Monolithic mtesla-level magnetic induction by self-rolled-up membrane technology

Route to obtaining high-density, monolithic 3D coils

As shown in Fig. 1, the structural design of S-RuM high-density 3D coils is relatively simple, and the processing requires only three lithography steps (see details in Materials and Methods and in section S1). From a practical perspective, no strict requirements must be imposed on the substrate or conductive layer materials. In the experiments reported here, sapphire wafers and Cu are chosen as the substrate and conductive materials, respectively. Note that Cu is prevalent in integrated circuit interconnect. Step 1 in Fig. 1 illustrates the deposition of the thin-film stack including the germanium (Ge) sacrificial layer, the Al₂O₃ protection layer, and the SiN_x strained bilayer. Generally, the sacrificial layer needs to have a relatively large Young’s modulus so as to avoid absorbing strain energy from the SiN_x strained layer and have a smooth surface so as to prevent reducing the conductivity of the Cu layer from surface roughness accumulation. When compared with previously reported S-RuM passive electronic platforms, incorporating an Al₂O₃ protection layer, by atomic layer deposition (ALD), on top of the sacrificial layer proved to be the most reliable approach to solving the PECVD SiN_x pinhole issue. The compressive and tensile stress produced during the PECVD growth of the low-frequency (LF) SiN_x and high-frequency (HF) SiN_x are intentionally maximized to provide sufficient momentum for the thick Cu layer to roll up. The first lithography level (step 2 in Fig. 1) serves to define the mesa, whereas the second lithography level (step 3 in Fig. 1) defines the 2D coil patterns on the mesa before rolling. In this work, the thickness of Cu strips varied from 150 to 250 nm, and the width varied from 250 to 300 μm so as to obtain a cross-sectional area from 37.5 to 75 μm². The number of Cu strips was chosen to be up to six. Long and wide Cu strips are used to reduce DC resistance because the alternative of rolling up micrometer-thick Cu strips is extremely challenging with the stress level in the SiN_x film. However, preferential etching of corners for these wide Cu strips led to detouring while rolling. Therefore, a rounded corner design for the Cu strip was introduced to solve this issue (see details in section S2). An Al₂O₃ film, grown by ALD and much thinner than previous work, served both as the cover layer and the second protection layer to avoid device failures due to the existence of pinholes in the PECVD-grown SiN_x layers. The last lithography process (step 5 in Fig. 1) opens an etching window on the far end of the mesa through the Al₂O₃ cover layers so as to ensure rolling in the desired direction. Note that if the substrate is not chemically inert to XeF₂ etch (e.g., silicon), photoresist (PR) can be coated on the exposed surface of the substrate to avoid corrosion, for example, ~100-μm-thick PR provided sufficient protection from XeF₂ corrosion for at least 1 hour in our experiment. Each of the rolled-up metal strips is known as a cell, and the requirement for an even number of cells in S-RuM structures follows from the imperative for balancing the input and output currents on both sides. Tight rolling with zero gap between turns of the same cell is desired for achieving good electrical performance tolerance. However, note that air gaps ranging in size from a few tens of nanometers to a few micrometers have been observed in most fabricated samples. By matching the simulated resonance frequency with measured values, electromagnetic modeling suggests that the average value of the air gap is approximately 1 μm.

Route to integrating a magnetic core into monolithic 3D coils

S-RuM 3D microtube architectures inherently provide a cylindrical cavity for ferrofluid integration, a natural geometrical advantage unavailable to conventional planar processing. Ferrofluids were successfully incorporated in energy harvesters and actuators (31, 32); however, the methods used in these devices were beyond the domain of microelectronics fabrication, both in dimension and compatibility. For S-RuM 3D coil core-filling in this work, ferrofluid composed of nanoscale ferromagnetic, or ferrimagnetic, particles suspended in a carrier fluid (usually an organic solvent) was used. It is known that superparamagnetic nanoparticle suspension can be directly injected by fine-point syringes or transferred by a probe tip, taking advantage of the surface tension of the liquid dispersant. Capillary action directly aids liquid injection into a microtube by drawing ferrofluid introduced at the open end of the S-RuM microtube toward the center, enabling a high fill factor naturally. Suitable ferrofluids must have an appropriate surface tension and viscosity to be drawn into the air core by capillary forces at the desired speed. Uniformity, stability, and mass density are the primary requirements for the dispersion of nanoparticles in the liquid carrier.

