Abstract—This paper presents the design and optimisation of high quality (Q) factor inductors using Micro/Nano Electro-Mechanical Systems (NEMS/MEMS) technology for 10GHz to 20GHz frequency band. Three inductors have been designed with rectangular, circular and symmetric topologies. Comparison has been made amongst the three to determine the best Q-factor. Inductors are designed on Silicon-on-Sapphire (SOS) because of its advantages including high resistivity and low parasitic capacitance. The effects of various parameters such as outer diameter (OD), the width of metal traces (W), the thickness of the metal (T) and the air gap (AG) on the Q-factor and inductance performances are thoroughly investigated. Results indicate that the symmetric inductor has highest Q-factor with peak Q of 192 at 12GHz for a 1.13nH.
Keywords-High Q inductor; Micro/Nano Electro-Mechanical Systems (MEMS/NEMS); Silicon-on-sapphire
I. INTRODUCTION Wireless systems, and in general, communications
systems, are composed of several off-chip, bulky passive RF components, such as high Quality (Q) factor inductor, ceramic and filters, varactors diode and discrete PiN diode switches [1, 2]. Such off-chip components make the wireless systems larger and consume higher power consumption. Future wireless sensor communication circuits require highly integrated RF front-ends, featuring small size, high performance, low power consumption and low cost. However, quality (Q) factor and frequency limitations of the present components still limit RF front-end circuitry to a large number of discrete passive components and make RF front-end module integration very crucial [3].
Micro/Nano Electro-Mechanical Systems (MEMS/NEMS) is a promising technology to yield a new generation of high-performance RF-MEMS passive components which can replace the off-chip components in wireless communication systems [2, 4]. Power consumption of communication transceivers can be greatly reduced by using high-Q MEMS passive components especially the inductor which is designated as ‘the most crucial passive’ [5]. High-Q inductors are the essential part in designing components of RF frontend such as voltage-controlled oscillator (VCO) and low noise amplifier (LNA). However, designing an optimum on-chip inductor is still a major bottleneck because it is suffer from low Q-factor and high parasitic effects due to substrate losses.
Existing research indicates that the MEMS/NEMS-based RF components such as L and C can achieve very high Q, thus enabling a single on-chip solution for wireless receivers with better performance [6-9]. In addition, MEMS/NEMS has achieved a good level of integrability and compatibility with standard semiconductor processes making it suitable for large scale production and low costs [10].
In the past, there are several suspended inductors have been proposed. In [11], suspended inductor has been designed with different air cavity structures together with pillar support that possesses highest Qmax of 6.6 at 2GHz. Another suspended inductor is proposed in [12], in which silicon substrate is removed, leaving the metal inductor suspended 60μm above the microwave substrate. This design contributed Q-factors from 45 to 100 with measured self-resonance frequency are between 5GHz to 34.8GHz. Suspended inductor has been implemented in LNA which reported in [13] and this inductor offer high Q-factor, inductance and frequency of operation when compared to monolithic spiral planar inductor. However, further research is needed to achieve higher Q factors in fully on-chip inductor designs.
This paper presents the design and analysis of on-chip high Q suspended inductors using MEMS/NEMS technology for RF application. This paper is organised as follows: Section II presents the inductor design; Section III is on simulation and analysis of parameters. Section IV presents results summary of the inductors followed by the conclusion in section V.
II. INDUCTOR DESIGN The performance of suspended inductors in this design
has been investigated on a silicon-on-sapphire (SOS) substrate using MEMS/NEMS technology in order to develop a very high Q-factor inductor to integrate wireless module. SOS is formed by depositing a thin layer of silicon onto sapphire (Al2O3) wafer. Inductor coil is designed using copper as the material on SOS substrate. Three metal layers are needed to build these inductors. The first metal layer forms the base of an underpass of the inductor and interconnection with the rest of the spiral. The second metal layer is used for the vertical via connected to the underpass. The third metal layer completes the inductor which is suspended above the surface of the substrate.
Inductors have been designed using several architectures namely circular, square and symmetrical and are shown in
2010 Fifth IEEE International Symposium on Electronic Design, Test & Applications
Fig. 1. Outer diameter (OD), the width of metal traces (W), the thickness of the metal (T) and the air gap (AG) are the key parameters of the inductor.
Fig. 2 shows the lumped physical model developed for these suspended inductors. L0 and R0 are series inductance and resistance due to conductor losses and dissipation by the induced eddy currents in the substrate. Cs is an inter-turn fringing capacitance and a metal overlap coupling capacitance between the spiral and underpass metal layers. Rsub and Csub are the resistance and parasitic capacitance of the sapphire substrate respectively. A high-resistivity sapphire substrate was used to minimise the substrate losses and eddy currents.
