# Fabrication and characterization of 3D micro-coils with hybrid manufacturing methods

Hakan Alaboz, Andras Kovacs, Daniel Johannes Förster, Lucas Werling, Jajnabalkya Guhathakurta, Julien Petit, Morgan Madec, Luc Hébrard, Ulrich Mescheder

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Hakan Alaboz, Andras Kovacs, Daniel Johannes Förster, Lucas Werling, Jajnabalkya Guhathakurta, et al.. Fabrication and characterization of 3D micro-coils with hybrid manufacturing methods. Journal of Manufacturing Processes, 2025, 145, pp.190 - 200. 10.1016/j.jmapro.2025.04.040. hal-05051870

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# Fabrication and characterization of 3D micro-coils with hybrid manufacturing methods

Hakan Alaboz<sup>a, *,</sup>, Andras Kovacs<sup>a, b</sup>, Daniel Johannes Förster<sup>c, d</sup>, Lucas Werling<sup>e</sup>, Jajnabalkya Guhathakurta<sup>f</sup>, Julien Petit<sup>a</sup>, Morgan Madec<sup>e</sup>, Luc Hébrard<sup>e</sup>, Ulrich Mescheder<sup>a, g</sup>

## ARTICLE INFO

### Keywords:

* Micro-coil
* 3D structuring
* Laser structuring
* µNMR
* PEDOT:PSS

## ABSTRACT

This study presents novel fabrication steps and hybrid approaches that combine contemporary methods with modified manufacturing strategies for fabricating 3D micro-coils on tubular surfaces. Although several methods have been developed in the last decade, most of them still rely on complicated multi-step lithography processes or sophisticated devices. In this article, rapid, simple, and straightforward approaches are presented for fabricating micro-coils directly on curved surfaces. The hybrid fabrication methods in this study provide an alternative solution to reduce the complexity in fabrication steps, provide better control over aspect ratios and the homogeneity of thin film coatings on tubular surfaces. Micro-coils from copper and conductive polymer with outer diameter of 2.5 mm and line width of 40 µm and a separation of 110 µm were designed, produced, and characterized. Magnetic fields inside the coils made of copper and conductive polymer were measured as 11 and 2.5 µT, respectively. The developed coating and structuring methods will open new avenues not only in application fields such as analytical characterization methods of fluidic samples with miniaturized nuclear magnetic resonance (µNMR) systems, but also for 3D sensor fabrication on curved surfaces.

## 1. Introduction

Miniaturized metal coils have applications in diverse fields, especially µNMR systems, thanks to their exceptional performance in detecting low sample volumes and maintaining uniform and high-density magnetic field [1]. They are also utilized in micro transformers and relays, because of their low resistance, high coupling coefficient, and quality factor [2–5]. Furthermore, these coils are integrated into MEMS devices for DC-DC boost converters [6], serve as high Q integrated coils in oscillators [7], and even function as antennas in smart implants [8]. Despite the numerous application fields, their fabrication process remains intricate, necessitating multiple complex steps or specialized equipment. This makes the miniaturization of such coils very complex and hinders the potential of integrating and using the full potential of these coils.

Miniaturization is, in general, crucial for lab-on-a-chip devices and especially for the analytical characterization of microfluidic samples using µNMR. One of the well-known technologies for µNMR systems is the use of planar micro-coils due to their mature planar fabrication steps (e.g., lithography) which have good compatibility with MEMS technology and provide various integration possibilities [9]. On the other hand, planar coils suffer from poor homogeneity and distortions of the magnetic field induced by its windings [10]. Because of these drawbacks, researchers have been looking in the last decade for new alternatives therefore have focused on 3D micro-coils. Since then, both theoretical and experimental studies [11] have shown that 3D micro-coils can provide better sensitivity than planar micro-coils for µNMR systems. Several studies have indicated the advantages of using 3D micro-coils in especially small volume µNMR spectroscopy [12], which increases the sensitivity [11,13–15] and provides better field homogeneity [7]. In

<footnote><sup>a</sup> Institute of Microsystems Technology (iMST), Furtwangen University, 78120 Furtwangen, Germany</footnote>

<footnote><sup>b</sup> Mechanical and Medical Engineering, Furtwangen University, 78120 Furtwangen, Germany</footnote>

<footnote><sup>c</sup> LightPulse Laser Precision, Maybachstrasse 17, 71263 Weil der Stadt, Germany</footnote>

<footnote><sup>d</sup> Department of Applied Sciences and Mechatronics, Munich University of Applied Sciences HM, 80335 Munich, Germany</footnote>

<footnote><sup>e</sup> ICube Laboratory, University of Strasbourg/CNRS, Strasbourg, France</footnote>

<footnote><sup>f</sup> CT-Lab UG, 70569 Stuttgart, Germany</footnote>

<footnote><sup>g</sup> Associated to the Faculty of Engineering, University of Freiburg, Freiburg, Germany</footnote>

