Skip to main content
SpringerLink
Log in

Circuits and magnetics co-design for ultra-thin vertical power delivery: A snapshot review

  • Review
  • Published:
MRS Advances Aims and scope Submit manuscript

Abstract

This paper presents a comprehensive overview of circuits and magnetics co-design for point-of-load voltage regulator modules (VRMs), which delivers power to microprocessors such as CPUs and GPUs that require low voltages and high currents. We examine the recent shift from the 12-volt to the 48-volt architecture to achieve higher efficiency and power density, and discuss the challenges associated with direct 48-volt power conversion to the point of load below 1 volt. Power delivery architectures for 48-volt VRMs are systematically reviewed and categorized, with emphasis placed the opportunities and challenges of circuits–magnetics co-design for energy efficiency, power density, and control bandwidth. Magnetic components, such as inductors and transformers, are essential components in VRMs, and a discussion on available materials and their limitations is provided. A comprehensive design approach for ultra-thin vertical multiphase coupled magnetics, including modeling magnetic core losses with machine learning, is detailed. This review paper aims to disseminate the progress and challenges in circuit and magnetics co-design, while outlining a vision for future advancements in device technology, magnetic materials, and packaging techniques including hybrid-switched-capacitor and coupled magnetics technologies.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability

Not applicable.

References

  1. K. Radhakrishnan, M. Swaminathan, B.K. Bhattacharyya, Power delivery for high-performance microprocessors—challenges, solutions, and future trends. IEEE Trans. Components Packaging Manuf. Technol. 11(4), 655–671 (2021). https://doi.org/10.1109/TCPMT.2021.3065690

    Article  CAS  Google Scholar 

  2. R. Dennard, F. Gaensslen, H.N. Yu, V. Rideout, E. Bassous, A. LeBlanc, Design of ion-implanted MOSFET’s with very small physical dimensions. IEEE J. Solid-State Circ. 9(5), 256–268 (1974). https://doi.org/10.1109/JSSC.1974.1050511

    Article  ADS  Google Scholar 

  3. D. Disney, Z.J. Shen, Review of silicon power semiconductor technologies for power supply on chip and power supply in package applications. IEEE Trans. Power Electron. 28(9), 4168–4181 (2013). https://doi.org/10.1109/TPEL.2013.2242095

    Article  ADS  Google Scholar 

  4. C.O. Mathúna, N. Wang, S. Kulkarni, S. Roy, Review of integrated magnetics for power supply on chip (PwrSoC). IEEE Trans. Power Electron. 27(11), 4799–4816 (2012). https://doi.org/10.1109/TPEL.2012.2198891

    Article  ADS  Google Scholar 

  5. K. Rupp, 50 years of microprocessor trend data. https://github.com/karlrupp/microprocessor-trend-data

  6. Preventing chips from burning up during test. https://semiengineering.com/preventing-chips-from-burning-up-during-test

  7. P. Sandri, Increasing hyperscale data center efficiency: a better way to manage 54–V48-V-to-point-of-load direct conversion. IEEE Power Electron. Magaz. 4(4), 58–64 (2017). https://doi.org/10.1109/MPEL.2017.2760113

    Article  Google Scholar 

  8. A. Bindra, Driven by density, efficiency at low cost, power integration reaches new heights: PSiPs and PwrSoCs are growing faster than the traditional power supplies. IEEE Power Electron. Magaz. 9(1), 14–19 (2022). https://doi.org/10.1109/MPEL.2022.3141293

    Article  Google Scholar 

  9. S. Jiang, S. Saggini, C. Nan, X. Li, C. Chung, M. Yazdani, Switched tank converters. IEEE Trans. Power Electron. 34(6), 5048–5062 (2019). https://doi.org/10.1109/TPEL.2018.2868447

    Article  ADS  Google Scholar 

  10. St 48v power conversion turnkey solution for servers. https://www.st.com/content/ccc/resource/

  11. Max16610: Switched Tank Converter (STC) controller with integrated drivers. https://www.maximintegrated.com/en/products/interface/controllers-expanders/MAX16610.html

