Additive Manufacturing of Magnetic Components for Heterogeneous Integration

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1 Additiv Manufacturing of Magntic Componnts for Htrognous Intgration Yi Yan 1, 2, Lanbing Liu 1, Chao Ding 1, Luu Nguyn 3, Jim Moss 3, Yunhui Mi 4 1, 4, 5, and Guo-Quan Lu 1 Dpartmnt of Matrials Scinc and Enginring, Virginia Tch, Blacksburg, VA USA 2 Cntr for Powr Elctronics Systms, Virginia Tch, Blacksburg, VA USA 3 Txas Instrumnts Inc., 2900 Smiconductor Driv, Santa Clara, CA USA 4 School of Matrials Scinc and Enginring, Tianjin Univrsity, Tianjin, China 5 Th Bradly Dpartmnt of Elctrical and Computr Enginring, Virginia Tch, Blacksburg, VA USA addrss:gqlu@vt.du Abstract In an ffort to simplify th procss of intgrating magntic componnts to powr lctronics circuits, an additiv manufacturing (AM) procss, or commonly known as 3Dprinting, for fabricating magntic componnts is studid in this work. A commrcial multi-xtrudr past-xtrusion 3D printr was valuatd for making magntic componnts. W dvlopd two matrial systms for printing magntic cors: (1) curabl powdrd iron past systm; and (2) sintrabl frrit systm. W usd commrcial nanosilvr past for th conductiv winding. A half pic of constant-flux inductor (CFI) and a planar inductor wr fabricatd in this study. magntic cors and lctrical conductor windings that mak up magntic componnts ar fabricatd sparatly in multipl, complx stps [5-7]. For xampl, to mak a soft frrit inductor, th cor is firstly formd by a high-prssur powdr-compaction procss followd by sintring at high tmpraturs (typically > 900 o C), and thn coppr wirs ar hand-wound around th cor. This mthod of fabrication rsults in bulky parts, limits th bttr dsign of th magntic componnts, and is incompatibl with othr procsss usd in assmbly of th circuits, which lavs magntics intgration to rmain as a challng in th fild of PE. For th half pic CFI, 3D-printing was usd with nanosilvr past and low-tmpratur curabl powdrd iron past. Th printd winding was sintrd at 250 o C for 30 minuts firstly and thn magntic past was printd to covr th sintrd winding. Th magntic past was curd at 230 o C for on hour without any xtrnal prssur to form th structur. Two printd pics wr connctd to form th full siz CFI. Inductanc of th CFI was masurd to b about 3.5 µh. Th DC rsistanc of th winding was 59 mω. For th planar inductor, 3D printing was usd with nanosilvr past and high-tmpratur sintrabl frrit past. It was sintrd at 920 o C for 14 hours without any xtrnal prssur to form th structur. Th inductanc of th planar inductor was masurd to b about 792 nh. Th DC rsistanc of th winding was 15 mω. Microstructurs of th printd inductors wr xamind by scanning lctron microscopy (SEM). Both th winding and cor magntic proprtis can b improvd by adjusting th fd past formulations and thir flow charactristics and fintuning th printr paramtrs. Kywords: additiv manufacturing; powr lctronics intgration; magntic componnts; magntic pasts; htrognous intgration I. INTRODUCTION Today s powr lctronics (PE) circuits ar customdsignd and fabricatd by intrconncting discrt componnts of powr smiconductor dvics (silicon or futur WBG), capacitors, inductors, and transformrs [1-3]. Among all of ths componnts, magntic componnts (inductors and transformrs) ar usually th havist and largst ons [4]. As shown in Fig. 1, magntic componnts can tak up 50% of th circuit surfac ara. Nowadays, Fig. 1. Insid of a powr convrtr. Htrognous intgration of sparatly manufacturd componnts into a highr lvl assmbly nabls nhancd functionality and improvd