<footnote>* Corresponding author.
E-mail address: hakan.alaboz@hs-furtwangen.de (H. Alaboz).</footnote>
<table><caption>**Table 1**
A brief overview of fabrication methods for 3D micro-coils.</caption><thead><tr><th>Fabrication method; references</th><th>Advantages</th><th>Disadvantages</th></tr></thead><tbody><tr><td>Wire bonding</td><td>— Have a potential for mass production<br/>— Direct approach</td><td>— Serial process<br/>— Aspect ratio limitations<br/>— Mechanical stability<br/>— Low compatibility to various substrates<br/>— Complex exposure systems<br/>— Multi step lithography process with special resists<br/>— Low compatibility to various substrates<br/>— Resist related inhomogeneities (i.e., pin holes, swelling side walls).<br/>Need additional support structures for high aspect ratio coils</td></tr><tr><td>• Kratt et al. [17]<br/>• Badilita et al. [18]<br/>Lithography</td><td>— Higher compatibility to existing fabrication processes</td><td></td></tr><tr><td>• Laser assisted Kaneko et al. [19], Meng et al. [20]</td><td>— Some process has good control over aspect ratio and thickness</td><td></td></tr><tr><td>• MEMS based Gel et al. [21], Uchiama et al. [22], Yang et al. [23]</td><td>— Some process has high repeatability</td><td></td></tr><tr><td>Localized electrodeposition</td><td>— Possibility to make coils with smaller diameters<br/>— Good repeatability for small scale coils</td><td>— Requires a conductive base layer<br/>— Aspect ratio limitations<br/>— Complex systems<br/>— Repeatability and uniformity problems for high turn coils<br/>— Low compatibility to various substrates<br/>— Relatively slow deposition</td></tr><tr><td>• Ren et al. [24],<br/>• Ercolano et al. [25]</td><td></td><td>— Repeatability and reliability are affected by the nature of the transfer material<br/>— Multi-step fabrication process<br/>— Alignment and homogeneity problems<br/>— Multi-step process<br/>— Low conductivity and mechanical stability</td></tr><tr><td>Micro contact printing</td><td>— Relatively low cost<br/>— Has a potential for mass manufacturing<br/>— Can be applied to curved surfaces</td><td></td></tr><tr><td>• Rogers et al. [26,27].</td><td></td><td></td></tr><tr><td>Miscellaneous</td><td>— Relatively low cost<br/>— Relatively fast production<br/>— Screen or inkjet-based approaches suitable for large area applications</td><td></td></tr><tr><td>• Hydrogel incorporated self-assembly; Kar- naushenko et al. [28]</td><td></td><td></td></tr><tr><td>• Self-rolling up structures; Yu et al. [29]</td><td></td><td></td></tr><tr><td>• Screen or inkjet printing with conductive ink; Qi et al. [30], Meissner et al. [31]</td><td></td><td></td></tr><tr><td>Hybrid Methods in this article</td><td>— Reduced fabrication complexity (two step fabrication) and manufacturing time<br/>— Better control over aspect ratio<br/>— Better compatibility to various substrates<br/>— Suitable for curved surfaces</td><td>— Aspect ratio is limited by spot size, electrodeposition parameters and viscosity of the conductive liquid</td></tr></tbody></table>

order to grasp the importance of the miniaturization of 3D coils, the relationship between coil parameters and coil performance must be considered. For instance, the on-axis sensitivity ($B_1/i$) of a single layer solenoid with more than one turn is directly related to the aspect ratio of the coil and is defined by the magnetic flux ($B_1$), [16] as given in Eq. (1):

$$B_1 = i \left( \frac{(\mu_o \times n)}{d_{coil} \times \left( \sqrt{1 + \left[ h/d_{coil} \right]^2} \right)} \right) \quad (1)$$

where $i$ is the current, $\mu_0$ is the permeability of free space, $n$ is the number of turns, $d_{coil}$ is the coil diameter, and $h$ is the coil length. From Eq. (1), it can be concluded that a compact design (small diameter) with many turns will provide higher on-axis sensitivity. Deviations in coil parameters such as coil width and thickness will affect $h$ and $d_{coil}$, therefore the magnetic field. The mass sensitivity $S_m$ of µNMR systems with micro-coils is defined [1] by Eq. (2).

$$S_m = \frac{SNR}{m \times t_{acq}^{1/2}} \quad (2)$$

where SNR is the signal to noise ratio, $m$ is the sample mass that can be observed with a coil during $t_{acq}$ which is the total acquisition time. Some applications are volume limited (hundreds of picolitres), therefore, employing a micro coil will increase the mass sensitivity of the µNMR system when the mass of the material is limited [12]. The realization of a compact 3D coil featuring many turns faces several fabrication challenges.

The main motivation to deliver a reliable technology for the fabrication of 3D micro-coils, especially for µNMR applications, is even more relevant today due to proven capabilities of 3D micro-coils in other applications that were mentioned in the beginning. The current state of the art for fabrication strategies and an overview of 3D micro-coils fabricated with 3D structuring strategies are shown in Table 1. As shown in Table 1, a fabrication method that is rapid, less complex and

can achieve high aspect ratio structures with good coating thickness homogeneity is still on demand. In order to overcome the mentioned challenges in the beginning, the aims of this work can be summarized as follows.