  12. Lmg5200: 48 to 1 v or 40 a single-stage converter reference design. https://www.ti.com/lit/ug/tiduc72a/tiduc72a.pdf

  13. 48v datacenter solutions DC/DC power conversion for datacenter, open compute & AI applications. https://media.monolithicpower.com/48v-solution-product-brochure.pdf

  14. Infineon ZSC topology. https://www.infineon.com/cms/en/applications/communication/computing-and-data-storage/48v-power-distribution/zsc-topology/

  15. Power stamp alliance. https://powerstamp.org

  16. Vicor, PRMTM regulator high efficiency converter. PRM48BH480x250A00 (2020). Rev. 1.7

  17. Vicor, VTMTM current multiplier sine amplitude converterTM (SACTM). VTM48MP010x107AA1 (2017). Rev. 1.5

  18. C.R. Sullivan, B.A. Reese, A.L.F. Stein, P.A. Kyaw, On size and magnetics: why small efficient power inductors are rare. In: 2016 international symposium on 3d power electronics integration and manufacturing (3D-PEIM) pp. 1–23 (2016). https://doi.org/10.1109/3DPEIM.2016.7570571

  19. J. Li, A. Stratakos, A. Schultz, C. Sullivan, Using coupled inductors to enhance transient performance of multi-phase buck converters. Nineteenth Annu. IEEE Appl. Power Electron. Conf. Exposition 2, 1289–1293 (2004). https://doi.org/10.1109/APEC.2004.1295989

    Article  Google Scholar 

  20. P.L. Wong, P. Xu, P. Yang, F. Lee, Performance improvements of interleaving VRMs with coupling inductors. IEEE Trans. Power Electron. 16(4), 499–507 (2001). https://doi.org/10.1109/63.931059

    Article  ADS  Google Scholar 

  21. Q. Li, Y. Dong, F.C. Lee, D.J. Gilham, High-density low-profile coupled inductor design for integrated point-of-load converters. IEEE Trans. Power Electron. 28(1), 547–554 (2013). https://doi.org/10.1109/TPEL.2012.2196525

    Article  ADS  CAS  Google Scholar 

  22. W. Huang, B. Lehman, Analysis and verification of inductor coupling effect in interleaved multiphase DC-DC converters. IEEE Trans. Power Electron. 31(7), 5004–5017 (2016). https://doi.org/10.1109/TPEL.2015.2479191

    Article  Google Scholar 

  23. M. Chen, C.R. Sullivan, Unified models for coupled inductors applied to multiphase PWM converters. IEEE Trans. Power Electron. 36(12), 14155–14174 (2021). https://doi.org/10.1109/TPEL.2021.3088083

    Article  ADS  Google Scholar 

  24. H. Li, S.R. Lee, M. Luo, C.R. Sullivan, Y. Chen, M. Chen, Magnet: a machine learning framework for magnetic core loss modeling, pp. 1–8 (2020). https://doi.org/10.1109/COMPEL49091.2020.9265869

  25. H. Li, D. Serrano, T. Guillod, S. Wang, E. Dogariu, A. Nadler, M. Luo, V. Bansal, N.K. Jha, Y. Chen, C.R. Sullivan, M. Chen, How magnet: machine learning framework for modeling power magnetic material characteristics. IEEE Trans. Power Electron. 38(12), 15829–15853 (2023). https://doi.org/10.1109/TPEL.2023.3309232

    Article  ADS  Google Scholar 

  26. M.H. Ahmed, C. Fei, F.C. Lee, Q. Li, Single-stage high-efficiency 48/1 V sigma converter with integrated magnetics. IEEE Trans. Industrial Electron. 67(1), 192–202 (2020). https://doi.org/10.1109/TIE.2019.2896082

    Article  Google Scholar 

  27. A. Kumar, K.K. Afridi, Single-stage isolated 48V-to-1.8V point-of-load converter utilizing an impedance control network for wide input range operation, pp. 2003–2009 (2017). https://doi.org/10.1109/ECCE.2017.8096402

