A resistance meter normally works by sending a small, precise current through the resistance to be measured. Then it measures the voltage drop. Once the meter knows the current and voltage, it applies Ohm’s law to derive resistance. Ohm’s law says that resistance is voltage divided by current, or R = V/I.
For example, if there is a 10 mA (0.01 A) current going through a resistor and there is a voltage drop of 1 V over the resistor, then the resistor is R=V/I = 1 V / 0.01 A = 100 ohms.
Different test conditions may have different impacts on resistance measurements. In this article, we will discuss some common mistakes that result in resistance measurement error and ways to counter them.
Trap 1. Impact of Temperature on Resistance
From the R=V/I equation, you might think that making an accurate resistance measurement on a material sample is trivial, but in reality, this may not be true. The reason for this is that the resistivity of all materials varies with temperature. When you attempt to measure a sample’s resistance, you inevitably heat it up to some extent. This is referred to as the Joule self-heating effect.
Joule self-heating makes resistance measurements a tricky balance between two factors:
- To keep the resistor from heating up and the resistance value from changing, you need to keep the current (= power) low.
- Small currents mean that we need to measure smaller voltages, which in-turn requires a higher voltage measurement resolution.
How Much Power Can I Apply to a Structure?
After understanding the effect of temperature on the resistance measurement, how do you establish the relationship between temperature and resistance? We just learned that temperature change is directly proportional to the power applied to the DUT. We also know that Power = Voltage x Current. The expression of the voltage across a resistor in terms of applied power and resistance is shown in the equation below.
To determine the maximum power we can apply to a structure without changing its resistance, we need to know something about its thermal characteristics. Let’s look at an example of copper. We know that the resistance of copper changes by about 0.35% for every degree Celsius change in temperature. For a 10 mm by 10 mm sample and resistance tolerance of 0.1%, we can see that maximum allowable power is about 0.04 mW:
Plugging this back into the top equation, we see that this amount of power creates a voltage change of approximately one microvolt, which tells us roughly how much voltage measurement resolution the instrumentation needs to have.
Trap 2. Thermo EMF in Resistance Measurement
Another factor to consider when making any type of measurement (not just resistance measurements) is thermo electromotive force (or EMF). Thermo EMF is a transient voltage pulse that is generated when a reed relay switch opens or closes. Since virtually all SMUs employ reed relays, thermo EMF effects are something that you need to consider when making sensitive low-level measurements.
The picture shown in Figure 1 is of a commercial grade relay chart. It is NOT characteristic of the relays used in SMUs, which are specially designed to minimize EMF. We can see thermo-EMF is generated over the time period when a relay is operating. This EMF can have a significant impact on low resistance measurements; it will distort the resistance value measured.
Figure 1. Thermo-EMF example of general reed relay.
Now let’s take a look at how to perform a modified Kelvin measurement that can eliminate the effects of thermo EMF, as well as the effects of any offset voltages in your circuitry. Figure 2 shows a picture of a standard Kelvin measurement on a resistor R with the EMF and offset voltages modeled as voltage sources.
Figure 2. Modified Kelvin resistance measurement.
First, set up one SMU as a current source and source current through the resistor you want to measure. Then use another measurement resource (either a voltmeter or an additional SMU) to measure the voltage across the resistor. After calculating the resistance, reverse the current flow and repeat the measurement. Then take the two resistance values that you have measured and average them.
If you check this by going through the KVL and KCL equations for this circuit, you will see that by measuring twice with both positive and negative current, the EMF and offset voltages cancel out. Of course, when making this measurement, you also need to make sure that you do not apply too much power to the resistor so that thermal effects do not alter its resistance value.
Trap 3. Floating vs. Grounded Measurements
In electrical circuits, voltage is always measured between two points: a point of high potential and a point of low or zero potential.
The term “reference point” denotes the point of low potential because it is the point to which the voltage is referenced. A floating measurement is a differential measurement that is not referenced to ground (zero potential). It can be a concern if anyone is mistakenly making a floating measurement while expecting a ground measurement.
Let’s examine the counter measures to address this concern. As you can see from Figure 3 below, the configuration using a Keysight B2980A electrometer for these two cases is quite different.
If you are floating your DUT with respect to earth ground (such as in the top left of Figure 3), you can measure the resistance between the high terminal and the low terminal. Parasitic resistances and capacitances may provide a “sneak path” to ground on the low side. You can mitigate measurement errors by connecting the negative terminal of Vs source to the low terminal. In this way, the ammeter and the DUT low terminal have a “common” reference point.
The bottom left shows the circuit diagram that corresponds to a floating device measurement. The test device is connected between the VS positive output and the Ammeter input. Since the Ammeter measures very low currents and is very noise-sensitive, it should be measured close to ground potential in order to shield the test device for better measurement results.
On the top right, you can see the case where the DUT is grounded. Since the low side is grounded, the applied test voltage and the current measurement must both occur at the DUT's high side terminal. The bottom right shows the circuit diagram that corresponds to a grounded device measurement. In this configuration, the Ammeter is connected to the VS positive output because the device is grounded on one side.
Neither one of these configurations is necessarily “better” than the other, and you can obtain good high resistance measurement results using either setup.
Figure 3. Floating vs. grounded measurement.
Temperature, thermo EMF and floating measurement affect your resistance measurements. Learning more about these impacts will help you get more accurate measurements in your work. For more tips related to resistance measurement, download the Resistance Measurements application note.