Abstract—This paper presents a new modeling technique, enti-tled extended MagPEEC model, which can be used to simulate ar-bitrary three-dimensional conductor-magnet structures of any ge-ometry with direct conductor-magnet interfaces included. The newmodel was validated using a sample coaxial transmission line struc-ture and was applied to investigate a group of super compact six-layer stacked spiral radio frequency integrated circuits (RFICs) in-ductor structures with various magnetic media integrated inside.This new modeling technique can be used to assist design of com-plex conductor-magnet structures including various magnetic-en-hanced inductors for RFIC applications.
RADIO frequency integrated circuits (RFIC) technolo-gies enjoy unprecedented advancements in recent years
thanks to the proliferation of wireless communication appli-cations. While RFIC technology continuously benefits as ICtechnologies migrates into the very-deep-sub-micron (VDSM)regime, lack of compact size high-performance high-frequencyon-chip RF inductors (e.g., inductance nH and qualityfactor at multiGHz) hinders the realization of RFsystem-on-a-chip (SoC) for commercial applications. Thismotivates great research efforts in developing high-perfor-mance inductors for RFIC applications. However, despiteof all the efforts, only incremental improvements have beenachieved in making high-quality RFIC inductors, particularly inmain-stream commercial CMOS technologies. To date, manydifferent types of spiral IC inductors have been reported withlarge inductance values and high quality factor values. Unfor-tunately, they mainly use some exotic structures and fabrication
Manuscript received August 31, 2004; revised December 22, 2004. This workwas supported by the 973 Research and Development Project of China underGrant G1999033105, by the National Science Foundation (NSF) of China underGrant 60171015, and by the U.S. NSF under Grant 0302449. The review of thispaper was arranged by Editor B. Zhao.
H. Long, Z. Feng, and X. Zhang are with the Department of Elec-tronic Engineering, Tsinghua University, Beijing 100084, China (e-mail:[email protected]).
H. Feng is with RF Micro Devices, San Diego, CA 92122 USA.A. Wang is with the Integrated Electronics Laboratory, Department of
Electrical and Computer Engineering, Illinois Institute of Technology (IIT),Chicago, IL 60616 USA (e-mail: [email protected]).
T. Ren, J. Bao, F. Liu, and C. Yang are with the Institute of Microelectronics,Tsinghua University, Beijing 100084, China.
Digital Object Identifier 10.1109/TED.2005.850662
techniques that are not compatible to commercial CMOStechnologies. For example, one possible solution to improvethe -factor is to include magnetic media into the inductorstructures to preserve the magnetic energy that will compensatethe electrical losses due to resistance and substrate couplingeffects. Various micro-electro-mechanical system (MEMS)techniques have been used to make such inductors with mag-netic media inside. However, any MEMS techniques can stillnot be integrated into the CMOS technologies. In addition, ICinductors made by such techniques are typically very large insizes (i.e., m m or several times of a typicalIC bonding pad), hence are not suitable for RF SoC design.Apparently, it is highly desirable to develop super compact(i.e., transistor-size) high-performance inductors for RF SoCdesigns. Since shrinking in the inductor size will increase theresistive loss inevitably, novel techniques to integrate magneticmedia into such super compact inductors are essential to recov-ering the electric energy lost from the magnetic field. To thisend, some initial work has been reported [1]–[3]. Nevertheless,more research is needed to ensure super gigahertz operationof such inductors with magnetic media that is required byRFIC applications and to develop novel fabrication techniquesthat can be seamlessly integrated into the commercial CMOStechnologies. The challenges lying ahead are the following.First is to find suitable magnetic materials that can operatein multiple-gigahertz spectrum. Second is to explore novelinductor structures with magnetic media integrated. Third is todevelop suitable process procedures to make such inductors incommercial CMOS technologies. To achieve all these goals, itis imperative to develop a new modeling technique and simu-lation software that would be able to handle three-dimensional(3-D) arbitrary electro-magnetic structures in general, andRFIC inductor in particular, with magnetic media integratedinside in various formats. Especially, electro-magnetic (E-M)modeling technique that can analyze conductor-magnet (C-M)structures with direct conductive-magnetic material interfaces(i.e., no gap between conductors and magnetic materials) isrequired to model complex 3-D conductor-magnet structuresand to guide design of magnet-integrated RFIC inductors.