oprating charactristics. Thrfor, htrognous intgration of magntic componnts has th potntial to furthr incras powr dnsity and fficincy in powr lctronic convrtrs [8]. On possibl way to fabricat th inductor/transformr into packag lvl for as of intgration of th componnts into a modul intgration procss is to us an additiv manufacturing (AM) procss for fabricating th magntics. AM is a layr-by-layr procss of making products and componnts from a digital modl. Its potntial has bn dmonstratd for applications in various industris. Som ky bnfits of AM ar shortr lad tims, mass customization, rducd parts count, mor complx shaps, lss matrial wast, and lowr lif-cycl nrgy us [9]. Rcntly, som rsarch groups xplord application of AM in powr lctronics. For xampl, Oak Ridg National Laboratory (ORNL) rsarchrs [10, 11] rportd in 2014 a 3D-printd aluminum hat sink and a plastic lad fram for a 10-kW powr invrtr and thn in 2016 a frrit E-cor with rlativ prmability of about 2; Wi Liang t al. [12] 3D-

2 printd a plastic structur as a mold for making a uniqu strling-silvr inductor; Proto-pasta [13] introducd an ironpowdr filld polylactic-acid (PLA) filamnt for us with a fusd-dposition-modl (FDM) 3D printr to mak magntic cors with rlativ prmability of about 1.5; and Yunqi Wang t al. [14] dvlopd a NiZn-frrit-filld ABS filamnt for th FDM printr with rlativ prmability of about 2. In 2016, our rsarch group firstly dmonstratd th fasibility of using a multi-xtrudr past-xtrusion 3D printr for procssing a slf-formulatd low-tmpratur curabl (< 250 o C) magntic past and a commrcial lowtmpratur (< 250 o C) sintrabl nanosilvr past invntd in our laboratory to fabricat a planar inductor and a toroid inductor. Howvr, th prformanc of th printd componnts was limitd by th formulation of th magntic past and th post-curing procss. Th rlativ prmability of th low-tmpratur curabl magntic past was about 10 [15, 16]. Aiming at flxibl fabrication and htrognous intgration of high prformanc magntic componnts, w stick to th mthod of using a multi-xtrudr past-xtrusion 3D printr to procss both magntic past and conductiv past into magntic componnts. W dvlopd two magntic past systms and applid to th 3D printr as fd matrials: a modifid low-tmpratur (< 250 o C) curabl iron-powdr past systm as wll as a high-tmpratur (> 900 o C) sintrabl frrit past systm. For th conductiv winding fd stock, w usd a commrcial nanosilvr past. Half pic of a constant-flux inductor (CFI) was 3D-printd by using th nanosilvr past and th modifid lowtmpratur curabl iron-powdr past. A planar inductor was 3D-printd by using th nanosilvr past and th hightmpratur (> 900 o C) sintrabl frrit past. Proprtis of th printd inductors, both th inductanc and DC winding rsistanc wr masurd. Microstructurs of th inductors wr also charactrizd by scanning lctron microscopy (SEM). (a) (b) Fig. 2. (a) Multi-xtrudr past-xtrusion 3D printr and (b) UV curing systm was affixd to th syring xtrudr. Prmalloy powdr (from ESPI Mtals) with an avrag particl siz of 12 μm, and th othr is flak-shapd Mtglas 2705M powdr with an avrag particl siz of 150 μm. Th composition of th past consists of 92 wt% of th magntic fillrs, 8 wt% of th monomr. Othr organic componnts, such as disprsant and solvnt wr addd to crat uniform suspnsions of th magntic fillrs in th organic systm. Fig. 3 is dmonstration of printing th iron-powdr past into a toroid shap. II. EQUIPMENT AND MATERIALS PREPARATION A. Commrcial multi-xtrudr past-xtrusion 3D printr Th multi-xtrudr past-xtrusion 3D printr shown in Fig. 2 (a) was purchasd from Hyrl 3D [17]. It