• Development of a relatively simple, reliable, and versatile 3D micro-coil fabrication method using a coating on glass tubes combined with laser processing, reducing the complexity of manufacturing compared to the complex state-of-the art processes given in Table 1.

• Providing a detailed insight about in-line (of the coating along one line) and cross-sectional thickness homogeneity (3D coating thickness homogeneity across the surface of borosilicate glass) by using modern measurement technologies such as focused ion beam scanning electron microscopy (FIB-SEM) and computer tomography (CT).

• Presenting an insight about how to achieve better coating (e. g., thickness homogeneity) and how to employ potential new coating materials (such as conductive polymers) via hybrid fabrication methods.

• Investigating the important properties of 3D micro-coils (e.g., magnetic field intensity) fabricated with hybrid methods.

## 2. Materials and methods

### 2.1. Conductive material coating on a tubular surface

Hybrid fabrication methods that are proposed in this work address the common challenges mentioned in the introduction and the brief comparison is presented in Table 1. Coating a conductive layer on a curved surface is one of these challenges due to common issues such as coating homogeneity, thickness, and adhesion etc. As a substrate, borosilicate glass tubes with 2.5 mm outside diameter, and 100 mm length were coated via so-called hybrid methods, and these different approaches are described in Fig. 1. All borosilicate glass tubes were cleaned with isopropyl alcohol prior to processing. In method 1, first, the
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Fabrication steps for copper and conductive polymer micro-coils on borosilicate glass tubes. Optical images of the tubes fabricated via related methods are given at the bottom of each method. The red and blue scale bars in the optical images indicate 500 µm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

coating was applied, followed by laser processing. The coating process includes a physical vapor deposition (PVD) coating of titanium (5 nm) as an adhesion-promoting layer and a thermally evaporated thin copper layer (40 nm) as a seed layer followed by electrodeposition of a copper layer on the same borosilicate glass. Both vacuum processes were conducted via a mounted rotary holder without introducing air to the vacuum chamber in between coating processes. A schematic representation of the developed fabrication steps is shown in Fig. 1.

Details of the thermal evaporation and the electrodeposition conditions are provided in Table 2, and a schematic representation of the electrodeposition setup is shown in Fig. 2.

In order to reduce inhomogeneity both in-line and cross-sectional, a crucial modification was made to the electrodeposition system. Rather than using a flat anode or a rotary cylindrical cathode system for tubular coating, a hollow anode was used (Fig. 2).

The rate of copper deposition on the surface of borosilicate glass was simulated using COMSOL Multiphysics, and the thickness values were measured experimentally via CT scan. COMSOL simulation was used to investigate the influence of advection (called the convection parameter in COMSOL) and diffusion on the transport-limited electrodeposition of a 3D copper layer. The layer thicknesses of electrodeposited copper were investigated at a defined length (1 cm from the end of the borosilicate

<caption>**Table 2**</caption>

Conditions for thermal evaporation of the seed layer and copper electrodeposition.

<table><tbody><tr><th colspan="2">Thermal evaporation</th></tr><tr><td>Power (W)</td><td>100 DC</td></tr><tr><td>Distance (mm)</td><td>170</td></tr><tr><td>Base pressure (mbar)</td><td>2.10<sup>-6</sup></td></tr><tr><td>Rotating speed (RPM)</td><td>50</td></tr><tr><th colspan="2">Electrodeposition</th></tr><tr><td>Current (A)</td><td>0.05</td></tr><tr><td>Anode-cathode distance (mm)</td><td>5</td></tr><tr><td>Agitation with magnetic stirrer (RPM)</td><td>300</td></tr><tr><td>Temperature (°C)</td><td>25</td></tr><tr><td>Rate (nm/s)</td><td>14</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Schematic representation of the electrodeposition setup with a hollow copper anode.</figcaption></figure>

tube) in a cell of interest where copper deposition occurred (length, width and height assigned as 1.2, 0.3 and 0.0015 cm, respectively). The current density distribution on the electrode surface for this cell is governed by the Péclet number $P_e$, which is a dimensionless quantity that relates the advective (convective) transport to the diffusion. The Péclet number is defined as the ratio of the advective and diffusive transport rates and is given by Eq. (3):

$$P_e = \frac{hu_{pe}}{D} \qquad (3)$$

where $h$ is the channel height, $u_{pe}$ is the velocity of the flow and $D$ is the diffusion coefficient of copper ions in the electrolyte. As electrodeposition in method 1 takes place on a non-structured surface in the investigated cell, we consider the distance between the hollow anode and the tubular cathode as characteristic height $h$. In this 3D model, a concentration dependent Butler-Volmer expression is used to describe the current density at the cathode. Copper deposition is solved in a time-
dependent simulation. Different Péclet numbers are investigated, and a comparison is presented in Fig. 6. Further details about these models can be found in the literature [32] and the details of these models are beyond the scope of this work. The hollow copper anode was cleaned before electrodeposition with 10% NaOH (v/v) solution for an hour at 45 °C followed by 5% H₂SO₄ (v/v) solution for one minute, and consecutive rinsing steps were performed in between. The cathode was placed inside a hollow copper anode, and the distance between them was set to 5 mm. Both the anode and cathode were dipped in a commercial copper electrolyte (NB Semiplate Cu 100 from Microchemicals GmbH), and a constant current was applied (galvanostatic electrodeposition). After electrodeposition, the metallized tube was laser structured to create a coil structure on the surface of the tube.

