Analysis of Horizontal and Vertical Couplings in Bonding Wire InterconnectionsUsing EFIE with Cylindrical Conduction Mode Basis Functions

Ki Jin Han, Madhavan Swaminathan, and Ege EnginSchool of Electrical and Computer Engineering, Georgia Institute of Technology

266 Ferst Drive, Atlanta, Georgia 30332, U.S.A.{kjhan, madhavan, engin} ece.gatech.edu

Abstract For clear understanding of complicated electricalTo clarify the initial step of 3-D interconnection design couplings in SiP, this paper analyzes parallel and vertical

this paper shows electrical characteristics of vertically and couplings in bonding wires, and discusses effects of wirehorizontally coupled bonding wire interconnections. For configuration and dimensional parameters on the electrical

efficient analysis, solving EFIE with cylindrical CMBF is perfonmances of SiP interconnectons.used, and additional approximation methods and matrix Overview of the Analysis Methodmanipulation are discussed. As authors proposed in [4] and [5], the method of solving

introduction EFIE with cylindrical CMBF improves accuracy and reduces

In the design of three-dimensional (3-D) packaging or computational effort, so can be an efficient way of obtainingfull coupling model of 3-D bonding wire interconnections. By

bonding wires and through-hole vias (THV) are critical using a similar procedure with conventional partial elementcomponents for achieving high efficiency of signal equivalent circuit (PEEC) method [6], the proposed method

transmission.t Wiorng betwee terminals onfstackedintegrated models the interconnections with circular cross section astransmission. Wirng between terminals on stacked integrated floigeuvln oa otg qaincircuits (ICs) and planar interconnections on substrate usually Zivalentmda±jotI Lresults in complicated 3-D bonding structures as shown in IjqRp ipd,j + COY imdj,jn = Vid ()Figure 1, so electrical couplings among the interconnectionsare difficult to characterize. Furthermore, high-frequency wherelosses due to skin and proximity effects affect wideband R1jjnq= *(7B w) ~ (4,W)dVj,applications required in a SiP. a=,i

Focusing on the electrical characteristics of bonding wires,various analysis and modeling methods have been proposed. Lpfim jnq = "IJ d (fJ, w) ojnq(F,w)G Fi§ )dVjdViJ andFast and simple analytic methods are found to be useful for ViVJinitial design [1]. However, they are sometimes inaccurate v =- brv)W,w)dSespecially incapable of describing high-frequency effects [2]. S

On the other hand, full-wave models based on are partial resistance, partial inductance, and modal voltage,electromagnetic (EM) solvers [3] are better in accuracy, but respectively. Cylindrical CMBF are defined ashuge computational effort may be needed to obtain full r^cos(n(j - j)) F jcoupling models of interconnections in stacked ICs. In this ij q(F,W)= )) F Eelpaper, for efficient analysis of full coupling model of bonding 0 elsewherewires, electric field integral equation (EFIE) combined with in the (n, q) mode of thejth conductor. Aj1 is the effective areacylindrical conduction mode basis functions (CMBF) [4] are for normalization, J. is the nth order Bessel function, andused for simulation and modeling. a' = -jo,ua [4].

The above modal voltage equation (1) is defined for eachstraight cylindrical conductor segment. To apply theprocedure to bended structures such as bonding wireinterconnections, we approximate the curvature of each wireto a collection of straight cylinder segments as shown inFigure 2(a). In the cylinder segments model, the equivalentnetwork of each segment conductor is connected as in Figure2(b), where only skin-effect mode networks are connectedtogether with other proximity-effect mode networks separatedto form closed loops.

Instead of obtaining a simplified equivalent circuit,calculating partial components for each conduction mode is amain source of computational efforts in the proposed method.

FIgure An example of 3-D wire bon integatio. (PhotoIn special, numerical integrals for all mutual inductances over

Figure 1. An example of 3-D wire bond integration. (Photo alfrqecswpponsmyeuiehgcmutincourtesy ofAmkorTechnology Inc.) all frequency sweep points may require huge computation

time. Fortunately, it is found that mutual coupling betweenconductors that are far separated each other can be

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approximated to simple frequency-independent formulas [7].One example is the following thin-filament approximation. Z

L,, =J GQt ,b)dzjdzi. (2)

