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First Published in EOS/ESD Technology Dec 1988/Jan 1989 Measure Resistance Instead, Part 1 Resistivity and
decay measurements can mislead users Link to Measure Resistance Instead, Part II Ben Baumgartner EOS/ESD Technology Editor's note: In the first part of this two-part article, Ben Baumgartner discusses the nature of resistivity measurements and shows why the results of such measurements can sometimes be misleading and difficult to repeat. In part two, to be published in our next issue, Baumgartner completes this discussion and outlines a simple measurement technique that is less confusing. Resistivity and static-decay data are often used to describe the ESD-protective characteristics of materials. However, because even engineers sometimes have difficulty with the concepts and terminology involved, such data often gives a confusing picture of the material being described. Indeed, resistivity and decay data collected on the same or similar materials often contain significant differences, and a number of papers have been written addressing these discrepancies (Ref 1,2). Unfortunately, it has become common to think of resistivity or static decay rate as actually defining the protection offered by a particular bag or tote, when this is almost never the case. Reality is complex, and factors such as device sensitivity, circuit configuration and the magnitude of anticipated electrostatic events all effect the amount any type of protection required. Even though we know that protection isn't a simple matter, we must often be satisfied with measurements of the properties of barrier materials, bags, totes, etc. that are thought to best describe the protection offered to ESD-susceptable devices. Unfortunately, this is also complicated; commonly used test methods frequently deliver the differing data referred to above. What's needed is a test method that resolves as many measurement and terminology problems as possible. We will present such a method in Part II of this article. Characterization Confusion Characterizing ESD-protective materials through measurement can be difficult for at least two reasons. The first, knowing what to measure, relies on understanding what is meant by resistance o resistivity Unlike resistance, resistivity is a property of an area or volume, and is not confined to wires or leads, which can be accessed and measured directly and unambiguously. Thus, if these terms are poorly understood and defined, measurements can result in error, and the errors can find their way onto data sheets. The second difficulty is that many materials don't lend themselves to measurement by conventional methods-- or to other available methods, for that matter. For the data taken to accurately reflect a material's properties, both the measurement method and the material tested must conform to laboratory practice and adapt to the theory of ideal resistivity measurement. ESD-protective materials vary in shape, size, construction and composition. This is unfortunate because for easy and accurate characterization, a material should be homogeneous, have a well-defined surface and a solid volume. Thus, resistance and resistivity measurements challenge our ability to apply such concepts to ESD-protective materials. This is especially true when data is taken on composites, laminates and foams; there is often a good deal of confusion as to exactly what the measured values represent. Resistance and Resistivity Resistance to the flow of electric charge determines a material's ability to dissipate a charge over time. The lower the resistance, the faster a charge flows, and the more rapidly potential equalizes on or in the material. Resistivity is the most important property of a material for determining resistance to the flow of these electric charges, both surface and volume. Although resistivity determines the rate of charge dissipation and the magnitude of static-charge field shielding, it theoretically has no relation to a material's tribocharging properties (Ref 3, see sidebar). Provided that certain conditions exist, control and charge flow is assumed to protect ESD-sensitive parts. The assumed conditions that charge (current) neither flows through bipolar devices at a destructive rate nor creates a voltage drop across the gate oxide of a metal oxide semiconductor that succeeds its oxide-breakdown potential. For certain surfaces or volumes, such currents must be limited, while for others, they must be relatively unlimited to provide optimum protection. Limiting current by specifying resistance will limit dissipation rate if the current travels through a device. Unlimited current on a surface provides shielding to the device it encloses.