In method 2, the borosilicate glass was first structured with a laser, and then the conductive polymer was coated with a modified dip coating method. One of the traditional ways to form conductive lines, such as filling trenches [33] via electrodeposition, is a challenging task (i.e., preventing void formation inside trenches) and requires special settings, materials, setups, and multi-step processes. In order to tackle this challenge, a more direct approach was developed. The coil trenches were made via a laser structuring process and filled with a modified dip coating method. To provide better in-line and cross-sectional homogeneity, a modified dip coating system was used. Borosilicate tubes were connected to an custom built automated dip coating system with a rotary component (Fig. 3) and dipped into a conductive polymer solution. A commercial 25 ml test tube was filled with conductive polymer and placed under the borosilicate tube. The tube was dipped completely inside the solution via an automated movement system.

Conductive polymers, especially Poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) has been used in solar cell technologies [34] and proved its performance as an electrode material. To improve control over the trench profile and aspect ratio while addressing lithography and electrodeposition challenges, trenches were laser-structured and filled with Clevios™ FET, a PEDOT:PSS-based conductive polymer from Heraeus, using the modified dip-coating method. Therefore, the aspect ratio and trench profile depend on different parameters, such as the laser spot size, viscosity of the conductive polymer, withdrawal speed in the dip coating process and properties of the substrate surface (e.g., surface energy and roughness). The properties of the coating material as well as the coating conditions are given in Table 3.

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Schematic representation of the automated and modified dip coating system. The red arrow indicates the direction of the rotation, and the blue arrow indicates the direction of withdrawal and pull-down. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<caption>**Table 3**</caption>

Conductive polymer coating conditions with the modified automated dip coating system.

<table><thead><tr><th colspan="2">Properties of conductive polymer</th></tr></thead><tbody><tr><td>Material</td><td>PEDOT:PSS</td></tr><tr><td>Conductivity of dried layer (S/cm)</td><td>200</td></tr><tr><td>Viscosity (mPa s)</td><td>20-80</td></tr></tbody><thead><tr><th colspan="2">Coating conditions with modified automated dip coating machine</th></tr></thead><tbody><tr><td>Withdrawal speeds (mm/s)</td><td>2.5, 4.3, 7.8</td></tr><tr><td>Rotation speeds (RPM)</td><td>400, 450, 500, 550, 600</td></tr><tr><td>Dip duration (s)</td><td>10</td></tr><tr><td>Drying duration (h)</td><td>48</td></tr><tr><td>Temperature (°C)</td><td>25</td></tr></tbody></table>

## 2.2. Femtosecond laser structuring

Laser structuring [35–37] was performed for both different approaches described in Fig. 1. In method 1, laser structuring was used as the final step to remove the copper layer, while in method 2, it was used as initial step to engrave the glass tubes. For both methods shown in Fig. 1, a femtosecond laser with a wavelength of 515 nm and a pulse duration of 900 fs was used. As shown in Fig. 4, the glass tube was mounted on a rotary axis (C-axis) for laser structuring. The focused laser beam was aligned perpendicularly to the cylinder surface. While rotating, the tube was moved along the x-axis to create a spiral path on top of the cylinder surface.

To control the structuring width and the taper angle of the grooves, a trepanning optic (GFH GmbH) was used to incline the laser beam and adjust the diameter of the beam path. The 1/e² diameter of the laser beam amounted to 18 µm, while the diameter of the beam path was varied (trepanning diameter). In method 1, the trepanning diameter was 24 µm and a pulse energy of 13 µJ, a repetition rate of 66.6 kHz and velocities for C- and X-axis 10 rpm and 26.7 µm/s were used.

In method 2, the trepanning diameter was 80 µm and a pulse energy of 25 µJ, a repetition rate of 40 kHz and velocities for C- and X-axis 20 rpm and 53.3 µm/s were used. While the laser process was carried out for a coil length of 2.5 mm (without contact pads), the coil length principally is limited by only the traveling length of the x-axis, which amounts to 500 mm for the used laser machine. That length corresponds to h in Eq. (1) and this technique provides more flexibility to create various aspect ratios.

## 2.3. Characterization methods for the fabricated coils

Tubular or curved surfaces bring a new challenge for measuring the thickness homogeneity of these surfaces. Current methods such as optical detection methods fall short due to low signal intensities due to material or substrate related reflections. Other common instruments such as surface profilometers and atomic force microscopes (AFMs), are also not suitable due to difficulties of positioning probes on curved surfaces. Additionally, most commercial AFMs have small scanning areas that require multiple scans and stitching and are therefore not desirable for large areas. Existing investigation methods usually provide reliable information for very small areas or provide very high resolutions for structures that have smaller aspect ratios. Therefore, detailed investigations of both thickness homogeneity for in-line and cross section were performed by CT scan and FIB-SEM. While CT scan provides extensive details for both cross-sectional profile and in-line profile. The thickness homogeneity of the copper along the line was investigated by FIB-SEM, which offers a resolution in nm.

