1694 半导体学报 第27卷 GHz CMOS LC VCO.Chinese Journal of Semiconductors, [10]Lopez Villegas J M,Samitier J,Cane C,et al.Improvement of 2005,26(5):867 the quality factor of RF integrated inductors by layout optimi- [2]Hussein A I.A 2 4-GHz bluetooth CMOS transceiver for zation.IEEE Trans Microw Theory Tech,2000,48:76 wireless LANs.IEEE International Midwest Symposium on [11] Tiemeijer L F,Leenaerts D.Record Q spiral inductors in Circuits and Systems,2003,3:1251 standard CMOS.IEDM Technical Digest of International E- 3 Niknejad A M,Meyer R G.Analysis,design,and optimization lectron Devices Meeting ,2001,2~5:40.7.1 of spiral inductors and transformers for Si RF ICs.IEEE J [12]Jian Hongyan,Tang Zhangwen,He Jie,et al.Analysis and op- Solid-State Circuits,1998,33:1470 timum design of differential inductors using the distributed [4 Burghartz J N.Progress in RF inductors on silicomunder capacitance model.Chinese Journal of Semiconductors,2005, standing substrate losses.International Electron Devices 26(6):1077 Meeting,1998,6-9:523 [13]Cockcroft J D.Skin effect in rectangular conductor at high 5 Chen KJ,Hon W C,Zhang Jinwen,et al.CMOS-compatible frequency.Proc Royal Soc,1929,122 :533 micromachined edge-suspended spiral inductors with high Q- [14]Faraj-Dana R,Chow Y.Edge condition of the field and ac re- factors and self-resonance frequencies.IEEE Electron Device sistance of a rectangular strip conductor.Proc Inst Elect Eng, Lett,2004,25:363 1990,137(2):133 [6 Chen P Q,Chan Y J.Improved microwave performance on [15]Stracca GB.A simple evaluation of losses in thin microstrips. low-resistivity Si substrates by Si ion implantation.IEEE IEEE Trans Microw Theory Tech,1997,45(2):281 Trans Microw Theory Tech,2000,48(9):1582 [16]Tiemeijer L F,Havens R J,Bouttement Y,et al.The impact [7 Kuhn W B,Ibrahim N M.Analysis of current crowding of an aluminum top layer on inductors integrated in an ad- effects in multiturn spiral inductors.IEEE Microw Theory vanced CMOS copper backend.IEEE Electron Device Lett, Tech,2001,49:31 2004,25(11):722 [8 Ooi B L.Xu D X,Kooi P S.et al.An improved prediction of [17]Faraji-Dana R,Chow Y L.AC resistance of two coupled series resistance in spiral inductor modeling with eddy-current strip conductors.IEE ProceedingsH Microwaves,Antennas effect.IEEE Trans Microw Theory Tech,2002,50:2202 and Propagation,1991,138(1):37 9 Sia CB,Ong B H,Chan K W,et al.Physical layout design op- [18]Danesh M,Long J R.Differentially driven symmetric mi timization of integrated spiral inductors for silicombased RFIC crostrip inductors.IEEE Trans Microw Theory Tech,2002, applications.IEEE Trans Electron Devices,2005,52:2559 50(1):332 Suppressing of On-Chip Inductor Current Cro wding by a MultiCurrent-Path Method Liu Ket,Jian Hongyan,Huang Chenling,Tang Zhangwen,and Min Hao (State Key Laboratory of ASIC System,Fudan University,Shanghai 201203.Chinal Abstract:From the view of the electromagnetic theory,we examine the current redistributions of an inductor.We conclude that metal with a small cross-section has a weak skin effect and that inductors with a smaller ratio of the turn width to the space between turns have a weak proximity effect.The inductors are fabricated in 0.35um four-metal CMOS technology.A turn of the differential inductor is divided into multi-shunt tracks,which keep the symmetry of the two ports of the inductor. Compared with a single-current-path configuration,the multi-current-path inductor offers a 40%greater maximum quality factor and a narrower range of operating frequencies,which we interpret here in detail. Key words:omchip inductor;quality factor;skin effect;proximity effect;multi-current-path;self-resonant frequency EEAC℃：2140；1205；1350 rticle ID:0253-4177(2006)091690-05 Corresponding author.Email:keliu @fudan.edu.cn Received 18 January 2006,revised manuscript received 27 February 2006 2006 Chinese Institute of Electronics半 导 体 学 报 第 27 卷 GHz CMOS LC VCO. Chinese Journal of Semiconductors , 2005 ,26 (5) :867 [ 2 ] Hussein A I. A 2142GHz bluetoot h CMOS transceiver for wireless LANs. IEEE