диафрагмированные волноводные фильтры / e689898c-4723-4bd7-98b3-c092d17ae01d

A. Design of components

We use the fabrication process and filter structures presented in [8] as the starting point for our analysis. The designs and fabrication process are briefly summarized here for reader convenience.

The filter designs are based on classical waveguide filter topologies similar to the ones shown in [10], [11]. The filters were synthesized using FEST3D 6.9.7 by Aurorasat. The lowpass filters (LPFs) are realized with periodic and symmetric capacitive irises in the E-plane. The used iris thickness is 100m. The filters are designed for a highest transmission frequency of 280 GHz with return loss >20 dB. The band-pass

The gold-plated SOI -wafer pairs containing half waveguide structures are bonded together using wafer-level optically aligned Au-Au thermocompression bonding. Finally the 1724- m thick wafers are cut into chips using narrow preetched cutting trenches on the dicing streets and combined with mechanical dicing from both wafer sides. The BPFs structures are processed only in the lower silicon wafer, and then capped with a flat upper silicon wafer (see Fig. 1(b)) using the same Au-Au thermocompression process. The band pass filters are fabricated having the H-plane along the wafer surface. The structures are formed using a single depth DRIE - etch step. The BPFs are processed on 882 μm thick SOI

wafers with 430 μm thick structure layers. The SOI wafers containing the BPF structures are capped with flat 400 μm thick DSP (Double Side Polished) wafers.

C. Measurement setup

S-parameters of the fabricated waveguides and filters were measured with Agilent PNA-X vector signal analyzer with V03VNA2 millimeter wave extenders from Oleson Microwave Labs for 220 325 GHz frequency band. Brass sample holders were fabricated (Fig. 2) for connecting the silicon samples to the waveguide interface of the measurement setup. Thru-reflect-line (TRL) calibration was performed at the waveguide interface [13].

Fig. 2. Measurement setup for the fabricated silicon dies: (a), (b) sample holder for dies with side entry [8].

Scanning electron microscope (SEM) Zeiss LEO 1525 FEG and optical profilometer Bruker Contour GT-X are used to study the dimensions and surface roughness of walls of the manufactured waveguides and filters.

III.RESULTS

A.RF performance of the filters

The simulation and measurement results of the waveguides and the filters are presented in [8]. As a summary, the measured (simulated) insertion loss for the LPF at 270 GHz is 3.3 dB (0.3 dB), whereas the return losses are >15 dB (>20 dB). For the BPF the insertion loss is 5.6 dB (0.5 dB) and return loss is >13 dB (>20 dB) at 270 GHz. In simulations, the walls were considered as gold without any roughness.

B.Filter parameters analysis

1)Surface roughness: To avoid losses in signal transmission, metal on waveguide structures must have low surface roughness [15]. It was found that DRIE process is critical for metal surface roughness on sidewalls. During DRIE -process the SF6 is used to etch silicon, while C4F8 provides a protective polymer on the sidewalls. This alteration of etching and passivation steps introduces unwanted modulation of the sidewall profile as it is shown in Fig. 3(a). Measurement shows that for not optimized DRIE process surface roughness of the metal were 1.3 μm for sidewalls and 90 nm for waveguide bottom. To achieve lower surface roughness, a special etching receipt was developed. Additionally, oxidation of Si was done before gold sputtering. The developed process allowed to reach 350 nm roughness of metal on sidewalls (see Fig. 3(b)).

Fig. 3. Regular sidewall modulation due to DRIE process before smoothing

(a). SEM picture of 350 nm roughness of sidewall metal (b).

Impact of metal surface roughness on losses was investigated by using 3D EM simulator Ansys HFSS v. 15. The HFSS provides two different models for surface roughness; Groisse model [16] and a more advanced Huray model. In Groisse model, surface impedance of a rough surface is scaled with a factor which depends on skin depth and surface roughness (in e.g. μm). The Groisse model is applicable to problems where the surfaces are highly polished. In cases where the roughness of the deposited metal is considerably higher, Huray model should be used [16]. It is based on visible features such as irregular collection of conductor nodules in a SEM image. The skin depth is also included in the model. From a SEM image, a nodule radius (a) and a Hall-Huray Surface Ratio (HHSR) can be determined, which are set as input parameters. The HHSR is calculated from the number of nodules (N), having a typical radius a, per specific unit cell area (A).

Simulation results of the BPF with Groisse roughness model are shown in Fig. 4. The |S21| is between -0.8 dB and -1 dB at 270 GHz when roughness value is varied form 200 nm to 1000 nm. Parameters for the Huray model can be estimated from a SEM image shown in Fig. 3(b). For a unit area of 2 μm × 2 μm the number of nodules with an average radius of about 100 nm is about 380. This results in as HHSR=12. Simulation results of the BPF with Huray roughness model are shown in Fig. 5. The |S21| is between -0.5 dB and -5.5 dB at 270 GHz when nodule radius (a) is varied form 0 nm to 350 nm. The skin depth at 270 GHz is 150 nm and of the same order of magnitude as the gold nodules. It is shown in the next section that losses predicted by the Huray model are in good agreement with experimental results with the parameters extracted from SEM image, i.e. nodule radius a 60 nm.

Fig. 4. Simulated |S21| of the BPF with different surface roughness values in the Groisse model.

Fig. 5. Simulated |S21| of the BPF with different nodule radiuses (a) in the Huray model.

