Science Advances

Supplementary Materials

The PDFset includes:

  • Section S1. Detailed fabrication flow
  • Section S2. The “round corner” design of Cu strip
  • Section S3. Detailed core-filling method
  • Section S4. Detailed mechanical FEM for inner diameter estimation
  • Section S5. Electrothermal modeling of S-RuM architecture
  • Section S6. Electromagnetic FEM modeling of S-RuM architecture
  • Section S7. IR imaging of S-RuM architecture
  • Section S8. Structural dimension of all S-RuM power inductor samples
  • Section S9. HF measurement details of S-RuM power inductors
  • Fig. S1. Mask-level depiction of the planar inductors.
  • Fig. S2. Capillary core-filling material and method for S-RuM architecture.
  • Fig. S3. Electrical-thermal modeling of S-RuM architectures.
  • Fig. S4. Electromagnetic FEM modeling of S-RuM architecture skin effect.
  • Fig. S5. LF (<~100 MHz) equivalent circuit of S-RuM architecture with ferrofluid core with enhanced inductance and introduced additional loss from FMR represented as LFL and RFMR, respectively.
  • Fig. S6. The complete FEM model in HFSS to simulate the S parameters and the intensity of magnetic induction in the core of the S-RuM architecture.
  • Fig. S7. IR imaging of S-RuM architectures.
  • Fig. S8. Temperature profiles measured across the white dotted line of the exemplary structure shown in Fig. 2E (also the batch 2 device) with DC current of 325 mA.
  • Fig. S9. Open-through de-embedding patterns and their corresponding lumped equivalent circuits.
  • Fig. S10. Mathematical procedure to do the open-through de-embedding.
  • Table S1. Material property set in FEM modeling simulation.
  • Table S2. Parameters for COMSOL simulations.
  • Table S3. Primary dimensional parameters of all batches.

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Other Supplementary Material for this manuscript includes the following:

  • Movie S1 (.mp4 format). Ferrofluid filled into a short S-RuM architecture.
  • Movie S2 (.mp4 format). Ferrofluid filled into a long S-RuM architecture.
  • Movie S3 (.mp4 format). The rolling progress of a 1-cm-long S-RuM architecture observed with 10× real speed.
  • Movie S4 (.mp4 format). The rolling progress of 1.6-mm-long S-RuM architecture array observed with 10× real speed.

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