A fundamental property of insulators is resistivity. The resistivity may be used to determine dielectric breakdown, dissipation factor, moisture content, mechanical continuity and other important properties of a material. The volume resistivity of some insulators such as sapphire and Teflon can be as high as 1e16 to 1e18 ohm-cm.
Due to the large magnitudes involved, our experience in working with customers has shown that proper test methods and instrumentation are vital when measuring the resistivity of insulators. One test method we see used frequently is ASTM-257, “DC Resistance or Conductance of Insulating Materials.” Instruments called electrometers are used to make this measurement because of their ability to measure extremely small current.
Let’s take a look at what’s involved. Of course, if you already have a handle on these measurements and want to see how its done, feel free to jump to the end of this post for an information video I put together on using the Keithley Model 6517B electrometer and Model 8009 resistivity test chamber for these measurements.
There are two methods to make a resistance measurement. One is to source a current and measure the voltage drop, then use Ohm’s law to calculate the resistance. The other is to source a voltage, measure the resulting current and then calculate the resistance.
In general, the first method (source current and measure voltage) is used to measure resistances lower than 1G ohm (1e9 0hms). The second method (source voltage and measure current) is generally used to measure higher resistances.
There are two reasons for this approach. One is the voltage coefficient. Since the magnitude of the applied voltage can affect the resistivity of materials, sometimes a few different voltage levels are used to get a better idea of how the material reacts to different levels. The other is the fact that most voltmeters do not have a high enough input impedance to avoid impacting measurements.
For example, if you’re testing a 1 G ohm sample and the input impedance of the voltmeter is 10G ohms, it will load down the measurement by a factor of 10%. Because of this, making high resistance measurements requires using the second method (source voltage measure current).
Resistivity measurements are basically resistance measurements with the geometric dimensions of the sample taken into consideration. Let’s take look at two different methods of resistivity measurements.
Volume resistivity – Volume resistivity is the measure of the resistivity through the sample. This means the voltage is applied from one side of the sample to the other side of the sample and the current through the sample is measured. It is defined as the electrical resistance through a 1 cm cube of insulating material and is expressed in ohm-cm.
Surface resistivity –Surface resistivity is a measure of the resistivity across the sample. It is defined as the electrical resistance of the surface of an insulator. This means the voltage is applied across the sample and the resulting current is measured.
Once the resistance is measured, the resistivity can be calculated.
The volume resistivity can be determined by the following equation:
P = AV / tI
Where V is the applied voltage
I is the measured current
A is the effective area of the guarded electrode for the particular electrode arrangement is cm squared.
T is the average thickness of the sample is cm.
The surface resistivity G, can be calculated from the following equation.
G = PV / gI
Where V is the applied voltage
I is the measured current
P is the effective perimeter of the guarded electrode of the particular arrangement used.
G is the distance between the electrodes
Ultra High Resistivity Measurements
Now that you have a basic understanding of resistance and resistivity measurements, what else do you need to be aware of for ultra high resistivity measurements? As it turns out, quite a bit. All of the previous information is pertinent for measuring ultra-high resistivity, but with the additional considerations I’ve outlined below.
Let me be up front. Not all measurement equipment is the same and getting it right is of utmost importance. The current to be measured at high resistivity could easily be lower than 1pA. A standard DMM (Digital Multimeter) would not have the capability for this measurement. Nor would a standard ammeter. Only a picoammeter or electrometer have the sensitivity and accuracy to make this small current measurement.
Most picoammeters have sensitivity to well below 1pA. With an accuracy of about 0.5pA. Most electrometers have current sensitivity to well below 1fA(1e-15A) and accuracy of about 3fA(3e-15A).
This is what’s required to make the current measurement of an ultra-high resistivity measurement.
Of course, the higher the applied voltage the higher the measured current. But ASTM-D257 recommends a 500V applied voltage. The ability of the sample to handle high voltage must also be taken into consideration.
Guard or guarding is a technique where the high impedance point in the circuit is surrounded by a low impedance signal of the same magnitude. With no potential between the two points current can’t flow and therefore no current can leak away.
This is important when measuring below about 10nA (1e-8A). And guess what, when measuring ultra-high resistivity, the measurement current will be much smaller than 10nA.
Electrometers and picoammeters have a built in guard feature. The inner shield of the triax connector on electrometer and the BNC shield on the picoammeters is at guard potential. This connection needs to be surrounding the low current signal all through the configuration. I should point out that Keithley Model 6517B electrometers and Model 8009 resistivity chambers have this capability and are well-suited for ultra-high resistivity measurements.
Time to let a small current settle and charge any capacitance in the test circuit is critical to obtaining repeatable and stable readings. The higher the resistivity the smaller the current. The smaller the current, the more time it takes to settle.
Consider charging a capacitor with 10mA up to the rated voltage. This should take very little time to charge completely. Now charge the capacitor with 10pA of current instead of 10mA. Of course, it would take much longer to completely change the capacitor. This is the same principle when measuring ultra-high resistivity. There is capacitance within the circuit, however small it might be. The lower the current the more time it takes for the current to charge everything in the circuit and therefore settle.
Alternate polarity method
The alternating polarity resistance/resistivity test is designed to improve high resistance/resistivity measurements. Unfortunately, these measurements are prone to large errors due to background currents. By using an alternating stimulus voltage, it is possible to eliminate the effects of the background currents. The higher the resistivity the more chance of background currents residing in the sample.
When this test is run, the V-source will alternate between two voltages (V-OFS + V-ALT) and (VOFS- V-ALT) at timed intervals (MEAS-TIME). Current measurements are taken at the end of each of these alternations and after calculation of Icalc resistance values are computed. Icalc is a weighted average of the latest four current measurements, each at the end of a separate alternation. The resistance value is then converted to a resistivity value if the meter has been configured for resistivity measurements.
For reference, Keithley Model 6517A and 6517B electrometers and Model 6487 picoammeter/source have the alternate polarity feature.
When making resistivity measurements the true measurement is current. So the current measurement range is of vital importance. If the range is physically set to 20mA and the current magnitude is 10pA then the measurement will be on the lowest part of the range and therefore be subject to noise and inaccuracy and maybe even negative values.
Paying attention to the current measurement range is important to making proper measurements. Auto range is fine if the magnitude of the resistivity is not known. But always monitor the current measurement range for the most accurate readings.
A resistivity chamber such as the Keithley Model 8009 applies a certain amount of pressure on the sample to obtain proper connections to the sample. The amount of pressure can range from 2 pounds to 23 pounds depending on the thickness and rigidity of the sample. In general, the higher the pressure the lower the measured resistivity. This affects volume resistivity much more than surface resistivity.
The ambient temperature and humidity affect the resistivity measurements. In a high humidity environment, the sample could contain more moisture and thus affect the measurement. Temperature is also a factor, but typically has more impact on the measurement instruments than the sample.
If the temperature is outside of the rated rage of the instrument, a temperature coefficient must be applied to ensure the accuracy of the measurement.
For simplified monitoring of the test environment, Keithley electrometers have built-in temperature and humidity measuring functions.
Making the measurements
Now that you understand the requirements and considerations for making ultra-high resistivity measurements, take a look at the video I mentioned earlier to see how easily they can be performed using the Keithley Model 65178B electrometer and Model 8009 resistivity test chamber.
Dale Cigoy is a lead application engineer at Keithley Instruments.