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© 2008 Wiley Periodicals, Inc.

ON-CHIP SPIRAL INDUCTOR WITHNOVEL GRADUALLY CHANGEDSTRUCTURE

Jing Liu,1,2 Yanling Shi,1,2 Xiuzhi Wen,1,2 Dawei Chen,1,2

Tian-Xing Luo,1,2 HaoHuang,3 Hongbo Ye,3 and Yong Wang3

1 East China Normal University, Shanghai 200062, People’s Republicof China2 State Key Laboratories of Transducer Technology, China Academyof Sciences, Shanghai, 200050, China3 Shanghai IC Research and Development Center, Shanghai 201203,China; Corresponding author: lj598yy@hotmail.com

Received 25 December 2008

ABSTRACT: On-chip spiral inductors with sufficient quality factorsare very important in many RF circuits. Based on the magnetic fieldintensity of a spiral inductor increasing gradually from outside to in-side, this article presents a novel inductor structure with graduallychanged metal width and space. Some design rules of this new structurehave been obtained from a large number of data analyses. The sum ofmetal width and space of each coil is fixed while the ratio of the metalwidth to space is gradually reduced from outside to inside. Inductorshave been fabricated and the obtained experimental results have verifiedthe proposed design method. For a 7-nH inductor on high-resistivitysilicon at 2.1 GHz, Q factor of 10 is 23.5% higher than the conven-tional inductor with fixed metal width and space, and is also 13.6%higher than the single gradually changed inductor with fixed space andgradually changed metal width. © 2008 Wiley Periodicals, Inc.Microwave Opt Technol Lett 50: 2210–2213, 2008; Published online inWiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23611

Key words: on-chip spiral inductor; quality factor; gradually changedstructure; metal losses; magnetically induced losses

1. INTRODUCTION

The quality of RF spiral inductors, as one of the key factors oflow-cost RF integrated circuits, have been gotten more and moreattention [1, 2]. Unfortunately, the parasitic effects, such as cou-pling capacitance and losses related to the integration substrate,will degrade their performance [3]. Therefore, the parameterswhich will influence the quality factor of on chip inductor havebeen analyzed and some guidelines of optimization have beenproposed [4, 5]. Some kinds of new layout structures have alsobeen presented [6, 7].

For a conventional spiral inductor with fixed metal width andspace, the influence of magnetically induced losses is much moreimportant in the inner turn of the coil, where the magnetic fieldreaches its maximum. According to this, some authors proposedthe elimination of the central turns to reduce losses [8]. After that,a single gradually changed structure with fixed space but graduallyreduced metal width from outside to inside has been proposed byLopez—Villegas J M [3]. The obtained Q factor of inductor withthis structure and the substrate removal is 60% higher than con-ventional inductor with the same layout size. It is also confirmedin that article that inductors with gradually changed structure canobtain better performance if they are properly designed.

There are many structure parameters which will susceptiblyinfluence the inductor’s Q factor, such as the metal width, space,inner opening diameter, outer opening diameter and so on. So it isnecessary to analyze these parameters and get some design rules toobtain better performance. Based on a large number of simulationand experimental results analysis, this article presents a novelgradually changed structure with the fixed sum of the metal widthand space of each turn while the ratio of the metal width to spacegradually reduced from outside to inside. According to this designrule, inductors have been fabricated and the obtained experimentalresults verify the proposed method.

2. PERFORMANCE ANALYSIS OF THE GRADUALLYCHANGED INDUCTOR

Q factor of inductor can be defined as follows:

Q ��Ls

Rs�

Rp

���Ls/Rs�2 � 1�Rs

� �1 �Rs

2�Cs � Cp�

Ls� �2Ls�Cs � Cp��

(1)

�Ls/Rs, the first item in Formula (1), accounts for the storedmagnetic energy and the energy losses in the series resistance. Ls

represents the series inductance of the inductor coil; Rs representsthe series resistance. They will both change with the structureparameters. The other two items in Formula (1) stand for substratelosses factor and self-resonance factor, respectively.