has a fdcartridg assmbly with four xtrudrs that can print four diffrnt past matrials stord in syrings. Fig. 2 (b) shows our UV curing systm was affixd to th syring xtrudr holdr. Th UV curing systm has four UV LEDs (LZ1-00UV00, LdEngin, Inc.) with pak wavlngth of 365 nm soldrd on a customizd PCB. Th PCB and th hat sink ar togthr connctd to th xtrudr holdr through a 3Dprintd PLA adaptor. B. Two magntic past systms 1) Low-tmpratur (< 250 o C) curabl iron-powdr past systm W dvlopd an iron-powdr past systm consisting of Trimthylolpropan triacrylat (TMPTA) (from Sigma- Aldrich Co. LLC) monomr solution and two kinds of magntic fillrs. On of th magntic fillrs is a kind of Fig. 3. Dmonstration of a 3D-printd toroid cor from an iron-powdr past. To charactriz magntic proprtis of th iron-powdr matrial, th toroid cor was mad by pouring th past into a mold and hatd to 230 o C for on hour undr ambint prssur to polymriz th TMPTA monomr. Aftr dmolding, th rlativ prmability of th cor was charactrizd ovr a frquncy rang from 100 khz to 110 MHz at zro dc bias by using a prcision impdanc analyzr (4294A; Agilnt, Santa Clara, CA) with a magntic matrial tst fixtur (16454A; Agilnt, Santa Clara, CA). Thn, th cor-loss dnsity was masurd at 1 MHz using a stup spcifically dsignd to masur th loss of a toroid cor at high lvls of magntic fild xcitation [18, 19]. Fig. 4 (a) is a plot of rlativ prmability vrsus frquncy of th toroid

3 100 ility b a rm P10 tiv la R µ Frquncy (MHz) (a) ) T = 25 o C C /C W (m ity s n 1000 D s o L r o C Bpak (mt) (b) Fig. 4. (a) Plot of rlativ prmability vrsus frquncy of th iron-powdr toroid cor and (b) Plot masurd at 1 MHz of th iron-powdr toroid cor at room tmpratur. cor, which shows that th rlativ prmability of th ironpowdr past is stabl at 22 till on mgahrtz. Fig. 4 (b) shows th cor-loss dnsity plot masurd at 1 MHz of th cor at room tmpratur. 2) High-tmpratur (> 900 o C) sintrabl frrit past systm W also workd on a UV-curabl frrit past systm that consists of 95 wt% NiCuZn frrit powdr (Powdr Procssing & Tchnology, LL) with an avrag particl siz of 0.5 µm, 4.9 wt% pntarythritol ttraacrylat as monomr, and 0.1 wt% of phnylbis (2, 4, 6-trimnthylbnzoyl) phosphin oxid as photo-initiator. Solvnt was addd in th mixtur to obtain a frrit past that can b printd out smoothly by th 3D printr. As shown in Fig. 5, a toroid-shapd structur was 3Dprintd from th frrit past. Th printd toroid cor was hatd to 920 o C for 14 hours undr ambint prssur to burn out th organic compounds and sintr. Aftr sintring, th cor was charactrizd. Fig. 6 (a) shows a plot of rlativ prmability vrsus frquncy of th sintrd cor, which shows th cor has a stabl rlativ prmability valu of 70 byond 10 MHz. Fig. 6 (b) shows th cor-loss dnsity plot masurd at 1 MHz of th cor at room tmpratur. Fig. 5. Dmonstration of 3D-printd toroid cor from as-fabricatd frrit past. (a) (b) Fig. 6. (a) Plot of rlativ prmability vrsus frquncy of th frrit toroid cor and (b) Plot masurd at 1 MHz of th frrit toroid cor at room tmpratur. C. Nanosilvr past To print lctrical winding, w tstd th commrcial nanosilvr past which was dvlopd for chip bonding [20, 21]. Th matrial can b sintrd at tmpraturs blow 250 o C to rsult in xcllnt thrmal and lctrical proprtis. Fig. 7 shows that th nanosilvr past can b adaptd to th 3D printing platform and xtrudd out to form a winding structur. Th nanosilvr past can achiv a crack-fr 3D printd singl layr thickr than 200 µm. Tabl 1 lists th lctrical rsistivity of th 3D-printd winding aftr lowtmpratur and high-tmpratur sintring procsss.

