The simulation study of high-performance micro-inductors Based on MEMS 3D coils

With the development of flexible electronics and microsystems, the demand for the miniaturization of electronic components is becoming increasingly urgent. Due to the advantages of miniaturization, low power consumption, and easy integration, the micro-inductors fabricated by microfabrication technology get more and more attention. However, the traditional two-dimensional inductors are no longer able to meet the growing needs of today’s society in terms of occupied areas, inductance values, and packaging costs. So, this paper proposes a three-dimensional structure thin film solenoid micro-inductor based on MEMS and analyzes it by using finite element method (FEM). The simulation focuses on recording the inductance values and quality factors of the micro-inductors with varying parameters in the frequency range of 0-2, 000 MHz. Additionally, the maximum current values corresponding to the micro-inductors with different parameters are recorded at the operating temperature of polyimide, specifically addressing the current-carrying capacity. The simulation result has certain theoretical guidance for high-performance micro-inductors design.


Introduction
The market has expressed an urgent need for the development of high-power and low-loss integrated micro-inductors as microsystems, and flexible electronics move toward higher performance and smaller sizes.For academics both domestically and internationally, enhancing the performance of microinductors has emerged as a research priority.The construction of integrated micro-inductors with benefits such as low resistance, high inductance, high-quality factor, low cost, and mass manufacturing can be accomplished by integrating thin film technology into MEMS technology [1, 2, and 4].The potential for development of MEMS-based micro-inductors is enormous, and in the future, they are expected to gradually replace traditional inductors, becoming key components in RF and other fields.This will drive the development of electronic products towards integration and intelligence.
Currently, both domestically and globally, there have been numerous papers on micro-inductors, the majority of which concentrate on thin film inductors with two-dimensional planar designs.However, there presently exists a lack of knowledge on three-dimensional micro-inductors.He et al. researched decoupling and coupling inductors with multi-layer magnetic cores.Selvaraj, S.L. et al. reported the design and fabrication of an on-chip solenoid inductor with a novel thin film magnetic core for highfrequency DC-DC power conversion applications [3].All existing reports have underscored the substantial utility of micro-inductors in integrated devices, as well as the relatively advanced research on micro-inductors.However, to date, there has been inadequate research on the simulation of 3D structural micro-inductors.

Simulation and analysis
We need to investigate the effects of many variable factors on the electromagnetic and thermal properties of the three-dimensional solenoid inductor to further improve its performance [5].During the investigation of thermal correlation characteristics, the study records the maximum current passing through the coil of an inductor with varying parameters at the insulation layer's operating temperature.The primary parameters under consideration are the magnetic core size and coil size of the inductor.
Figure 1 depicts the structure of a three-dimensional solenoid inductor, where a coil is wound around a magnetic core in space, forming a solenoid structure.Figure 1 (b) illustrates the implementation of a cuboid connecting column on both sides of the magnetic core for electrical connection.In Figure 1 (c), the transparent section above the silicon substrate represents the polyimide material serving as an insulating layer.

Effect of magnetic core size
We change the thickness and width of the magnetic core within the size range of conductor coil encirclement.The thickness of the magnetic core is set within the range of 20 to 45 μm, while the width of the magnetic core is fixed between 780 μm and 880 μm.By computing and analyzing these parameters, we aimed to gain insights into the inductor's performance characteristics.Figures 2-5 depict the simulation results illustrating the impact of both magnetic core thickness and width on the performance of the micro-inductor.In Figures 2 and 4, the inductance of the micro-inductor improves as the thickness and width of the magnetic core expand.This is because a larger magnetic core allows more magnetic flux to pass through, thereby enhancing the inductance value.Additionally, Figure 2 demonstrates that the maximum quality factor of the micro-inductor also increases with an increase in the magnetic core thickness.However, in Figure 4, the maximum quality factor initially decreases and then increases with an increase in the magnetic core width.Nevertheless, the overall change amplitude is not significant and remains around 24-25.
Furthermore, Figures 2 and 4 demonstrate a significant negative correlation between the quality factor in the high-frequency band and the thickness and width of the magnetic core.This is due to the increased size of the magnetic core, which elevates the series capacitance value, thereby reducing the inductor's ability to store magnetic energy at high frequencies.However, changes in core thickness and width in Figures 3 and 5 have almost no effect on the current-carrying capacity of the micro-inductor.This is because the current-carrying capacity of an inductor is primarily linked to its resistance, and altering the core size only modifies the capacitance value, which does not significantly impact the maximum current allowed to flow through it.
Based on the conclusion, it is evident that alterations in the thickness and width of the magnetic core have a substantial impact on the inductance of the micro-inductor, and increasing the size of the magnetic core proves to be an effective means of enhancing the inductance value.

