On Miniaturizing On-Chip Microstrip Inductors Using...

Hindawi Publishing CorporationInternational Journal of Microwave Science and TechnologyVolume 2007, Article ID 86583, 5 pagesdoi:10.1155/2007/86583

Research ArticleOn Miniaturizing On-Chip Microstrip Inductors UsingEmbedded Radiating Dipoles

Chungpin Liao, Hsien-Ming Chang, and Jeng-Shin Hsu

Received 7 January 2007; Revised 6 March 2007; Accepted 7 March 2007

Recommended by Kamya Yekeh Yazdandoost

As RF mixed-signal and patch-antenna-equipped SOC devices are becoming the dominant products worldwide, concerns over thelarge real-estate consumption by the spiral inductors (including those for microstrip antennas and impedance-matching induc-tances), as well as their generally Q-low (quality factor) performance, are now being discussed more than ever. Liao et al. haverecently addressed the Q-low issue via using location-selective proton beam bombardment, whereby Q-improvements of 100%–300% were evidenced. That success, nevertheless, is at times tarnished by some undesirable features, that is, the explosive rises ofinductances near certain frequencies, which practically cut short the Q-enhancement and were identified to be due to resonantinteractions between the inductor-propagating EM wave and the proton-caused defect dipoles. In this paper, however, the authorsattempt to turn this resonance-caused undesirability to favor by proposing a new way to greatly shrink down the needed inductorsize through dipoles engineering.

Copyright © 2007 Chungpin Liao et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. INTRODUCTION

As RF mixed-signal and patch-antenna-equipped RF SOC(system-on-chip) devices are becoming the dominant prod-ucts worldwide, concerns over the large real-estate consump-tion by the desired spiral inductors, as well as their gener-ally Q-low performance, are now being discussed more thanever. In fact, owing to these concerns, RF circuit designershave already resorted their impedance-matching and signal-filtering needs to RC type of work, rather than LC style of de-sign, even though the latter, in many situations, may rendersuperior circuit performance and design flexibility. The in-ductor Q-low problem has recently been attacked by Liao etal. (see, e.g., [1, 2]) via using location-selective proton beambombardment, and Q-value improvements of 100%–300%were shown to be readily achievable (see the obtained induc-tance spectral behavior in Figure 1 and Q-improvement inFigure 2). However, the real-estate consumption issue has re-mained unresolved.

Economically, it will be much celebrated if commonlyneeded inductance values can be realized on inductors offairly smaller physical sizes. On the other hand, occasionally,high-inductance-value on-chip inductors are convenient tohave for some special applications. Unfortunately, however,it is also well known that, other than topology, the induc-tance value is entirely determined by the electrical properties

(including skin effects) of the spiral metal line and the un-derlying substrates such as silicon [3]. In this paper, the au-thors attempt to explore the possibility of greatly enhancingthe inductance value of an ordinary spiral inductor by meansof dipoles engineering.

This innovative idea actually came from the first au-thor’s aforementioned experience with proton-enhanced de-vice isolation and inductor Q-improvement [1, 2]. Althoughimplementing the new idea itself no longer relies on anyproton beam effort but more likely relies on VLSI or ULSI(ultra-large-scale integration), modern nanotechnology, orother new methods to emerge. That is, in spite of numer-ous evidenced successes of proton bombardment treatmentin both the device isolation and the inductorQ-improvement[1, 2] (see Figures 1 and 2) on already-manufactured mixed-mode IC wafers (prior to packaging), it was also found thatoccasionally there showed several undesirable and puzzlingfeatures in the obtained inductance spectral behaviors forsome large inductors post the proton irradiation. Amongothers, there are explosive rises of inductance (and the rel-ative dielectric coefficient) near certain frequency (or fre-quencies) [4, 5] (see Figures 3 and 4). A theory identifyingthe cause to be resonant interaction between the inductorEM wave and the proton-created defect dipoles (or displacedcharge imbalance) has explained the observation quantita-tively [4, 5], should the electromagnetic mass of electron [6]

2 International Journal of Microwave Science and Technology

0 2 4 6 8 10 12 14 16×109Frequency (Hz)

−60

−40

−20

0

20

40

60

×10−

9In

duct

ance

(H)

2.5-turn circle3.5-turn circle4.5-turn square

Figure 1: Inductance spectral behaviors of various aluminum spi-ral inductors (of different L(0)’s) subjected to an identical protonfluence of 1015 15 MeV protons/cm2.