In [4], we reported a new modeling technique, entitledMagPEEC, which is a modified method to include the magneticmedia coupling effect into the partial element equivalent circuits(PEEC) method, to analyze arbitrary 3-D conductor-magnet(C-M) structures that, however, cannot handle general C-Mstructures with direct conductive-magnetic material interfaces
LONG et al.: A NEW MODELING TECHNIQUE FOR MAGNET STRUCTURES 1355
(C-M interface) as required in practical RFIC inductors withmagnetic media inside. This paper describes a new modelingtechnique that extends the MagPEEC model, called extendedMagPEEC model, to deal with arbitrary 3-D complex C-Mstructures in any C-M contact formats. In this new extendedMagPEEC model, the fictitious magnetized currents are stillassumed to flow on the surfaces of magnetic materials. Whilethe real conductive currents flow in conductors are dividedinto two types: 1) when the skin depth of the conductor is farsmaller than the dimension of the conductor cross-section, thereal conductive currents are treated as surface currents, whichonly flow through the conductor surfaces and 2) when the skindepth is greater than or comparable to the dimension of theconductor cross-section, the real conductive currents are treatedas bulk currents flowing in the bulk conductors.
In [5], we reported design of the first transistor-size supercompact six-layer stacked spiral RFIC inductor fabricated ina commercial 0.18- m CMOS technology with Copper inter-connects, where a simple polysilicon pattern grounded shield(PGS) between metal 1 and the substrate was used to reducesubstrate-coupling effect. This transistor-size (22 m 23 minductor delivers an adequate 9.5-nH inductance with a veryhigh self-resonant frequency of GHz achieved dueto very small parasitic capacitance of about 7 fF according tothe equation of . However, its -factorneeds to be improved by introducing magnetic media into theinductor, which is a current project we are working on to designand fabricate a magnetic-enhanced super compact inductorthat can be integrated into commercial CMOS technologies.The goal of developing such a magnetic-cored inductor is toachieve adequate inductance and -factor values in a tran-sistor-size inductor structure in CMOS process, where thesmall inductor size will ensure very low parasitic capacitancethat in turn guarantees a very high self-resonant frequency sothat its operating frequency will be well into multiGHz rangeas required in most RFIC applications. The critical tasks in thisresearch are to find the right magnetic materials, to exploresuitable conductor-magnet inductor structures and to develop amanufacturing procedure that can be seamlessly integrated intoCMOS processes. For this purpose, E-M modeling and sim-ulation are essential to guide the design practice. Applicationof the new extended MagPEEC modeling technique to designsuch magnetic-enhanced super compact inductors with variousgeometries is discussed in this paper. The paper is organized asfollows. Section II discusses the extended MagPEEC modelingtechnique. Section III depicts the capability of the new model tohandle conductor-magnet structures with direct C-M interfaces.Application of the new modeling technique to design varioussuper compact magnetic-enhanced inductors is described inSection IV, followed by a Conclusion in Section V.
II. AN EXTENDED MAGPEEC MODELING TECHNIQUE
In conductor-magnet structures, the sources of resistive andinductive effects are electric currents. For conductors, thereare real conductive currents flowing inside the bulk conductor,while in high-frequency the conductive currents are regarded asflowing through its surfaces. For isotropic and linear magnetic
Fig. 1. (a) A c-type hexahedron cell and a c-type quadrangle cell. (b) A x-typequadrangle cell (with x = p, f ).
materials, the inductive-resistive coupling effect is associatedwith the fictitious magnetized currents flowing through thesurface of the magnetic materials. Three types of mesh cells aredefined as follow: the -type (quadrangle/hexahedron) cell hasonly locally-uniform-distributed real conductive (surface/bulk)currents flowing through; the -type (quadrangle) cell hasboth locally-uniform-distributed real conductive and fictitiousmagnetized (surface) currents flowing through; and the -type(quadrangle) cell has only locally-uniform-distributed fictitiousmagnetized (surface) currents flowing through.
