Rapid Estimation Method Of Dk & Df Parameters For AME Materials

The primary objective is to create a methodology for measuring \( D_k \nonumber \) and \( D_f \nonumber \) values over a frequency range of up to \( 10MHz\nonumber \). The results would be structured into a text file that can be imported into simulation tools and be used as material data for simulations including AME materials.

We will employ a blend of experimental and computational methods for data measurements and evaluation. On the experimental side, planar capacitors, as test structures, will be printed and their capacitance and \( Q\nonumber \) factor will be measured using an RLC meter. Computationally, we will derive \( D_k \nonumber \) and \( D_f \nonumber \) values from these measurements and compare them with measurements provided by the manufacturer tested in the dedicated lab for dielectric materials.

The presented approach requires minimal time, logistical effort, and financial investment for printer owners Yet, the output holds significant value. In theory, it's precise enough in the frequency range that we investigate in our methodology. An added benefit will be a step by step guide to replicate the process, allowing the wider community to validate and build upon our results.

A dielectric material, when placed in an external electric field, has the ability to store energy. In a scenario where a DC voltage source is connected to a parallel plate capacitor, inserting a dielectric material between the plates leads to an increased charge accumulation on these plates. This enhanced charge storage is more significant compared to t he scenario where the space between the plates is a vacuum. This is due to the dielectric material neutralizing charges at the electrodes that would otherwise contribute to the external field. The increase in storage capacity of the capacitor is mathematically related to\( D_k \nonumber \)The capacitance of a parallel plate capacitor with a dielectric material (\( C\nonumber \)) is related to the capacitance without a dielectric material (\( C_0\nonumber \)) as can be seen in Figure 1 [1].

In the image\( C\nonumber \)and\( C_0\nonumber \)are the capacitance with and without the dielectric,\( \varepsilon_r\nonumber \)real dielectric constant and\( A\nonumber \)and\( t\nonumber \)are the area of the capacitor plates and the distance between them as shown in Figure 1. The presence of a dielectric material enhances a capacitor's ability to store electrical energy by counteracting the charges at the electrodes, which would otherwise add to the external electric field. This boost in storage capacity is mathematically connected to the dielec tric constant, as demonstrated by the equations provided.

When an AC sinusoidal voltage source is applied across the capacitor, the current comprises a charging current (\( I_c \nonumber \)) and a loss current (\( I_l\nonumber \)). The losses in the material can be represented as a conductance (\( G\nonumber \)) in parallel with a capacitor (\( C\nonumber \)). The complex dielectric constant (\( k\nonumber \)) consists of a real part (\( k^{'}\nonumber \)) representing storage and an imaginary part (\( k^{''}\nonumber \)) representing loss, as can be seen in Figure 2 [1] below.

Delving deeper into the electromagnetics point of view the electric displacement (or electric flux density) (\( \vec{D}\nonumber \)) is defined as:

\( \vec{D}=\varepsilon\cdot \vec{E} \)

\( \varepsilon = \varepsilon_r\cdot\varepsilon_0 \)

where\( \varepsilon \nonumber \)is the absolute permittivity ,\( \varepsilon_r\nonumber \)is the relative permittivity, and\( \vec{E}\nonumber \)is the electric field strength. This equation above is fundamental to understanding how a material interacts with an electric field. The loss tangent (\( \tan(\delta)\nonumber \)) is defined as the ratio of the imaginary part of the dielectric constant to the real part as can be seen in Figure 3 [1]. It represents the relative "loses" of a material, i.e., the ratio of the energy lost to the energy stored. The quality factor (\( Q\nonumber \)) is the reciprocal of the loss tangent and is used to assess the performance of electronic microwave materials.

Dielectric materials, as showcased in Figure 4 [1], possess an intricate nature. They comprise electric charge carriers that shift when influenced by an electric field, leading to a polarization effect with opposite charges moving against each other corresponding to the electric field Delving deeper, multiple microscopic dielectric mechanisms emerge. Especially at microwave frequencies, phenomena like dipole orientation play a significant role. Water molecules, being permanent dipoles, rotate in response to alternating electric fields, resulting in high loss tangent, explaining efficiency in microwave heating . On the other hand, atomic and electronic mechanisms are not affected by those frequencies and remain relatively constant across this spectrum. Each mechanism possesses a unique “cutoff frequency”. As we increase frequency, slower mechanisms recede, causing peaks in the loss factor (\( \varepsilon_r^{''}\nonumber \)). Materials such as water show a marked decline in their dielectric constant around \( 22GHz\nonumber \), while PTFE's permittivity remains consistent even in higher frequency domains.

In essence, while resonant effects are usually tied to electronic or atomic polarization, relaxation effects are predominantly link ed to orientation polarization Based on the theory already discussed, a practical method can be set up. The last section highlights the importance of being able to measure the dielectric properties over a frequency band. A suitable method will be explained in the next section

Within the context of accelerated material development in the AME industry, it becomes important to establish a systematic method that can measure vital parameter values for materials, especially when such information is missing.