0 2 4 6 8 10 12 14 16×109Frequency (Hz)

−15

−10

−5

0

5

10

15

20

Qva

lue

2.5-turn circle3.5-turn circle4.5-turn square

Figure 2:Q-value spectral behaviors of various aluminum spiral in-ductors (of different L(0)’s) subjected to an identical proton fluenceof 1015 15 MeV protons/cm2.

be taken into account [4, 5]. Its relevant importance to thecurrent work is manifested through the high frequency partof the inductance L, L = L(0) + L(ω), where L(0) and L(ω)are the low-frequency and high-frequency components, re-spectively. Namely, it was found analytically [4, 5] that thehigh-frequency component of the inductance (L(ω)) of theinductor sitting on the now proton-treated substrate is pro-portional to the new defect-dipoles-modified relative dielec-tric coefficient (ε̃r) of the substrate (a more elaborate expla-nation is offered for this paper at the end of this section, or

0 2 4 6 8 10

Frequency (GHz)

0

10

20

30

40

50

Ind

uct

ance

(nH

)

1× 1015 protons/cm2No proton irradiation

Figure 3: Anomalous inductance spectral behaviors of a 4.5-turn copper circular spiral inductor subjected to 1015 15 MeVprotons/cm2.

see [4, 5]). Accordingly, the proton-conditioned inductanceL also explodes near the resonance frequency of ε̃r . The reso-nance of ε̃r will be elaborated in the following section.

It thus occurred to the authors that if such observed ex-plosive spikes in inductance can be arranged in a prepro-grammed fashion so that an on-chip inductor is virtuallycushioned frequency-wise by an array of dipole resonators ofincrementally separated resonant frequencies, then the resul-tant inductance can be made very large, possibly to the extentinaccessible by any traditional VLSI means.

Prior to entering the main issue, a more elaborate ex-planation of the proposed theory [4, 5] relating the dipole-modified substrate dielectric coefficient (ε̃r) and the high-frequency part inductance (L(ω)) of the inductor on theformer substrate is now due. Other than the already pre-sented somewhat complicated mathematical demonstrationinvolving solution of the system equations associated witha quasi-TEM approximation [4, 5], here, rather, an expla-nation based on more intuitive physical arguments is given.First of all, a quasi-TEM wave traveling along the inductormetal line and its underlying substrate would excite dipoles(embedded within the substrate) of natural resonance fre-quency matching the wave frequency, in a fashion much likethe resonant excitation among tuning forks. This newly es-tablished energy exchange channel then dominates the spec-tral redistribution of the inductor EM wave energy pattern byconcentrating considerable proportion of the EM wave en-ergy to around the resonance frequency, which is effectivelythe work of a trapping action imposed on an EM wave by ahigh ε̃r (or high-refractive-index) material. In other words,the reaction of the now resonantly excited dipoles (of a to-tal polarization moment) would drag and slowdown the EMwave to facilitate such efficient energy exchange around theresonance frequency, and this effectively would enhance themagnetic flux linkage (in azimuthal direction with respect

Chungpin Liao et al. 3

0 0.5 1 1.5 2 2.5

Normalized frequency (x = ω/Ω)

−100−80−60−40−20

0

20

40

60

80

100

Die

lect

ric

coeffi

cien

tε y

Figure 4: An example of explosive spectral behavior in themicrostrip-perpendicular dielectric coefficient with respect to thenormalized frequency (x = ω/Ω), where Ω/2π is the dipole naturalfrequency.

to the wave propagation vector), and thus inductance (L),around the resonance frequency. Secondly, as shown in [4, 5],the scaling of the observed explosive rise in the inductancespectral behavior (see Figure 3) is aroundω4, that is, with L(0)

the low-frequency part of the inductance, the high-frequencycomponent of the inductance is [4, 5]

L(ω) ∝√εyω4L(0)2

c6(1)

(quite unlike the relatively smooth rise of ordinarily evi-denced inductance spectral behavior near the self-resonancefrequency), which is the typical characteristic of dipole radia-tion oscillations [7]. Additionally, effort of computer simula-tion on such inductor-dipole coupling is being planned, andthe results will be published elsewhere. To this point, reve-lation of the cause of the explosive rise of substrate relativedielectric coefficient (ε̃r) is now in order.