Step 7 of Fig. 1 shows the three-step postfabrication core-filling process involving iron oxide nanoparticles as the magnetic material for an S-RuM Cu 3D coil air-core inductor. The three steps of this process are aligning, filling, and detaching. The tip of the micropipette (black shadow on the left) is first aligned with the S-RuM 3D coils. Then, one end of the S-RuM power inductor is attached to the ferrofluid droplet dangling from the tip of the micropipette. Core filling is triggered by the strong capillary interaction between the liquid carrier droplet and the microscale tubular air-core structure, and the result is the delivery of ferrofluid into the core of the inductor in a few seconds (movies S1 and S2). After the core is fully filled, the tip of the micropipette is retracted and detached from the end of the S-RuM 3D coils as shown, and the ferrofluid-filled tubular structure is left to dry. The core of an S-RuM 3D coil can also be filled multiple times after successive drying steps to evaporate the dispersant (cf. core-filling method in section S3). The core-filling process requires only that a micropipette, the ferrofluid delivery tool, has an exit diameter close to that of the S-RuM structure(s), resulting in a process that is simple, fast, clean, controllable, and reversible.

Underlying mechanics and general design approach

Experimental results and computational modeling suggest that the design of 3D S-RuM architectures for strong magnetic induction requires comprehensive mechanical/electrical/thermal management for predictable and optimized performance. Finite element analyses throughout every aspect of design provide context for general, rule-based procedures for obtaining magnetic induction systems with the desired performance. Consequently, these analyses have been found to be an essential element of the design process for practical applications. As shown in Fig. 1, the structural design of S-RuM 3D coils includes the vertical layer construction of layers and the horizontal layout before rolling. The coil inner diameter, the key parameter throughout the design process, is dictated by the properties and thicknesses of the material layers adopted for the vertical construction design. Given these data, a quasi-dynamic finite element method (FEM) is then used to accurately predict the value of the inner diameter based on the vertical construction of the layers (19). Figure 2A shows a simulated rolled-up membrane structure comprising a layered material stack as indicated, with an inner diameter of 140 μm. Figure 2B shows the tilted and side view (inset) scanning electron microscopy (SEM) images of the corresponding fabricated device, demonstrating agreement between the experimental and simulated values. The results of Fig. 2 (A and B) are representative of those obtained throughout these studies, thus providing support for the reliability of the quasi-dynamic FEM (details of the modeling can be found in section S4).