Charge Decay and Resistivity Static-decay time is another way of describing ESD-protective materials. As measured by Fed. Test Method STD 101C, Meth. 4046, static-decay time determines the charge-dissipation rate of a material only when it is related to surface resistivity. As an aside, during measurement the charge on the material (Ref 5) often was originally created by tribocharging, but now it is applied using a 5-kV power supply through the electrodes supporting the material being tested. The original tribocharging method of electrifying the specimen has led to the mistaken belief that the test also measured tribocharging properties. The static-decay test is a dynamic-resistance measurement expressed in units of time for a 3 x 5 in specimen. The test measures decay time, which for an ideal material is related to surface resistance and resistivity of the sample. When applied to MIL-B-81705 Type-2 polyethylene materials, decay time has been shown to have a direct relationship to surface resistivity (Ref 6). When the decay test is applied to nonhomogeneous materials, or to those having layers with different resistivities, a field-suppression effect can cause ambiguous measurements. This effect results in a mistaken indication of low surface resistivity and a discrepancy in the measured decay time vs. the actual surface-charge-dissipatioon time. For example, a composite material's charge-dissipation time will be longer than the indicated charge-decay time. This occurs because the instruments don't measure charge directly, but instead measure electric-field intensity. For some materials, electric-field suppression time can be below the instrument's measuring range, even though surface resistivity is the insulative range. And the characteristic of materials in the dissipative range can't be measured using this method because the instruments can fail to respond to fast field changed. Despite these limitations, some product data sheets report very fast decay times for ESD-protective materials. These fast decay times cannot be useful in determining charge dissipation for anything but a Method-4046-size specimen unless the decay time is converted into a material property of resistivity. Thus, the decay test has serious limitations (Ref 6,7). Also, volume-resistivity data cannot be generated by the decay-test method. To determine the dissipation properties of any material, both volume- and surface- resistance or resistivity measurements must be made. So the decay test cannot be a substitute for a resistivity or a resistance measurement (Ref 4). Taking and Using Resistivity Data ESD-protective materials have both surface and volume paths that can carry current, but neither surface nor volume current encounters a discrete resistance. Instead, the sum of these resistive paths must be known in order to calculate the total resistance that determines current. The shape of the measurement electrode determines these paths and the effective resistance through control of field-line configuration. The resistance then measured is a function of current flow for an applied voltage; it is converted to a resistivity value by either the instrument or a calculation. Although such resistivity measurement method are theoretically sound, they work only when measuring ideal specimens. Still, such resistivity ideal specimens. Still, such resistivity data can be of value to package designers when properly sized material specimens are prepared and measured. In practice, the field configuration in the material is seldom known or worth the time to determine. Therefore, resistivity data have much less value to the end user because arc-discharge points and the associated paths are not known in advance.
Limits of Resistivity Measurements Resistivity measurements produce data usable for engineering purposes only when the shape, surface and thickness of the test specimen are controlled. Materials so characterized also must be uniform and homogeneous. For example, foam materials are not ideal and cannot have a true resistivity because there are holes or cells throughout the material. With ideal materials, the presence of surface and volume currents does not cause large errors in measurements, providing the material is an insulator. A guard ring is used in some instruments to improve the measurement accuracy. The ASTM D-257, Standard Test Method for DC Resistance or Conductive of Insulating Materials, surface-resistivity measurement is intended for measuring high-resistivity (volume) materials only. The surface resistivities of these insulative materials tend to be lower than their volume resistivities. This results in relatively small errors in surface or volume measurements, even if the measurement is unguarded. A guarded-electrode measurement system can properly compensate for these conditions, and surface measurements will produce usable results for ideal insulative materials. This isn't always the case for more conductive materials. Some instrumentation will measure black carbon-loaded materials as insulators, while the same material might measure about 20 kW with an ohmmeter and pointed test probes. Thus, even guard-electrode instrumentation can produce measurement errors in conductive-range materials beyond the design range of the instrument. If the characteristics of the material are not suspected in advance, such an error won't be detected without additional measurements. Except in theory, there is no such thing as surface resistivity. Physics handbooks list surface resistivity values for dielectrics (no values below 108W/square), but no surface resistivity values are listed for conductive materials. Volume resistivity values are given for both insulators and conductors. Insulators have very thin (i.e., several molecular layers thick) conductive surfaces; but the surface conductivity of a conductor's surface is indistinguishable from its volume conductivity. On an insulative substrate such as sapphire, a thin conductive conductive film has a surface resistivity related to its thickness. Generally, one should not assume that surface and volume resistivities are related.
Surface Resistivity Correction Factor To understand material and
instrumentation problems, we must review the electrode correction
and normalization factors used in resistivity measurement. Resistance
values are calculated from Equation 1, and surface resistivity from
Equation 2. The voltage, V, is divided by the current, I, to find
the measured surface resistance, Rs, in ohms. Rho
(RS) is the resistivity in ohms/square
and K is a correction factor. A surface resistance value assumes that no volume conductivity is involved. Any square electrode configuration used on an ideal material will measure a resistance in ohms that has the same numerical value as resistivity in ohms/square.
Fig. 1 shows that by adding equal resistance squares, the same value is obtained as for the original square, providing the electrode configuration remains square. To find surface resistivity (RS), RS is multiplied by correction factor, K, which is the width-to-length ratio, and which for a square electrode is always a convenient K=1, and thus, RS = RS For other shapes, K must allow for electrode configuration. For circular electrodes, K must account for the number of squares being measured in parallel (Fig 2). Large spacing between concentric-ring electrodes produce trapezoid-like sections that result in a slight error for different-sized electrodes, but it is not significant (Ref 1). K need not be a whole number. Equation 3 calculates K for concentric-ring electrodes for the diameters given in 3a and 3b.
