диафрагмированные волноводные фильтры / a369dd12-f901-4415-a2f6-f3e05f1e7735

Abstract—Three waveguide band-pass filters are designed based on three different resonant cavity structures, operating at WR-2.2 (0.33~0.5THz), WR-1.5 (0.5~0.75THz) and WR-1.0 (0.75~1.1THz) frequency band separately. Terahertz filters are all fabricated using the deep reactive ion etching (DRIE) silicon micromachining technique. For more accurate designs, the conductivity of the metal film with the roughness surface is investigated in the terahertz frequency band, using the HB and the modified Huray model. The measurements are performed using the vector network analyzer (VNA) with corresponding frequency extenders. Measured insertion losses within pass band are about 1.9dB, 2dB and 3.4dB respectively, which are in good agreement with simulations and therefore verifies the accuracy of the analysis above.

I. INTRODUCTION

There is a growing interest in the Terahertz (THz) system for the appealing potential applications in security scanning, communication and atmospheric monitoring ranging from 0.3 THz to 10 THz [1]. Waveguide filters have advantages over the planar transmission line filters, which have been investigated more than 15 years [11], due to their lower losses, higher factors and higher power handling capacities in the THz region. Moreover, their standard waveguide sizes make them easy to interconnect with the measurement system and other THz solid systems [2].

The micromachining technique has an advantage over the computer numerical control (CNC) metal machining, due to its highly accurate dimensional control as well as its potential for highly accurate batch fabrication, reducing the cost per components [3]. Therefore, the micromachining technique, such as the DRIE technique, has been widely used for the fabrications of THz components.

As the frequency increases, the common value of metal conductivity used in microwave and millimeter-wave frequency band is not any more applicable. And the effect of the surface roughness on the metal conductivity should be investigated for more accurate designs.

In this paper, the effective conductivities of the metal film with different roughness surfaces are investigated in the terahertz (THz) frequency band for more accurate designs of THz components. Three filters are designed according to the analysis of conductivity and fabricated using the DRIE micromachining technique, which are operating at the 0.33~0.5THz, 0.5~0.75THz and 0.75~1.1THz frequency band separately. Measurements are in good agreement with the simulations, which verifies the accuracy of the analysis. The designs of filters are valuable for the metal waveguide components at 0.3~1.1THz frequency band or higher frequencies.

II. CONDUCTIVITY OF THE METAL FILM AT THE TERAHERTZ

FREQUENCIES

The complex conductivity of smooth bulk metal can be in a large majority of cases described by the Drude model, in which

ω = 2π f ; τ 0 is a frequency-independent part of the scattering relaxation time of the free electron and β describes the frequency dependence . At the microwave frequency band, the conductivity σ (ω ) is represented by σ 0 because the relation between ω and τ meets ωτ 1. And the value of σ 0 is also adopted in the commercial full-wave electromagnetic simulation software (Ansoft HFSS). While the frequency is up to the terahertz frequency band, (1) should be adopted for obtaining more accurate conductivity.

According to the classical relaxation-effect model, the skin depth of homogeneous metals has the general forms given by [5]

formula (3), the skin depth of the smooth gold film is less than 0.15 μm from 0.3THz to 1.1THz.

When the surfaces of the metal films are smooth, the Mie-scattering-based model is more accurate [6]. When the surface roughness exceeds the skin depth, the conductivity σ (rough) of the rough metal surface can be captured by a frequency dependent correction factor Krough [7]

Rq to the skin depth δ is less than 4, Krough can be expressed using the HB model [8], which is shown in (4). According to the (4), factor Krough is less than 2 no matter how big the surface roughness is.

When Rq is much larger than δ , the HB model is not accurate. In this situation, the modified Huray model is proposed based on the Huray model [9] to calculate the

conductivity of rough metal surface. The 3-D “snowball” structure of metal surface, which is shown in Fig. 1, is used to simulate the rough surface [10]. The correction factor Krough in this method, which relates to the metal surface topography and the frequency, is expressed in (5).

Fig. 1 3-D “snowball” structure of metal surface

where r is the radius of the ball, Af is the area of the equivalent hexagon of the “snowball” structure.

According to the formula (3~5), the effective conductivity decreases while the surface roughness increases, no matter which method is used.

III. DESIGNS OF WAVEGUIDE BAND-PASS FILTERS

IV. FABRICATION PROCESS

Three filters are all fabricated using the DRIE micromachining technique. First of all, filter 1 is split into two halves symmetrically in E-plane and each half is etched on a polished silicon wafer. Filter 2 and filter 3 are both etched on one silicon wafer and another silicon wafer just plays the role of a cover. Next, the surfaces of two wafers are both metalized by electroplating gold layer to a thickness of 3 ȝm. Then two silicon wafers are bonded together by applying a gold-to-gold thermocompression bonding process. Because the close bonding between two silicon wafers can be well completed, the electromagnetic effect from the air gap between two wafers can be ignored, which is not ideally guaranteed using conventional metal machining in general. Finally, the end surfaces of the bonded testing structure are sputtered with a gold film of several nanometers to ensure the good electric connection to the measurement system.