2) Dimensions errors: The main reason for dimension errors is accuracy of the etching process. In the SEM image of a BPF interresonator wall in Fig. 6(a), the wall width is 103 μm and 98 μm (design 100 μm) on the top and bottom sides, respectively. So the accuracy of utilized DRIE process is about 3 m.

Fig. 6. SEM images of BPFs showing manufacturing accuracy of interresonator walls with different etching parameters. (a) straight wall, (b) tapered wall.

The effect of etching accuracy on BPF filter is shown in Fig. 7. The interresonator wall width is increased by 0 μm, 2 μm, or 4 μm. The center frequency is shifted upwards by 2.2 GHz (0.8 %) at maximum. The shift is due to decreased lengths of the resonating cavities.

Fig. 7. Simulated |S21| of the BPF with varied interresonator wall width.

Parameters of the DRIE process are critical for sidewall accuracy. In Fig. 6(b) a SEM image shows a deformed BPF interresonator wall as a result of different etching parameters. Filters in Fig. 6(a) and 6(b) have the same geometry but interresonator wall width varies from 98 μm up to 154 μm in subfigure (b). In addition, verticality of the wall edges varies from 0.3 to 2.3 degrees. Such differences in interresonator wall dimensions have a strong impact on filter performance. To study the effect of wall verticality, Fig. 8 shows the |S21|

when interresonator wall width is 120 μm (Fig. 6(b)) on the bottom side and is varied on the top side from 100 μm to 160 μm with 20 μm steps. The center frequency is shifted upwards by 12 GHz (4%). Also the frequency response is changed and the bandwidth is decreased. Fig. 8 shows also the measured |S21| (solid line with markers). The measurement result agrees well with simulation in which interresonator wall width of 120/160 μm (bottom/top side) are used. The dimensions are very close to the measured ones from SEM image (120/154 μm in Fig. 6(b)). In simulations, the Huray model with a = 60 nm is used as surface roughness. The insertion loss, 2.5 dB at 290 GHz, agrees well with the measurement, and the used nodule radius is reasonable when looking at the small Au particles in Fig. 3(b). At least in this case the Huray model predicts the realised losses very well and is more accurate than the Groisse model.

Fig. 8. Simulated |S21| of the BPF with varied interresonator wall verticality. Measurement result is shown as solid line with markers.

3) Wafer to wafer misalignment: wafer alignment with high accuracy is needed for fabrication of LPF. Utilized technology allows to reach 3 μm alignment accuracy. The wafer-to-wafer misalignment was simulated and the results are presented in Fig. 9. The results show that misalignment of 3 μm has a negligible effect on the frequency response of the LPF. With ±20 μm misalignment, the center frequency is shifted only about 1 GHz (0.4 %).

Fig. 9. Simulated |S21| of the LPF with varied misalignment between the two wafers.

4) Gaps in the corners due to notching effect in the DRIE process: It was found for components from some manufacturing lots that the final oxidation step did not successfully fill the 2- m gap in the metallization at the waveguide corner due to over etching of silicon dioxide [8]. Simulations were done with a 2- m or 4- m gap in gold in the corners of the waveguide for the band-pass filter. It was observed that the simulated results with a 2- m gap comply

very well with the measured results. The measured insertion loss was as high as 6 dB at 270 GHz.

5) Misalignment between the BPF and the extenders waveguides: Due to very high frequencies, misalignment between the filter and the extender waveguides may have an effect on the measurement results. This was investigated with simulations by misaligning the input/output waveguides simultaneously with respect to the BPF along E-plane. The results are shown in Fig. 10. Is can be seen that when misalignment is varied from 50 m to 250 m, the insertion loss of the BPF is increased from 2.5 dB to about 8 dB with ripples in the frequency response. In addition, the stopband attenuation is decreased from 60 dB [8] down to 30 40 dB. The measured |S21| is solid line with markers. The E-plane misalignment has a significant effect on stop-band behaviour, and explains the measurement results at least partly.

Fig. 10. Simulated and measured |S21| when the measurement waveguides are misaligned along E-plane with respect to the BPF.

In addition to E-plane misalignment, simulations were done for H-plane and longitudinal plane misalignment between the extender waveguides and the BPF. With 5 μm to 55 μm misalignment in H-plane, the |S21| remained almost constant. With the same misalignment range in the longitudinal plane, the |S21| varies between -2.7 dB and -4.4 dB at 290 GHz (Fig. 11). The gaps have no significant effect on the stopband behaviour. It can be concluded that misalignment is more critical in E-plane and longitudinal plane than in the H-plane of the filter.

Fig. 11. Simulated |S21| when the extender waveguides are misaligned in longitudinal plane with respect to the BPF.

IV. CONCLUSIONS

Impact of fabrication processes and electrical interfaces with external waveguides on parameters of silicon micromachined sub-THz waveguides, low-pass and band-pass filters at frequency range 225–325 GHz were studied. Based

on results, it can be concluded that an accurate etching process with wall verticality better than 0.5 degrees is required. In addition, for accurate characterization of the fabricated components, alignment between the sample-under-test and the extender waveguides is also important. Simulations with Huray model for surface roughness described the measured values well with the physical parameters obtained from SEM images. Results obtained in this work are also applicable for other types of devices based on micromachining waveguides.

ACKNOWLEDGMENT

This work has been financially supported by the Academy of Finland under grant MilliRAD, number 314541.

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