Figure 2. A lumped physical model of a on-chip inductor
III. SIMULATION AND ANALYSIS The MEMS/NEMS inductor was designed and simulated
using the Coventorware® software from Coventor Inc. MemHenry Solver is used to derive the equivalent inductor (L0) and the series resistance (R0). Parameters for the inductors layout such as outer diameter, width of metal, air gap and thickness of metal have been optimised accordingly in order to improve the Q-factor and inductance. Innovative design and suitable materials are needed in order to improve the inductor performance which has been analysed in section below.
A. Analyse effects of change in Outer Diameter Outer diameter of the inductors has been analysed to see
the effect on inductance and Q-factor performances. Outer diameter for all three inductors is varied between 400μm to
1500μm. The results, shown in Fig. 3 and Fig. 4, correspond to a 3-D inductor with metal line width of 60μm, metal thickness of 5μm and air gap of 20μm. As observed in both figures, that as the outer diameter increase, Q-factor decreases and inductance increases. This is due to the fact that, larger inductors require a longer inductor coil which increases the series resistance and inductance. Symmetric inductor illustrates highest Q-factor of 140 at 1220μm of outer diameter. Amongst these three inductor architectures, rectangular inductor has the highest inductance value because it has longest track length, which result in higher inductance and resistance.
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Figure 3. Effects of change in Outer Diameter on Q-factor
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Figure 4. Effects of change in Outer Diameter on Inductance
Increase in the outer diameter contributes to larger area resulting in larger current in the substrate which causes the high-frequency losses to increase. Literature suggest that inductor with large diameters are usually preferred to minimize degradation of inductor performance due to formation of conductor eddy effect [14].
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B. Analyse effects of change in Track Width The effects of width of metal on Q-factor and inductance
are analysed with the thickness, air gap and outer diameter are fixed. Inductors have been designed and simulated on SOS substrate with metal line width varying from 20μm to 80μm, metal thickness of 5μm and suspended 20μm above the substrate. Fig. 5 and Fig. 6 show the effects of change in width on Q-factor and inductance respectively.
Fig. 5 shows that Q-factor for symmetric and circular inductor considerably increases with the metal line width from 20μm to 60μm and decrease for 80μm of metal width. However, Q-factor for rectangular inductor increases from 20μm to 150μm and decrease for 170μm. The frequency for Qmax also decreases with the metal line width for all three inductors. This is due to the fact that, large metal width induces bigger capacitance, which reduces the self resonance frequency (SRF), and increases the coupling of current into the substrate. At high frequencies, electrical conduction is confined to the a skin depth [15], where the resistance per unit length is given by (1), where is the resistivity of copper and is skin depth.
)2(
0δ
ρW
R = (1)
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RectangularCircularSymmetric
Figure 5. Effects of change in Width on Q-factor
From Fig. 6, it can be seen that increasing the metal width reduces the inductance for three inductors. Resistance also decreases when the width of metal increases which is a good way to improve the Q-factor.
The symmetric inductor achieved the maximum Q-factor of 140 while circular inductor has least Q-factor of 71 at 10GHz. The optimum width for symmetric and circular inductors is 60μm while for the rectangular inductor is 150μm which contribute the Q-factor of 135 at 10GHz. The larger surface area of the inductor with wide conductor metallisation results in higher parasitic capacitance, which lowers the inductors SRF and increases the substrate dissipation [16]. Consequently, the Qmax of the inductor shifts to a lower frequency as the conductor width increases.
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Width(μm)
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RectangularCircularSymmetric
Figure 6. Effects of change in Width on Inductance
C. Analyse effects of change in Air Gap The variation of air gap has been fully analysed for all
three inductor structures and are illustrated in Fig. 7 and Fig. 8. It can be clearly seen from Fig. 7 that symmetric inductor has highest Q-factor and decrease with air gap from 20μm to 70μm because it is has lowest capacitance coupling. Q-factor for circular inductor decreases from 20μm to 50μm of air gap and increase for 70μm of air gap. However, Q-factor for rectangular inductor increases with air gap. It is clearly show that different inductors architecture has different air gap influences to the inductor performances. This is significant improvement which can reduce the capacitances from the metal layer to substrate and the fringing capacitance between the metal lines.
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Figure 7. Effects of change in Air Gap on Q-factor
However, Fig. 8 reveals that inductance increases with the air gap for three inductors because inductance is directly proportional with air gap. Hence, inductor suspended 20 m above the SOS substrate is found to reduce the effect of substrate proximity on the performance of the symmetric and
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circular inductor structure which leads to higher Q-factor value and self-resonant frequency.
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Air Gap( m)
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Figure 8. Effects of change in Air Gap on Inductance
D. Analyse effects of change in Thickness Fig. 9 and Fig. 10 show the effects of increasing the
thickness of the inductor coil from 5 m to 40 m on the Q-factor and inductance of the inductors.