4 Fig. 7. Commrcial nanosilvr past for past-xtrusion 3D printr. Tabl 1. Elctrical rsistivity of sintrd 3D-printd silvr winding and that of pur silvr wir. Elctrical rsistivity Matrials (10-8 Ω m) o 250 C sintrd 3D-printd 4.8 silvr winding 920oC sintrd 3D-printd 2.4 silvr winding Pur silvr wir 1.6 III. Tabl 2. Dsignd dimnsions of half pic CFI for printing. Winding Outr radius Innr radius of numbr of winding winding j=1 9.2 mm 7.6 mm j=2 7.2 mm 5.8 mm j=3 5.4 mm 4.4 mm j=4 4 mm 3 mm Winding spac 0.4 mm j=3 Winding j=4 0.5 mm thicknss Cor lngth 20 mm j=2 j=1 Cor thicknss 1.5 mm B. Fabrication procdurs Fig. 9 (a)-(f) show th 3D-printing procss to form th CFI, th sintring profil usd to dnsify th nanosilvr past, th hating profil to hardn th magntic past, and a 3D-printd half pic CFI. Th low-tmpratur curabl iron powdrd past is th fd matrial for th magntic cor and th nanosilvr past for th winding. A fram for maintaining th shap of th CFI was printd by using a silicon past. Th singl printing layr thicknss of th nanosilvr past was 0.2 mm. Convrsly, singl printing layr thicknss of magntic past was 1.6 mm. CONSTANT-FLUX INDUCTOR FABRICATION WITH CURABLE POWDERED IRON PASTE SYSTEM A. Structur dsign Th constant-flux concpt is lvragd to achiv high magntic-nrgy dnsity, lading to bttr utiliz th cor matrial and thn rduc th volum of th inductor [22]. On dsign vrsion of th constant-flux inductor, which is shown in Fig. 8, is configurd with spiral windings mbddd in th magntic cor, and rquirs a prcis control of th diffrnt widths and sam spac btwn ach turn of th spiral. Th hight of th dsignd inductor can b two tims lowr than that of convntional products and th targt working frquncy for th inductor is 1 MHz [23]. Howvr, th intricat configurations and gomtris of windings posd challngs in fabricating this inductor by using convntional fabrication mthod. Th paramtrs for a half pic of th CFI ar listd in Tabl 2. Fig. 9. Procss of 3D printing as-dsignd half pic constant-flux inductor. Fig. 10. Full siz constant-flux inductor. Fig. 8. Gomtry of a dsign vrsion of constant-flux inductor. Fig. 9 (a) showd nanosilvr past printd to form a winding structur. Aftr th winding structur was fabricatd in th printr, it was sintrd in a programmabl muffl furnac basd on th sintring profil shown in Fig. 9 (b). A fram around th sintrd winding for maintaining th cor shap was printd by using th silicon past, which is

5 shown in Fig. 9 (c). Fig. 9 (d) shows th magntic past was filld in th fram by th printr to covr th sintrd nanosilvr winding and thn compltd half pic of CFI. Th magntic past was hatd in a programmabl muffl furnac basd on th curing profil shown in Fig. 9 (). Fig. 9 (f) shows th half pic of th CFI aftr post polishing procss. Th full siz CFI, shown in Fig. 10, was fabricatd by conncting two printd pics togthr with 60 µm thicknss Kapton tap as an insulator btwn th windings. C. Charactrization 1) Inductanc and DC winding rsistanc of th 3Dprintd CFI For th dsignd CFI, th finit lmnt analysis (FEA) was carrid out to simulat its inductanc and DC winding rsistanc. Th conductivity of th winding for simulating is thr tims than that of th pur silvr. Th rlativ prmability of th magntic matrial for simulating is 22. Th dfind gap btwn th two windings in th modl is 60 µm. Th inductanc and DC winding rsistanc of th inductor modl wr found to b 3.6 µh and 19.6 mω rspctivly. A high prcision impdanc analyzr was usd to masur th inductanc and th DC winding rsistanc of th 3D-printd CFI. Th masurd inductanc and DC winding rsistanc of th inductor wr 3.5 µh and 59 mω, rspctivly. Th masurd inductanc is only 3% lowr than th inductanc prdictd by simulation. Howvr, th masurd DC winding rsistanc of th CFI is around thr tims highr than of th DC winding rsistanc prdictd by simulation. Th contact rsistanc cam from conncting th two half CFI pics may rsult in th high DC rsistanc of th printd CFI 2) Microstructur Fig. 11 is th SEM imag of th 3D-printd CFI. It shows silvr winding forming dns layr with som lvl of porosity. Voids can b found in th curd magntic past part. Magntic flaks ar randomly distributd in th cor, which will lowr th rlativ prmability of th cor. IV. PLANAR INDUCTOR FABRICATED WITH SINTERABLE FERRITE PASTE SYSTEM A. Structur dsign To dmonstrat th fasibility of fabricating magntic componnts with th as-fabricatd sintrabl frrit past and nanosilvr past, w tstd it by printing a planar inductor. Fig. 12 shows th dsign of th planar inductor. Th inductor has on turn winding mbddd in th cor. Th dsignd planar inductor had th following dimnsions: Cor diamtr = 20 mm; cor thicknss = 2.25 mm; winding width = 0.5 mm; winding thicknss = 0.25 mm. Fig. 12. Dsign of on turn mbddd planar inductor for 3D-printing B. Fabrication procdurs Fig. 13 (a)-(c) show th 3D-printing procss to form th planar inductor, th sintring profil usd to dnsify th nanosilvr past and frrit past, and a finishd planar inductor. Singl printing layr thicknss of both nanosilvr past and frrit past wr 0.2 mm. Fig. 13 (a) shows that th frrit past was printd layrby-layr to form th cor part and in ach layr th nanosilvr past was also printd out to build th winding structur. During th layr-by-layr printing procss, both th cor and winding matrials wr drid on a 50 o C -hatd build-plat. Additionally, th frrit layr was xposd to UV light to spd up its transition into a rigid layr. Aftr 3D structur of th planar inductor was fabricatd in th printr, it was hatd in a programmabl muffl furnac to simultanously sintring th frrit past and th nanosilvr winding. Th sintring profil is shown in Fig. 13 (b). Fig. 13 (c) shows th finishd 3D-printd planar inductor aftr polishing. Fig. 11. SEM imags of 3D-printd constant-flux inductor (CFI). Fig. 13. Procss of 3D printing a on turn mbddd planar inductor.