The strength of magnetic induction for the microcoil technology described here clearly depends on their current handling ability. However, increasing current also raises the level of Joule heating, and the magnitude of the temperature rise depends primarily on the out-of-plane structural details. The physical dimensions of the rolled-up coil structure, such as the inner diameter and width of the metal strip and the layered structure design, play crucial roles in determining the rate at which temperature rises with increasing current. Joule heating in the copper strips was simulated using COMSOL by applying a range of currents from 100 to 225 mA (details of the model can be found in section S5). Shown in Fig. 2C is the modeled electrical-thermal profile of a representative S-RuM 3D coil architecture sitting on a sapphire substrate at an input current of 175 mA. As can be seen, there is a temperature distribution along the axial direction, with the uppermost sections of the inductor (furthest from the substrate) being the hottest, whereas the temperature distribution is uniform across the entire tube length. Figure 2D plots the modeled maximum temperature rise (taken along the dotted line at the top surface of the tube inductor in Fig. 2C) together with the experimental value from infrared (IR) measurements, as a function of input current in the range of 50 to 250 mA. The modeled and the experimental data do show a similar trend, i.e., increasing temperature rise with increasing current, but the modeled values clearly overestimate the temperature rise, and the discrepancy becomes larger at higher input current level. However, as shown in the inset of Fig. 2D, the match is excellent between the measured DC resistance of the 3D coil as a function of input current and the estimated values from the simulation. This validates the modeled Joule heating contribution because the rise in resistance with current can be attributed to the self-heating within the 3D coil at these current values (100 to 225 mA) and the positive temperature coefficient of resistance of copper. The overall thermal transport model from COMSOL needs to be refined to have an accurate estimation of all the thermal dissipation mechanism of the material system of S-RuM architecture, including thermal radiation, air convection, etc. Nonetheless, the model helps guide the thermal design of the S-RuM 3D coil architecture under a wide range of biasing conditions, along with input from IR temperature measurements for various structures.

Once the structural dimension and current handling ability are determined, the strength of magnetic induction can then be estimated by the FEM electromagnetic modeling for S-RuM 3D coil architectures. Because the metal strips used in the present S-RuM coil designs are much wider than the previously reported S-RuM radio frequency (RF) devices, the skin effect must be taken into consideration in the electromagnetic (EM) simulation to better describe the dependence of the resistivity on frequency, especially at HF. We note that for spherical Fe₃O₄ nanoparticles (d ≈ 10 nm) dispersed in a fluid, superparamagnetic behavior emerges, which is distinctly advantageous in HF applications because the single domain nanoparticle magnetic moments of the single-domain nanoparticles reorient more rapidly than their ferromagnetic counterparts because of Néel relaxation and Brownian motion. Furthermore, the nanoparticles require a magnetic field of lower magnitude to be applied for magnetization, and they do not suffer from the same losses as thin-film magnetic materials (33–35). Because detailed analytical or FEM modeling of the magnetic behavior of ferrofluids is problematic, in this work, the relationship between important ferrofluid material properties [energy loss due to the ferromagnetic resonance (FMR) and permeability] and frequency is first derived from the measured S parameters of a given ferrofluid material, and those for the ferrofluid loaded into a S-RuM coil with known geometry and dimensions. A model based on the experimentally established relationship is then integrated into the FEM S-RuM coil EM model to predict the performance of other designs (see details in section S6). Figure 2E shows the modeled magnetic flux density distribution of a representative two-cell three-turn S-RuM structure with an inner diameter of 140 μm both with and without the ferrofluid core, respectively. The maximum intensity of the magnetic induction inside the tubular structure is simulated accordingly with an input signal power of 0.813 W at 10 MHz with DC resistance of 7.7 ohms, which only increases the maximum operating temperature of the structure by 40°C (see details in section S7). The calculations show a maximum magnetic induction of 0.873 mT with air core and 1.9× improvement of the relative permeability with ferrofluid core. Figure 2F shows the corresponding raw S₁₁ parameter between the modeled and the measured data in the Smith chart up to a frequency of 20 GHz and 500 MHz with the air-core and ferrofluid-core devices, respectively. In addition, the variation of the relative permeability and the FMR energy loss of the inductors with frequency are shown for two ferrofluid structures. The latter is represented as a resistance, and the results are given in a frequency range of 30 to 100 MHz where the cross-talk capacitance (19) between turns can be ignored. Structure 1 is the two-cell three-turn structure shown in Fig. 2E and the upper figure in Fig. 2F. Structure 2 is a four-cell 14-turn structure that has a larger volume to store ferrofluid. Moreover, structure 2 was filled three times, with time in between to dry the ferrofluid. As a result, structure 2 shows ~2× improvement of the relative permeability of the core material, as shown in the lower figure in Fig. 2F, indicating that multifilling effectively increases the volume of the magnetic nanoparticles. However, the FMR resistance of structure 2 is much larger than that of structure 1, which can be attributed to the more serious interparticle interaction loss (e.g., collision and friction) in the aggregated polydomain magnetic material.