  28. J. Baek, Y. Elasser, K. Radhakrishnan, H. Gan, J.P. Douglas, H.K. Krishnamurthy, X. Li, S. Jiang, C.R. Sullivan, M. Chen, Vertical stacked LEGO-PoL CPU voltage regulator. IEEE Trans. Power Electron. 37(6), 6305–6322 (2022). https://doi.org/10.1109/TPEL.2021.3135386

    Article  ADS  Google Scholar 

  29. Y. Elasser, J. Baek, K. Radhakrishnan, H. Gan, J.P. Douglas, H.K. Krishnamurthy, X. Li, S. Jiang, V. De, C.R. Sullivan, M. Chen, Mini-LEGO CPU voltage regulator. IEEE Trans. Power Electron. (2024). https://doi.org/10.1109/TPEL.2023.3337171

    Article  Google Scholar 

  30. N.M. Ellis, R.A. Abramson, R. Mahony, R.C.N. Pilawa-Podgurski, The symmetric dual inductor hybrid (SDIH) converter for direct 48V-to-PoL conversion. IEEE Trans. Power Electron. (2023). https://doi.org/10.1109/TPEL.2023.3259949

    Article  Google Scholar 

  31. G.S. Seo, R. Das, H.P. Le, Dual inductor hybrid converter for point-of-load voltage regulator modules. IEEE Trans. Ind. Appl. 56(1), 367–377 (2020). https://doi.org/10.1109/TIA.2019.2941945

    Article  CAS  Google Scholar 

  32. R.C.N. Pilawa-Podgurski, D.J. Perreault, Merged two-stage power converter with soft charging switched-capacitor stage in 180 nm CMOS. IEEE J. Solid-State Circ. 47(7), 1557–1567 (2012). https://doi.org/10.1109/JSSC.2012.2191325

    Article  ADS  Google Scholar 

  33. D.M. Giuliano, M.E. D’Asaro, J. Zwart, D.J. Perreault, Miniaturized low-voltage power converters with fast dynamic response. IEEE J. Emerg. Select. Topics Power Electron 2(3), 395–405 (2014). https://doi.org/10.1109/JESTPE.2014.2331671

    Article  Google Scholar 

  34. Y. Chen, P. Wang, H. Cheng, G. Szczeszynski, S. Allen, D.M. Giuliano, M. Chen, Virtual intermediate bus CPU voltage regulator. IEEE Trans. Power Electron. 37(6), 6883–6898 (2022). https://doi.org/10.1109/TPEL.2021.3130213

    Article  ADS  Google Scholar 

  35. Y. Zhu, T. Ge, Z. Ye, R.C. Pilawa-Podgurski, A Dickson-squared hybrid switched-capacitor converter for direct 48 V to point-of-load conversion, pp. 1272–1278 (2022). https://doi.org/10.1109/APEC43599.2022.9773567

  36. P. Wang, Y. Chen, G. Szczeszynski, S. Allen, D.M. Giuliano, M. Chen, MSC-PoL: hybrid GaN-Si multistacked switched-capacitor 48-V PwrSiP VRM for chiplets. IEEE Trans. Power Electron. 38(10), 12815–12833 (2023). https://doi.org/10.1109/TPEL.2023.3293022

    Article  ADS  Google Scholar 

  37. N.M. Ellis, R.C. Pilawa-Podgurski, A symmetric dual-inductor hybrid dickson converter for direct 48V-to-PoL conversion, pp. 1267–1271 (2022). https://doi.org/10.1109/APEC43599.2022.9773452

  38. K. Nishijima, K. Harada, T. Nakano, T. Nabeshima, T. Sato, Analysis of double step-down two-phase buck converter for VRM, pp. 497–502 (2005). https://doi.org/10.1109/INTLEC.2005.335149

  39. M. Halamicek, T. McRae, A. Prodić, Cross-coupled series-capacitor quadruple step-down buck converter, pp. 1–6 (2020). https://doi.org/10.1109/APEC39645.2020.9124412