A. MagPEEC Conception and Derivation of Basic Equations
In the high-frequency range, the skin depth of conductor isfar smaller than the dimension of the conductor cross-section.Hence, the conductive currents can be treated as surface cur-rents that only flow on the conductor surfaces. The conductorsurfaces excluding the direct C-M interfaces are discretized into
-type quadrangle cells, as shown in Fig. 1(a). The relatedparameters for the th unit of -type quadrangle cells includecurrent direction , electrical voltage , quadrangle area
, surface current crossing width , and length .The conductive surface current density and total conductive cur-rent along the direction in this cell are denoted asand , respectively. The direct C-M interfaces are discretizedinto -type quadrangle cells, as shown in Fig. 1(b). The re-lated parameters for the th unit of such -type quadrangle cellsinclude current direction , quadrangle’s normal direction
, electrical voltage , quadrangle area , surfacecurrent crossing width , and length . For conve-nience, the normal direction of the cell is defined as pointingfrom side to side, as shown in Fig. 1(b). andare the permeabilities at each sides. and are therelative permeabilities. The fictitious magnetic surface currentdensity and total fictitious current of the th quadrangle cellare denoted as and , respectively. The conduc-tive surface current density and total conductive current of the
th quadrangle cell are labeled as and , respec-tively. The magnetic material’s surfaces excluding the directC-M interfaces are discretized into -type quadrangle cells,as shown in Fig. 1(b). The related parameters for the th unitof such -type quadrangle cells include current direction ,quadrangle’s normal direction , quadrangle area ,surface current crossing width and length . Thedenotation for the permeability is similar to that for -type quad-rangle cells. The fictitious magnetic surface current density and
1356 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 52, NO. 7, JULY 2005
total fictitious current of this quadrangle cell are denoted asand , respectively.
Analogous to the current distribution problem in free space,the magnetic vector potential is expressed as
(1)
where , , is field point and is source point.The magnetic flux density is extracted by the equation
. Considering the voltage of conductor quadranglecells similar to the process in [6], we obtain
(2)
where (with , ) is the partial resistance of the th-type cell due to the th -type cell and (with , and
, , ) is the partial inductances of the th -type cell dueto the th-type cell. The formulas for the partial resistance andpartial inductance will be discussed in Section II-B. Similar tothe derivation of (2), we can deduce
(3)
The magnetic boundary condition in the th quadrangle cellon C-M interfaces is given by
(4)
where is the surface conductive current density of thiscell. The and are the approaching the and side of the
quadrangle cell, respectively. The total real conductive currentflowing through the cell is
(5)
Next, substituting (1) into (4), then substituting (4) into (5), weobtain
(6)
where the matrix element (with , and , , ),which is the control coefficient of the current-controlled conduc-tive current source of the th -type cell due to the th -typecell. The formulas for will also be introduced in SectionII-B. Similar to the derivation of (6), the total real conductivecurrent (apparently equals to zero) flowing through the -typequadrangle cells can be expressed as
(7)
Then (2), (3), (6), and (7) can be compactly expressed in a matrixform as
(8)
(9)
(10.1)
(11)
After introducing a unit matrix , (10.1) can be transformedinto
(10.2)From (8)–(11), the relations between the conductive currentsand voltages can be expressed as
(12)
where the matrix is called inductance matrix, which char-acterizes the resistive and inductive effects of the electromag-netic structures.
LONG et al.: A NEW MODELING TECHNIQUE FOR MAGNET STRUCTURES 1357
When the skin depth of the conductor is greater than or com-parable to the dimension of the conductor cross section, the con-ductor bodies are discretized into -type hexahedron cellswhose dimensions of the cross section should be smaller than orequal to the skin depth, as shown in Fig. 1(a). The related param-eters for the th hexahedron cell include current direction ,electrical voltage , bulk , cross section area ,and length . The bulk current’s density and total currentof the th hexahedron cell are denoted as and , re-spectively. Since the conductive currents carried by the conduc-tors are bulk currents, the conductive surface currents densityon the direct C-M interfaces equals to zero. Hence, all magneticmaterial’s surfaces including the direct C-M interfaces can bediscretized into -type quadrangle cells. In this case, theexpression of magnetic vector potential is reduced to
(13)
Then (8) and (11) are reduced to
(14)
and
(15)
The corresponding inductance matrix can then be extractedfrom (14) and (15).