The photographs of three micromachined filters are shown in Fig. 3. The size of the filter 1 is given by 3 mm×5 mm×1 mm. Sizes of the filter 2 and 3 are both given by 2 mm×3 mm×1 mm. The test fixtures are fabricated for measurements, which are also shown in Fig. 3.

Fig. 3 The photographs of the micromachined filter and corresponding test fixture (a) the filter 1 (b) the filter 2 (c) the filter 3

Fig. 2 Structures of the (a) filter 1 (b) filter 2 (c) filter 3

Filter 1 is designed based on four circular resonant cavities the coupling between resonant cavities is completed by inductive irises, operating at the 0.33~0.5THz frequency band. The filter 2 is operating at the 0.5~0.75THz frequency band, and a transmission zero is introduced into the filter 2 through the cross coupling, improving the rejection of the stop-band. Filter 3 is composed with two inter-coupling rectangular cavity resonators, operating at the 0.75~1.1THz frequency band.

As shown in Fig. 2, the standard WR-2.2 (559 μm×279 μm), WR-1.5 (381 μm×191 μm) and WR-1.0 (254μm×127μm) rectangular waveguides are adopted as the input and output waveguides. For the purpose of interconnecting the measurement system conveniently and simplifying the fabrication, the etching depths of three filter structures are 279μm, 191μm and 127μm respectively. The effective conductivities in the simulation models are set according the analysis above. The optimization is carried out using the full-wave electromagnetic simulation software (Ansoft HFSS) and the values of relative conductivities are set according to the analysis above.

V. MEASUREMENTS AND RESULTS

S-parameter measurements are carried out using Agilent N5245A VNA with OML 0.325~0.5THz, VDI 0.5~0.75THz and VDI-VNAX 0.75~1.1THz frequency extenders, as shown in Fig. 4. The system are all calibrated by TRL standards with the insert loss less than 0.1 dB and the return loss better than 30 dB. Measured results are shown in Fig. 5, compared with the simulations.

Fig.4 S-parameter measurement setups (a) with OML 0.325~0.5THz frequency extenders (b) with VDI 0.5~0.75THz frequency extenders (c) with VDI-VNAX 0.75~1.1THz frequency extenders

From Fig .5 (a), the insertion loss of the filter 1 within the pass band is less than 1.9dB and the relative bandwidth is 5.3%. The measured center frequency shifts downward to 416 GHz

from 419 GHz, and the band width expands to 22 GHz from 16 GHz.

From Fig .5 (b), the best insertion loss of the filter 2 within the pass band is about 2dB and the relative bandwidth is 6.3%. The measured center frequency is at 629GHz, shifting downward 2GHz compared with the simulation. The measured transmission zero is at 660GHz.The high return loss in pass band is probably caused by alignment errors of the whole screwed assembly.

From Fig .5 (c), the average insertion loss of the filter 3 within the pass band is about 3.4dB and the relative bandwidth is 2.1%. The measured center frequency is at 1.033THz, which shifts downward 0.002THz compared with the simulation.

Freq./THz

(c)

Fig. 5 Measured results of (a) filter 1 (b) filter 2 (c) filter 3, compared with simulations

In a word, the measured insertion losses of three filters are basically in accord with the simulations. Therefore, the metal conductivity and surface roughness loss are the main reason of the deterioration of the insertion loss. The center frequencies shift downward and the bandwidths expand, compared with the simulations. There are two main reasons for these phenomena. Firstly, the fabrication deviation of resonant cavity volume is the main reason. Secondly, the transverse etching in the DRIE micromachining process leads to the non-vertical sidewalls and then causes changing of the cavity volume, which consequently shifts the center frequency of the filter. While the etching time is longer than the passivation time in the Bosch process of the DRIE, the upper surface of the etched groove is narrower than the bottom surface. Conversely, the upper surface will be wider than the bottom surface.

VI. CONCLUSION

In this paper, three waveguide band-pass filters operating at WR-2.2, WR-1.5 and WR-1.0 frequency band are designed according to the analysis of the metal conductivity with surface roughness, and are fabricated using the DRIE micromachining technique. The measured results are in good agreement with simulations, which verifies that the analysis and the design are applicable to high-performance THz passive components.

ACKNOWLEDGMENT

The authors would like to thank Haotian Zhu, Peng Wu, and Quan Xue, Department of Electronic Engineering, City University of Hong Kong, for the measurement and helpful discussion. This work was supported by the National Natural Science Foundation of China (61371054).

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