Overview of the process:

• Autodesk Fusion 360 - Design parametric planar capacitors
• Nano dimension Flight Control SW - Slicing and preparing models to print.
• Nano dimension DF IV Printer - Printing models
• “Rohde & Schwarz” RLC LCX200 with license up to \( 1MHz\nonumber \) Electrical measurements.
  • Measurement tolerance up to 2% over whole supported frequency range.
  • R&S LCX Z3 SMD test fixture adaptor.
• Keyence microscope Visual dimensions verification
• Microsoft excel Data analysis (include VBA scripting)
• Python Overall script creation for combining all csv files and computation of\( D_k \nonumber \)from capacitance.
• Measurements table of\( D_k \nonumber \)and\( D_f \nonumber \)values from the manufacturer for DI 1092 ink.

Materials used:

• Dielectric ink (DI) material: NNDM DI 1092
• Conductive ink (CI) material: NNDM AgCite ® 90072

Experimental procedure:

1. Design the planar capacitor in fusion 360.
   1. Make parametric design with dielectric material thickness as a parameter.
   2. Export conductive and dielectric structures as object file.
2. Import four different variations of capacitors into Flight SW to place and slice them.
   1. Each version was printed 14 times using two rows of 7 capacitors as can be seen in Figure 5.
3. Printing on DF IV printer
   1. Using the standard High Quality (HQ) recipe.
   2. Basic calibrations set: registration, start position and slice thickness calibration.
4. Electrical measurements using RLC meter LCX200.
   1. Marking each printed model with a serial number.
   2. Frequency sweep with step size of \( 10kHz\nonumber \).
   3. Export as csv format for each sample measurement.
5. Visual inspection of the printed model dimensions using the Keyence microscope.
   1. Include cutting two first models of each variation to get insight for dielectric thickness.
   2. Getting xGetting x-y dimensions for all the samplesy dimensions for all the samples.
6. Creating Creating pythonpython script for merging the data from different tables to one script for merging the data from different tables to one table that include\( D_k \nonumber \),\( D_f \nonumber \),frequency and serial number.
7. VBA scriptscript for rapid graph creation to check initial results.
8. Based on visual analysis before getting to numerical analysis decided to run a supportive test based on current models.
   1. Check heating influence on\( D_k \nonumber \)and and\( D_f \nonumber \)graph.
   2. Take 2 samples from each variant and run a heating sequence with measurements before and after.
   3. The heating sequency included 2 soldering sequences in a row up to\( 160^0C\nonumber \)peak with linear rise and cooldown, Overall each sequence took half an hour.
   4. Run VBA analysis again to see the effect of the additional step.
9. Conclude the results and suggest future investigations based on the results.

As mentioned in the procedure, we had two dependent steps. We first present straightforward results from two stages of our experiment, followed by a concise discussion on additional printing process effects and their impact on our methodology.
The geometry of the printed samples shown in Figure 6.
The distance between the planes corresponds to the designed distances of 500, 600, 700, and 800\( \mu m \nonumber \).

To evaluate the solvent's impact within the Conductive Ink, capacitors with consistent dielectric thickness, but varying conductive plane thicknesses, should be printed. This will allow for a comparison in capacitance differences based on the effect we assumed during this work Testing this effect should include various recipes and different stages of the Conductive Ink curing process to define the behavior of this effect Additionally, it's essential to determine whether the conductive structure influences capacitance. This mean s maintaining the same Conductive Ink volume but varying the plane structure, including different grids, hole sizes and 3D structures. It's also crucial to assess the impacts of humidity and temperature on product shelf life using different printing recipes. This is important for the Technology Readiness Level (TRL) of AME, as it influences storage environments and conditions.

Conclusion

This study introduced and evaluated a cost effective approach to obtain\( D_k \nonumber \)and\( D_f \nonumber \)values The results indicate that within the AME process, when combining a conductive material with a dielectric material, additional effects may occur during the printing process. As at least one of the material s is not in its bulk state , it's essential to consider additional effects arising from the printing process that affect the material properties It's noteworthy that while the \( D_k \nonumber \) parameter of Dielectric ink remains in its limits according to data provided from the manufacturer , the potentially added parasitic capacity in the conductive ink introduces a new and different behavior of the materials To predict circuit behavior accurately, it's essential to simplify the printing process, examining the effects of the printing process on material behavior both individually and in combination . Once these effects are isolated, they can be integrated into the 3D circuit design process. Furthermore, the study highlighted that the current measurement setup cannot separate the effects of the individual materials, indicating a need for further investigation.

References:

1. Keysight Technologies. 2020. Basics of Measuring the Dielectric Properties of Materials. Application Note, Keysight Technologies. Literature number 5989 2589EN
2. Nano-dimension Ltd. 2023. AME Materials Technical Datasheet. Rev 03. Literature number DOC0000543