B. Fast and Accurate Integral Techniques for CalculatingPartial Elements
In Part A, we have deduced three types of partial elementsfor partial inductance, partial resistance and partial coefficientsof currents, respectively. When the related th -type cell is aquadrangle cell, the partial resistance is calculated by
(16.1)
where and are the conductivity and skin depth of the con-ductor, respectively. When the th -type cell is a hexahedroncell, is expressed as
(16.2)
When the related th -type cell and the related th -type cellare both quadrangle cells, the partial inductance can be cal-culated by
(17.1)
When the related th -type cell is a hexahedron cell and therelated th -type cell is a quadrangle cell, the is then cal-culated by
(17.2)
When the related th and th -type cells are both hexahedroncells, the can be calculated by
(17.3)The is derived as
and
(else).(18)
When the related th -type cell and the related th -type cellare both quadrangle cells, the corresponding coefficientis calculated by
(19.1)
When the related th -type cell is a quadrangle cell and therelated th -type cell is a hexahedron cell, the can be cal-culated by
1358 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 52, NO. 7, JULY 2005
(19.2)
While the above expressions for the partial element formulasinclude complex multistage integrals over quadrangle areas orhexahedron bodies, fast integral techniques can be used to solvethe equations. Equations (17.1), (17.2), and (19.2) can then besimplified by using the following:
(20)
(21)
where the parameters , , , , , , etc. are definedin [7]. The fast and accurate integral technique for (17.3) wasgiven in [8]. Equation (19.1) can also be simplified using thefollowing:
(22)
(23)
where the parameters in (22) and (23) are defined in [7] and [9].The accuracy of these fast integral techniques has been ver-
ified by comparing their calculation results with that obtainedusing the commercial software Mathmatica, where good agree-ment was observed. Our techniques are more efficient and takeonly several seconds per partial element compared to many min-utes when using the Mathmatica.
III. VALIDATION OF MAGPEEC MODEL INCLUDING
DIRECT C-M INTERFACES
To verify the accuracy of the new extended MagPEEC mod-eling technique in analyzing a conductor-magnet structure with
Fig. 2. Cross section of the coaxial line, where � is the relative permeabilityof the magnetic materials and � is the conductivity of copper (5.8�10 S=m).
direct C-M Interfaces, it is applied to model a piece of coaxialtransmission line with magnetic materials filled inside, with itscross section shown in Fig. 2, to extract its unit-length induc-tance and resistance in a gigahertz frequency range.A coaxial line is used for validation because it is a classic andsymmetrical structure, and the analytical formulas to calculateits unit-length inductance and resistance are readily available inmany classic microwave textbooks [10]. The numerical simu-lation results obtained by using the new MagPEEC model willbe compared with the analytical results derived using the classicformulas.
To extract the distributed-parameters of this transmission line,the length of the coaxial line must be far greater than theouter radius of the cross section and the skin depth of copperin the operating frequencies must be far smaller than the innerradius . We evenly divided both the inner and outer C-M inter-faces into equal-length segments, respectively, along the axesdirection of the coaxial line. We denote the voltage and conduc-tive current of the segment as and , where
. In order for the new extended MagPEEC model tobe able to process these circular surfaces, the circular surface isapproximated by a 20-side polygon cylinder so that each seg-ment is naturally divided into 20 -type quadrangle cells. Thevoltage and conductive current in these quadrangle cells are de-noted as and , where and
. A voltage source is applied between innerconductor and outer conductor at one end of the coaxial line,while at the other end, the inner conductor and the outer con-ductor are electrically shorted to each other. It is assumed thatall current flows are in the direction of the axes of coaxial linewith the conductive current direction in the inner C-M inter-face pointing to the shorted while that of outer C-M interfaceto the opposite direction. We denote the total currents of innerconductor and outer conductor as and . With the assump-tion of no current leakage along the cross-section, symmetry ofcoaxial line and the mesh scheme, we obtain
(24)
(25)
Using the extended MagPEEC model, (13) is reduced to
(26)
LONG et al.: A NEW MODELING TECHNIQUE FOR MAGNET STRUCTURES 1359
TABLE ISIMULATED UNIT-LENGTH INDUCTANCE AND RESISTANCE OF THE
COAXIAL LINE AS A FUNCTION OF FREQUENCY BY DIVIDING
A L = 100 mm COAXIAL LINE INTO N = 9 SEGMENTS, WITH
a = 0:45 mm, b = 1:5 mm AND � = 4
The impedance of this one-end-shorted coaxial line can be ex-tracted as
(27)
The unit-length resistance and inductance are extracted as
(28)
From classic microwave textbooks, the analytical formulas aregiven as
(29)The comparison between simulation results using the new ex-tended MagPEEC model and the data from the analytical equa-tions for the unit-length inductance and resistance is given inTables I and II, which shows good agreement, hence, validatesthe new extended MagPEEC model.
