Models for Long Bond Wires and Large Multi-port Capacitors

Analytical modeling has been performed on bond wires and multi-port capacitors and has been compared with electromagnetic simulation and microwave measurements. A transmission line model and a Green's function capacitor model were found to be the most accurate and efficient. INTRODUCTION For high-frequency and high-power integrated circuit simulation, accurate and efficient models are needed for bond wires and multi-port capacitors with dimensions approaching a significant fraction of the wawelength. Previously reported lumped [1,2,3] and distributed [4] bond wire models were found inadequate for such large and complicated geometries. Distributed multi-port capacitor models were simply non-existent. RESULTS To develop our own model, the characteristics of 25 pm diameter Au wires was simulated using em, a 3D full-wave electromagnetic simulator from Sonnet. The simulation was performed on symmetrical and non-symmetrical wires 1 to 4 mm long and 0.3 to 1.5 mm in span. Wire span is defined as the ldistance between the bonding pads. Figure 1 shows that for short Wires the simulated characteristics agree with the measured results but not with those calculated by the formula in reference [ 11. With the em simulation validated, LCR and transmission line models (Figure 2) were then extracted from the simulated S-parameters using EEsof's LIBRA program. Figure 3 shows that the extracted wire inductance values were lower than any existing formula would predict. With an empirical expression, the wire inductance can be expressed as: L(nHl= -0.15 + t?.46S+ 0.69H, where S and H are wire span and height in mm. It was found that a similar expression can not be written using only the total wire length. For the wires located above substrates with E,= 140 the extracted Laand Eaparameters of the transmission line model are shown in Figures 4 and 5 . Figure 6 shows that for long wires the LCR model is valid only up to approximately 16 GHz, while the transmission line model agrees with the em simulation at aJ frequencies. Multi-port capacitors can also be simulated using em. however, it is rather time consuming and leaves no room for optimization if the capacitor is a part of a larger circuit. Another drawback is the absence of tic analysis capability making large-signal analysis impossible. To develop our own model, we iusume the current density in the port area is uniform and apply an open boundary condition: dV/dn=O. As a result, the impedance matrix of a N-port circuit is given as: where G is the Green's function. For a rectangular pattern shown in Figure 7: 7r 7r k,=m-, kn-nk 2 = p e u , ( , , E , = l for m,n=O, otherwise .$,,.$,=fi. a b'