Double integral in the above formula is not related to CMBF 0and frequency, and can be calculated in analytic way for anytwo straight conductor segments [8]. The accuracy of the thin- Xfilament approximation is ensured when the absolute distancebetween conductors are sufficiently large. Figure 3 shows therelative errors in coupling coefficients between the thin- 0filament approximation and integration with CMBF, wherewe can use about 500 um as a threshold distance between twoconductors to maintain relative error less than 103. Another Impedances with CMBFapproximation is called center-to-center formula [7], which (frequency dependent)also can be used when more loss of accuracy is permitted. Impedances with approximation

(frequency independent)Conductor segment Figure 4. Structure of the entire matrix with skin- and proximity-

approximation effect mode impedances.of a bonding wire

When two conductors are closely located together, weneed to return to finding accurate numerical integral in (1).However, the required number ofmodes is different accordingto the strength of coupling between conductors, which can bedetermined by a) minimum distance between conductors or b)coupling coefficient of the skin-effect modes. For use ofcriteria a), an algorithm of calculating minimum distance oftwo cylinders can be useful [9]. By choosing the requirednumber of bases, the whole sub matrix of higher-ordercomponents become sparse matrix as shown in Figure 4. Thesparse property of Zpp makes inversion ofZpp more efficient.

'rLoops"fiom In addition, since the frequency-independent approximateproximity-effect modes formula are in the off-diagonal of dense skin-effect mode

matrix (Zss), computational effort of generating this densematrix can be reduced to those of generating a banded matrix.

'Branches" J Analysis of Horizontal and Vertical Couplings in Bondingfrom skin-effect modes Wire Interconnections

Figure 2. Conductor segments approximation of bonding wires and The proposed method in the previous section is applied to

their equivalent circuits. All voltage sources represent inductive analyze horizontal and vertical couplings in five bondingcoupling among branches and loops. wires in this section. Quantifying two kinds of coupling is

important since interconnections in SiP can be coupled to0 others in arbitrary orientation. Actually, horizontal coupling is

mte 4 n 2 10 a popular type of coupling mechanism in general packagingEdiameter 40 um E EI= 100 PMr , T-L2ttMn AmI design or radio frequency (RF) circuit design. In contrast,

-10X T T rrX n n] -7X 500 I'm : vertical coupling is an emerging issue in modern 3-D1

- Rf I~ 1000 pMI° - E I I TE T E T0 O interconnections, and just a few authors discussed about this

rI

TLIE

-D EIJS-0pm topic [10]..° 1-2 F T Tr r T n~nTm X - t1Ipl

10 EHIE-EEBE conductor lengthq Simple structures for companing honizontal and vertical8 t couplings are shown in Figure 5. The shape of each bondingF 10r TTYVHHr T: wires is modeled as a circular arc, and each arc isu F F E:TF R E TR q4 T T L- approximated to nine straight conductor segments. The radius

7VI I T VTI and span angle are variables that determine the wire length*m10 i::eL L and the pitch between wires. Electrical configuration is also

aI V a L V 2 shown in Figure 5, where the loop inductance from two wiret Itt tt\t¢t m t It I T ti -t L T 7 T T U r T7 pairs are observed with the center conductor grounded. By

102 3 4 5 6 using this coupling structure, we can maintain constant

Distance ( 1m) lengths, so can fairly compare effects of two kinds ofFigure 3. Relative errors in coupling coefficient between parallel two couplings.cylindrical conductors.

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O&W,1.5 horizontal coupling 15 vertical coupling

-e-- 30./An -& 30 pAn-65 lin -~~~~65 pAn

100 /An - ~~~~~~100 /on

p~~~~~~~~~~~~~

span angle . ' 0.5 4 0.5': :"~~~~~~~~~~~~~~~~~~l' 10 6 lo ' i o lo 104 16 lo'8 01O

frequency (Hz) frequency (Hz)1.5 1.5

(a) Horizontally coupled bonding wires

Figures5.pGeometrical andgelectrical configurations offive -30 nr30Anr0.6 65 An 0.6 65 lAn<~~~~~~~~~~~~~~~~~ 10 /n 5 100 /An3+l n

type bonding wires. For all cases, the length of the center grounded 8 5-F°3conductor is 1 mm. 1lilililililililil0