Representative S-RuM 3D strong magnetic induction devices

DC/DC power converters are widely used in Internet of Things and cyber-physical system units to regulate the input levels of the voltage supply from a few volts to tens of volts. Following Moore’s law, the transistor node has been scaling down toward 3 nm, resulting in highly integrated logic control circuit; however, the bulky power inductors still dominate the overall size of power converters because of the extreme difficulty in scalability. The key specification requirements in the design and fabrication of compact power converters become more stringent. On the other hand, the switching frequency of emerging power converters has been pushed to as high as tens to hundreds of megahertz, which substantially reduces the inductance requirements down to tens to hundreds of nanohenries. Whether the power system in packaging (PSiP) or on-chip (PSoC) approach is used for power inductor design and fabrication, the planar spiral structure has almost always been the single best choice because of the prerequisite compatibility with planar semiconductor processing technologies. However, low inductance density and serious substrate parasitic effects, such as eddy current and parasitic capacitance effects associated with the planar design and fabrication regime, inherently limit the inductance density and the switching frequency.

With the S-RuM strong magnetic induction schemes outlined above, S-RuM power inductors with diverse geometry parameters and wide-ranging electrical performance can be realized in many different 2D layout designs using a variety of core materials. Here, we present five batches of S-RuM power inductors with Cu thicknesses of 150 to 225 nm and different numbers of cells, and each cell has the same width of 250 μm but different lengths scaled from 0.8 to 10 mm. Summarized in Fig. 3A is the length comparison of all batches before rolling with the scale indicated on the left y axis. The corresponding side-view SEM images of fully rolled-up batch 1, 2, and 4 devices, with the number of turns indicated, are shown on the right side. The most number of turns is obtained from the batch 5 design, which is ~23 turns with an inner diameter of ~140 μm with the total rolling length of each Cu strip of 1 cm.

A critical enabler of the scaling scheme to increase the number of turns, by rolling-up centimeter and beyond long strips, is to use XeF₂ dry etch to release the Ge sacrificial layer instead of using wet etching solutions. The dry etching releasing method produces a rolling speed of ~750 μm/min (movies S3 and S4), which is over 500 times faster compared with any wet etching methods previously reported (28). The fast rate provides the rolling momentum for a much heavier load such as Cu strips with hundreds of nanometers in thickness, hundreds of micrometers in width, and centimeters in length. In addition, the superfast dry releasing speed bypasses the overwhelming pinhole issues that used to trigger detouring and failure during the rolling progress even when the rolling length was under 1 mm long.

Figure 3 (B to D) demonstrates the three-step core-filling process. First, the ferromagnetic fluid is drawn into a 28-gauge micropipette by capillary action, with a droplet hanging onto the tip of the pipette. Second, the pipette is lowered until it is nearly leveled with the inductor tube and is moved toward the tube to make contact. Last, once the contact is made between the inductor and the micropipette, the ferrofluid inside the pipette is drawn into the inductor tube, which has an even smaller diameter, by capillary action. Figure 3E shows an optical image of a six-cell, 21-turn inductor before and after being core-filled with the ferromagnetic fluid. For visual purpose, a single inductor device sitting on a piece of sapphire wafer was cut off from the rest of the inductor tubes in the array by a laser cutter and placed beside a U.S. penny for size comparison in Fig. 3F. A 3 × 3 array of fully fabricated and core-filled two-cell S-RuM inductor tubes is shown in Fig. 3G.

