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Voltmeter Manual Questions

Techniques for Bulk Material Resistivity Measurements

Electrical resistivity is a basic property that defines how well a material conducts current. It’s determined by measuring the resistance of a material sample, and then applying geometry factors. The three basic types of bulk materials—metals, insulators, and semiconductors—have different ranges of resistivity. Metals are good conductors of current with typical resistivities of about 10-6 ohm-cm. Insulators are poor conductors with typical resistivities from about 109 to 1020 ohm-cm. Semiconductors conduct current better than insulators but not as well as metals; they may fall anywhere from about 10-3 to 107 ohm-cm.

 

Measuring the Resistivity of Good Conductors. Characterizing a metal’s resistivity requires the measurement of very low resistances (and therefore, low voltages) accurately. The techniques described here can also be used in applications involving other small voltage measurements, such as those needed in measuring the resistance of superconductors, nanowires, carbon nanotubes, graphene (a one-atom-thick form of carbon), and other nanomaterials in which applied power must be kept low to prevent material heating.

 

Imagine a conductive material sample in the shape of a thin block with thickness t, width w, and some arbitrary length. To find its volume resistivity, a current source is connected at both ends of the sample along its length. Voltmeter leads are placed a known distance apart, L, along the length of its surface. The resistivity can be found by sourcing a known current, I, measuring the voltage drop, V, then calculating the volume resistivity, r, from the measured voltage, the magnitude of the source current, the cross-sectional area, A, (=wt), and the distance between the voltmeter leads, L, using the equation:

 

r = (V / I) x (wt / L)

 

For metals and other good conductors, the voltage drop is usually just microvolts or nanovolts, so precise measurements are crucial. Potential error sources include test lead resistance, thermoelectric voltages, low frequency noise, external noise sources, Johnson noise, and the use of a voltmeter with insufficient sensitivity. Fortunately, special techniques can reduce the impact of these errors. For example, using the four-wire (Kelvin) measurement method, in which one set of leads are used to source the current and another set are used to measure the voltage drop across the sample, will eliminate the effects of lead resistance.

 

Thermoelectric voltages are a common source of error when making low voltage and low resistance measurements. These voltages are generated when different metals in the circuit are at different temperatures. To reduce thermoelectric voltages construct test circuits using the same materials for interconnects. Minimize temperature gradients within the test circuit and allow the test equipment to warm up and reach thermal equilibrium. Finally, use an offset compensation method to overcome these unwanted offsets, such as a current-reversal method or the delta mode offset compensation technique.

 

The delta mode technique for removing offsets and low frequency noise involves applying a current and measuring the voltage, then reversing the current and re-measuring the voltage. The difference between the two measurements divided by two is the voltage response of the sample to the applied current level. Repeating the process and using averaging reduces the noise bandwidth and therefore the noise. Although this was once a manual technique, which limited reversal speed to less than 1Hz, newer instruments, such as Keithley’s Model 2182A Nanovoltmeter and Model 6221 Current Source, now automate the technique. This increases the reversal speed, which sets the frequency that dominates the noise. Higher reversal speeds do a better job of removing low frequency noise and thermal drift, because these noise sources have lower power at higher frequencies.

 

External noise sources are interferences created by motors, computer screens, or other electrical equipment. They can be controlled by typical shielding and filtering techniques, or by simply eliminating the noise source. Because these noise sources are often at the power line frequency, avoid test frequencies that are exact multiples or fractions of 60Hz or 50Hz. When using DC instruments and reversal methods, the same result can be achieved by adjusting the instrument’s signal integration period for each measurement to an integer number of power line cycles.

 

In any electrical resistance, thermal energy produces the motion of charged particles. This charge movement results in Johnson noise. Johnson noise may be reduced by reducing the bandwidth using analog or digital filtering, or by reducing the temperature of the device.

 

When considering instruments for resistivity measurements keep in mind that most digital multimeters (DMMs)can’t measure microvolt- or nanovolt-level voltage drops accurately. Generally, an instrument with around 1nV sensitivity is a better choice, which can be found in a good nanovoltmeter.

 

Measuring the Resistivity of Insulators. The techniques used to measure the resistivity of insulators such as paper, rubber, and plastics are very different from those used for conductors. The resistivity of an insulator is determined by applying a voltage to the sample for a specified period of time, measuring the resulting current with an electrometer or picoammeter, then calculating the resistivity based on Ohm’s law and geometric considerations.