Do is the average diameter, g is the gap between the rings, D1is the outside diameter and D2 is the inside diameter. If the rings don't have knife edges, the contact point nearest the gap should be used as the measurement point. Fig 2 is to scale for the correction factors given, and shows the cells that approximate trapezoids. The cells are the proper length-to-width ratio when a circle is tangent to all sides.
Volume Resistivity Normalization Factor Equation 4 can be used to calculate
volume resistivity rv
is a normalized value that is numerically equal to the resistance
across the opposite faces of a 1-cm cube.
Volume resistivity is a normalized value since both thickness and area are not taken into account in its calculation. Normalization results in a data-sheet value that can be misleading (Fig 3). In Equation 4, any size (area) electrode used on any thickness of a material will produce a resistivity value for the unit cube shown. Normalization results if proper metrics are used in this equation. Resistivity and actual measured resistance have the same numerical value only if 1-cm2 electrodes are used to measure a 1-cm cube. This allows a materials' resistivity to be compared with that of others because it is normalized, and measurement data now refer to an intrinsic property of the material, regardless of sample shape. A volume-resistivity value gives a false sense of actual resistance for a large or small area. This value can be very misleading for an envisioned current path when a volume current is not desirable. For a material that is 4-mil (0.01-cm) thick, the actual resistance to a current though a 1-cm2 electrode is 2 orders of magnitude below this. For this 4-mil thick material, a 10 x 10-cm sheet would have 4 orders of magnitude less resistance. Measurement Problems Many problems, both real and imaginary, are attributed to the electrodes used in measurement. Should they have knife edges or offer broad contact? Should they be circular or square, metal, or conductive rubber, large or small? What pressure is needed to make a good contact? The problems are due to combinations of electrodes and materials, and thus blaming the equipment does not address the problems of the measuring system. Soft, hard or textured materials cannot be easily measured with the same electrodes, and even greater problems are caused by composite, laminate and foam materials since they are far from the homogeneous ideal. There are many other factors that could explain some of the variations in surface resistivity values, but, in practice, it is difficult to separate the variables. However, theoretical examples help us see what might cause measurement discrepancies. Fig 4 shows how incorrect surface-resistivity measurements might be caused by a buried conductive layer. E1 is a plain knife-edge electrode; E2 is a knife-edge electrode with a conductive-rubber center. The volume current is Iv adds to the surface current Is, and is not properly subtracted from the measurement by the guard electrode since this subtraction depends on the volume resistivity of the material contacting the guard electrode. This condition can exist where the top layer of a laminated specimen is relatively conductive and the bottom layer is an insulator. The resistance measurement is then practically independent of electrode spacing, which results in a surface-resistivity-measurement error. Electrode spacing determines the correction factor used to convert the resistance measurement to resistivity.
The variation can be greater for different electrode surface areas because the resistance measurement is proportional to electrode area; it is as if the measurement were one of volume. The dashed-line square in Fig 4 represents this larger effective electrode surface. For example, the ratio of the areas of an 0.125-in. rubber electrode and a knife-edged electrode is almost infinite. For measurements to be repeatable, circumference must also be taken into consideration. The area ration of a 25-in. circumference (approximately 8-in.-diameter EMI-gasket electrode) to a 1.5-in.-circumference (approx. 0.5-in.-diameter knife edge used in making measurements on small samples) makes comparable measurements difficult. The data in Table 1 show variations for several electrodes that are not as extreme as the above example.
Multilayer materials also cause problems for volume measurements because the various conductive layers often have different volume resistivities and are of unknown thickness. Fig 5 shows how the volume current (Iv) can be spread by a buried conductive layer if the top layer is more conductive than the bottom material. Electrode E1, which has a conductive-rubber center, is used to calculate the contact area for the Iv current. The other electrodes are the plate, E2, and the guard ring. This figure illustrates how, for composites and laminates, layer thickness and electrode design both affect the measurement. The guard ring does prevent surface current (Is) errors but is affected by the sample's internal conductive layer, which increases to Iv to the guard ring. The measurement may also be affected by the guard contact area ( dashed-line square), which can increase volume current to the guard electrode. In open- or closed-cell forms, volume measurements are confused because surface paths shunt volume paths. For foam materials it's not possible to separate the surface current from the volume current being measured. This is also a problem for materials such as composites, which contain random conductive wires, carbon-particle swirls (as in conductive flooring) or layers of different materials. References 1. D.C. Burdeaxu, C.L. Mott, "An Analytical
Approach to Surface Resistivity Measurements," Evaluation Engineering,
November 1986 (Table 3, p. 87; Summary, p. 97). |
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