Effect of wire size
The wire thickness varies between 20 μm and 50 μm, and the associated performance parameters of the inductor were calculated and analyzed.Figures 6-7 depict the simulation results illustrating the impact of wire thickness on the performance of the micro-inductor.Through simulation, it has been observed that the impact of wire width on inductor performance is similar to that of wire thickness, and therefore the influence of wire width is not depicted in a chart here.However, when considering Figure 6, it becomes evident that both the inductance and maximum quality factor of the micro-inductor decrease with an increase in wire thickness and width.As the coil width increases, the self-inductance coefficient of the inductor decreases, leading to a gradual reduction in the inductance value.
Upon further examination of Figure 6, it becomes evident that the quality factor in the high-frequency band experiences a slight increase with an increase in wire thickness and width.Additionally, Figure 7 illustrates an improvement in the current-carrying capacity of the inductor.This is attributed to the expanded cross-sectional area of the wire resulting from the increased thickness and width, which subsequently reduces the resistance loss.Based on these findings, it can be concluded that increasing the wire thickness and width can enhance both the quality factor and current-carrying capacity of the micro-inductor at high frequencies.However, it is important to note that excessive increases in wire thickness and width can lead to significant parasitic and eddy current losses, potentially negating the improvement in the quality factor and even causing a decline in performance.
It is critical to find a balance between size requirements and performance goals during the structural optimization design given the divergent impacts of wire size on the inductance, quality factor, and current-carrying capacity of the micro-inductor.To reach the required criteria, it is important to properly increase the wire's thickness and width.

Optimized inductor performance
The finite element method and diagram are used to analyze the relationship between the magnetic core thickness, magnetic core width, wire thickness, wire width, inductance, quality factor, and currentcarrying capacity of the micro-inductor.The results of the simulation calculations yield a direct basis for optimizing the dimensions and performance of micro-inductors.We compared the performance parameters of the optimized micro-inductors in this study with those of some published core-based micro-inductors, with the aim of highlighting the advantages of the device performance designed by us.Table 1 summarizes the relationship between radio frequency inductor performance and operating frequency, as reported in various literature on magnetic materials.It is important to note that our analysis is a first in that it takes current-carrying capacity into account.In our work, the micro-inductor in the high-frequency range exhibit significant advantages in terms of inductance value and quality factor.What's more, the micro-inductor we design boast excellent current-carrying capacity.

Conclusions
The specific findings came from studying and analyzing how various parameters affected the performance of the 3D solenoid-type micro-inductor.
Increasing the size of the magnetic core portion can increase the micro-inductor's inductance, but doing so will also lower its quality factor at high frequencies and have essentially little effect on its current-carrying capacity.In practical applications, it is required to combine the operating frequency, size requirements, and performance requirements, choose the appropriate material as the core, and suitably increase its size due to the opposing trend of inductance value and quality factor.
In the conductor coil section, increasing the wire size has the potential to enhance the quality factor and current-carrying capacity of the micro-inductor.However, it is important to note that this increase in wire size may result in a reduction in its inductance.Therefore, in practical applications, it is crucial to strike a balance between the desired performance requirements and the limitations of the current electroplating process.By considering both the size and performance requirements, it is possible to appropriately determine and increase the wire size.
In this paper, a novel simulation method of high-performance micro-inductors based on MEMS 3D coils is proposed.Through optimization techniques, the micro-inductor achieves impressive results, with a maximum inductance of 99.5 nH, a maximum current-carrying capacity of 0.936 A, and a maximum quality factor exceeding 21.These findings demonstrate that the inductor successfully attains the objectives of compact size, high inductance value, high current-carrying capacity, and superior quality factor simultaneously.In this paper, we not only focused on investigating the operating frequency, inductance value, and quality factor of the inductor but also took on the challenging task of enhancing

Figure 1 .
Figure 1.Schematic illustrations of an on-chip solenoid inductor.

Figure 2 .
Figure 2. The impact of magnetic core thickness on inductance value and quality factor.

Figure 3 .
Figure 3.The impact of magnetic core thickness on the current-carrying capacity of micro-inductor.

Figure 4 .
Figure 4.The impact of magnetic core width on inductance value and quality factor.

Figure 5 .
Figure 5.The impact of magnetic core width on the current-carrying capacity of micro-inductor.

Figure 6 .
Figure 6.The impact of wire thickness on inductance value and quality factor.

Figure 7 .
Figure 7.The impact of wire thickness on current-carrying capacity of micro-inductor.

Table 1 .
Performance of published inductors.