatively weak and generates no heat; therefore, it will not damage the material. Compared to contact measurement methods, such as four-point probes, eddy current technology has a number of advantages.

Eddy Current

Advantages of Eddy Current Technology

Compared to alternative methods of measuring sheet conductance, such as physically probing the material, eddy current technology has many advantages. These advantages are as follows:

  • Non-contact means no damage to the material
  • Insulating/non-conductive encapsulating layers do not affect measurements
  • Continuous and instantaneous readings
  • Ability to determine the bulk conductance of a sample

The Problem with Four-Point Probes

  • Often destroy the material they are measuring
  • Limited ability to measure the bulk value of the material
  • Cannot penetrate non-conductive coatings
  • Impractical for most process control applications

Potential Concerns for the Application of Eddy Current Technology

  • A minimum spot size of 1" x 1" (2.54 cm x 2.54 cm)
  • A caliper style sensor head—the top and bottom halves of these sensors must be close together
  • Sensitivity to temperature fluctuations


  • Sheet conductance is measured in Mhos/sq and sheet resistance is measured in Ohms/sq.
  • Sheet resistance is the inverse of sheet conductance. Measurements of sheet conductance and sheet resistance assume a perfectly square conductive sample.
  • Unlike measuring resistivity and conductivity, the user does not need to know the thickness of the conductive layer to determine its sheet conductance or sheet resistance.
  • For a conductance monitor, the size of the sample does not matter, as long as it is large enough to be viewed as an infinite sheet by the sensor (about 1" x 1" square).
  • The thickness of the material must be known to convert from Ohms/sq to Ohms-cm.

sheet conductance/Resistance, Resistivity, and Thickness

Consider the implied definition of resistivity, r (rho), given a bar of resistive material as shown below. Imagine measuring the resistivity across the length of this bar.

Length Width Height Block

As is intuitive, a longer bar is more resistive to flow. Similarly, a bar with a greater cross-sectional area provides more parallel flow paths and is thus more conducive to flow. From these observations, we infer that resistance equals resistivity times length, divided by Area. R=(ρ*L) ÷A. Resistivity is represented by the 17th letter of the Greek alphabet: Rho, ρ. Common physical tables list resistivity in units of Ohms-cm.

Now consider a square shape that could be cut out of a conductive film sheet or a coated glass panel with length (L), width (W) and thickness (T), as shown below.

We will use the formula we derived above. However, this time we will substitute area (A) with width (W) times thickness (T). Furthermore, since the sample is a perfect square, we can substitute length (L) for width (W). Therefore we get the following equation:

Resistance of a square sheet = (ρ*L) ÷ (L*T).
This can be simplified to Rs = ρ÷T

Length Width Height Block

Conductance of a square sheet is the inverse of above. Cs = T÷ρ. Therefore, for any perfectly square sample, sheet resistance is equal to resistivity divided by thickness. Similarly, sheet conductance is equal to thickness divided by resistivity. Sheet resistance is measured in Ohms/sq and sheet conductance is measured in Mhos/sq.

For many applications, the operator has a target resistance or conductance and does not necessarily care about the thickness of the coating. For these applications, the ability to directly measure in sheet conductance or sheet resistance—without first measuring thickness and resistivity—is quite useful.


Assume a Silicon wafer of resistivity ρ = 9.464 Ohms-cm and thickness T = 0.0615 cm. Rs = ρ÷T. Sheet resistance = 9.464 ÷ 0.0615 = 153.9 Ohms/sq (Cs = T÷ρ). Sheet conductance = 0.0615 ÷ 9.464 = 0.0065 Mhos/sq

Converting from Ohms/square to Ohms-centimeters

Ohms-cm refers to the volume or bulk resistivity of a material. The thickness of the material must be known to convert from Ohms/sq to Ohms-cm. The equation is sheet resistance (in Ohms/sq) multiplied by thickness (in cm) which equals volume resistivity (in Ohms-cm).

For example, consider a material that is 0.02 cm thick and has a sheet resistance of 3.00 Ohms/sq.
This material would have a volume resistivity of 0.02 cm times 3.00 Ohms/sq, which equals .06 Ohms-cm.

Best Practices

Below are some suggested best practices to ensure optimal use of a Delcom conductance monitor.

Ensure minimum required sample size. J and S series sensors require a sample area of at least 3 cm in diameter. C series sensors require a sample area of at least 9 cm in diameter.

Ensure sample is in center of sensor head gap. Due to the inherent field pattern within the head gap, the reading may be 5 % higher when the conductive layer is moved from the center of the gap towards one of the two poles of the sensor head. The sensor is calibrated with standards introduced into the center of the sensor head gap. Hence, for critical evaluation and comparison of a particular set of samples, register all test items such that the center of the bulk of the conductive material is located in the center of the sensor head gap.

Choose the appropriate range. If resolution requirements allow, and the expected values reside within the high range zone, the instrument should be used in that range since this will result in less temperature sensitivity.

Maintain stable temperature. In order to minimize the effects of temperature induced zero drift, the user may want to use the instrument in a temperature controlled environment.

Allow instrument to equilibrate to the room's temperature. Ensure the instrument (especially the sensor head) is the same temperature as the room to ensure minimal reading drift due to the instrument heating up or cooling down. If the sensor head has not been allowed to equilibrate to the room environment, it will produce reading drift at a rate of approximately 2.3 millimhos/degree centigrade.