2. PROPOSED APPROACH: PREPROGRAMMEDSUBSTRATE WITH EMBEDDED DIPOLERESONANCES

2.1. Dipole resonance theory

When a host material is programmed with numerous dipolesof one kind, say, by normal front side proton bombardment(to create defect charge distribution—dipoles, as previouslyaccidentally found) or better, by embedding of a selected typeof molecular dipoles, an anisotropy is imposed upon the hostsubstrate and manifested through its dielectric coefficient ε(say, in y direction, upward perpendicular to the inductorspiral). Let us pay attention to the y-dimension to whichdipoles are assumed to dominantly align. Beneath the spi-ral inductor, each dipole is subjected to a time-varying elec-tric field of the EM wave propagating along the spiral induc-tor and penetrating down to the substrate. The latter causes

a time-varying displacement⇀r to the bound electron rela-

tive to its positive counterpart within each dipole. The corre-sponding equation of motion for the bound electron is

md⇀v

dt= −K⇀r − e

⇀E′ − 2νm⇀v , (2)

where m is the mass of electron, K is dipole restoring forceconstant, e is absolute electron charge, ν is a phenomenal

electron collision frequency, and⇀E′ =

⇀E +

⇀Pb/(3ε0) with

⇀E

the applied electric field,⇀Pb the electric dipole moment per

unit volume of dielectric, and ε0 the vacuum electric permit-

tivity. Note that it is this electric vector⇀E′ that has to be used

in dense media, that is, on the right-hand side of (2) in place

of⇀E (see [8] and references therein). Defining Ω2 = K/m,

as the squared dipole natural radian frequency, (2) can be

rewritten in terms of the displacement vector⇀r along the y

direction as

⇀̈r + Ω2

⇀r + 2ν

⇀̇r = −

(

e

m

)⇀E′. (3)

Employing⇀Pb = N · (−e) · ⇀r (N being the volumetric

dipole number density) and using the Fourier representation⇀Pb ∼

⇀̃Pbeiωt (with i =

√−1), the relation of displacementcurrent

⇀̃Dy = ε̃y

⇀̃Ey (with quantities over-barred by ∼ stand-

ing for complex amplitudes) gives

(

ε̃y/ε0 − 1)

(

ε̃y/ε0 +2) ≡ ε̃r−1

ε̃r + 2≡ Z

Z + 3= Ne

2

3ε0m· 1Ω2−ω2 +iγω ≡ξ,

(4)

where Z ≡ ε̃y/ε0 − 1 ≡ ε̃r − 1 and ε̃y/ε0 ≡ ε̃r . Further manip-ulation of (4) gives

ε̃r = 1 + 2ξ1− ξ . (5)

The explosive behavior of the real part of ε̃r can be seenin (5) as ξ approaches 1, while y is very small. The limit valueis usually obtained through numerical means (see Figure 4).Recall that the high frequency component of the inductanceL(ω) of the inductor above such dipole-engineered substrateis proportional to ε̃r and thus the inductance L explodes nearthe resonance frequency of ε̃r (as proved in [4, 5]).

2.2. Programmed matter with multiple resonancesof dipoles

When a host material is embedded with more than onekind of dipoles, the overall modified dielectric equation (4),can be described by the well-known Clausius-Mossotti equa-tion [8]:

ε̃r − 1ε̃r + 2

≡ ZZ + 3

= Ne2

3ε0m

∑

j

f jΩ2j − ω2 + iγ jω

, (6)

4 International Journal of Microwave Science and Technology

0 2 4 6 8×109Frequency (Hz)

0

10

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30

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50

Th

eim

agin

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(a)

0 2 4 6 8×109Frequency (Hz)

−3−2−1

0

1

2

3×101

Th

ere

alp

arto

fd

iele

ctri

cco

nst

ant

(b)

Figure 5: Absorption coefficient and relative dielectric coefficientfor a medium with more than one resonance (though the reso-nances are not very close to each other as proposed).

where f j is the number fraction of the jth type dipolesamong all, and thus

∑

j f j = 1. It is to be noted that, nor-mally, the real and imaginary parts of ε̃r are mathematicallyrelated by the well-known Kramers-Kronig integral relation(see, e.g., [9]). Namely, dispersion and absorption are inti-mately related. In the situations of interest here, however, theinterrelationship between real and imaginary parts of ε̃r is al-ready fully explicit as shown by (6) and therefore, effort fordirect application of the more implicit Kramers-Kronig rela-tion is saved.