The CT scans were performed with a cone beam reflection type X-ray source with a tube voltage at 80 kV and 31 µA. A flat panel detector with a resolution of 3200 × 2302 pixels was used to capture 5026 projection
<figure><img src="image_7.png" /><figcaption>Fig. 4. a) View of the system used for laser structuring with a rotational holder for tubes and a mounted borosilicate glass tube which was structured in its center. b) Sketch of the laser process for coil manufacturing c) Optical microscope image of a structured copper coil. The black bar in the inset indicates a length of 500 µm.</figcaption></figure>

images over 360° around the sample with an exposure time of 2.8 s for each projection image. The 3D reconstructed volume has a voxel resolution of 1.44 µm. The measurement conditions of the FIB-SEM measurements are given in the supplementary section. The coating thickness of the PEDOT:PSS coils were measured by Keyence VK-X3000 confocal laser scanning microscope.

Electrical properties of the coils (such as the inductance) have been investigated in the literature. In this work, the inductance of the copper coils was measured with a GwInstek 8110G LCR meter. Four wire Kelvin clips were used to reduce the parasitic effect. The contributions of the copper connection cables were also measured and subtracted. The measurement conditions of the experiment are summarized in the supplementary section.

Fukushima's equation for the theoretical calculation of the inductance was used by Webb [38] and compared with experimentally fabricated coil inductances in the literature. The same calculation was applied here by using Eq. (4) (adapted from [39]), and the results were compared with the measured values.

$$L = \frac{n^2 \times d^2}{(46 \times d) + (100 \times h)} \quad (4)$$

where L, n, d and h are the inductance of the coils in nH, number of turns, diameter of the coil and length of the coil, respectively.

The magnetic field inside the coils was also simulated with COMSOL Multiphysics software using the AC/DC module that implements Maxwell-Ampere equation ($\nabla \times H = J$ and $\nabla \cdot J = 0$). Where H and J are defined as magnetic field and electric current density. The simulation model was developed using a solenoidal coil with a square cross-section. At the center of the coil, a container with cylindrical shape and a radius of 1150 µm, length of 5800 µm was positioned. A 100 µm spacing was intentionally introduced between the coil and the sample to account for the thickness of the container. The entire setup was enclosed within a larger cylindrical air domain, carefully designed to minimize any distortion of the magnetic field generated by the coil. The outer boundaries of the model were assigned magnetic and electric insulation conditions. Both electrodes of the coil were positioned at the model boundaries, allowing the application of current, voltage, and grounding. Meshing was performed using tetrahedral elements, starting with a fine mesh for the coil, which represents the smallest domain in the model. A coarser mesh was then applied to the sample and the surrounding air to optimize computational efficiency while maintaining accuracy. Thickness values of the coil made of copper and PEDOT:PSS in the simulation were selected according to experimental data. Conditions of the

<table><caption>**Table 4**
Simulation conditions for copper and PEDOT:PSS coil.</caption><thead><tr><th></th><th>Copper coil</th><th>PEDOT:PSS coil</th></tr></thead><tbody><tr><td>Windings/turns</td><td>17</td><td>17</td></tr><tr><td>Coil diameter (µm)</td><td>2500</td><td>2500</td></tr><tr><td>Conductor width (µm)</td><td>40</td><td>40</td></tr><tr><td>Separation (µm)</td><td>110</td><td>110</td></tr><tr><td>Conductivity (S/m)</td><td>5.998 × 10<sup>7</sup></td><td>2 × 10<sup>4</sup></td></tr><tr><td>Input signal</td><td>2.45 mA</td><td>12 V</td></tr><tr><td>Filling sample and surrounding material</td><td>Air</td><td>Air</td></tr></tbody></table>

simulation were summarized in Table 4.

Magnetic and electric field (MEF) interface and measured experimentally by a custom built automated linear movement system equipped with a prototype Hall sensor. The experimental measurement setup is shown schematically in Fig. 5. For the copper coil and PEDOT:PSS coil constant current of 2.45 mA and constant voltage of 12 V were applied both in the simulation and the experiment, respectively. The prototype Hall sensor measure ±30G magnetic field with a resolution of 20 bits up to 1 kHz of bandwidth. The sensor was connected via a I²C buses to an Arduino board. More details about the characterization method were previously described in the literature [40].

## 3. Results

In this section, the properties of the coatings and fabricated coils are presented. The electrodeposition rate of copper was simulated using COMSOL Multiphysics simulation and the results were compared with extracted rate from the CT measurements.

