# Repeatable measurement of high-resistivity rubber and other materials.

High resistance and resistivity measurements are often made on rubber, other polymers and materials, for the purpose of determining their electrical characteristics as well as their structure, effects of additives, homogeneity, composition and other physical characteristics.

The accepted (classic) method of measuring high resistance is to apply a dc voltage to a sample and measure the current stimulated by the voltage in the sample. The current and voltage values are used to calculate the resistance (ohms), volume resistivity (ohm-cm) or surface resistivity (ohms per square) of high-resistance materials. For high resistance samples, the levels of measured current can be quite low, in the pA ([10.sup.-12] A) or pA ([10.sup.-15] A) region. Testing materials involving these low currents and getting repeatable results can be a challenge. Currents of the same order of magnitude or larger are generated by other effects, such as piezoelectric effects or charge storage in the sample or in test fixtures not designed for such sensitive measurements. These can easily obscure the stimulated current used to calculate resistance, surface resistivity or volume resistivity.

This article presents a method for selectively measuring a stimulated current in the presence of other currents that may be much larger than the stimulated current. This measurement method provides a much more repeatable measure of the current-voltage relationship. It can also be used to determine the dependence of the current-voltage relationship on time. This information can be used to more precisely determine electrical and other characteristics of rubber, other polymers and high-resistivity materials.

Test methods, systems and fixtures

Classic test method

A typical test system for resistivity consists of a dc voltage source to provide the stimulus voltage, a series ammeter to measure the stimulated current and a test fixture to connect the sample under test in series with source and the ammeter.

The biggest problem in this measurement process is typically that the ammeter measures current due to many effects, not just the stimulating voltage. The result can be high variability in the current reading and grossly incorrect values, such as a negative total current for a positive stimulating voltage. Some sources of these extraneous currents are dc or transient currents generated in the test fixture, cabling or the sample itself.

Test fixture

Standard fixture parameters and dimensions have been defined by the American Society for Testing and Materials (ASTM) (ref. 1) for measuring volume and surface resistivity and are commercially available. Most are designed for samples at least two inches in diameter, less than four inches square, and less than 1/8-inch thick. It is important to apply a force to the sample to control contact resistance and keep it small compared to the sample resistance. The instrument applies 10 pounds of force to the sample.

In order to determine the effect of currents in the test fixture, one can measure the current in the fixture with no sample (air as the sample material) and compare this value to the stimulated current measured through the sample. If the current due to the fixture alone is much smaller than the sample current, this will not cause a significant error. This is shown in figure 2, comparing the fixture current to a rubber sample with resistivity of [10.sup.15] ohm-cm. In this case, the fixture leakage currents are lower than the sample currents by a factor of 1,000, causing less than 0.1% errors due to this problem.

[Figure 2 ILLUSTRATION OMITTED]

Sources of current

Extraneous background currents can be produced by many different phenomena, from piezoelectric effects to temperature induced pole relaxation to discharge of internal capacitive elements. Time constants vary from seconds to hours or days. In general, when measuring high-resistivity materials, there is always some background current, and it is usually decaying from some set of previous events. Figure 3 shows a typical background current and the sum of the background current and a stimulated current superimposed on it, resulting from a voltage step at time 0, using the classic method.

[Figure 3 ILLUSTRATION OMITTED]

As figure 3 indicates, the stimulated current is completely masked by the background current using this method. This would lead to the erroneous conclusion that the sample has negative absolute resistance, since the stimulating voltage is positive and the stimulated current is negative, at C and all regions right of B. At B, the point where the current crosses zero, the calculated resistance, V/I, is infinity. At A, and all points left of B, a positive number is obtained, but it is not correct, since the stimulated current is the difference between the background and measured current.

Alternating polarity method

The intrinsic problems with the classic method led to the development of the alternating polarity method, shown in figure 4. This also uses the block diagram of figure 1. In this method, the voltage is reversed (or put at another level) at a selected time, and the change in the stimulated current in response to the change in stimulating voltage is measured. The change in current is taken between measured points shown as solid squares. These points were measured just before the voltage was reversed. It has been shown (ref. 2), that by measuring four currents just prior to each of four successive alternations of the stimulus voltage, the value of the background current, its slope and curvature may be corrected for in calculating the change in current.

[Figure 1 and 4 ILLUSTRATION OMITTED]

In figure 5, the "X"s indicate one-half the calculated change in current due to the stimulus voltage. The values of the first four measured currents are needed to calculate the first change in current, correcting for value, slope and curvature, as indicated above. It is clear by examining the calculated points (the "X"s), that this technique provides much more repeatable results than measuring current directly using the classic method (the solid squares), in spite of the large background current and change in sign of the stimulated current as measured using the classic method.

[Figure 5 ILLUSTRATION OMITTED]

This system is capable of making very repeatable measurements. For example, using an FR-4 epoxy sample, the short-term repeatability is within 0.3%, as seen in figure 6.

In the classic method, the basic measurement technique is usually the limiting factor, due to the impact of background currents, as discussed earlier. Often the calculated resistivities vary over decades, even in the short term, and include negative values. Using the alternating polarity method, the limitation is usually the temperature dependence of the sample. We found this to be the case in testing rubber, vinyl and epoxy samples. The advantage of the alternating polarity method is that it is sufficiently repeatable to permit investigation of the dependence of the sample on temperature, pressure, humidity, additives, processing or other parameters. Using this method, it is possible to determine such cause-and-effect relationships confidently, without being limited by the measurement method. For example, on the sample used in figure 6, the temperature coefficient of resistivity was measured as being (8% [+ or -] 1%)/ [degrees] C. Figure 7 shows the curves from which this calculation was made.

[Figure 6-7 ILLUSTRATION OMITTED]

Implications in measuring resistivities of rubber

Applying this method to rubber samples, we found that samples that measured [10.sup.14] to [10.sup.15] ohm-cm, with some negative readings, using the classic method, could be measured with 4% repeatability, which was limited primarily by the temperature coefficient of 5%/[degrees] C, determined by the same method as in figure 7. Figure 8 shows short-term noise.

[Figure 8 ILLUSTRATION OMITTED]

By using the proper test system, precise tests can be done to determine the effects of voltage level, frequency of the alternating voltage and bias voltage. The system could also have provisions to record temperature (as in figure 7) and relative humidity. This system would be a complete system for easily and precisely measuring the dependence of resistivity on test and environmental parameters. This can be used to quantify system errors, permitting statements of the uncertainty in test reports.

This method can be used to determine the effects of additives, processing and investigate any parameter that is related to resistivity or resistance of rubber on a quantitative basis. Using the classic method, it is only possible to get rough qualitative data. The alternating polarity method provides a tool for serious quantitative investigations of cause-and-effect relationships in rubber processing and compounding that could not be made using the classic method, due to lack of repeatability.

References

[1.] 1991 Annual Book of ASTM Standards, Volume 10.01 D257.

[2.] Adam C. Daire, white paper: "Improving the repeatability of ultra-high resistance and resistivity measurements," Keithley Instruments Inc., 1997.
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