Electrochemical Impedance Spectroscopy Beyond 300 GΩ

January 19, 2023 by Dino Klotz

Introduction

In electrochemistry, the characteristics of a given process can be assessed by electrochemical impedance spectroscopy (EIS). A semicircle in the Nyquist plot usually corresponds to electrochemical processes that can be modelled as a parallel connection of a resistor (R) and a capacitor (C). The diameter of the semicircle provides the value of R, while the associated time constant (also known as relaxation time) is given by RC. The activation energy of a process appears in the Arrhenius equation that links the conductivity (or the resistance) with temperature: for this reason, measuring the temperature dependence of a process is a popular strategy to identify its nature. Since temperature enters the Arrhenius equation in the exponent, however, small temperature differences can lead to large changes in the magnitude of the impedance.

The MFIA Impedance Analyzer can measure impedances up to 1 TΩ, as demonstrated using a commercial resistor in this blog post. What happens with more complicated devices under test (DUTs), such as an ion conducting thin film?

Here, we use EIS on the Gd-doped Ceria thin film studied in this blog post, where measurements were taken between 250°C and 450°C - leading to impedance magnitudes up to hundreds of Megaohms. Now we decrease the operating temperature to 60°C, 50°C and 40°C to increase the film's impedance up to hundreds of Gigaohms.

Measurements with the MFIA

The MFIA is a perfect fit for temperature dependence measurements, because it is specified for covering an impedance range that goes from 1 mΩ to 1 TΩ. Figure 1 shows the measurement results on a thin film ion conductor for three different temperatures. Measurements were taken from 100 Hz down to 10 mHz; each sweep required 30 to 35 minutes after waiting at least 30 minutes for the steady state to be reached following the temperature change (realized with a Linkam heater stage).

EIS at 60°C, 50°C, and 40°C

Figure 1: Measurements on a Gd-doped Ceria thin film at 60°C (blue), 50°C (orange), and 40°C (3x red). All spectra are measured from 100 Hz to 10 mHz with an amplitude of 2 V. The measurements at 40°C show significant noise, which is mainly attributed to temperature fluctuations as such a low temperature is more difficult to control and keep constant.

With reference to Figure 1, we see that the measurements at 50°C and 60°C show rather smooth semicircles with very little noise. The parameter R these measurements can be determined easily and with good precision: R is approximately equal to 300 GΩ and 160 GΩ, respectively. At 40°C, we see noise as well as differences between the three measurements included in the figure. These differences stem mainly from temperature fluctuations during the measurement, as the temperature stage is more sensitive to such fluctuations close to ambient temperature (which is room temperature in this case). Repeating the measurements can still provide a suitable estimate for the resistance at 40°C, and indeed we find approximately 600 GΩ for R - albeit with a much larger error bar.

Measurement Time

The relaxation time of a process scales with R times C. The capacitance C of the thin film considered here is dominated by the stray capacitance between film and substrate and is in the range of 10 pF; the value does not display a significant temperature dependence. Given that the resistance of the film follows the Arrhenius law (with an exponential temperature dependence), the relaxation time increases significantly at the lowest temperature. This explains why the semicircle almost converges to the real axis at 60°C, whereas it barely reaches the peak at 40°C. The time required to measure a full semicircle thus becomes an issue for large resistance values.

Reaching the Steady State

Another lesson that can be learned from these measurements is that we should leave enough time for the device under test (DUT) to reach the steady state after changing the temperature, especially in the lower temperature range, because of the longer relaxation times. On the MFIA, it is possible monitor the resistance of the film over time using the LabOne® Plotter module: you can set a low frequency such as 1 Hz and wait until the absolute magnitude of the impedance shows a flat line in the Plotter window, as is explained in this video.

Ensuring Steady Temperature Conditions

Since the impedance of the considered thin film at low temperatures is highly sensitive to temperature changes, it is important to make sure that the heater stage can provide a stable temperature. Small heater stages are prone to temperature fluctuations in the presence of airflows coming from ventilation systems, or even of airflows caused by people walking in the room. Additional enclosures such as large boxes can help to provide a stable ambient temperature and stagnant air.

Measurement Accuracy

The MFIA can measure up to 1 TΩ and has a rated accuracy of 10%, as shown in the instrument's accuracy chart. If necessary, this accuracy can be improved with a "Load-Load-Load" compensation. For the example considered in this blog post, an accuracy of 10% is more than enough for calculating the activation energy from measurements at different temperatures.

Conclusion

The MFIA Impedance Analyzer is well-suited to perform measurements up to 1 TΩ, even for complex DUTs such as ion conducting thin films where such values of the resistance occur at low temperatures. The LabOne Sweeper module can be used to build Bode and Nyquist plots, the latter being the most informative for EIS. The Plotter module is useful to check that there is a good contact on the DUT and that the steady state was reached.