An Equivalent Circuit for the Double Bonding. Wire Interconnection. F. Alimenti, P. Mezzanotte, L. Roselli, R. Sorrentino. Dipartimento di Ingegneria Elettronica e ...
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An Equivalent Circuit for the Double Bonding Wire Interconnection F. Alimenti, P. Mezzanotte, L. Roselli, R. Sorrentino Dipartimento di Ingegneria Elettronica e dell’Informazione, UniversitA di Perugia. via G. Duranti 93, 1-06125 Perugia, Italy. E-mail: alimentiOiste1.ing .unipg. it Abstract- This work proposes a quasi-static model for the double bonding wire interconnection. The wires have been assumed to be parallel, while their curvature has been described with an arc of circle. The model is based on the representation of the structure by means of four sections of a uniform, homogeneous transmission line. The characteristic impedance of this line can be evaluated analytically versus the wire spacing. A double bonding wire structure has been analyzed systematically. In order to determine the accuracy of the model, the same structure has been simulated with the FDTD technique. The quasi-static model has been found to be in good agreement with the full-wave‘model.
11. MODELLING In this section, an equivalent circuit of the double bonding wire will be proposed. The equivalent circuit is based on a quasi-static model of the structure.
A . Geometrical model The double bonding wire interconnection is depicted in Fig. 1. The total length of the structure is given by: db
= pi 4-d i
+ g + d2 4- p2
(1)
The curvature of the bonding wire has been approxiI. INTRODUCTION
HE bonding wire interconnection technique is cur-
T
rently adopted in the fabrication of hybrid and monolithic microwave integrated circuits [l]. It has the advantages to be inexpensive and robust, while allowing the thermal dilation of the bonded chips. The latter is a basic requirement for space-qualified components. In spite of its popularity, the application of such technique in millimeter-wave frequency ranges suffers a severe limitation because of the spurious reactances associated with the interconnection. The main reactive contribution is due to the wire bond inductance [2]. The conventional methods to reduce this inductance are based on multi-wire or ribbon configurations [3], [4]. To overcome the above frequency limitation, networks, capable to compensate for the wire bond inductance, must be realized on the bonded chips. Such networks embed the wire bond inductance in a a-type low pass filter, allowing the increase of the interconnection bandwidth. The value of the wire bond inductance can be controlled by adopting a double wire configuration and by adjusting the wire spacing as in [5]. This work proposes a quasi-static model for the double bonding wire interconnection alternative to that in [6]. Such model is suitable to be implemented in commercial microwave CAD tools allowing the design of the compensation networks. For validation purposes, the model has been compared with FDTD simulations of the double wire structure.
’A
Fig. 1. Double bonding wire interconnection.
mated with an arc of circle while the wires have been assumed to be parallel. With reference to the system of coordinates shown in Fig. 1, the height of the wire from the ground plane can be expressed as follows:
h(x) = ye + Jrz - (x - xe)2
(2)
In the above expression xcrye and r, are the coordinates of the center and the radius of the circle respectively.
633 0-7803-5135-5/99/$10.000 1999 IEEE
1999 IEEE MTT-S Digest
These parameters can be evaluated from the mechanical capacitances are, for i = 1 , 2 : dimensions of the structure as indicated in Tab. I.
