138 Telfor Journal, Vol. 4, No. 2, 2012.

1 Abstract — Methodology for extracting an effective dielectric

constant of microstrip transmission lines on multilayer substrates, from measured or simulated S-parameters data, using on-chip test structures, has been demonstrated. The methodology consists of: 1) building on-chip interconnect structures usually implemented in calibration and de-embedding procedures in microwave on-wafer test and measurements – transmission lines, stubs and pad launchers; 2) extracting the effective dielectric constant from the characteristic impedance and propagation constant of these structures, fully described by the measured or EM-simulated S-parameters. The demonstrated methodology is applicable for evaluation of dielectric and semiconductor multilayer substrates, both with lossy and lossless characteristics over a broad frequency band. Another advantage is implementation of very short transmission line structures with physical dimensions much smaller than a quarter wavelength of the highest investigated band frequency, thus preserving a valuable chip area in the test structures and being compatible with some of the calibration TRL elements.

Keywords — Calibration and de-embedding structures, characteristic impedance, effective dielectric constant, multilayer substrates, on-wafer test and measurements, propagation constant, S-parameters.

I. INTRODUCTION HE continued growth of personal communications with wireless applications has generated a great demand for

portable and highly integrated components and subsystems. As a consequence, these applications challenge semiconductor and packaging technologies to integrate high density 3-D mixed-signal integrated circuits on complex multilayer semiconductor substrates, assembled in multilayer packages and modules.

Frequently these substrates possess an inherently lossy characteristic, which deteriorates their performance or puts the accuracy of active and passive elements modeling under question. At frequencies where the dimensions are not electrically small, it is necessary to use complex distributed models. General full wave numerical methods such as FDTD, FEM, MoM and PEEC have been applied to model these structures successfully. The basic key to build successful models and perform genuine electromagnetic simulations of topology layout is the

Radosvet G. Arnaudov is Head of MMIC Department with the company “RaySat BG” and Associate Professor in TU-Sofia at the dept. of Microelectronics, both in Sofia, Bulgaria (phone: +359 2 9625665, e-mail: RadosvetA@gilat.com).

Radoslav B. Borisov is MMIC Designer at “RaySat BG” and currently making his Ph.D. in the field of Microeletronics (e-mail: RadoslavB@gilat.com).

knowledge of complex characteristic impedance and propagation constant in transmission line structures on the upper interconnect levels. Ultimately, it is necessary for the IC industry to characterize these losses and novel dielectric properties of such sequenced isolation and semiconductor layers, with different thickness and relative dielectric permittivity, in order to build a representative interconnect characterization database [1]. The most reliable information about wave propagation in multilayer metal/dielectric/semiconductor systems is knowledge of the effective dielectric constant, derived straightforwardly from the propagation constant, more precisely its imaginary part – the phase constant.

Previous research has demonstrated S-parameter characterization of interconnect transmission lines, based on two-port unbalanced measurements, Ri-Li-Gi-Ci modeling and extraction of characteristic impedance ZC and propagation constant γ [1], [2]. The core of our approach is the same but differs in some aspects from the well-known procedure: a) we rather implement and measure one-port open-end stubs instead of relatively long transmission lines with two ports); b) short-end stubs are not included in the measurement test set-up in order to eliminate the inserted parasitic inductance of grounding through-hole vias and existing obstacle to build them by some technologies; c) two-port measurements are conducted on a transmission line with the same length, width and contact pads (launchers) geometry as the open-end stub; d) ZC and γ are extracted directly from S-parameter data of the one-port capacitive (open) and inductive (short) stubs. In many cases, existing de-embedding structures and some of the TRL calibration standards in the test set-up could be easily implemented to acquire the necessary one-port stub S-parameters for calculations of the propagation constant. The effective dielectric constant is derived from the phase constant.

II. THEORY OF TRANSMISSION LINE STUBS Open and short stubs are widely used in microwave

transmission line designs as capacitors, inductors or resonator tanks to ground. For example many DC biasing circuits implement stubs to achieve higher isolation between power supply and the RF signal. The size of the stubs is small enough to build LC filters and matching networks, when their length is smaller or equal to n.(λline/4).

Conventional small signal z-, y-, and ABCD-parameters, are not quite suitable for high frequency interconnect characterization, because “open” and “short” terminations, required to measure this data, cannot be easily implemented in “on-wafer” applications and deteriorate performance by

On-Wafer Measurements for Extraction of Effective Dielectric Constant in IC

Transmission Lines on Multilayer Substrates Radosvet G. Arnaudov, Member, IEEE, and Radoslav B. Borisov, Member, IEEE

T

Arnaudov and

insertion of terminations pvias, while “opfringing effectS-parameter mreflected wavreliably charac

The inputtransmission simulated or the S-parameideal ground information ashorted to groleft open.

From tranequations Zinpl < λ/4 the inpcircuit in Fig.

Fig. 1. Equsimple Г-typ

On the otheone regular when the loapresented as:

The first eqlayers and inconnected toleakage in thconductivity σ

Let us equThe same is vwork from no

stushortinputZ

After mulZinput short andobtain the foimpedance ZC

d Borisov: On

impedance ppossess excesspen” ones havt of the edge e

measurements, es in a controcterize intercont impedance

line can bmeasured two

eters in a scheconnection a

about the inpuound. The sam

stushortinputZ

stuopeninputZ

nsmission liput short and Zinpput impedanc 1.

uivalent circupe representat

with leer hand, expretwo-conductoad ZL is 0 (

Z shortinput

Z openinput =

quation definncludes skin-eo the substrathe substrate σ. ualize input imvalid for (1b) aow further on w

shortinputub Z=

ltiplying (2ad Zinput open frofollowing expC, where Z0 is

inC Z=Z

1(1(

.0C Z=Z −+

n-Wafer Measu

parasitics. Thsive parasitic ive external capelectric field at

defined in terolled 50-Ω mennect high freq

Zin of a gbe readily do-port S-paramematic simulaat one of the ut impedanceme is valid if

ub SS

Z11

110 1

1.

