Measuring Dielectric Properties of Materials with Varying Thickness

Introduction

A dielectric is traditionally defined as an electrical insulator, with very poor conductivity at DC [1]. However, because of its polarizability, charges can be stored in a dielectric material, typically in the format of dipoles, in the low and medium AC frequency range. This ‘capacitive’ effect makes a dielectric useful in charge (and energy) storage (and dissipation).  One example is in a supercapacitor, where one aims at a high capacitance using the ultimate thinness of the electrochemical double layer (EDL) [2]. Another example is in a high-Q capacitor, where one targets at a low Ohmic loss. Even though the impedance is well studied in both cases, the dimension of the dielectric (whole or part of the DUT) is less defined, hence little is known in the (relative) dielectric constant (permittivity). To answer this question, in this blog post we will measure 3D printed dielectric disks using a dielectric test fixture, demonstrate how important the ‘dimension’ is, and emphasizes both the sample roughness and the instrument phase accuracy. With a careful non-contact air gap compensation, we find the dielectric constant of white polylactic acid (PLA) as 2.7 at 1 kHz, and the dissipation factor as 0.0003.

 

Measurement setup

To prepare dielectric samples, we 3D print a white biodegradable PLA (polylactic acid) wire (Best Value PLA Filament 1.75 mm) into discs in a diameter of 49 mm and a thickness from 0.5 mm to 2.5 mm. This allows us to easily insert the disc samples into a third-party dielectric test fixture, with an unguarded bottom electrode diameter of 56 mm. The top electrode of the fixture is guarded and has a diameter of 38 mm to define the area of the sample under test. As shown in Fig. 1, the fixture is directly connected to an MFIA impedance analyzer to lower the parasitic impedance.

Fig. 1 Sketch of the MFIA with a third-party dielectric test fixture, where a rough PLA disc sample is inserted in using a non-contact air gap method. The orange dashed lines indicate a direct connection without any cables in between. t is the sample thickness and ta includes additional air gap created (more details later). A test signal of 3 V is used in this blog post.

 

Increase the measurement speed with the latest one-period averaging feature

For simplicity, dielectrics are often studied at a few fixed frequencies such as 50 Hz, 1 kHz, 1 MHz, and so on, despite in many applications they work at DC or very low frequencies. However, measurements at low frequencies take long and can be even worse if we consider a narrower bandwidth of the low-pass filter used to reject noises [4]. The waiting time not only demands additional material and energy costs to stabilize the measurement environment but also can result in frustration and inconvenience to users.

The latest LabOne 20.07 release contains a brand new one-period feature to alleviate this problem. When this feature is activated (Fig. 2), LabOne will calculate the impedance by dividing the averaged raw voltage (if in 4-terminal configuration) to the averaged current over one period. As the low pass filter is not necessary for this new process, the measurement speed can be hugely increased, reaching a theoretically fastest possible time. Fig. 2 shows a measurement at a fixed frequency of 100 mHz, where we can see that the measured impedance quickly settles without waiting for the RC delay of the low-pass filter.

Fig. 2 LabOne screenshot showing the Plotter module, measured at a fixed frequency of 10 mHz, using the one-period feature. The one-period averaging button locates in the IA tab, and the LED next to it indicates if the feature is running or not. Tooltips are also available to help you quickly master how to work with it.

 

When running a full frequency sweep across the cutoff frequency (default at 13 Hz), the one-period will be automatically deactivated while standard sweeper settings being activated. This ensures a smooth measurement without any breaks. A comparison of one-period and standard sweep in the 2.5-mm-thick sample is shown in Fig. 3. Using the LabOne Sweeper module, we start the measurement from 100 mHz as it is already close to 1 TOhm (upper bound of the MFIA reactance chart). In addition to the impedance parameters such as phase, the capacitance (Cp) can also be extracted in real-time using built-in circuit models in LabOne. In one-period mode, the sweep takes ~1.3 min in contrast to about 15 min in standard mode. We can also see that, as a minor trade-off of such a fast speed, the measurement precision is slightly sacrificed in the one-period mode, yet the accuracy is not affected. The difference between the two measurements becomes only visible when zooming in at around -90 deg.

Fig. 3 LabOne screenshot showing frequency sweeps of the 2.5-mm-thick sample in standard mode (colored) and in one period (greyed).

 

Start the measurement without any user compensations

In low impedance measurements [5], we have shown that a short-load user compensation is needed to define a low measurement baseline. A dielectric sample however shows a high impedance, especially at low-mid frequencies. This means standard user compensation procedures will not help, and we can simply start our measurements as it is (more details in the next section). The result of different samples is plotted in Fig. 4. To better compare with literature references, we start all measurements here from 1 kHz, even though this frequency may not be meaningful. A quick glimpse at Fig. 4 tells that the measured capacitance in the 2.5-mm-thick sample is ~11 pF and in the 0.5-mm-thick sample ~35 pF. This does not scale inversely with the sample thickness (a factor of 3, not 5), hinting the dielectric constant is not a constant anymore. We also find that the measured dissipation factor strangely keeps increasing with thickness. So what could be the reason for the discrepancy here?

Fig. 4 LabOne screenshot showing the capacitance and dielectric loss of PLA samples in different thicknesses measured from 1 kHz to 5 MHz. The thickness of each colored trace can be found in the history tab.

