Fig. 1: Scaling laws for planar and three-dimensional microinductors and experimental realization of RuMi inductors.
a Schematic of a conductor of length l configured as microinductors in various geometries. In each pair, the first configuration (cases 1, 3, and 5) shows the pure conductor (yellow) as a straight line, a 2D spiral, and a 3D wound structure, respectively, while the second (cases 2, 4, and 6) depicts the corresponding configuration with an additional magnetic layer (blue). b, c Calculated self-inductance and mutual inductance (b) and inductance density (c) versus conductor length for cases 1–6. d Schematic of the proposed RuMi inductor with 6 coil cells rolled up from a planar meander configuration. The equivalent circuit model is shown with Lcell, Rcell and Ccell as the inductance, resistance and capacitance of a single coil cell, Cgap and Mgap as the capacitance and the mutual inductance between the adjacent coil cells, Rs and Cs as the parasitic resistance and capacitance of the substrate, respectively. e Electron microscope image of a fabricated 6-cell RuMi inductor. Scale bar, 100 μm. f Optical image of an array of 40 RuMi inductors. Inset: Optical image of a single RuMi inductor cut from the wafer and placed at the tip of a nipper. Scale bars, 1 mm. g Measured inductance and the Q-factor for 4-cell and 6-cell RuMi inductors with a rolling length of 10 mm. Inset: Optical images of the corresponding 4-cell and 6-cell RuMi inductors. Scale bar, 500 μm. Source data are provided as a Source Data file.