The simulation results indicate that the deposition rate lies between 9.29 nm/s and 38 nm/s according to only diffusion-based model and advection diffusion-based model. The CT measurement results show that electrodeposition rate of copper was 14.4 nm/s. Even though the experimental results tend to align with only diffusion-based mechanisms, Fig. 6 shows that for deposition times larger than 600 s, corresponding to layer thicknesses larger than 7 µm, advection diffusion-based model must be considered. A good fit between the simulation and experimental results is found for Péclet numbers between 30 and 40, and the best fitting rate is 15.1 nm/s with 35 Péclet numbers.

The laser ablation process of the electrodeposited copper layer on the tubular surface is shown in Fig. 4. A copper coil with a line width of 40 µm, separation of 110 µm and total length of 2.5 mm was produced via laser structuring. The separating trenches are parallel, thus providing a
<figure><img src="image_8.png" /><figcaption>Fig. 5. Magnetic field intensity test setup.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Comparison between simulated and measured electroplated copper rates. The dots and straight lines show data points and linear fits for the simulation and measurements, respectively. Simulations were performed with different Péclet numbers, for a model considering diffusion and advection. For comparison, only diffusion-based model is also plotted.</figcaption></figure>

uniform coil geometry needed for uniform magnetic field strength in µNMR. This is also proven by the magnetic field intensity measurement results. The coils made from method 2 and with PEDOT:PSS has also 17 windings, line width of 40 µm and a separation of 110 µm. They were produced by laser structuring and modified dip coating.

Thickness uniformity of the coils was investigated in detail with CT scans and FIB-SEM. The CT scan shows 3D thickness profile of the copper coil and indicates only 1 µm deviation. The in-line homogeneity of the thickness was also validated by FIB-SEM images (see the supplementary section) which were aligned with 1 µm deviation along 2.5 mm scanning range.

High purity coating is needed to ensure consistent conductivity for the coil and directly related to performance of the coil. Therefore, copper content of the electroplated coating was investigated by EDS measurements and results are shown in the supplementary section. Both the cross-sectional and line homogeneity of the electrodeposited copper thickness were measured after structuring and the results are shown in

<figure><img src="image_10.png" /><figcaption>Fig. 7. a) 3D CT scan of the copper coil fabricated with method 1 on borosilicate glass b) cross-sectional evaluation of the thickness homogeneity of the coil windings after laser structuring c) thickness distribution of the coil windings.</figcaption></figure>

Fig. 7. A comparison of different dip-coating conditions, both with and without rotation, was conducted for unstructured PEDOT:PSS coatings on borosilicate tubes. Additionally, the effect of rotation speed on coating thickness was analyzed and is presented in Fig. 8. Furthermore, trench filling, coating thickness, and surface quality at the same rotation speed were compared between samples with and without rotation (Fig. 9). Therefore, the impact of the modified dip-coating method was examined on both unstructured curved surfaces and laser-structured surfaces.

Fig. 7a, b and c shows 3D, cross sectional thickness profile and
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** a) Thickness of PEDOT:PSS coatings on unstructured borosilicate tubes with different withdrawing speed for rotated and stationary samples. Red and blue lines represent linear fit for the respective data. b) Thickness of PEDOT:PSS coatings for different rotation speeds. Red line represents polynomial fit for the data. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

thickness distribution for the copper coil that is made by method 1. Thickness distribution indicates a homogeneous electrodeposition of copper on a borosilicate capillary tube. Distribution of thickness shows that electrodeposited copper layer thickness falls into 8 ± 1 µm regime. Various thickness (6.97 and 12 µm) of the electrodeposited copper were measured by CT method and showed similar coating homogeneity (see Supplementary section).

The samples were fully immersed in PEDOT:PSS and then withdrawn at different speeds. Immediately after withdrawal, the samples were spun at 400 RPM, while the stationary ones remained still. Fig. 8a illustrates that coating thickness increases with higher withdrawal speeds for both rotated and stationary samples. To evaluate the effect of rotation speed, the withdrawal speed was kept constant (4.3 mm/s) while the rotation speed was adjusted from 400 to 600 RPM. After the coating step, three scratch lines were carefully made on the coated borosilicate tube at distances of 1.3, 1.5, and 1.7 cm from the bottom point. Measurements were conducted using a confocal laser scanning microscope at 20× magnification with nanometer-scale vertical resolution. Step height calculations for each line were performed using the Mountains SPIP software, following ISO 5436 standards. The rotation speed of the DC

motor was determined using a DT-2234C tachometer with a resolution of 0.1 RPM. Fig. 8b demonstrates that increasing the rotation speed at a constant withdrawal speed (4.3 mm/s) results in thinner coatings. For PEDOT:PSS with a viscosity range of 20–80 mPas, applying rotation immediately after withdrawal enables precise thickness control.