 

Both volume and surface resistivity measurements can be made on insulators. Volume resistivity is a measure of the leakage current directly through the insulator. To set up this measurement, picture a sample of arbitrary shape, but with a known uniform thickness t. Two electrodes, each having the same area, A, are placed on the top and bottom of the sample. The lower electrode is connected to the high terminal of a voltage source, V. The low terminal of the voltage source is connected to the low terminal of an ammeter. The high terminal of the ammeter is connected to the top electrode. Although the magnitude of the applied voltage usually depends on the material under test, it is often 500V DC (per ASTM D257). After a specified electrification time, usually 60 seconds, the current, I, is measured using an ammeter capable of measuring nanoamps or lower. Volume resistivity, r, is calculated based on the area, A, of the electrodes and the thickness, t, of the sample using the equation:

 

r = (V / I) x (A / t)

 

Surface resistivity is the electrical resistance on the sample’s surface. This measurements is conducted on a sample of any thickness and length, but fabricated with a constant width, w. Two electrodes are placed across the width of the sample, separated by a constant distance, L. An ammeter’s high terminal is placed on one electrode; the voltage source’s high terminal is placed on the other. The low terminals of the ammeter and voltage source are connected together. A potential difference, V, is applied for a known period of time and the ammeter measures the resulting current, I. The surface resistivity, s, is calculated from:

s = (V / I) x (w / L)

 

Potential error sources when characterizing an insulator’s resistivity include choosing an ammeter without sufficient sensitivity, and using an inappropriate electrification time or test voltage. Other error sources include electrostatic interference, background currents due to charge stored in the material, and static or triboelectric charge, or piezoelectric effects.

 

Electrostatic interference occurs when an electrically charged object is brought near an uncharged object. High resistance materials do not allow the charge to decay quickly and unstable measurements may result. Electrostatic shielding will help to minimize these effects. Shield the material by using a conductive shielded enclosure and connecting the low terminal of the ammeter to the shield.

 

Background currents can equal or exceed the current stimulated by the applied voltage. To counter the effects of these spurious currents, an alternating polarity technique can be used. In this technique, a bias voltage of positive polarity is applied, then the current is measured after a specified delay. Next, the polarity is reversed and the current is re-measured using the same delay. This process can be repeated any number of times. The resistance is calculated based on a weighted average of the most recent current measurements. By calculating a weighted average current, the background current is cancelled out. Some instruments, such as Keithley’s Model 6517B Electrometer, have a built-in test sequence that automates this alternating polarity technique.

 

A high-quality electrode system that provides good contact to the test sample is essential. Conductive rubber on these electrodes enables good contacts to the sample, especially if the sample is a rigid material. Avoid electrodes that will add appreciable resistance to the measurement circuit or could contaminate the sample. Choose an electrode configuration that supports calculating the resistivity from the measured resistance. Several commercial systems now available provide this type of resistivity measurement.

 

Measuring Semiconductor Resistivity

The four-point collinear probe technique is the most common way of measuring the resistivity of semiconductor materials, particularly wafers being tested at a probe station. This technique involves the use of four equally spaced (collinear) probes in contact with the material sample. The outer probes (1 and 4) source current; the inner probes (2 and 3) measure the resulting voltage drop across the sample’s surface. The volume resistivity is calculated thus.

ρ = (π / ln2) x (V / I) x (tk),

where ρ = volume resistivity (ohm-cm), V = voltage between 2 and 3, I = source current from 1 to 4,
t = sample thickness (cm), and k = a correction factor based on the ratio of the probe to wafer diameter, and on the ratio of wafer thickness to probe separation. Using four probes in this manner eliminates measurement errors due to the probe and lead resistance, the spreading resistance under each probe, and contact resistance between each metal probe and the semiconductor material.

Another technique for measuring the resistivity of semiconductors is the van der Pauw method, which involves applying a current and measuring voltage using four small contacts on the circumference of a flat, arbitrarily shaped sample of uniform thickness. The current is forced between two adjacent terminals of the sample. The voltage is measured on the opposite pair of terminals. This method is particularly useful for measuring very small samples because the dimensions of the sample and the spacing of the contacts are unimportant. It requires making eight measurements around the periphery of the sample to compensate for offsets and geometric considerations. These measurements are combined mathematically to compute the resistivity.

Typical sources of error for van der Pauw measurements include voltage drops due to lead and contact resistances, voltage offsets, and incorrect instrumentation choices. In semiconductor material research, a parametric tester is often the instrumentation of choice when characterizing material resistivity. These systems often include a switch matrix to switch the current source and voltmeter to all sides of the sample, which facilitates measurement automation. Parametric test systems also include software to completely automate the measurements and perform resistivity calculations.

Special considerations must be taken into account when measuring semiconductor materials with resistances of hundreds of kilo-ohms or higher:

* To avoid leakage currents, use a 4-point collinear probe with excellent isolation between the probes to avoid leakage current errors.

* Choose a current source with high output impedance (≥1E14 ohms) to avoid loading errors, and with a built-in guard circuit to reduce the effects of shunt capacitance.

* Use voltmeters with high input impedance (≥1E14 ohms).

* Always shield the sample and all sensitive circuitry, and use shielded cabling to prevent errors due to electrostatic interference; connect the shield to the instrumentation’s low terminal.

* To avoid errors from common mode currents, use differential voltage measurement techniques. 

Summary

In such a brief article it is impossible to address all of complexities that help ensure the accuracy of bulk materials resistivity measurements. For more details, view Keithley’s free webinar on this topic at the following link: How to Make Electrical Resistivity Measurements of Bulk Materials.

About the Author

Mary Anne Tupta is a senior applications engineer at Keithley Instruments, Inc., headquartered in Cleveland, Ohio. She earned a Bachelor of Science degree in physics/electronic engineering and a Master of Science degree in physics from John Carroll University in Cleveland. She has assisted Keithley customers with instrument applications since 1988.

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