IV. APPLICATION IN DESIGNING SUPER COMPACT STACKED
SPIRAL RFIC INDUCTORS WITH MAGNETIC MEDIA IN CMOS
A CAD software, entitled L-Simulator [11], was developedbased upon the new extended MagPEEC modeling technique,which can accurately simulate magnetic-cored/covered/buriedRFIC inductors of 3-D arbitrary geometries. L-Simulator wasfirst used to simulate the super compact six-layer stacked spiralRFIC inductor we designed [5], as shown in Fig. 3, using our
TABLE IISIMULATED UNIT-LENGTH INDUCTANCE AND RESISTANCE OF THE COAXIAL
LINE AS A FUNCTION OF RELATIVE PERMEABILITY � BY DIVIDING
A L = 100 mm COAXIAL LINE INTO N = 9 SEGMENTS, WITH
a = 0:45 mm, b = 1:5 mm AND FREQUENCY = 2 GHz
Fig. 3. Super compact six-layer stacked spiral inductor structure: Metal layerthicknesses for M1, M2, M3, M4, M5, and M6 are 0.3, 0.3, 0.45, 0.45, 1, and 1�m, respectively. The width and spacing of the coplanar metal stripe is 1�m and0.5 �m, respectively. D , D , T are the inner diameter, outer diameter ofcoils and the thickness of the metal structure, respectively. (a) The whole view.(b) Cross-section view.
original 3-D MagPEEC model and the simulation results agreewell with the measurement data [11], hence experimentally ver-
1360 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 52, NO. 7, JULY 2005
Fig. 4. Cross-section view of the five types of magnetic integration schemescombined with the six-layer metal structures. (a) Type-1 with a W �W � Tmagnetic layer. (b) Type-2 with two W � W � (T=2) magnetic layers. (c)Type-3 with a W �W � T magnetic bar core and W < D . (d) Type-4with two W �W � (T=2) magnetic layers plus one W �W � 8:4 �mmagnetic bar core. (e) Type-5 with a W �W � T magnetic tank formed bymagnetic multilayers and W > D .
ified the new modeling method. Yet the main motivation of thisresearch was to develop a new modeling and simulation tech-nique that can guide one in designing very complex C-M struc-tures, such as magnetic-cored RF inductors. As an example ofa real-world application, the L-Simulator was used to guide thedesign of five improved versions of similar super compact mag-netic-enhanced RFIC inductors, therefore, to assist us in se-lecting proper magnetic materials, designing optimal inductorstructures with magnetic materials integrated and developingsuitable process steps for CMOS technology. Fig. 4 shows thecross-sections of the five proposed magnetic-enhanced stackedspiral inductors with magnetic cores inside, and/or magneticmedia partially/fully filled to improve the inductor performanceby forming a closed magnetic circuit. Fig. 4(a) shows the in-ductor structure Type-1 that has a single magnetic film on topor at bottom. Fig. 4(b) shows a Type-2 structure that has mag-netic films both on top and at bottom with the metal spirals sand-wiched in between. Fig. 4(c) shows the Type-3 structure with amagnetic core inside the metal coils. Fig. 4(d) shows the struc-ture Type-4 that is the combination of Types 2 and 3.Fig. 4(e)
TABLE IIISIMULATED INDUCTANCE DATA FOR THE TYPES 1 TO 5 INDUCTOR STRUCTURES
AS A FUNCTION OF RELATIVE PERMEABILITY � WITH T = 8:4 �m AND
W = 40 �m FOR TYPES 1, 2 & 4; WITH T = 8:4 �m AND W = 11 �mFOR TYPE-3; AND WITH T = 8:4 �m AND W = 40 �m FOR TYPES-5
TABLE IVSIMULATED INDUCTANCE DATA FOR TYPES 1, 2 AND 4 INDUCTOR STRUCTURES
AS A FUNCTION OF MAGNET THICKNESS T WITH � = 16 AND W = 40 �m
shows the Type-5 inductor structure that has the metal spiralsimmersed inside a magnetic media solid with direct C-M inter-faces around.