  40. M. Ursino, R. Rizzolatti, G. Deboy, S. Saggini, K. Zufferli, High density hybrid switched capacitor sigma converter for data center applications. 2022 IEEE Appl. Power Electron. Conf. Exposition (2022). https://doi.org/10.1109/APEC43599.2022.9773659

    Article  Google Scholar 

  41. A. Dago, M. Leoncini, S. Saggini, S. Levantino, M. Ghioni, Hybrid resonant switched-capacitor converter for 48–3.4 V direct conversion. IEEE Trans. Power Electron. (2022). https://doi.org/10.1109/TPEL.2022.3186790

    Article  Google Scholar 

  42. Z. Ye, R.A. Abramson, T. Ge, R.C.N. Pilawa-Podgurski, Multi-resonant switched-capacitor converter: achieving high conversion ratio with reduced component number. IEEE Open J. Power Electron. 3, 492–507 (2022). https://doi.org/10.1109/OJPEL.2022.3181338

    Article  Google Scholar 

  43. C. Steinmetz, On the law of hysteresis. Proc. IEEE 72(2), 197–221 (1984). https://doi.org/10.1109/PROC.1984.12842

    Article  Google Scholar 

  44. D. Serrano, H. Li, S. Wang, T. Guillod, M. Luo, V. Bansal, N.K. Jha, Y. Chen, C.R. Sullivan, M. Chen, Why magnet: quantifying the complexity of modeling power magnetic material characteristics. IEEE Trans. Power Electron. 38(11), 14292–14316 (2023). https://doi.org/10.1109/TPEL.2023.3291084

    Article  ADS  Google Scholar 

  45. H. Li, D. Serrano, S. Wang, M. Chen, Magnet-AI: Neural network as datasheet for magnetics modeling and material recommendation. IEEE Trans. Power Electron. 38(12), 15854–15869 (2023). https://doi.org/10.1109/TPEL.2023.3309233

    Article  ADS  Google Scholar 

  46. E. Stenglein, B. Kohlhepp, D. Kübrich, M. Albach, T. Dürbaum, GaN-half-bridge for core loss measurements under rectangular AC voltage and dc bias of the magnetic flux density. IEEE Trans. Instrum. Measure 69(9), 6312–6321 (2020). https://doi.org/10.1109/TIM.2020.2972140

    Article  ADS  CAS  Google Scholar 

  47. V. Thottuvelil, T. Wilson, H. Owen, High-frequency measurement techniques for magnetic cores. IEEE Trans. Power Electron. 5(1), 41–53 (1990). https://doi.org/10.1109/63.45998

    Article  ADS  Google Scholar 

  48. J. Li, T. Abdallah, C. Sullivan, in: Conference record of the 2001 IEEE industry applications conference. 36th IAS annual meeting (Cat. No. 01CH37248), 4, pp. 2203–2210. (2001). https://doi.org/10.1109/IAS.2001.955931

  49. R.P. Davies, C. Cheng, N. Sturcken, W.E. Bailey, K.L. Shepard, Coupled inductors with crossed anisotropy \({\rm cozrta/sio}_{2}\) multilayer cores. IEEE Trans. Magn. 49(7), 4009–4012 (2013). https://doi.org/10.1109/TMAG.2013.2237892

    Article  ADS  CAS  Google Scholar 

  50. J. Baek, Y. Elasser, M. Chen, MIPS: multiphase integrated planar symmetric coupled inductor for ultrathin VRM. IEEE Trans. Power Electron. 38(5), 5609–5614 (2023). https://doi.org/10.1109/TPEL.2023.3236152

    Article  ADS  Google Scholar 

  51. W.J. Lambert, M.J. Hill, K. Radhakrishnan, L. Wojewoda, A.E. Augustine, Package inductors for intel fully integrated voltage regulators. IEEE Trans. Components Packaging Manuf. Technol. 6(1), 3–11 (2016). https://doi.org/10.1109/TCPMT.2015.2505665

    Article  Google Scholar 

  52. T. Sen, Y. Elasser, M. Chen, Origami inductors: foldable 3-D polyhedron air-coupled inductors for mhz power conversion, pp. 397–404 (2023). https://doi.org/10.1109/APEC43580.2023.10131510