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Figure 9. Effects of change in Thickness on Q-factor
It can be clearly seen that, symmetric inductor obtains the maximum Q-factor of 192 with 30 m of metal thickness as this thickness of metal significantly contributed to the reduction of the series resistance. Furthermore, the optimum thickness for circular inductor is 5μm which results in highest Q-factor of 112 at 10GHz. The Q-factor of rectangular inductor increased with thickness of metal from 5μm to 15μm but has fluctuates from 15μm to 40μm of the metal thickness. As a result, the optimum metal thickness for rectangular inductor is 15μm with Q-factor of 145 at 10GHz.
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Figure 10. Effects of change in Thickness on Inductance
The effect of thickness of metal on resistance can be seen in Fig. 11. It is clear that resistance is proportional to Q-factor. Resistance in the high Q-factor region is further reduced by the increase of sidewall height in the metal line. By thickening the metal, the Q-factor can be increased because of the reduced series resistance caused by the increased metal sidewall areas of current. In fact, inductance is inversely proportional to the thickness of the conductor.
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Figure 11. Effects of change in Thickness on Resistance
Hence, the inductance decreases with increasing metal thickness, lowering the Q-factor. The Q-factor of the spiral inductor could therefore be improved by increasing the metal thickness. By using thicker metal, the Q-factor increases because of the reduced series resistance due to the increased metal sidewall areas of current [17].
IV. RESULTS The analysis of the three MEMS/NEMS inductors show
that the Q-factor of these inductors can be improved by optimising design parameters, including outer diameter,
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width of the metal tracks, air gap from the substrate and metal thickness. From a series of design analysis it is shown that increasing the outer diameter and metal width of an inductor linearly increases the Q-factor but decreases the SRF. However, SRF increases with increase the air gap and thickness. Furthermore, inductance linearity decreases with increasing the metal width and thickness of metal but inductance increases with air gap and outer diameter. These results are summarised in Table 1, where OD is outer diameter, W is metal width, AG is air gap, T is thickness of metal, Qmax is maximum Q-factor, L is inductance, FSRF is resonant frequency, C is circular inductor, R is rectangular inductor and S is symmetric inductor.
TABLE I. SUMMARY OF PARAMETERS EFFECT ON INDUCTORS PERFORMANCE
Parameters Qmax L (nH) FSRF
C R S C R S C R S
OD
W
AG -
T
Note: , increase; , decrease; –, almost constant The performance of the Q-factor for all three inductors
designed using MEMS/NEMS technology is presented in Table 2.
TABLE II. INDUCTORS PERFORMANCE
Parameters Cir (a) Rec (b) Symm (c)
Outer Diameter (OD) 640 m 640 m 1220 m
Width (W) 60 m 60 m 60 m
Air Gap (AG) 20 m 70 m 20 m
Thickness (T) 5 m 15 m 30 m
Spacing (S) 100 m 100 m -
Qmax @ GHz 112 @ 10 154 @ 16 192 @ 12
L(nH) @ Qmax 0.90 1.19 1.13
Q @ 10 GHz 112 145 190
L (nH) @ 10 GHz 0.90 1.19 1.13
R @ 10 GHz 0.5037 0.5160 0.37384
After thoroughly analysing the effects of the various
parameters effect on inductor performance, the optimum parameters for the 1.13nH symmetric inductor are metal thickness of 30 m, metal width of 60 m, air gap of 20 m, and outer diameter of 1220 m, which results Q-factor of 192 at 12GHz. However for the rectangular inductor the optimum parameters are metal thickness of 15 m, metal width of 60 m, air gap of 70 m, and outer diameter of 640 m which result inductance of 1.19nH with Q-factor of 154 at 16GHz.
Finally, the optimum parameters for circular inductor are with metal thickness of 5 m, metal width of 60 m, air gap of 20 m, and outer diameter of 640 m which results in an inductance of 0.90nH with Q-factor of 112 at 10GHz.
The optimum design result has been showed in Fig. 12. The results show that symmetric structure has the optimum inductor performance with high Q-factor followed by rectangular and circular inductor.
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Figure 12. Q-factor and Inductance versus Frequency
V. CONCLUSION Symmetric, rectangular and circular inductors are
designed, simulated and analysed and their performance compared. In addition to reduce the parasitic effects of the substrate, air gap has been used directly below the inductor. Moreover, the use of high resistive sapphire substrate provides inductors with high SRF and high Q factor. Result shows that symmetric inductor structure consumes more area but acquires higher Q-factor when compared to rectangular and circular inductor structure. A Q-factor of 192 has been achieved for 1.13nH symmetric inductor at 12GHz for a suspended MEMS/NEMS inductor. This evaluation of inductors in MEMS/NEMS technologies recommends that the proposed inductor is the best candidate to achieve higher Q-factors required for low power low cost RF applications.
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