The important feature of interest here is that the imagi-nary part of ε̃r can be confined near the resonance frequen-cies, while the real part contributes at all frequencies nearand below the resonances (see Figure 5 with arbitrary or-dinate scale). Namely, away from the resonance frequencies,the real part of relative dielectric coefficient (i.e., εy ≡ Re(ε̃r))(or refractive index n = (εy)1/2 for nonmagnetic materials)is constant and the medium is approximately nondispersiveand nonabsorptive. More importantly, each resonance con-tributes a constant value to the refractive index at all frequen-cies smaller than the lowest resonance frequency [9] (seeFigure 5 in arbitrary scale). Note that, for the overall relativedielectric coefficient, the final resonant curve similar to thatin Figure 5 cannot be obtained by simply adding togethereach resonant curve associated with one dipole kind. It hasto be secured rigorously through solving (6) numerically.

Now, as our proposal, if these resonance frequencies Ω j ’scan be arranged in such a way that they are very close to eachother, then the distinctive feature of sharp peaks in Figure 5will no longer be discernable, and correspondingly, εy belowand away from the resonances can be significantly enhanced.Accordingly, inductance of the spiral inductor residing onsuch a cushion of predefined dipoles can also be greatly en-hanced, since L ∝ εy as proved in [4, 5] and explained inSection 1.

3. NUMERICAL SIMULATION RESULTS

Numerical simulation efforts were launched for an on-chipinductor sitting on 5 types of permanent dipoles embed-ded within a normal Si substrate, and the result is given inFigure 6, in terms of the functional relationship between thedipoles-modified relative dielectric coefficient (εy) versus fre-quency (since high frequency component of the inductance isproportional to εy) [4, 5]. The adopted parameters were totaldipole number density N = 1× 1014 cm−3 with f j = 0.2 uni-formly, where the first type of dipoles has its resonance fre-quency (Ω1/2π) set at 52.19 GHz, and then subsequent reso-nances incremented by 48.72 MHz were arranged for the rest4 types of dipoles. The normalized attenuation (damping)coefficients yj (with respect to Ω j) were all set to be 1×10−3.

It was found that the ordinarily small and roughly con-stant relative dielectric coefficient (εy) of Si, around 12, couldthen be raised to about 250–500 in the approximately flatregime of around 3–6 GHz (i.e., away from resonances inFigure 6). Thus, using the proposed multi-dipole-cushionapproach, the significantly increased real part of the rela-tive dielectric coefficient εy , together with the favorably smallimaginary part εrI away from the fast-varying region, canlead to super large inductances and extraordinarily high Qvalues for all on-chip inductors, according to the formulaL ∼ L(ω) ∝ ε1/2y obtained in [4, 5] (see (1)), where L(ω) isthe high frequency component of the inductance associatedwith the spiral inductor lying on the cushion of dipoles.

More importantly, from the economic point of view, thisalso implies that it is possible to obtain normally needed in-ductance values of several nanohenries (nH) by on-chip spi-ral inductors of much smaller physical sizes. For example, forsimplicity, if the inductance value of a traditional spiral isroughly proportional to the square root of its spanned area(see [3] for more accurate but complex calculations), thenthe same inductance may be achieved by a multi-dipoles-cushioned inductor of ∼50 times smaller. In other words, atraditional inductor spanning 500 μm × 500 μm can now bereplaced with the new one spanning merely 70 μm × 70 μm,approximately.

Still, some may argue that the explosive rise of the di-electric coefficient of Si near certain frequencies should notbe considered as the real contribution to the inductance ofan originally metal inductor on silicon. However, the authorsbelieve that it is what the network analyzer actually measuresas a whole (including metal lines and dipoles-embedded sub-strate underneath) that really counts. In other words, fromthe widely used standard inductance measuring procedure

Chungpin Liao et al. 5

0 2 4 6 8 10×109Frequency (Hz)

−8−6−4−2

0

2

4

6

8×103

Th

ere

alp

arto

fd

iele

ctri

cco

nst

ant

(a)

0 2 4 6 8 10×109Frequency (Hz)

0

2

4

6

8

10

12×103

Th

eim

agin

ary

par

tof

die

lect

ric

con

stan

t

(b)

Figure 6: Great enhancement in real part of the relative dielectriccoefficient εr , which would lead to very large inductance if the in-ductor size is kept unchanged.

and machinery, it is known that the network analyzer simplywould never be able to distinguish between two pedagogicalinductors of identical characteristics but of different topol-ogy and contents. Besides, it is how an inductor (in whateverform of practical desirability) will behave that’s really rele-vant, and never its topology.