Table III shows the simulated inductance data for all five in-ductor structures as a function of the relative permeability ofthe magnetic materials inside with fixed geometry parameters
, , or , as shown in Fig. 4. The simu-lation data clearly show that the inductance values increase asthe increases initially for all five structures, indicating thenecessity of finding the proper magnetic materials for the struc-tures. However, it is observed that, as the increases beyondsome value, this improvement in inductance rapidly saturatesfor Type 1, 2, and 3 structures, while continuous enhancementcan still be achieved for the Type 4 and 5 structures. This indi-cates that the Type 4 and 5 inductor structures shall be the candi-dates for better inductors in design. Table IV shows another datacomparison for the Type 1, 2, and 4 structures, where the induc-tance is compared against different magnetic film thicknesswith fixed and . Again, the trend of inductance improve-ment for Types 1 and 2 structures saturates as increases, whilecontinuous enhancement in a Type-4 structure can be achieved.This again suggests that Types 1 and 2 are not suitable struc-tures, while a Type 4 can be a good candidate. Figs. 5 and 6show the simulated inductance enhancement characteristics ofthe Type-3 and -5 structures as a function of the magnetic mediawidth and thickness, respectively. Fig. 5(a) shows that the in-ductance continuously improves for the Type-3 structure as thebulk magnetic media width gets wider and approaches to themetal coil inner diameter . Fig. 5(b) shows that the improve-ment in inductance for the Type-5 inductor becomes weaker andweaker as increases, particularly as it becomes far largerthan the outer diameter of the metal spiral and the trendsaturates at about m. In addition, the improvement
LONG et al.: A NEW MODELING TECHNIQUE FOR MAGNET STRUCTURES 1361
Fig. 5. Simulated inductance data as a function of the magnet widthW orWwith � = 16: (a) data for Type-3 structure and (b) data for Type-5 structure.
Fig. 6. Simulated inductance data as a function of the magnet thickness T orT with� = 16: (a) data for Type-3 structure and (b) data for Type-5 structure.
trend slows down as the increases and saturates as it reachesm. Fig. 6 shows that the inductance enhancement of
the Type-3 and -5 structures saturates as the magnetic media
Fig. 7. Simulated and measuredQ-factor for Type-5 inductor structure schemewith W = 40 �m and T = 8:4 �m.
thickness increases beyond some critical value. It seems thatthe saturation in inductance improvement as the magnetic mediadimensions increase generally occurs as the magnetic field be-comes weak. This observation shall be helpful in designing thedimensions of such magnetic-enhanced stacked spiral inductors,for example, the dimensions of m and mfor the magnetic media seem to be preferred in such design. Ap-parently, a very high self-resonant frequency is preferred in de-signing such magnetic-core inductors and a 18.6–GHz self-res-onant frequency was achieved in one of our super compact in-ductors designed in [5] because of its extremely low parasiticcapacitance. Fig. 7 shows the simulated -factor versus fre-quency curves for such super compact six-metal stacked spiralinductors with various , where corresponds to theinductor we designed in [5] extracted after de-embedding. Theother curves in Fig. 7 have included the silicon substrate andPGS effects. Fig. 7 shows that using magnetic materials not onlyincrease the inductance and the -factor, but also decrease theself-resonant frequency dramatically. However, the super com-pact inductor we proposed has a very high initial self-resonantfrequency that can afford being reduced when using magneticmaterials to improve the inductance and -factor as confirmedby the simulation. In general, using the new extended MagPEECmodeling technique and L-Simulator can be very helpful in de-signing various conductor-magnet structures, particularly mag-netic-enhanced RFIC inductors with arbitrary 3-D geometries.
V. CONCLUSION
We report a new extended MagPEEC modeling technique thatcan analyze 3-D arbitrary conductor-magnet structures with di-rect C-M interfaces. The new technique has been verified usingseveral C-M structures. Application of this new modeling tech-nique to designing super compact 3-D stacked spiral RFIC in-ductors proves to be very useful in practical design.
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Haibo Long received the B.S. degree from the De-partment of Electronic Engineering, Tsinghua Uni-versity, Beijing, China, in 2000, where he is currentlypursuing the Ph.D. degree, conducting research onelectromagnetic fields and microwave technologies.
His current research focuses on novel electromag-netic numeric solution for modeling RF IC inductorswith magnetic media integrated and electromagneticsimulation of signal integrity in printed circuit boardsfor mobile handset applications.
Zhenghe Feng received the B.S. degree in radioand electronics from Tsinghua University, Beijing,China, in 1970.
Since 1970, he has been with the Departmentof Electronics Engineering, Tsinghua University,where he is currently a Professor and DepartmentChair. His main research areas include numericaltechniques and computational electromagnetics, RFand microwave circuits and antennas, wireless com-munications, smart antennas, and spatial-temporalsignal processing.