  53. S. Prabhakaran, C. Sullivan, T. O’Donnell, M. Brunet, S. Roy, in: 2004 IEEE 35th annual power electronics specialists conference (IEEE Cat. No.04CH37551), vol. 6, pp. 4467–4472 (2004). https://doi.org/10.1109/PESC.2004.1354790

  54. N. Sturcken, E.J. O’Sullivan, N. Wang, P. Herget, B.C. Webb, L.T. Romankiw, M. Petracca, R. Davies, R.E. Fontana, G.M. Decad, I. Kymissis, A.V. Peterchev, L.P. Carloni, W.J. Gallagher, K.L. Shepard, A 2.5D integrated voltage regulator using coupled-magnetic-core inductors on silicon interposer. IEEE J. Solid-State Circ. 48(1), 244–254 (2013). https://doi.org/10.1109/JSSC.2012.2221237

    Article  ADS  Google Scholar 

  55. N. Sturcken, R. Davies, H. Wu, M. Lekas, K. Shepard, K.W. Cheng, C.C. Chen, Y.S. Su, C.Y. Tsai, K.D. Wu, J.Y. Wu, Y.C. Wang, K.C. Liu, C.C. Hsu, C.L. Chang, W.C. Hua, A. Kalnitsky, Magnetic thin-film inductors for monolithic integration with CMOS, pp. 11.4.1–11.4.4 (2015). https://doi.org/10.1109/IEDM.2015.7409676

  56. K. Bharath, K. Radhakrishnan, M.J. Hill, P. Chatterjee, H. Hariri, S. Venkataraman, H.T. Do, L. Wojewoda, S. Srinivasan, in, 2021 IEEE 71st electronic components and technology conference (ECTC), pp. 1286–1292 (2021). https://doi.org/10.1109/ECTC32696.2021.00208

  57. A.J. Hanson, J.A. Belk, S. Lim, C.R. Sullivan, D.J. Perreault, Measurements and performance factor comparisons of magnetic materials at high frequency. IEEE Trans. Power Electron. 31(11), 7909–7925 (2016). https://doi.org/10.1109/TPEL.2015.2514084

    Article  ADS  Google Scholar 

  58. P. Thakur, D. Chahar, S. Taneja, N. Bhalla, A. Thakur, A review on MnZn ferrites: synthesis, characterization and applications. Ceram. Int. 46(10), 15740–15763 (2020). https://doi.org/10.1016/j.ceramint.2020.03.287

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  59. L.G. Petrescu, M.C. Petrescu, V. Ionita, E. Cazacu, C.D. Constantinescu, Magnetic properties of manganese-zinc soft ferrite ceramic for high frequency applications. Materials 12(19), 3173 (2019). https://doi.org/10.3390/ma12193173

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  60. A. Costa, E. Tortella, M. Morelli, R. Kiminami, Synthesis, microstructure and magnetic properties of Ni-Zn ferrites. J. Magn. Magn. Mater. 256(1), 174–182 (2003). https://doi.org/10.1016/S0304-8853(02)00449-3

    Article  ADS  CAS  Google Scholar 

  61. Y. Zhu, Z. Ye, T. Ge, R. Abramson, R.C.N. Pilawa-Podgurski, A multi-phase cascaded series-parallel (CaSP) hybrid converter for direct 48 V to point-of-load applications, pp. 1973–1980 (2021). https://doi.org/10.1109/ECCE47101.2021.9596032

  62. M. Ursino, S. Saggini, S. Jiang, C. Nan, High density 48V-to-PoL VRM with hybrid pre-regulator and fixed-ratio buck, pp. 498–505 (2020). https://doi.org/10.1109/APEC39645.2020.9124561

  63. P.L. Wong, Q. Wu, P. Xu, B. Yang, F. Lee, Investigating coupling inductors in the interleaving QSW VRM. Fifteenth Annu. IEEE Appl. Power Electron. Conf. Exposition (Cat. No.00CH37058) 2, 973–978 (2000). https://doi.org/10.1109/APEC.2000.822807