B. Quasi-static model A quasi static model of the bonding wire has been derived considering the interconnection as a non-uniform, inhomogeneous transmission line [5], [7]. The nonuniformity is due to the curvature of the bonding wire, while the inhomogeneity is due to the dielectric substrates (sections BC and EF of Fig. 1). In order to simplify the model we neglect the inhomogeneity of sections BC and EF. Under this assumption, the cross section of the transmission line describing the double bonding wire consists of two circular wires over a ground plane. The wires are at the same electric potential. The characteristic impedance of this line has been computed in [8] and is given by:
where:
hw,i =
h (P1/2) - h l ,
ifi= 1
h ( d b - p 2 / 2 ) - h2, if i = 2
(9)
In the above formulas pi is the length of the i-th soldering region, while Z8,i and cs,i are the characteristic 2,= Z c ( h , s , T w , q )= 4R rl log (2h,,,,,) ( 3 ) impedance and the effective dielectric constant of the i-th microstrip line. Note that C s , i / p i and 2 L , , i / p i are the capacitance and the inductance per unit length of In this expression s is the spacing between the two wires, the microstrip line. The fringing capacitance C!,i has h is the height of the wires from the ground plane, r , been used to represent the i-th open microstrip end. is the wire radius and q is the wave impedance of the The equations (6)-(8) have been derived by modelling medium. each soldering region as a pair of transmission lines sharThe non-uniformity can be considered by introducing ing a line conductor. Such common conductor is con(2) in (3). The local characteristic impedance of the line stituted by the microstrip metallization, while the other is thus expressed by the following function: two line conductors are the wires (which are at the same potential) and the ground plane. In first approximation Z ( X ) = z c ( h ( X ) s, , T w , v) (4) we neglect the coupling between these lines. The two port description of each soldering region is obtained by To account for the non-uniformity, the interconnection properly terminating the two lines, i.e. by connecting has been divided in four intervals corresponding to the the wires to the microstrip metallization at the soldersections BC, CD, DE and EF of Fig. 1. Each section ing point and by loading the open microstrip end with has been represented with a uniform transmission line the fringing capacitance. The T networks have been deas shown in Fig. 2 . The characteristic impedances of rived by further simplifying above the two port descripthese lines have been computed by evaluating the local tion under the approximation of small electrical lengths. impedance at the midpoints between B and C, C and D, D and E, E and F respectively. The characteristic 111. RESULTS parameters of these uniform lines have been quoted in To determine the accuracy of the proposed quasiTab. 11. static model, a double bonding wire interconnection between two Ai203 substrates has been analyzed. The scattering parameters of the structure have been computed versus the wire spacing s. The magnitude of 5’11 is shown in Fig. 3 (solid line) for two different values A B c D E F 0 of s. The dimensions of the interconnection are indicated in the caption of the figure. In order to provide Fig. 2. Equivalent circuit. a reference dataset, the same structure has been simulated with the FDTD method, as illustrated in [3]. The The soldering regions (sections AB and FG of Fig. 1) results are plotted in Fig. 3 (dashed line). The agreecan be modelled as two lumped T networks (see Fig. 2), ment between the quasi-static model and the full-wave accounting for the parasitic inductances and capaci- model is in the order of f 1 . 5 d B in the frequency range tances associated. The value of these inductances and 5 - 50 GHz.
634
0
--
50
-5
I
i..................................
_
i..................................
Q-
40 .................................
-1 0
-
quasi-static model FDTD model i.................................. i............................... i -10d0
-1 5 %
E
’0
-20
5
10
15
20
25 30 35 frequency [GHz]
40
50
45
0 0.2
Fig. 3. Comparison between S l l estimated with the quasi-static model and that computed with the full-wave FDTD simulator. The dimensions of the structure are: rw = 17pm, w = w1 = dl E,,Z
= 244pm, db = 470pm, g = 224pm, PI = p 2 = = d2 = 67pm, hb = 344pm, hl = hz = 254pm, = 9.86.
i.................................. ----E?
[ ..............-. -15d0 ~
----E-
_-- ...;-.-.--
10 ............................
-25
w2
20 .................................
.n
--
.......
I -20dB4
--;-+----*----................... ..........................
’
0.4
0.6 0.8 normalizedwire spacing
Fig. 4. Bandwidth of the double wire interconnection versus the normalized wire spacing s / w .