The measured frequency dependence of the inductance and the Q factor of all batches of devices without the core filled is shown in Fig. 4 (A and B) (see detailed structural dimension of all batches in section S8). Just as it was the case for S-RuM RF inductors reported previously (19, 28), inductance shows a superlinear relationship with the number of turns. The batch 5.2 device has an inductance as large as 140 nH at 10 MHz, a maximum working frequency at 2 GHz, and a maximum Q factor of 2.3 at 250 MHz. Compared with the batch 1 device, the inductance per cell is improved by 46.7× by increasing the length of the Cu strip by 12.5×. The resonance frequency continues to drop from batch 1 (>20 GHz) to batch 5.2 (>1.3 GHz), but with rapidly decreasing rate because of the weakened influence of cross-talk coupling capacitance between turns (19). This implies that, unlike the planar counterparts, the operating frequency of S-RuM power inductors can still be high even when larger inductance is obtained. The maximum Q factor at 250 MHz is ~2.85, improved by 11.4× from the previously reported best result of ~0.25 (30), because vapor-phase releasing enabled large cross-sectional area Cu strip rolling. Once the air core is filled by ferrofluid, the operating frequency drops because of the FMR of the available iron oxide nanoparticles used for this study. To better study the performance of S-RuM power inductors at ultralow frequency below 10 MHz, the data collected from Keithley Clarius and Copper Mountain Technologies vector network analyzer (CMT VNA) are combined to show the relationship between the inductance and the Q factor versus frequency (Fig. 4C). It can be seen that the inductance reaches 1.24 μH at 10 KHz, and the maximum Q factor is 0.9 at 10 MHz for the batch 5.2 device. The corresponding inductance area and volume density are 3 μH/mm² and 23 μH/mm³, respectively. Compared with the air-core devices, the maximum inductance and Q factor enhancement due to ferrofluid core filling at LF are ~9× and 3×, respectively. The improvement of the Q factor is not as much as that of inductance because of the FMR loss. To examine whether the air core is filled by the ferrofluid to the limit, the batch 4.2 device was filled and measured three times. Slight improvement was shown after the second filling, but nearly the same inductance (and Q factor) versus frequency was found between the second and third rounds of filling, as shown in Fig. 4 (C and D), indicating that two-time core filling is sufficient for this case. Figure 4E shows the resonant frequency of the batch 4.2 and 5.2 devices, which are both above 500 MHz. Compared with the bulk iron oxide material, monodomain iron oxide nanoparticle has much large FMR frequency, implying an important application when high power and HF are both required. Figure 4F benchmarks the inductance area density versus the operating frequency, plotted on a double log scale, of the S-RuM power inductor devices against state-of-the-art planar counterparts from literature as cited. Clearly, the S-RuM devices show much higher inductance density across the entire frequency range. Furthermore, they demonstrate unique capability in HF operation, which fits the need of the next generation of power device with a switching frequency range of 100 to 500 MHz. The S-RuM power inductor performance can be further improved by scaling the rolling length of the metal strips longer, wider, and with better conductivity.

Current handling ability is determined by measuring the thermal profile along the axial direction on top of the device using an IR thermometer. Shown in Fig. 4G is the thermal map of a batch 4 air-core device. The background temperature was set to 50°C to obtain a reasonable signal-to-noise ratio. The input current was set to 250 mA with measured maximum temperature of ~400°C without destroying the device (see details in section S7). This indicates that the maximum power the batch 4 S-RuM power inductor can handle is at least 0.94 W, with corresponding power density of ~8.5 W/mm² and a simulated maximum magnetic induction of 12 mT in the core at 10 MHz.

On the basis of the above representative demonstration, it is clear that the S-RuM architecture is unique in that it enables the concentration of a magnetic field through the center axis of a hollow cavity, which can support a fluid and confine it through capillary action. This feature allows the integration of a unique class of core materials, ferrofluids, which can be optimized for higher frequencies than what is possible with planar-deposited magnetic alloys. Theoretically, the thermal conductivity of the oil-based ferrofluid is much larger than that of air, which implies a positive impact on helping distributing the Joule heating.