Precisely measuring resistances of samples in ultra-low temperature and other extreme environments can present a number of signal-to-noise issues and other measurement challenges that complicate obtaining accurate and repeatable results.

This article will discuss some of these challenges and how a unique characterization system from Lake Shore Cryotronics, the M81-SSM synchronous source measure system, can help overcome them. The system is optimized specifically for low-level measurements and is unique in a number of ways, including the ability for the user to switch easily between AC (up to 100 kHz), DC and lock-in detection modes with up to three source and measure channel pairs.

Modular in its design, the M81-SSM includes a controller instrument that at this time integrates four different types of source and measurement modules. These include: a constant voltage source module; a balanced or differential constant current source module; a greater than 1 TΩ input impedance voltage measurement module; and a voltage type current measurement module featuring programmable DC bias. (Additional module types are in development for other measurement applications, and when available, will be able to be seamlessly integrated into existing customer systems in the field.)

Figure 1: The M81-SSM can easily calculate resistance measurement results by computing voltage divided by current in both DC and AC modes. Source: Lake Shore Cryotronics

In addition, because the system includes both voltage/current source and measure capabilities, the M81-SSM can easily calculate resistance measurement results by computing voltage divided by current in both DC and AC modes. Highly precise measurements of a sample’s electrical resistance can be quickly configured leveraging the M81-SSM’s differential current source and voltage measurement module combinations, which enable user-specified levels of voltage or current stimulus.

Before this article goes into more detail about some of the additional M81-SSM resistance measurement capabilities, let’s examine the common approaches and specific difficulties encountered with making precision and low-level signal type resistance measurements.

Basic approaches to resistance measurements (R=V/I)

Source current, measure voltage (measured voltage [V] proportional to resistance):

• Generally preferred for low resistances from 1 MΩ to sub-milli-, micro- and nano-ohm levels
• Constant current sourcing allows control over device heating and device power, and avoids overcurrent situations where device resistance is variable, such as an active device
• Source voltage, measure current (measured current [I] inversely proportional to resistance):
• Generally preferred for high resistances from 1 MΩ to giga-, tera- and higher ohm levels
• Constant voltage sourcing improves settling speed as well as provides control over the amplitude of device voltages, which can avoid damage to voltage-sensitive devices

Typical low-resistance measurement challenges

In general, the central challenge is a signal-to-noise optimization process for measuring the low voltages developed across particularly sub-ohm devices when applying a known current. These include significant amplitudes of unwanted signals, such as thermal offset voltages due to dissimilar metal connections that in the presence of heat flow can often be larger than the voltage signal of interest from the device itself.

In cryogenic and other cases where the stimulus currents must be minimized, the voltage resulting from the device resistance can be very small (milli-, micro- and nano-volt levels) and thus challenging to measure in the case of lower resistance samples (including temperature sensors).

Typical high-resistance measurement challenges

The challenges for high-resistance applications when using a known voltage stimulus method include measuring very low currents using ammeters that do not alter the voltage across the device as well as having adequate accuracy, sensitivity, noise and settling performance. So-called feedback or zero-burden voltage ammeters provide best accuracy and settling performance when measuring resistance in excess of mega-, giga- and tera-ohm levels because these types of ammeters do not reduce the voltage across the device.

The use of DC techniques

While modern DC instrumentation provides highly sensitive and accurate source and measure capabilities to characterize both high- and low-value resistances, they are vulnerable to the thermal offsets, leakage and other parasitic effects as mentioned above. Using current and voltage reversal techniques can reduce or eliminate interfering DC signals. However, these methods can add significant settling time and complexity to the process while also, in some cases, impacting the stability of the device under test (DUT).

Precision DMMs with DC resistance functions do not generally allow the user to fully specify the level of stimulus current or voltage applied to the sample or device. This limitation results in the user not having complete control over the power and, in turn, self-heating effects that may create additional errors and complications when trying to control sample temperatures. The M81-SSM solves this issue by allowing the user to specify voltage or current source amplitudes and by including many options for filtering measurements to optimize total SNR.

The use of AC techniques

Generally, AC measurements using lock-in amplifiers have been a commonly used technique for measuring low-value resistances with a level of certainty. They do this by directly detecting the voltage across the device as the result of AC current applied to it at the designated reference frequency. Lock-ins, by their nature, completely reject DC signals, such as thermal offsets, and noise at frequencies other than the user-selected reference frequency. As such, they provide many controls and tuning options for each given setup and for addressing unique interfering noise situations.