International Midwest Symposium on Circuits and Systems ,2003 ,3 :1251 [ 3 ] Niknejad A M ,Meyer R G. Analysis ,design ,and optimization of spiral inductors and transformers for Si RF ICs. IEEE J Solid2State Circuits ,1998 ,33 :1470 [ 4 ] Burghartz J N. Progress in RF inductors on silicon2under2 standing substrate losses. International Electron Devices Meeting ,1998 ,6～9 :523 [ 5 ] Chen K J , Hon W C , Zhang Jinwen ,et al. CMOS2compatible micromachined edge2suspended spiral inductors wit h high Q2 factors and self2resonance frequencies. IEEE Electron Device Lett ,2004 ,25 :363 [ 6 ] Chen P Q , Chan Y J. Improved microwave performance on low2resistivity Si substrates by Si + ion implantation. IEEE Trans Microw Theory Tech ,2000 ,48 (9) :1582 [ 7 ] Kuhn W B , Ibrahim N M. Analysis of current crowding effects in multit urn spiral inductors. IEEE Microw Theory Tech ,2001 ,49 :31 [ 8 ] Ooi B L ,Xu D X , Kooi P S ,et al. An improved prediction of series resistance in spiral inductor modeling wit h eddy2current effect . IEEE Trans Microw Theory Tech ,2002 ,50 :2202 [ 9 ] Sia C B ,Ong B H ,Chan K W ,et al. Physical layout design op2 timization of integrated spiral inductors for silicon2based RFIC applications. IEEE Trans Electron Devices ,2005 ,52 :2559 [ 10 ] Lopez2Villegas J M ,Samitier J ,Cane C ,et al. Improvement of t he quality factor of RF integrated inductors by layout optimi2 zation. IEEE Trans Microw Theory Tech ,2000 ,48 :76 [ 11 ] Tiemeijer L F , Leenaerts D. Record Q spiral inductors in standard CMOS. IEDM Technical Digest of International E2 lectron Devices Meeting ,2001 ,2～5 :40. 7. 1 [ 12 ] Jian Hongyan , Tang Zhangwen , He Jie ,et al. Analysis and op2 timum design of differential inductors using t he distributed capacitance model. Chinese Journal of Semiconductors ,2005 , 26 (6) :1077 [ 13 ] Cockcroft J D. Skin effect in rectangular conductor at high frequency. Proc Royal Soc ,1929 ,122 :533 [ 14 ] Faraji2Dana R ,Chow Y. Edge condition of t he field and ac re2 sistance of a rectangular strip conductor. Proc Inst Elect Eng , 1990 ,137 (2) :133 [ 15 ] Stracca G B. A simple evaluation of losses in t hin microstrips. IEEE Trans Microw Theory Tech ,1997 ,45 (2) :281 [ 16 ] Tiemeijer L F , Havens R J ,Bouttement Y ,et al. The impact of an aluminum top layer on inductors integrated in an ad2 vanced CMOS copper backend. IEEE Electron Device Lett , 2004 ,25 (11) :722 [ 17 ] Faraji2Dana R , Chow Y L. AC resistance of two coupled strip conductors. IEE Proceedings2H Microwaves , Antennas and Propagation ,1991 ,138 (1) :37 [ 18 ] Danesh M , Long J R. Differentially driven symmetric mi2 crostrip inductors. IEEE Trans Microw Theory Tech , 2002 , 50 (1) :332 Suppressing of On2Chip Inductor Current Crowding by a Multi2Current2Path Method Liu Ke ­ , Jian Hongyan , Huang Chenling , Tang Zhangwen , and Min Hao ( S tate Key L aboratory of A S IC & S ystem , Fudan Universit y , S hanghai 201203 , China) Abstract : From t he view of t he electromagnetic t heory ,we examine t he current redistributions of an induct or. We conclude t hat metal wit h a small cross2section has a weak skin eff ect and t hat induct ors wit h a smalle r ratio of t he turn widt h t o t he sp ace between turns have a weak p roximity eff ect. The induct ors are f abricated in 0135μm f our2metal CMOS technology. A turn of t he diff e rential induct or is divided int o multi2shunt tracks ,which keep t he symmetry of t he two p orts of t he induct or. Comp a red wit h a single2current2p at h configuration , t he multi2current2p at h induct or off e rs a 40 % greater maximum quality f act or and a na rrowe r range of ope rating f requencies ,which we inte rp ret here in detail. Key words : on2chip induct or ; quality f act or ; skin eff ect ; p roximity eff ect ; multi2current2p at h ; self2resonant f requency EEACC : 2140 ; 1205 ; 1350 Article ID : 025324177 (2006) 0921690205 ­Corresp onding aut hor. Email :keliu @f udan. edu. cn Received 18 J a nua ry 2006 ,revised ma nuscript received 27 Februa ry 2006 2006 Chinese Institute of Electronics 4961