4. SUMMARY AND CONCLUSIONS

The verified success of proton bombardment treatment inboth the device isolation and the inductor Q-improvement[1, 2] (see Figures 1 and 2) on already-manufactured mixed-mode IC wafers (prior to packaging) has also uncovered newphenomena, especially the explosive rises of inductance nearcertain frequency (or frequencies) [4, 5] (see Figure 3). Apreviously proposed theory identified the cause to be res-onant interaction between the inductor EM wave and theproton-caused defect electric dipoles [4, 5]. Based on suchunderstanding, this paper aims at providing a new possibil-ity of greatly enhancing the effectiveness of on-chip inductorsvia having them cushioned by multiple dipoles of small-stepincremented resonance frequencies.

These preprogrammed dipoles can be carefully designedpermanent dipoles in the form of molecules oriented in thepreferred direction(s), or could be achieved by employingother artificial ULSI molecules, such as tiny pn-junctions and

Schottky diodes [10]. Further, if active biases could be neatlyapplied upon these dipole molecules, their dipole restoringforce constant Kj ’s and thus the natural resonance frequen-cies (Ω2j = Kj/m) can be more actively tuned. Realization ofthis new concept may likely have to rely on the particle-by-particle construction manner of the coming more advancednanotechnologies, including the self-assembly and the pro-grammable atoms [11].

REFERENCES

[1] C. Liao, M.-N. Liu, and K.-C. Juang, “Crosstalk suppression inmixed-mode ICs by the π technology and the future with anSOC integration platform: particle-beam stand (PBS),” IEEETransactions on Electron Devices, vol. 50, no. 3, pp. 764–768,2003, special issue on RF and SOC.

[2] C. Liao, T.-H. Huang, C.-Y. Lee, et al., “Method of creating lo-cal semi-insulating regions on silicon wafers for device isola-tion and realization of high-Q inductors,” IEEE Electron DeviceLetters, vol. 19, no. 12, pp. 461–462, 1998.

[3] H. M. Greenhouse, “Design of planar rectangular microelec-tronic inductors,” IEEE Transactions on Parts, Hybrids, andPackaging, vol. 10, no. 2, pp. 101–109, 1974.

[4] C. Liao, C.-W. Liu, and Y.-M. Hsu, “Observation of explo-sive spectral behaviors in proton-enhanced high-Q inductorsand their explanations,” IEEE Transactions on Electron Devices,vol. 50, no. 3, pp. 758–763, 2003, special issue on RF and SOC.

[5] C. Liao and C.-H. Hsu, “Proton-caused particle-beam standand novel dipole engineering in SOC integration,” in Si-BasedSemiconductor Components for RF Integrated Circuits, W. Z.Cai, Ed., chapter 9, p. 243, Transworld Research Network, Ker-ala, India, 2006.

[6] C. A. Mead, Collective Electrodynamics: Quantum Foundationsof Electromagnetism, The MIT Press, Cambridge, Mass, USA,2000.

[7] E. Hecht, Optics, Addison-Wesley, New York, NY, USA,4th edition, 2002.

[8] G. Bekefi and A. H. Barrett, Electromagnetic Vibrations, Waves,and Radiation, The MIT Press, Cambridge, Mass, USA, 1977.

[9] B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, JohnWiley & Sons, New York, NY, USA, 1991.

[10] Patent application in progress by NFU and ARBL.

[11] W. McCarthy, Hacking Matter, Perseus Book Group/BasicBooks, New York, NY, USA, 2003.

AUTHOR CONTACT INFORMATION

Chungpin Liao: Graduate School of Electro-Optic and MaterialScience, National Formosa University (NFU), 64 WenHua Road,Huwei 632, Taiwan; Advanced Research & Business Laboratory(ARBL), No. 6C, 88-8, Ta-Tun 20th Street, Taichung 407, Taiwan;[email protected]

Hsien-Ming Chang: Graduate School of Electro-Optic andMaterial Science, National Formosa University (NFU), 64 WenHuaRoad, Huwei 632, Taiwan; [email protected]

Jeng-Shin Hsu: Graduate School of Electro-Optic and MaterialScience, National Formosa University (NFU), 64 WenHua Road,Huwei 632, Taiwan; [email protected]

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