6 C. Charactrization 1) Inductanc and DC winding rsistanc of th 3Dprintd planar inductor For th dsignd planar inductor, th finit lmnt analysis (FEA) was also carrid out to simulat its inductanc and DC winding rsistanc. Th conductivity of th winding for simulating is on and a half tims than that of th pur silvr. Th rlativ prmability of th frrit for simulating is 70. Th inductanc and DC winding rsistanc of th inductor modl wr found to b 843 nh and 13.8 mω, rspctivly. Th masurd inductanc and DC winding rsistanc of th inductor wr 792 nh and 15 mω, rspctivly. Th masurd inductanc is only 6% lowr than th inductanc prdictd by simulation. Th masurd DC rsistanc of th planar inductor is around 8.7% highr than th DC rsistanc prdictd by simulation. 2) Microstructur Fig. 14 is th SEM imag of th 3D-printd planar inductor. It shows that th cor and silvr winding ar dns, but aprturs can b found in th intrfac btwn th winding and th cor. Also, som dfcts can b found in th big grain siz. Fig. 14. SEM imags of 3D-printd on turn mbddd planar inductor. V. SUMMARY In ordr to raliz th htrognous intgration of th magntic componnts in th futur, w dmonstratd th fasibility of additiv manufacturing magntic componnts by printing both th magntic cor and conductiv winding using a commrcial multi-xtrudr past-xtrusion 3D printr. Two past systms wr dvlopd for th magntic fdstock, on bing a low-tmpratur (< 250 o C) curabl iron powdrd systm and th othr a high-tmpratur (> 900 o C) sintrabl frrit systm. Both wr shown to b compatibl with th 3D printr. Th commrcial lowtmpratur sintring nanosilvr past, dvlopd in our arlir studis, srvd as th fdstock for th winding. A constant-flux inductor was dsignd and 3D printd by using th low-tmpratur curabl iron-powdr past and th nanosilvr past, whil a planar inductor was dsignd and 3D printd by using th high-tmpratur sintrabl frrit past and nanosilvr past. Th inductanc and DC winding rsistanc of th printd inductors wr masurd and compard with thos simulatd by a finit-lmnt analysis of th inductor modls. Th microstructurs of th printd inductors wr charactrizd, and th dfcts in th printd componnts should b liminatd to furthr improv th prformanc of th 3D-printd magntic componnts. ACKNOWLEDGMENT Financial support from th following organizations is gratly apprciatd: th Institut of Critical Tchnology and Applid Scincs at Virginia Tch; th High Dnsity Intgration Consortium of th Cntr for Powr Elctronics Systms at Virginia Tch; Txas Instrumnts; and th Scinc and Tchnology Offic of Tianjin Municipal Govrnmnt, China. REFERENCES [1] M. Ludwig, M. Duffy, T. O'Donnll, P. McClosky, and S. C. Ó. Mathùna, PCB intgratd inductors for low powr DC/DC convrtr, IEEE Transactions on Powr Elctronics, vol. 18, no. 4, pp , [2] S. O'Rilly, M. Duffy, T. O'Donnll, P. McClosky, S. C. Ó. Mathùna, M. Scott, and N. Young, Nw intgratd planar magntic cors for inductors and transformrs fabricatd in MCM-L tchnology, Th Intrnational journal of microcircuits and lctronic packaging, vol. 23, no. 1, pp , [3] H. Sarnago, O. Lucia, A. Mdiano, and J. M. Burdio, Dsign and implmntation of a high-fficincy multipl-output rsonant convrtr