The samples were fully immersed in PEDOT:PSS then withdrawn at the constant speed (4.3 mm/s) and coated with the coating conditions specified in Table 3. Immediately after the withdrawal step, the samples were spun at 400 RPM, while the others remained stationary. To analyze both in line and cross-sectional homogeneity and account for depth variations caused by the laser process, 17 trench depths were measured along four different lines (every 90°) on the tube, both before and after the dip coating process. The differences between coated and uncoated trench depths were then plotted for samples with and without rotation. To better illustrate the difference between these two cases, the percentage-based interquartile range was calculated. The first quartile (Q1, 25 %), mean line (M), and third quartile (Q3, 75 %) were marked in Fig. 9a and b. The region between Q1 and Q3 was shaded in gray in the graphs, representing the core deviation zone. For the cases without and with rotation, the Q1, M, and Q3 values were determined as 5.11, 4.20, and 2.62 µm, and 4.36, 3.41, and 3.07 µm, respectively. Consequently, the core deviation zone ranged from 5.11 to 2.62 µm without rotation and from 4.36 to 3.07 µm with rotation. This indicates that applying rotation during the dip-coating process reduced the core deviation zone, leading to improved homogeneity in the coil produced using method 2. The results for trench filling exhibited the same trend as shown in Fig. 8 for samples dip-coated with and without rotation. In general, rotation influences coating thickness, with rotated samples consistently forming thinner coatings than non-rotated ones, regardless of the presence of trenches.

The electrical properties of the fabricated coils were also investigated. The inductance of the copper and PEDOT:PSS coils were measured at 100 kHz as 550 nH and 42 mH, respectively. The inductance of the copper coil is consistent with the theoretical calculations in the literature [21,38]. The theoretically calculated inductance for the copper coil from Eq. (4) is 428 nH, and the measured inductance is approximately 350 nH in the frequency range of 1 to 10 MHz. The difference between the calculated and measured value is due to the contribution of the contact pads and transmission line between the coil and contact pads. For comparison, the inductances of a similar 3D coil (fabricated using lithography) in the literature and the copper coil in this work are shown in Fig. 10.

Experimental results for the magnetic field intensity measurement corroborate quite well with the COMSOL simulation results. Magnetic field distribution is shown in Fig. 11. Simulation result shows magnetic field intensity of 14 µT at the center of the copper coil, and measurement shows 11 µT. Simulated magnetic field intensity of 3.3 µT at the center of the PEDOT:PSS coil, and measurement shows 2.5 µT.

## 4. Discussion

3D micro-coils were successfully fabricated via hybrid methods and characterized in this article. The most important advantages of the proposed fabrication processes are reduced fabrication complexity, duration, better control of the aspect ratio as well as better homogeneity of the coating along with promising magnetic field inside the coils.

Both hybrid methods proposed in this work require only two fabrication steps. This means, that artefacts and limitations that come from intermediate steps, such as problems regarding trench filling [33] by conventional methods (swelling resist profiles, and void formation during electrodeposition), have no influence on the hybrid fabrication methods proposed in this work. Therefore, the thickness of the conductive lines in 3D coils depends only on the laser structuring and the dip coating process. The trench profile especially for method 1 (i.e., shape and depth) is related to the laser structuring process and depends only on the laser spot size and substrate material. As an example, two
Thickness variation of 17 trenches on
borosilicate glass after dip coating

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

Step height analysis of laser scanning
microscope images

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

Surface image of coated trenches

<figure><img src="image_17.png" /><figcaption>Fig. 9. a) Thickness variation of 17 trenches for a) non-rotated samples after dip coating b) rotated samples c) reconstructed 3D surface profile from confocal laser microscope image and measurement line for the trenches. Optical image of measurement line 2 ablated on borosilicate tube as an inset d) step height calculation from software Mountains SPIP for each trench according to ISO 5436 e) confocal microscope image of the coated surface for trench number 14. and 15. for non-rotated f) rotated sample.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig. 10. Inductance of copper coil from the literature (extracted data from [21]). b) Inductance of the fabricated copper coil with method 1 in this work between 100 kHz and 10 MHz.</figcaption></figure>

different aspect ratios and sidewall profiles are presented in the sup-
plementary section. The presented results especially for method 2 show
that with the proposed hybrid process, better control of the thickness is
possible because it depends mainly on the viscosity, withdrawal, and
rotation speed.

Coating homogeneity (impurities, thickness variations or changes in coil dimensions) may create distortion in terms of magnetic field strength inside the coil therefore making it impossible to use the coils in some applications (e. g., µNMR). However, there is limited information in the literature about thickness profile after the fabrication process of 3D micro-coils. In this work, better control of coating parameters, such as in-line and cross-sectional homogeneity of the coating over curved surfaces, was established. For hybrid method 1, both cross-sectional and in-line thickness homogeneities are 11 %. Although there is limited information in the literature regarding coating thickness homogeneity for 3D micro-coils, the value established in this study surpasses previously reported values [41] achieved using more complex fabrication methods. Compared to conventional lithographic methods, the approaches used in this work require fewer fabrication steps, enabling rapid production while also reducing the use of hazardous chemicals— all without sacrificing coil performance, including nH-level inductance and homogeneous magnetic field distribution inside the coil. For hybrid method 2, an increase in withdrawal speed resulted in thicker films. This behavior