Figure 6 shows effects of different pitches on self 0.2 frequency (Hz) frequency (H)z)inductances and mutual coupling in vertically and horizontally Figure 6. Self inductances and coupling coefficients with differentcoupled bonding wires. In case of a small pitch (30 microns), pitches. For all cases, the span angle of wires is 180 degrees.differences between vertical and horizontal couplings are notobserved. As the pitch increases, however, the self inductanceof the outer bonding wire pair begins to drop in lower Conclusionsfrequencies. The frequency dependence of inductance is To clarify the initial step of 3-D interconnection design,usually small in practical applications, but the variations can this paper showed electrical characteristics of vertically andbe a reason of imbalance in bonding wire characteristcs, horizontally coupled bonding wire interconnections. ForFigure '7 shows effects of different span angles on self efficient analysis, solving EFIF with cylindrical CMBF isinductance and mutual coupling in vertically and horizontally proposed, and additional approximation methods and matrixcoupled bonding wires. Since the center conductor is always manipulation are discussed. Compared to the hoizontalset to 1 mm, different span angle actually means different coupling effect, the vertical coupling is found to generatebending effect. In case of the horizontal coupling, increased possible imbalance that makes difficulty in electrical design ofbending lowers self inductances and mutual coupling since the 3-D interconnections.bending structure makes magnetic flux diverge. In contrast, For more practical analysis of SiP or 3-D interconnecions,wire bending in vertically coupled wires does not effect on the proposed method should be improved in memory anddiverging of magnetic flux, so the self inductances are similar speed. In additon, wideband performance should be analyzedfor different span angle. In high fequencies, the self by including capacitive coupling and finite ground effect.inductances and couplings are almost same for vertical and Acknowledgments

beoareasonta ofiblneinbnigwracaatrsis. hrznalyculdsnin.ieitronetos o

horizedbontlae wires.Sincethecentercoductorisalways manipulaThiswork was supported by the Mixed Signal DesignTools Consortium (MSDT) of the Packaging Research Canter,Georgia Tech, under project number 2126QOR.

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0.75 0.75 [6] Ruehli, A. E., "Equivalent Circuit Models for Three-Dimensional Multiconductor Systems," IEEE Trans-MTT,Vol. 22, No. 3 (1974), pp. 216-221.

0.65 \ 0.65 \ [7] Antonini, G. et al, "Fast Multipole and MultifunctionPEEC Methods," IEEE Trans. Mobile Computing, Vol. 2,

X0.6 \ 0.6 Xo No. 4 (2003), pp. 288-298.3 0.55--130 deg.530 deg. [8] Ray, S. et al, "Closed Form Expression for Mutual Partial

1 30deg , 0.551 30deg.ZInductance between Two Skewed Linear Current4 6 8 o 6 8 Segments," Proc. Antennas and Propagation Society

frequency (Hz) frequency (z) International Symposium, pp. 1278-1281, July 1999.horizontal coupling vertical coupling [9] Lennerz, C. et al, "Efficient Distance Computation for

1 l Quadratic Curves and Surfaces," Proceedings of0.95< 0 eE~ 95 __Geometric Modeling and Processing, pp. 60 - 69, July

2002.i 0.9 nb 0.9 ED [10] Lin, H. -G. et al, "Model Extractions of Coupled

Bonding-wire Structures in Electronic Packaging," Proc.APMC 2005, Vol. 1, Dec. 2005.

. 9 30 deg. -e.330 deg.< 3<,0.8 - 105 deg. h<Z 0.8 105 deg.

1 180 deg. ,180 deg.10.7 4 106 lo' 10lO 0.71 4 106 lo' 10l

frequency (Hz) frequency (Hz)0.6 .0.6

-e--30 deg. -e-30 deg.0.58 - 105 deg. 0.58 --105 deg.

5180deg. @ fi 180 deg.

0.56 / 0.56

°o0.54 at 0.54

0.52 et 0.52

0.54 = s 0.5104 106 10 10ol 104 106 10 10

frequency (Hz) frequency (Hz)

Figure 7. Self inductances and coupling coefficients with differentspan angles. For all cases, the pitch between of wires is 30 microns.

References[1] Patterson, H., "Analysis of Ground Bond Wire Arrays for

RFICs," Proc. Radio Frequency Integrated CircuitsSymposium, pp. 237-240, June 1997.

[2] Ruehli, A. E. et al, "On Modeling Accuracy ofEMIProblems using PEEC," Proc. IEEE InternationalSymposium on Electromagnetic Compatibility, Vol. 1, pp.341-346, November 2003.

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[4] Han, K. J. et al, "Wideband Electrical Modeling of LargeThree-Dimensional Interconnects using AcceleratedGeneration of Partial Impedances with CylindricalConduction Mode Basis Functions," accpetedforpresentation in IEEE International Microwave Symposium2008.

[5] Han, K. J. et al, "Electnic Field Integral Equation withCylindrical Conduction Mode Basis Functions forElectrical Modeling of Three-dimensional Interconnects,"submitted to Design Automation Conference.

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