 

Non-contact air gap compensation of sample surface roughness

To fully understand the problem, we extract the dielectric constant from samples in different thicknesses using the well-known parallel-plate capacitor model and plot them as blue dots in Fig. 5a. Surprisingly, the dielectric constant at 1 kHz keeps rising and reaches a plateau at ~2.7 in 2-mm-thick and 2.5-mm-thick samples. This value (2.7) agrees with most literature references [6], but we do notice that there are lower (some) or higher (few) values reported [7]. Except for the difference in sample preparation methods, one critical aspect that has often been forgotten is the sample surface roughness. Thin samples are more prone to the roughness as surface effects tend to dominate. In other words, bulk PLA properties are not accurately measured in our samples thinner than 2 mm.

Fig. 5 Thickness-dependent dielectric constant (a) and dissipation factor (b) of PLA at 1 kHz without (blue dots) and with (orange triangles) the non-contact air gap compensation.

 

For rough samples prepared by 3D printing (roughness noticeable even by naked eyes), air gaps exist between the sample and the electrodes in the test fixture, as illustrated in Fig. 1. This argument is supported by comparing the 2.5-mm-thick sample with the 1-mm-thick and 1.5-mm-thick samples stacked together, where the latter reveals a smaller capacitance and dissipation factor due to the additional air gap in between.  However, since the thickness of the ‘intrinsic’ air gap is not uniform, to quantify the error we need to manually add an air gap in a known thickness, by use of the micromanipulator on the fixture. In doing so, we can imagine this layer as a thin film capacitor in series with the PLA sample, and derive the compensated dielectric constant as well as dissipation factor using Equation 1 and 2. This non-contact approach requires two separate measurements for each sample, one with air only, and another one with the sample inserted. Notice that the thinner the added air gap is to the sample thickness, the more effective the compensation will be. Nonetheless, limited by the spatial resolution of the micromanipulator (0.01 mm), here we only fix this gap to 1% of the sample thickness. This explains why thinner samples still could not reach the bulk dielectric constant at 2.7 after the compensation. We can also confirm that the dielectric constant of ~2.7 in the 2.5-mm-thick sample as decreasing from 1% to 0.2% leads to no further improvements.

In terms of the dissipation factor, in addition to the surface roughness concern, the phase accuracy of the impedance analyzer should also be considered. The MFIA has a basic phase accuracy of 2 mdeg in a resolution of 10 udeg, and can reach a Q up to 100000 (D down to 0.00001) on the low-parasitic MFITF fixture [3].  Even with the third-party dielectric test fixture, we can measure a D at 0.0001 level at 1 kHz from air, which sets the baseline of all samples, according to Equation 2. Compensation with this equation leads to an order of magnitude decrease in the measured dissipation factor, reaching 0.0003 at 1 kHz in the sample. At higher frequencies, the dissipation factor (e.g. 0.007 at 1 MHz) increases agreeing with the literature [8], hence it is necessary to confirm the baseline from the instrument to understand if the measurement is meaningful or not.

Eq. 1 Compensated dielectric constant using the non-contact air gap method. Ca stands for the measured capacitance from the air gap alone, and Cam for the capacitance with the sample inserted.

Eq. 2 Compensated dissipation factor using the non-contact method. Da stands for the measured dissipation factor from the air gap alone, and Dam for the dissipation factor with the sample inserted.

 

Conclusion

In this post, we show that 3D printed PLA has a bulk dielectric constant of 2.7 and a dissipation factor of 0.0003 at 1 kHz. Surface roughness is found important in the measurement and should be compensated carefully with the non-contact method. In addition, a high phase accuracy of the MFIA is essential to reach a low baseline in the dissipation factor and to ensure the dielectrics being correctly measured. Most importantly, thanks to the latest one-period in the 20.07 LabOne release, measurement speed at low frequencies can be greatly increased.  Don’t waste time to enjoy in your future measurements!

If you have any questions or suggestions, please feel free to get in touch.

 

References:

  1. Wikipedia dielectric entry https://en.wikipedia.org/wiki/Dielectric
  2. Zurich Instruments blog https://blogs.zhinst.com/tim/2016/11/01/using-the-mfia-impedance-analyzer-to-characterize-the-esr-of-a-super-capacitor/
  3. Zurich Instruments blog https://blogs.zhinst.com/tim/2017/01/30/measuring-esr-and-q-of-100-pf-commercial-capacitors-using-the-mfia-impedance-analyzer/
  4. Zurich Instruments white paper principle of lock-in detection https://www.zhinst.com/ch/resources/principles-lock-detection
  5. Zurich Instruments blog https://blogs.zhinst.com/tim/2019/06/10/measuring-low-esl-and-low-esr-of-a-dc-link-capacitor-with-the-mfia-impedance-analyzer/
  6. Hegde, V. (2017). Dielectric study of biodegradable and/or bio-based polymeric materials (Doctoral dissertation).
  7. Behzadnezhad, B. et al. (2018). Dielectric properties of 3D-printed materials for anatomy specific 3D-printed MRI coils. Journal of Magnetic Resonance, 289, 113-121.
  8. Veseley, P et al. (2018). Study of electrical properties of 3D printed objects. IOP Conference Series: Materials Science and Engineering, Volume 461, 5th International Conference Recent Trends in Structural Materials.