Insulate sensor from radiant heat and cold. Samples that are extremely hot or cold may radiate heat or cold which could heat or cool the sensor head. This may result in reading drift.

Prevent deformation of sensor head. Excessively thick substrates or other forces that result in either increasing or decreasing the gap separation are considered abnormal and will affect reading accuracy. Delcom produces various sensor head models to accommodate most applications.

Recalibrate as needed. Instruments are calibrated with the use of NIST traceable standards to an accuracy value of plus or minus 2 %. Due to shipment shock, optional high sensitivity models may have to be recalibrated before usage.

Do not modify or replace sensor cable. The sensor is attached by a cable to the console. The cable cannot be indiscriminately lengthened or shortened—any change in the distributed capacitance value of the cable will affect the instrument's performance. Similarly, for critical readings, the cable should be allowed to rest for several minutes after being disturbed and before a low range zero is attempted. Cable motion can result in sub-picofarad capacitance changes that can affect the readings when measuring in the more sensitive ranges.

Reading Confidence

When deciding on what instrument range to purchase, potential operators should select a range that encompasses the entirety of the range of readings they expect to read for the material they are working with. Furthermore, the instrument should be selected such that the anticipated sheet resistance of the material is in the center of the range for the instrument. The closer each instrument gets to the high resistance end of its range, the lower the confidence is of the reading generated by the instrument. This characteristic of a conductance monitor is best explained by working in Mhos/sq. For this example, let us use a x10 instrument operating in low range (.00001 to .19999 Mhos/sq).

If we put a sample with a true value of .11111 Mhos/sq into this instrument, we are likely to see the display of the instrument reading any of the following values .11110, .11111, or .11112 Mhos/sq. The last significant digit is always likely to move one count on either side of the true value. This equates to a confidence error of roughly 1/10000 = .01 %. This means the user should have very good confidence in the value they are reading.

Now, let us put a sample with a true value of .00001 Mhos/sq into the same instrument. The last significant digit will likely move one count on either side of the true value. This will generate the following readings: .00000, .00001, or .00002 Mhos/sq. Each of these movements in the reading could equate to a confidence error of 1/1 = 100 %. This means that the value being read may not be very useful to the user.

The confidence error for each of the instrument ranges is listed in the chart below:

Mhos/sq .00001 .0001 .001 .01 .1 1 10 100
Ohms/Sq 100k 10k 1,000 100 10 1 .1 .01
÷100 10-100% 1-10% .1-1% .01-.1% .001-.01%
÷10 10-100% 1-10% .1-1% .01-.1% .001-.01%
x1 10-100% 1-10% .1-1% .01-.1% .001-.01%
x10 10-100% 1-10% .1-1% .01-.1% .001-.01%

Performance Caveats

A number of factors may complicate or render meaningless readings using Delcom conductance monitors.

Ferromagnetic Behavior in the Material

The placement of a non-conductive, ferromagnetic material between the faces of the sensing head can reduce the reading value. If the instrument is zeroed, the effect can be seen as a negative conductance value. As an example, the antiquated 5.25 inch DSDD computer floppy disk produces a value of approximately -0.0002 Mhos/sq.

Dielectric Loss Tangent

A material may have a small conductance when measured at DC or low frequency; however, it can exhibit a large conductance at an RF frequency of several Megahertz. Water is an example of a material with this behavior. Pure water is relatively non-conductive at low frequencies, but at RF and microwave frequencies it is an effective power absorber. Even though this type of conductance monitor operates in the low Megahertz region, certain oxides of titanium and other metals do have high dielectric losses and consequently high apparent conductance values.

Spatial Non-Uniformity of the Conductive Material

Materials that exhibit cracking, crazing, striated surfaces, non-isotropic properties, and island-like structures can cause apparent conductance variations. A DC four contact conductance measurement responds to the unidirectional current flow over a given area of material. If the given area is composed of islands, which are isolated from each other by surface cracks, the DC conductance value can be small. However, because the confined circulating currents induced by this eddy current type monitor can reside within an island structure, the dynamic conductance can be larger than DC measured values. Similarly, a striated or non-uniform metalized film can produce reading differences of between one and two orders of magnitude.

Non-Linear Behavior

Non-linear behavior of conductance is observed in semiconductors, dielectric-metal mixtures, and loosely bound dielectric materials because they can exhibit tunneling, electron hopping, and current decrease due to large compliance voltages, heating, electromigration and high current densities. Consequently, correlation between the RF/dynamic and the four contact DC measurement technique depends on measurement conditions.

Skin Effects

At high frequencies, electrical currents are unable to deeply penetrate conductive materials. Consequently, the effective resistance of conductors can sometimes rise to excessive levels. However, the frequency chosen for this device is such that the skin depth properties should rarely affect accuracy.

Free Carriers in Silicon Wafers

Silicon wafers exhibit short term reading instability. This characteristic has been noted and documented by others, including the NIST laboratory in Gaithersburg, Maryland, USA. For some values of conductance, the time period to achieve a stable reading can be one minute, for some it can be as long as six minutes. The phenomena is not understood well, and some maintain that all wafer testing and calibration should be done in a dark environment due to the release of photon stimulated carriers.