56pm, +,I
=
From the analysis of the previous example it has been found that the quasi-static model produces reliable results only if the fringing capacitances Cf,j is computed accurately. Several models of the open ended microstrip are available in the literature (see, for example [9]). When the open microstrip end is close to the substrate edge, however, such models are no longer applicable. In our case the distance of the substrate edges form the microstrip ends are of only 67pm. For this reason, we compute the fringing capacitance by means of a full-wave FDTD simulation. A capacitance of about Cf = 7fF has been obtained. Finally, the bandwidth of the interconnection has been evaluated versus the wire spacing. The bandwidth has been defined as the maximum frequency for which IS111 < A . The bandwidth behaviour is shown in Fig. 4 for A = -10, -15 and -20dB. It is worth noticing that the bandwidth of the interconnection increases as the spacing between the two wires approaches the width of the microstrip. For the un-compensated interconnection proposed, a bandwidth greater than 40 GHz is difficult to achieve.
wave models is of the order of f 1 . 5 d B for the scattering parameter $1 in the frequency range 5 - 50GHz. The proposed model is suitable to be implemented in commercial microwave CAD tools. REFERENCES [l] W. Menzel, “Interconnection and packaging for MMIC’s,” in 27-th European Microwave Conference, vol. 1, (Jerusalem (Israel)), pp. 649-654, Sep. 1997. [2] S. Nelson, M. Youngblood, J . Pavio, B. Larson, and
R. Kottman, “Optimum microstrip interconnections,” in IEEE International Microwave Symposium, vol. 3, (Boston), pp. 1071-1074, Jun. 1991. [3] F. Alimenti, P. Mezzanotte, L. Roselli, and R. Sorrentino, “Multi-wire microstrip interconnections: a systematic analysis for the extraction of an equivalent circuit,” in IEEE International Microwave Symposium, vol. 3, (Baltimora (MD)), Jun. 1998. [4] W. Menzel, “Packaging and interconnect techniques for com-
[5]
[6]
[7]
IV. CONCLUSIONS I81
L
In this work, a quasi-static model of the double bonding wire interconnection has been proposed. A systematic, FDTD simulation of such interconnection has been used to determine the accuracy of the quasi-static model. The agreement between quasi-static and full-
1
[9]
635
plex millimeter-wave front-ends,” in 28-th European Microwave Conference, vol. l,(Amsterdam (NL)), pp. 497-502, Sep. 1998. U. Goebel, “DC to 100 GHz chip-to-chip interconnects with reduced tolerance sensitivity by adaptive wirebonding,” in 3rd Topical Meeting on Electrical Performance of Electronic Packaging, (Monterey, CA), pp. 182-185, Nov. 1994. A. 0. Harm, K. Mouthaan, E. Aziz, and M. Versleijen, “Modeling and simulation of hybrid rf circuits using a versatile compact bondwire model,” in 28-th European Microwave Conference, vol. 1, (Amsterdam (NL)), pp. 529-534, Oct. 1998. F. Alimenti, U. Goebel, and R. Sorrentino, “Quasi static analysis of microstrip bondwire interconnects,” in IEEE Znternational Microwave Symposium, vol. 2, (Orlando, FL), pp. 679682, May 1995. W. Hilbern. Electrical Characteristics o f Transmission Lines. Dedham, Gassachusetts: Artech House; 1979. N. G. Alexopoulos and S.-C. Wu, “Frequency-independent equivalent circuit model for microstrip open-end and gap discontinuities,” IEEE Trans. Microwave Theory Tech., vol. 42, pp. 1268-1272, JuI 1994.
a = l - - hb - h2
b = -2db
hb - h i
4, .'={-e, i f a = ~
ifA>O
section
=
UC
hi
2 (hb - hl)
characteristic impedance
+ $)
BC
(Pl
CD
z(xc+:+dl)
DE
- h: - x,"
(". 2' +P1
dl
c
= di
+ ( h i - h2) (hb - h2) rc = hb - yC
electrical length
Po dl
PO ( x c - PI - d l )
+
EF
)
PO (PI+ di + g - 2 , )
Po d2
636
