IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 17, NO. 9, SEPTEMBER 2007
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Equivalent Lumped Elements of DC-Biased Thin Film Microstrip Line in MMICs Hung-Wei Wu, Student Member, IEEE, Min-Hang Weng, Member, IEEE, Yan-Kuin Su, Fellow, IEEE, Ru-Yuan Yang, Student Member, IEEE, and Cheng-Yuan Hung, Student Member, IEEE
Abstract—This letter investigates the equivalent lumped elements of the thin film microstrip line (TFML) with different dc-bias voltages for the first time. The wide-band frequency-dependent characteristic impedance 0 ( ) and equivalent lumped elements such as ( ), ( ), ( ), and ( ) are accurately characterized for dc-biased TFML on a 20- m thick low dielectric constant ( ) polyimide up to 50 GHz. The experimental results shows the dc-biased TFML can be extensively applied to the voltage-controlled passive and active integrated circuits. Index Terms—DC-bias, low , monolithic microwave integrated circuit (MMIC), polyimide, thin film microstrip line (TFML).
I. INTRODUCTION
HE integration of a large number of passive devices with low loss and high reliability is as important as the advancement in active devices technologies. However, the low-resis10 cm) silicon substrate used in standard CMOS tivity ( technology for most monolithic microwave integrated circuits (MMICs) has limited the integration of high- passive devices due to the high loss of the low-resistivity silicon substrate [1], [2]. Recently, thin film microstrip line (TFML) has gained popularity for applications in silicon (Si) based MMICs and multichip modules (MCMs), with incorporation of the analog and digital circuits in a package, due to its high integration ability with active circuits and passive devices [3]–[8]. TFML can solve this problem because it shields the line from the substrate effects [3]–[5]. In recent year, the studies of TFML with a low dielectric constant ( ) dielectric layer have been characterized, and most of them focused on the fabrication process and attenuation performances without dc-bias [3]–[8]. Actually, these passive devices using TFML technology should meet the different dc-biased conditions when the active devices are operated. Therefore, to achieve the requirement of high quality factor ( ) Si-based MMICs, the microwave characteristics and models of dc-biased TFMLs are one of the important issues for interconnects integrated on system-on-chip (SOC) technology. Additionally, according to the reports of the international tech-
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Manuscript received March 30, 2007; revised April 18, 2007. This work was supported by the National Science Council of Taiwan, under Grant NSC 94-2622-E-492-001-CC3. H.-W. Wu, Y.-K. Su, R.-Y. Yang, and C.-Y. Hung are with the Advanced Optoelectronic Technology Center, Institute of Microelectronics, Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C. (e-mail:
[email protected]). M.-H. Weng is with the National Nano Device Laboratories, Tainan 30078, Taiwan, R.O.C. (e-mail:
[email protected]). Digital Object Identifier 10.1109/LMWC.2007.903458
Fig. 1. (a) Top view, (b) 3-D view, and (c) the lumped-element equivalent circuit of the TFML. The signal line width (W ) is 60 m, the spacing (S ) between signal and ground is 90 m, respectively. The polyimide thickness (hPI) is 20 m and the physical length (l ) is 2000 m.
nology roadmap for semiconductors (ITRS) [9], the supply voltages on RF/analog complementary metal-oxide-semiconductor (CMOS) devices will be equal to or less than 1 V after 2012. Therefore, in this study, the TFML has been successfully fabricated, as shown in Fig. 1(a) and measured with dc-bias voltages less than 1 volt. The accurate wide-band frequency-depen( ) and lumped elements, dent characteristic impedance such as , , and , of the transmission line model of dc-biased TFML have been carefully characterized and reported for the first time. II. EXPERIMENT The configuration of the TFML fabricated on 540 m thick -type low-resistivity silicon ( 10 cm) substrate with 1 0 0 crystal orientation is shown in Fig. 1(b). The polyimide 3 is Kapton HN-types polyimide (dielectric constant at 1 KHz), which the starting materials are dianhydride and diamine [10]. The 20 m thick polyimide was spin-coated on the low-resistivity silicon substrate. The 2 m thick aluminum
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IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 17, NO. 9, SEPTEMBER 2007
Fig. 2. Real characteristic impedance of the different dc-biased TFML. The slight variety range of characteristic impedance is still suitable used for voltagecontrolled active circuits in MMICs.
