Analysis from Modeling

We use the physically-based equivalent circuit model shown in Figure 2.3.1 to simulate the S-parameters. Lt and Rt are the series inductor and parasitic resistor from the long microstrip transmission line body, respectively. The symmetrical Rs and Cs at the input and output ports represent the RF signal loss to the ground plane, which should be large for the bulk microstrip line formed on VLSI-standard low resistivity Si substrate (10 Ω-cm) without ion implantation.

The measured and simulated S-parameters of the bulk and thin-film microstrip transmission lines, with or without implantation, are shown in Figure 2.3.2 (a) and Figure 2.3.2 (b). Good agreement is obtained between the measured and modeled S-parameters, suggesting that the equivalent circuit model in Figure 2.3.3 is appropriated.

The extracted substrate impedances, deduced from the Rs-Cs sub-circuits for both bulk and thin-film microstrip transmission lines, are shown in Figure 2.3.3. For the bulk microstrip lines on standard Si, the proton implantation can increase the substrate impedance by more than one order of magnitude. For the thin-film microstrip lines, the relatively high substrate impedance arises from the high resistivity SiO dielectric inside the microstrip line body.

We have also used a physically-based equivalent circuit model, shown in Figure 2.3.4 to simulate the RF characteristics of the ring resonator. The shunt Rs and Cs sub-circuits simulate the substrate loss, and Cox is the parasitic oxide capacitor underneath the resonator of the 1.5 µm SiO2 on the Si substrate. The capacitor C1 represents the gap-coupling capacitor, while the series L and R are the parasitic inductor and resistor from the ring and coupling metal stub. The series LC forms the resonator realized by these coupling lines and the ring body. Figure 2.3.4 shows the equivalent circuit simulated and measured RF characteristics of both the CPW and microstrip ring resonators with ion implantation. Excellent agreement between the measured and simulated S-parameters, shown in Figure 2.3.2 for both CPW and microstrip resonators, was achieved. This indicates the accuracy of the equivalent circuit model. Similar good matching between circuit-simulated and measured S-parameters was also obtained for the resonators without proton implantation in Figure 2.3.2 (b) and Figure 2.3.3 (b). Thus the equivalent circuit can be used to extract the substrate loss from Rs-Cs sub-circuits.

The extracted substrate impedance from the Rs-Cs sub-circuits is shown in Figure 2.3.5. Proton implantation increases the substrate impedances by more than an order of magnitude. The decreasing substrate impedance with increasing frequency is due to the effect of shunt capacitance to ground, which is also consistent with the

higher loss at higher frequency of the transmission line and filter loss in our previous publications.

2.4 Conclusions

We have achieved extremely low power loss for both bulk (0.4 dB/mm at 50 GHz) and thin-film (0.9 dB/mm at 20 GHz) microstrip transmission lines on VLSI-standard Si substrates and fabricated CPW and microstrip ring resonators on Si substrates with good RF performance at ~40 and ~30 GHz, was close to that for ideal IE3D-designed resonators. Proton implantation selectively transforms the low resistivity Si substrates of bulk microstrip transmission line into a high resistivity state.

The high performance of thin-film microstrip line results from the high-resistivity SiO2-dielectric being inside the microstrip line body. Both transmission lines can be integrated into RF circuits and distributed devices at a reduced size compared with using CPW lines. Without implantation such resonators have worse insertion and reflection loss and completely fail. By using equivalent circuit models and EM simulation we conclude that the substrate impedances are the major cause of the poor RF performance.

0 10 20 30 40 50 0

2 4 6 8 10

12 Measured Simulated

bulk microstrip line w/o implanation CPW line w/o implanation

bulk microstrip line with implanation GaAs simulation

Frequency (GHz)

Power Loss (dB/mm)

Fig. 2.1.1 The measured and EM-simulated power loss of 3 mm long bulk microstrip transmission lines. For comparison, results for a 1 mm long CPW line are included.

Implantation produces a large loss reduction, from 6.7 dB/mm to 0.4 dB/mm at 50 GHz.

4 8 12 16 20 0

1 2 3 4 5 6

measurement

equivalent circiut simulation IE3D simulation

Power Loss (dB/mm)

Frequency (GHz)

Fig. 2.1.2 The measured and EM-simulated power loss of 0.75 mm long thin-film microstrip transmission lines. The measured loss at 20 GHz is < 1 dB/mm, i.e. much lower than the bulk CPW (3 dB/mm) and microstrip lines (6 dB/mm) in Figure 1 without implantation.

1200µm

(a)

(b)

Fig. 2.2.1Images of fabricated (a) CPW and (b) microstrip ring resonators designed at 40 GHz and 30 GHz, respectively. The long surrounded stubs near the ring are to enhance the coupling efficiency.

30 35 40 45 50

Fig. 2.2.2 The measured S-parameters of CPW ring resonators (a) with and (b) without proton implantation. The EM and circuit simulated filter characteristics are shown for reference.

20 25 30 35 40

without implantation circuit simulation

S-parameter (dB)

Frequency (GHz)

(b)

Fig. 2.2.3 The measured S-parameters of 30 GHz microstrip line ring resonators (a) with and (b) without proton implantation. The EM-simulated and the equivalent circuit simulated filter characteristics are also shown for reference. No resonance is observed in (b) due to the substrate loss of ~40 dB.

Fig. 2.3.1 The physically-based equivalent circuit for the microstrip transmission lines.

The Lt represents the line inductor, and Rt the parasitic resistor of the transmission line. The substrate loss is modeled by the shunt Rs and Cs to ground.

0.5

S

S

with proton implantation w/o proton implantation Solid: measurement

Solid: m easurem ent O pen: sim ulation

Fig. 2.3.2 The measured and equivalent-circuit modeled S-parameters of (a) bulk and (b) thin-film microstrip transmission lines on Si substrates. The effect of proton implantation is shown in (a). The different curve lengths are due to different

0.1 1 10 100 10

10

10

bulk microstrip line

with (solid) or w/o (open) implantation thin-film microstrip line