They are generally less accurate in terms of traceability to recognized standards, but unless very tight repeatability is required for an experiment, this isn’t an issue in most cases. For high-resistance devices, care must be taken using lock-in amplifiers due to their typical input resistance of 1 MΩ to 10 MΩ, which can reduce the device’s resistance as a result of the lock-in’s parallel impedance. In such cases, additional preamplifiers may be needed to reduce this effect. Most lock-ins measure voltages with limited or no ability to directly measure currents, which means higher-value resistances measured with source voltage and current detection may require additional I to V amplifiers or instruments. The M81-SSM’s modularity and modules allow it to directly perform both current source and voltage source resistance measurements on up to three module pairs and three samples simultaneously and with each pair using unique lock-in frequencies.

Possible complications with AC techniques

Because a lock-in amplifier can only determine X and Y voltage amplitudes as presented to the input terminals of the lock-in, there can be errors caused by significant phase shifts between applied signals and measured signals depending on amplitudes and frequencies used to measure a given resistance. These errors are commonly due to cabling, fixturing and device inductance and capacitance effects, which can significantly affect measurements made with low-level signals. Detecting and correcting for such phase shift errors generally falls on the user because they are typically responsible for setting up the measurement system, including the source and measure components, and any associated error contributions.

Unique to the M81-SSM: Compensated AC resistance mode

As noted earlier, the M81-SSM system is a new concept in low-level device characterization. It was developed by Lake Shore Cryotronics specifically to provide a more complete measurement solution by including source and measure, voltage and current, and DC and AC capabilities. As a result, all the above resistance measurement setups are easy to implement for obtaining voltage, current and resistance measurements from nano-ohm to high tera-ohm levels.

However, it also goes further to address the type of AC setup as described above where there is a significant phase shift due to higher frequencies and device impedances, with a new feature: compensated resistance mode. This mode builds upon the M81-SSM’s synchronous sampling and lock-in detection capabilities and provides improved accuracy resistance measurements for cases where cabling and other unwanted phase shifts are significantly impacting measurement of true in-phase resistances.

While operating in this mode, the system directly measures and displays the shunt capacitance value, then corrects for the effects of it that may appear in parallel with the resistance of interest. Once the value of shunt capacitance is known, the M81-SSM performs a phase-correction algorithm, and then reports the true value of the resistance under test as if there were orders of magnitude less interfering capacitance in parallel with the sample.

How it can be used in a four-wire or Kelvin setup

Lock-in amplifiers are often used for resistance measurements due to their low-noise amplifiers and ability to extract small signals from the noise. Performing resistance measurements in some applications, such as in a cryostat where one has long cryogenic wires and cables, can add significant resistance and capacitance to the measurement. In these situations, experimentalists are well aware of techniques such as four-wire measurements to remove the effects of lead resistance or contact resistance.

However, the effects of parasitic capacitance are often ignored. In a lock-in measurement, the real and imaginary (or in-phase and out-of-phase) components are reported, where the imaginary component quantifies the effects of capacitance.

Take, for example, the case of a four-point probe measurement application where a current source and a voltage meter are used. A typical experimental setup has parasitic capacitance across the DUT, as well as from each line to ground. Potential sources include the capacitance from twisted pairs and BNC cables (which have capacitances of ~100 pF/m), breakout boxes, the input and output capacitance of sources and meters. A rough range of parasitic capacitance in a typical setup can range from ~100 pF to as much as 10 nF, depending on the setup, cable length and cable quality.

If the capacitance impedance becomes comparable to the device resistance, less current will go through the device, resulting in a lower voltage signal. A common practice to calculate resistance is to only consider the real component, or to use the magnitude of the lock-in measurement.

The M81-SSM’s built-in feature to calculate compensated resistance and capacitance follows an RC model as it both measures and sources synchronously and, therefore, takes into account both amplitude and phase of the signals applied to the sample. Setups with separate source and measure AC instruments do not have this information readily available, which means any such capacitance detection and compensation would either be ignored or have to be manually performed by the user. The M81-SSM performs this correction simply by invoking compensated resistance mode.

The details of how this new M81-SSM feature, which operates regardless of voltage/current source and measure setups, can be found in this application note. If, after reading it, users have additional questions or would like to see a live demonstration of this or other M81-SSM capabilities, please contact Lake ShoreFigure 2: The M81-SSM’s built-in feature to calculate compensated resistance and capacitance follows an RC model. Source: Lake Shore Cryotronics Cryotronics.

To learn more about the M81-SSM system, watch the YouTube video.

The video demo discusses the system’s components, including four types of amplifier modules that are combined with the M81-SSM instrument to enable low-level DC, AC and mixed AC/DC measurements. Also demonstrated is how quickly and easily the system can measure various values of resistance using very low DC and AC currents, illustrating the limitations of DC methods and the advantages of AC lock-in methods as the signal of interest becomes affected by thermal offsets and other parasitic effects.