used for conductor line and ground plane was deposited by sputtering on the surface of low-resistivity silicon substrate with 100-nm thick SiO buffer layer deposited first. The TFML pattern was defined through photolithography and inductive coupled plasma (ICP) etching technologies. Surface roughness of the polyimide observed from the scanning electron microscope (SEM) data was estimated around 0.3 m. Measurements were taken by an HP 8510C vector network analyzer up to 50 GHz. Short-open-load-through (SOLT) calibration was performed, with the de-embedding reference planes (A–A’ and B–B’) set to the ground-signal-ground (GSG) probe tip. The temperature of the laboratory during the measurements was set for 15–20 C. The dc-bias was simultaneously added at the end of the two ports of TFML. From the measured complex -parameters, the frequency-dependent propagation constant and ( ) of the dc-biased is the attenuation TFML were determined [11], where constant, is the angular frequency, is the velocity of light is the effective dielectric constant. in free space, and values of polyimide were constant averagely The extracted , , around 2.5 from 1 to 50 GHz [11]. The parameters , and were derived from and [12], as shown in Fig. 1(c). III. RESULTS AND DISCUSSIONS Fig. 2 shows the real ( ) of the TFML with 0, 0.1, 0.5, and 0.9 V. The extracted Re [ ( )] of the TFML without 50.2 dc-bias is maintained in the range of 47.5 from 0.5 to 50 GHz, which are suitable for integrated passive and active devices on the low-resistivity silicon. With increasing ( ) is progressively dc-bias voltages on the TFML, the real increased below 30 GHz, except that with 0.1 V bias, and be48.3 ) above comes a nearly constant (47.8 30 GHz. Fig. 3 shows the extracted ( ) of the TFML with different dc-bias voltages. For the TFML without dc-bias, the ( ) increases with the square root of frequency due to the skin effect [3]. When increasing the dc-bias voltages, ( ) with higher dc-bias voltages has higher values, but ( ) with different dc-bias voltages achieves nearly constant values in the range between 1.2 and 1.7 mm. As is known, The expression of the ohmic loss ( ) in MMIC-based transmission line could
Fig. 3. Extracted lumped equivalent resistance R (f ) of the different dc-biased TFML. The skin depth ( = 2=! ) is 0.364 m at 50 GHz.
Fig. 4. Extracted lumped equivalent conductance G (f ) of the different dc-biased TFML.
be expressed as [13]. indicates the losses in the metallization at low frequencies near dc condition. is frequency dependent current distribution across the width models series losses in the substrate of the conducting line. can and depends on the substrate resistivity. It is noted that be ignored since the polyimide can be defined as an insulator with very high resistivity in this work. Therefore, the dc-bias and simultaneously increase the ( ) might increase the [13]. Fig. 4 shows the extracted ( ) of the TFML with different dc-bias voltages. ( ) displays the similar behavior to ( ), namely, ( ) with higher bias voltages has higher values than that without dc-bias. It is clearly observed that ( ) is less than 1 mS/mm for all cases from 1 to 50 GHz. As is reported [3], the ( ) variation is effected by the polarization current in polyimide and uniformity and quality of polyimide. When increasing the dc-bias voltages, the polarization current in polyimide might be enhanced and uniformity and quality of polyimide might be reduced, thus the ( ) increases. Additionally, ( ) is also related with dielectric loss of the polyimide, described by the ). The average values of with difloss tangent ( ferent dc-bias voltages are found to be 0.008 (without bias), 0.014 (0.1 V), 0.026 (0.5 V) and 0.034 (0.9 V). Such results are very useful since considering the dielectric loss in the dielectric media with dc-bias is required when designing the passive devices. Fig. 5 shows the extracted ( ) of the TFML with different dc-bias voltages. Since the added electric field does not change
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IV. CONCLUSION In this letter, we have succeeded in extracting the wide-band ( ) and frequency-dependent characteristic impedance equivalent lumped elements of the TFML with different dc-bias voltages. This study provides an effective model for evaluating the circuit characteristic of dc-biased TFMLs which is appropriate for the design of high-frequency interconnects in MMICs.
Fig. 5. Extracted lumped equivalent inductance L (f ) of the different dc-biased TFML.
ACKNOWLEDGMENT The authors wish to thank Y. D. Lin, National Nano Device Laboratories, for sample preparation.
REFERENCES
Fig. 6. Extracted lumped equivalent capacitance C (f ) of the different dc-biased TFML.
the magnetic flux penetration in the dielectric media, the extracted ( ) displays nearly the same values of 0.128 nH/mm ( ) of the from 5 to 50 GHz. Fig. 6 shows the extracted TFML with different dc-bias voltages. The extracted ( ) of 0.1 volt-biased TFML, from 0.5 to 50 GHz, has larger values than those of other dc-biased TFML. While, the values of ( ) of the TFML with different dc-bias voltages are all larger than those without biasing when measured frequency is higher than 20 GHz. These results might be resulted from the polarization mechanisms of the polyimide under different dc-bias voltages [3]. At all events, in comparison with the previous work [12], the extracted ( ) of the TFML with different dc-bias voltages are smaller than 0.05 pF/mm, which is small enough to reduce the crosstalk and the power consumption associated with the multilayer interconnects system. Further works are progressing to understand more clearly the physical meaning of the variation of equivalent lumped elements for the TFML with different dc-bias voltages. Additionally, we should notice room for further evaluation of the average power handling capability on the dc-biased TFML.
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