suggests that the dip coating of PEDOT:PSS onto borosilicate capillary
tubes follows the draining regime in the Landau-Levich model [42].
Confocal laser scanning microscope images further revealed that rota-
tion contributes to a smoother coating inside the trenches of the coil
produced using method 2. Additionally, the modified coating system,
particularly the rotation step, provided enhanced thickness control,
which is crucial for coating curved substrates. Although, other
conductive liquids and materials have been tested in the literature for
coil production [30,31], PEDOT:PSS is employed for the fabrication of
3D coil process with using a hybrid method for the first time in this work.
The electrical and magnetic behavior of the PEDOT:PSS coils also
showed promising results. Even though the conductivity of the coated
part is not as good as copper coil, it can be improved by the strategies
mentioned in the literature [43]. PEDOT:PSS, as a semi-transparent
coating, has an additional advantage over reflective coil coatings,
which makes it easy to observe the sample inside the coil. Easy and rapid
fabrication steps make these hybrid methods suitable candidates for
many applications, such as lab-on-a-chip applications. The reduced
complexity of the presented processes is increasing the chance of
implementing these coils in microfluidic systems as well as various
sensor applications on curved surfaces.

The magnetic and electrical properties of the fabricated coils were investigated. As shown in the literature for a static magnetic field [44], inhomogeneity may change the NMR spectrum and make it difficult to detect some signals. Even though magnetic field inside the coil in this work is not static, every single asymmetry in the field generated by the coil might cause various deformation in the spectrum. Therefore, as an important performance parameter, homogeneity of magnetic fields inside the tubes were simulated and experimentally proven. Figs. 10 and 11 show that the properties of the fabricated coils are promising, and the simulations show excellent agreement with the measurements. For instance, the electrical and magnetic behavior of coils fabricated with method 1 align with theory and previously reported coil properties in the literature [21]. Magnetic field intensity of the copper coil presented in this work has great potential due to µT range magnetic field has been proved to be useful for NMR applications [45] in the literature.

**5. Conclusion**

In this work, different fabrication methods were combined to reduce
the number of fabrication steps for micro-coils. A custom build modified
dip coating device was built, and for the first time PEDOT:PSS was used
for 3D coil production. Rotational laser structuring is also used for
creating a better aspect ratio and eliminating the difficulties associated
with copper coils produced by the classical lithography technique.
Compared with existing methods, the methods proposed in this work
promise better integration possibilities, faster fabrication durations and
better sidewall.

As summarized in Table 1, the proposed methods offer several ad-
vantages over existing techniques. Compared to lithography, they
require fewer fabrication steps, use less hazardous materials, and pro-
vide greater flexibility in achieving a wider range of aspect ratios. Unlike
local electrodeposition, these methods do not require a base conductive
layer, allowing for broader substrate compatibility and enabling rela-
tively faster fabrication over larger areas. Additionally, in contrast to
microcontact printing, they offer higher repeatability, with results that
are independent of the transfer material. More specifically, the methods
proposed in this work have been proven to be effective alternative
methods for fabricating 3D micro-coils, without the issues such as trench
filling or dimension variations due to multiple lithography steps (i.e.,
swelling resist). However, further research can be conducted to better
understand the influence and limits of each parameter (i. e., viscosity,
spot size, substrate influence) on achievable trench depths and profiles.
Furthermore, PEDOT:PSS coating can be further optimized to achieve
better conductivity values therefore a better magnetic field inside the
coil. Application area of the fabricated coils is not limited to µNMR, and
<figure><img src="image_19.png" /><figcaption>Fig. 11. a) Simulated magnetic flux density of the fabricated copper coil b) Comparison of the simulated and measured magnetic field intensities of fabricated copper coil. c) Simulated magnetic flux density of the fabricated PEDOT:PSS coil. d) Comparison of the simulated and measured magnetic field intensities of the fabricated PEDOT:PSS coil. The black dots represent experimentally acquired data points, and the red curves indicate Gaussian fits of the data points. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

demonstrated methods can be implemented in several other fields such as flexible electronics and sensors.

### CRediT authorship contribution statement

**Hakan Alaboz:** Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Andras Kovacs:** Writing – review & editing, Visualization, Formal analysis. **Daniel Johannes Förster:** Writing – review & editing, Visualization, Resources, Investigation. **Lucas Werling:** Writing – review & editing, Visualization, Resources, Investigation, Formal analysis. **Jajnabalkya Guhathakurta:** Writing – review & editing, Visualization, Resources, Investigation. **Julien Petit:** Writing – review & editing, Investigation. **Morgan Madec:** Writing – review & editing, Resources. **Luc Hébrard:** Writing – review & editing. **Ulrich Mescheder:** Writing – review & editing, Supervision, Project administration, Funding acquisition.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

This research was supported by the European Regional Development Fund (ERDF) and the Interreg V Upper Rhine Offensive Sciences Program (Project 3.14 – Water Pollution Sensor). The work with FIB-SEM was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), within the program Major Research Instrumentation (Project number: 505067193) under GG91b and by the state Baden-Württemberg as well as by Furtwangen University. Author

gratefully acknowledges the assistance from Ms. Xeng in the copper evaporation process and Hochschule Furtwangen-Institute for Advanced Manufacturing (KSF) for the laser scanning microscope measurements.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jmapro.2025.04.040.

### Data availability

Data will be made available on request.

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