  64. J. Li, C. Sullivan, A. Schultz, Coupled-inductor design optimization for fast-response low-voltage DC-DC converters. Seventeenth Annu. IEEE Appl. Power Electron. Conf. Exposition (Cat. No. 02CH37335) 2, 817–823 (2002). https://doi.org/10.1109/APEC.2002.989338

  65. Y. Elasser, J. Baek, C.R. Sullivan, M. Chen, Modeling and design of vertical multiphase coupled inductors with inductance dual model, pp. 1717–1724 (2021). https://doi.org/10.1109/APEC42165.2021.9487344

  66. Texas instruments, using the LMG5200POLEVM-10 48V to point of load EVM. LMG5200POLEVM (2016). Rev. (Oct 2017)

  67. R. Das, G.S. Seo, D. Maksimovic, H.P. Le, An 80-W 94.6%-efficient multi-phase multi-inductor hybrid converter (2019). https://doi.org/10.1109/APEC.2019.8721952

  68. Z. Ye, R.A. Abramson, Y.L. Syu, R.C.N. Pilawa-Podgurski, MLB-PoL: a high performance hybrid converter for direct 48 V to point-of-load applications, pp. 1–8 (2020). https://doi.org/10.1109/COMPEL49091.2020.9265870

  69. Bel-Power, Main & satellite power stamp 48V-to-PoL isolated DC-DC converters. https://www.belfuse.com/resources/datasheets/powersolutions/ds-bps-48-v-to-pol-power-stamp.pdf

  70. J Zhu, D. Maksimovic, 48 V-to-1 V transformerless stacked active bridge converters with merged regulation stage (2020). https://doi.org/10.1109/COMPEL49091.2020.9265671

  71. H. Cao, X. Yang, C. Xue, L. He, Z. Tan, M. Zhao, Y. Ding, W. Li, W. Qu, A 12-level series-capacitor 48–1V DC-DC converter with on-chip switch and GaN hybrid power conversion. IEEE J. Solid-State Circ. 56(12), 3628–3638 (2021). https://doi.org/10.1109/JSSC.2021.3104328

    Article  ADS  Google Scholar 

  72. Analog Devices, 54VIN dual 25A, single 50A \(\mu \) module regulator with digital power system management. LTM4664 (2021). Rev. B

  73. Y. Zhu, T. Ge, N.M. Ellis, L. Horowitz, R.C.N. Pilawa-Podgurski, A 500-A/48-to-1-V switching bus converter: a hybrid switched-capacitor voltage regulator with 94.7% peak efficiency and 464-W/in3 power density, pp. 1989–1996 (2023). https://doi.org/10.1109/APEC43580.2023.10131359

Download references

Acknowledgments

The authors would like to acknowledge the Semiconductor Research Corporation (SRC), Google LLC, Intel Corporation, pSemi, the ARPA-E CIRCUITS program, the ARPA-E DIFFERENTIATE program, and the Princeton SEAS Industrial Collaboration Fund.

Author information

Authors and Affiliations

  1. Princeton University, Princeton, NJ, 08540, USA

    Youssef Elasser, Haoran Li, Ping Wang & Minjie Chen

  2. Intel Corporation, Chandler, AZ, 10587, USA

    Jaeil Baek & Kaladhar Radhakrishnan

  3. Google LLC, Mountain View, CA, 94043, USA

    Shuai Jiang & Houle Gan

  4. IBM T. J. Watson Research Center, Yorktown Heights, NY, 10598, USA

    Xin Zhang

  5. pSemi, a Murata Company, San Diego, CA, 92121, USA

    David Giuliano

Authors
  1. Youssef Elasser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haoran Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ping Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jaeil Baek
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kaladhar Radhakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Shuai Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Houle Gan
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Xin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. David Giuliano
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Minjie Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Youssef Elasser or Minjie Chen.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Elasser, Y., Li, H., Wang, P. et al. Circuits and magnetics co-design for ultra-thin vertical power delivery: A snapshot review. MRS Advances 9, 12–24 (2024). https://doi.org/10.1557/s43580-023-00724-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/s43580-023-00724-w

Search

Navigation