For high-resistivity silicon substrate, the dominative losses aremetal losses and magnetically induced losses. The metal lossesrelate to the sheet resistance of the metal strip, which can beexpressed as follows.

Rs � �n�1

N �rs� f �

Wn� cgn

2f2wn2�lnrs� f � (2)

Where rs (f) is the sheet resistance of the metal line, f is thefrequency, ln is the length of the nth turn of the coil, c is a constant,and gn is a function dependent on geometrical parameters such asN, ln, wn, and sn [3].

Since the sheet resistance of the metal strip is inversely pro-portional to the metal width, a wide metal strip width is expected

2210 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 8, August 2008 DOI 10.1002/mop

to decrease the metal losses. However, the magnetically inducedlosses depend on the magnetic-field flux through the metal strip.And the associated magnetic field has a maximum intensity in thecenter of the coil. Consequently, a narrow metal strip width wn isexpected to decrease the magnetically induced losses, especially inthe center of the coil.

In the other case, the magnetic field generated by neighboringlines will change the current distribution of the metal line. Whenthe inter-turn space value sn is smaller the magnetic field willbecome stronger, resulting in a more asymmetric current density inthe metal line. In addition, L-value is inversely proportional to theinter-turn space. When sn is larger the L-value will be reduced.Therefore, the inter-turn space values should be selected accord-ingly.

According to all of the above, both the metal width and inter-turn space should be properly chosen to get better performance.This article presents a novel gradually changed structure. The sumof the metal width and space is fixed while the ratio of the metalwidth to space is gradually reduced from outside to inside, asshown in Figure 1.

The structure parameters of the inductor include number ofturns (N), inner opening diameter (Din), outer opening diameter(Dout), metal line width of the nth turn (wn), conductor inter-turn

space (sn), and two metal layers (M1 and M2). In this structure, thenarrower metal lines in the inner turn can decrease magneticallyinduced losses while wider metal lines in the outer turn decreasemetal losses. Besides, the larger space can reduce the magneticfield in the inner turn while smaller space in the outer turncompensates the L-value of the inductor.

3. SIMULATION AND OPTIMIZATION

To evaluate the performance of this novel structure and get somedesign rules, a large number of inductors have been simulated byHFSS. Table 1 shows the comparison of three groups of inductorswith different structure parameters. Q1, Q4, Q7 represent theconventional inductors with fixed metal width and space. Q2, Q5,Q8 are the inductors with fixed space and gradually changed metalwidth, we call them single gradually changed inductors. And Q3,Q6, Q9 are the inductors with novel gradually changed structurepresented in this article. We use HFSS to analyze the electromag-netic field distributing, then extract their S parameters and obtain

Figure 1 Top view of a spiral inductor with gradually changed structure

TABLE 1 Comparison of the Inductors with Different Structure Parameters

Dout (�m)wn � sn

(�m) N Qn wn/sn

wn

(�m)sn

(�m) Qmax

fm(GHz)

L(nH) fsr (GHz)

Group I 400 � 400 30 3.5 Q1 1 15 15 11.61 1.8 7.4 5.5Q2 – 24 �

1510 12.25 1.6 6.8 5.4

Q3 4 � 1 24 �15

6 �15

13.25 1.6 7.0 5.2

Group II 400 � 400 30 4.5 Q4 1 15 15 10.73 1.5 8.6 4.7Q5 – 25 �

1510 12.04 1.4 7.7 4.9

Q6 5 � 1 25 �15

5 �15

12.45 1.3 8.0 4.5

Group III 400 � 400 40 3.5 Q7 1 20 20 11.07 1.9 5.0 6.0Q8 – 32 �

2010 12.14 1.6 4.6 5.9

Q9 4 � 1 32 �20

8 �20

13.40 1.8 4.9 5.8

Figure 2 Photograph of the inductor with gradually changed structure

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 8, August 2008 2211

the spiral inductance (L), the maximal Q factor (Qmax), frequencyat Qmax (fm), and self-resonant frequency (fsr), which are shown inTable 1. wn � sn is the sum of the metal width and space at the nthturn. wn/sn is the ratio of the metal width to space at the nth turn.For the gradually changed structure, this ratio is gradually reducedfrom outer turn to inner turn.