for induction hating applications faturing wid bandgap dvics, IEEE Transactions on Powr Elctronics, vol. 29, no. 5, pp , [4] R. L. Billings, D. W. Dahringr, and A. M. Lyons, Circuit lmnts dpndnt on cor inductanc and fabrication throf, U.S. Patnt No , [5] R. W. Lamp Jr, and G. J. Hays, Wir wound inductors, U.S. Patnt No , [6] A. Taghvai, H. Shokrollahi, M. Ghaffari, and K. Janghorban, Influnc of particl siz and compaction prssur on th magntic proprtis of iron-phnolic soft magntic composits, Journal of Physics and Chmistry of Solids, vol. 71, no. 1, pp. 7-11, [7] Y. Yan, K. D. Ngo, D. Hou, M. Mu, Y. Mi, and G.-Q. Lu, Effct of sintring tmpratur on magntic cor-loss proprtis of a NiCuZn frrit for high-frquncy powr convrtrs, Journal of Elctronic Matrials, vol. 44, no. 10, pp , [8] F. Roozboom, A. Kmmrn, J. Vrhovn, F. Van dn Huvl, J. Klootwijk, H. Krtschman t al., Passiv and htrognous intgration towards a Si-basd Systm-in- Packag concpt, Thin Solid Films, vol. 504, no. 1, pp , [9] I. Gibson, D. W. Rosn, and B. Stuckr, Additiv manufacturing tchnologis: Nw York: Springr, [10] M. Chinthavali, Additiv manufacturing tchnology for powr lctronics applications, Applid Powr Elctronics Confrnc and Exposition (APEC), [11] M. Chinthavali, C. Ayrs, S. Campbll, R. Wils, and B. Ozpinci, A 10-kW SiC invrtr with a novl printd mtal

7 powr modul with intgratd cooling using additiv manufacturing, IEEE Workshop on Wid Bandgap Powr Dvics and Applications (WiPDA), pp , [12] W. Liang, L. Raymond, and J. Rivas, 3D-Printd air-cor inductors for high-frquncy powr convrtrs, IEEE Transactions on Powr Elctronics, vol. 31, no. 1, pp , [13] Proto pasta. "Composit PLA - Rustabl Magntic Iron," [14] Y. Wang, F. Castls, and P. S. Grant, 3D printing of NiZn frrit/abs magntic composits for lctromagntic dvics, MRS Procdings, vol. 1788, pp. mrss , [15] Y. Yi, J. Moss, K. D. T. Ngo, M. Yuhui, and L. Guo-Quan, Additiv manufacturing of toroid inductor for powr lctronics applications, IEEE Enrgy Convrsion Congrss & Exposition (ECCE) [16] Y. Yi, K. D. T. Ngo, M. Yuhui, and L. Guo-Quan, Additiv manufacturing of magntic componnts for powr lctronics intgration, Intrnational Confrnc on Elctronics Packaging (ICEP), pp , [17] "Hyrl 3D 30M," [18] M. Mu, High frquncy magntic cor loss study, Ph.D Dissrtation, Virginia Tch Univristy, [19] M. Mu, and F. C. L, A nw high frquncy inductor loss masurmnt mthod, IEEE Enrgy Convrsion Congrss and Exposition (ECCE), pp , [20] J. G. Bai, Z. Z. Zhang, J. N. Calata, and G.-Q. Lu, Lowtmpratur sintrd nanoscal silvr as a novl smiconductor dvic-mtallizd substrat intrconnct matrial, IEEE Transactions on componnts and packaging tchnologis, vol. 29, no. 3, pp , [21] G.-Q. Lu, G. Li, and J. Calata, Nanoscal mtal past for intrconnct and mthod of us, U.S. Patnt No , [22] H. Cui, K. D. Ngo, J. Moss, M. H. F. Lim, and E. Ry, Inductor gomtry with improvd nrgy dnsity, IEEE Transactions on Powr Elctronics, vol. 29, no. 10, pp , [23] H. Cui, and K. D. Ngo, Inductor gomtris with significantly rducd hight, Applid Powr Elctronics Confrnc and Exposition (APEC), pp , 2013.

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