Haigang Feng (S’00) received the B.S. degree inelectrical engineering from Tsinghua University,Beijing, China, and the M.S. and Ph.D. degrees (withhonors) in electrical and computer engineering fromIllinois Institute of Technology, Chicago, in 1998,2001 and 2005, respectively.
He is currently with RF Micro Devices, San Diego,CA, as an RF IC Design Engineer. His research in-terests center on analog, mixed-signal and RF IC de-sign and ESD protection design. He has contributedto more than ten papers.
Albert Wang (M’95–SM’00) received the B.Eng.degree from Tsinghua University, Beijing, China, in1985 and the Ph.D. degree from the State Universityof New York at Buffalo, Amherst, in 1996, both inelectrical engineering.
He was with National Semiconductor Corporation,Santa Clara, CA, until 1998 when he joined the Fac-ulty of Electrical and Computer Engineering, IllinoisInstitute of Technology (IIT), Chicago, where he iscurrently an Associate Professor and directs the Inte-grated Electronics Laboratory. His research interests
center on analog/mixed-signal/RF ICs, advanced on-chip ESD protection, ICCAD and modeling, SoCs and semiconductor devices, etc. He is the author ofOn-Chip ESD Protection for Integrated Circuits (Norwell, MA: Kluwer, 2002)and more than 80 papers in the field, and holds several U.S. patents. He is afrequent speaker at various industrial/academic/international forums and a fre-quent consultant to the IC industry.
Dr. Wang received the CAREER Award from the National Science Founda-tion in 2002 and the Sigma Xi Award for Excellence in University Research fromIIT in 2003. He is an Editor for the IEEE ELECTRON DEVICE LETTERS, an Asso-ciate Editor for the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I, a GuestEditor for the IEEE JOURNAL OF SOLID-STATE CIRCUITS, and a Guest Editorfor the IEEE TrANSACTIONS ON ELECTRON DEVICES. He was an Associate Ed-itor for the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II. He is an IEEEDistinguished Lecturer for the Electron Devices Society and the Solid-State Cir-cuits Society. He serves as TPC Member, Committee Chair and Session Chairfor many conferences, e.g., IEEE CICC, RFIC, APC-CAS, ASP-DAC, ISCAS,ICSICT, and NewCAS.
Tianling Ren received the Ph.D. degree from the De-partment of Modern Applied Physics, Tsinghua Uni-versity, Beijing, China, in 1997.
He is currently a Professor and Director of theDevices Research Division, Institute of Microelec-tronics, Tsinghua University. His research areas areMEMS, nonvolatile memories, ferroelectric/piezo-electric devices, magnetic devices, and spintronics.He has published more than 90 papers and holds 15patents.
Junbo Bao received the B.S. and M.S. degreesin chemistry from the Qingdao University ofOceanology, Qingdao, China, in 1987 and 1990,respectively. He is currently pursuing the Ph.D. de-gree in microelectronics and solid-state electronicsat Huazhong University of Science and Technology,Wuhan, China, and conducts research at the Instituteof Microelectronics, Tsinghua University, Beijing,China.
Feng Liu received the B.S. degree from WuhanUniversity, Wuhan, China, in 1996, and the M.S.degree from the Huazhong University of Scienceand Technology (HUST), Wuhan, China, in 2001,both in mechanical engineering. He is currentlypursuing the Ph.D. degree at HUST and conductshis research at the Institute of Microelectronics,Tsinghua University, Beijing, China.
His research interests include MEMS, magneticmaterials and RF devices.
LONG et al.: A NEW MODELING TECHNIQUE FOR MAGNET STRUCTURES 1363
Chen Yang received the B.S. degree from the De-partment of Electronic Engineering, Tsinghua Uni-versity, Beijing, China, in 2003. He is currently pur-suing the Ph.D. degree at the Institute of Microelec-tronics, Tsinghua University.
His research interests include high-frequency inte-grated circuits and devices.
Xiao Zhang received the B.S. degree in communica-tion engineering from Huazhong University of Sci-ence and Technology, Wuhan, China, in 2002. Sheis currently pursuing the Ph.D. degree at the Depart-ment of Electronics Engineering, Tsinghua Univer-sity, Beijing, China.
Her research interests include design of super-conductive filter and EM modelling for RF IC novelspiral inductors.