The quality factors of all the inductors with gradually changedstructure are all higher then those exhibited by other inductors. Forthe inductor Q9 (wn � sn � 40 �m, wn/sn: 4 � 1), Qmax is up to10.4% better than the result of the single gradually changed in-ductor Q8 and is also 21.0% better than the result of the conven-tional inductor Q7. With Dout unchanged, good performance hasbeen obtained by this optimizing method.

Best set of wn/sn values from outside to inside should be chosenin order to obtain good performance. Several design rules havebeen concluded through a large number of simulations. First, forinductors with small number of turns (about 3 � 5 turns), theoptimum wn/sn should be in the range of 0.3 � 6. Second, wn/sn

gradually reduced from outside to inside and the optimum wn/sn of

outermost-turn should be in the range of 4 � 6 while that ofinnermost-turn in the range of 0.3 � 1.5.

4. EXPERIMENTAL RESULTS AND DISCUSSIONS

Based on these analysis, inductors on high-resistivity silicon sub-strate (� � 103 U cm) have been fabricated in the followingprocesses. Ti/Au metals �0.6 �m are evaporated and patterned toform the underpass of the inductors. Then a PECVD SiO2 layerabout 0.8 �m is deposited for isolation. Subsequently, 1.5-�mthick Ti/Au layer is evaporated and electroplated for patterningspiral coil of inductor. Figure 2 shows one photograph of thefabricated inductors with gradually changed structure, which is theQ6 inductor in Table 1.

Measurements are carried out at frequencies ranging from 100MHz to 10 GHz by E8363B network analyzer and Cascade on-wafer probe. The obtained Q factors versus frequency for theinductors in Table 1 are plotted on Figures 3 4 and 5, (a) for HFSSsimulations and (b) for experimental results.

Figure 3 Q factors versus frequency for the Inductors of Group I inTable 1

Figure 4 Q factors versus frequency for the Inductors of Group II inTable 1

2212 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 8, August 2008 DOI 10.1002/mop

The optimized gradually changed structure shows good perfor-mance from about 500 MHz to 4 GHz. For the 7-nH inductor (Q3in Group I), Qmax of 10 at 2.1 GHz is 23.5% higher than theconventional inductor Q1 with fixed metal width and space and itis also 13.6% higher than the single gradually changed inductor Q2with fixed space and gradually changed metal width. Same resultsare also obtained in the other groups. For Q6, Qmax of 9.4 at 2 GHzis 28.8% higher than the conventional inductor Q4. And for Q9,Qmax of 11 at 2.7 GHz is 19.6% higher than Q7. Good agreementshave been observed between measurements and simulations,which validates the proposed gradually changed structure.

5. CONCLUSIONS

This research is devoted to the further study of gradually changedstructure of RF spiral inductors. After analyzing the magnetic fielddistribution and considering about the influence of the metal widthand space on the performance of inductors, a novel structure of RF

spiral inductor has been presented. The sum of the metal width andspace of each turn is fixed while the ratio of the metal width tospace is gradually reduced from outside to inside. The obtainedexperimental results corroborate the validity of the proposedmethod. This structure, which considering metal losses, magneticinduced losses and parasitic effects, will develop the inductor’sperformance.

ACKNOWLEDGMENTS

This work was supported by Natural Science Foundation of China(No. 60676047, 60606010), Foundation of Shanghai Science &Technology Committee (075007033, 04QMX1419) and Shanghai-Applied Materials Research and Development Fund (No. 0522).

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© 2008 Wiley Periodicals, Inc.Figure 5 Q factors versus frequency for the Inductors of Group III inTable 1

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 8, August 2008 2213