−+

=

ub SS

Z11

110 1

1.

−+

=

ine theory put open for shore is defined fr

uits of Telegration of transmength Δl→0. ession of the ior and lossy (short) or ∞

(tanhZC= γ

(tanh/ZC= γ

nes the losses effect. The ste dielectric (tanδ) or som

mpedances frand (2b). For with:

stopeninputt Z;

a) and (2b) om equation pressions for the system im

sinputopennput Z.

1).(1).(

11

11

short

short

SSSS

−−++

urements for E

he “short” cinductance of pacitance, due

higher frequerms of incideneasurement syquency responsgiven intercoderived frommeters [2]. Plator and provports can giv

e, when the lione of the po

short

short

1

1

open

open

1

1

and Telegrrt lines with l

from the equiv

apher equation

mission line (TR

input impedantransmission (open), coul

)l⋅

)l⋅γ in the TRL m

second equatilosses, causeme semicond

rom (1a) and simplicity we

openinputtub Z=

and substit(1a) and (1bthe characte

mpedance 50 Ω

short

))

11

11

open

open

SS

Extraction of

circuit GND to the

encies. nt and ystem, ses. nnect

m the lacing viding ve us ine is orts is

(1a)

(1b)

apher ength valent

ns: RL)

nce of line,

ld be

(2a)

(2b)

metal on is

ed by ductor

(2a). e shall

n (3)

tuting ), we eristic Ω:

(4a)

(4b)

Af(1), (

whercons

Efand can bof th

Fr

we m

wherc0 is

Imcons

wherZinpuZinpu

A

II

A. EV

electmicrIn theffecimpe(MoMprob

Siare gof boGaAof 10 -

Filinesfrequ15 simuμm,

Sithe signiconsThislinesand

Effective Die

fter some alg(2) and (3) in

in

in

ZZ

=X

re X is a hstant γ multipl

ffective dielecelectro-physibe extracted f

he complete prrom λπβ /2=manage the fol

re ω – angularlight velocity

maginary part stant β. From (

γ

re l is physt short is the int open is the inpfter substitutio

II. EXPERIME

EM Simulationerification of tromagnetic sirostrip transmihe presented wctive dielectedances ZC aM) implemen

be station measimulation paragiven in Fig. 2oth substrates

As substrate is SiGe

30 S/m and inig. 3 and Fig.s on non-conduency range 1μm, 30 μm,

ulations were 100 μm, 150 imulated resulength of t

ificant effect stant varies fro

means that ws the capacitivbottom groun

electric Consta

gebra transfor(4) is obtained

in

opennput

shortnput Z=

hyperbolic taied by the phy

l =).tanh(γ

ctric constant cal transmissfrom the imagropagation con

lineλ where lineλllowing expre

=ε imageff

r frequency, γy in free space

of the propag(4d) the propa

tanh1al

=γ

sical length nput impedanput impedanceon of (6) into

ENTAL RESULT

ns of Semi-insthe proposed

imulations andission lines on

work, investigatric constantare achieved

ntation in EM surements. ameters of th2. The main di. In this worktaken σ = 0.2

substrates n our case σ =. 4 present thductive (semi- – 40 GHz an, 60 μm. Fperformed wμm, 200 μm a

ults for semi-ithe transmiss

over εeff anom 6.5 to 4.7

with the increave coupling bnd increases,

ant

rmations by sd:

inpC

shortnput

Z=

Z

angent of theysical line len

openinput

shortinput

ZZ

t is a functionsion line paraginary part (pnstant γ.

effe ελ /0 ==ession for εeff:

,).( 20

ω

γ cg

γ – propagation. gation constanagation consta

,openinput

shortinput

ZZ

of the trans

nce obtained fe obtained from(5) εeff is dire

TS AND MEAS

sulating Substd method was d measured S-n GaAs and Siation and comt εeff and

by method simulations a

he semiconducifference is th

k for the cond2 S/m. Typica

varies = 25 S/m. he simulations-insulating) su

nd line widths:or each wid

with varying and 300 μm. insulating Gasion line dond ZC. Effect7 with the chaasing width o

between the totoo. From el

139

substitution o

,openput

CZ

(4c)

e propagationgth l:

(4d)

n of the shapeameters and βhase constant

efffc ε./0=

(5)

n constant and

nt is the phaseant is:

(6)

smission linefrom (1a) andm (1b). ctly derived.

UREMENTS

trate GaAs done through

-parameters oiGe structures

mparison of thecharacteristicof moment

nd “on-wafer”

ctor substratehe conductivityductivity of theal conductivity

between

s of microstripubstrate in the: 5 μm, 10 μmdth additionalengths of 30

aAs prove thaoesn't have ative dielectricange of width

of transmissionop metal layelectromagnetic

9

of

)

n

)

e β t)

)

d

e

)

e, d

h of s. e c s ”

s y e y n

p e

m, al 0

at a c

h. n

er c

B

140

point of viewTEM-wave wactive conduc

Fig. 2. Muapplied in

S-parame

Fig. 3. Effeconductive

60 μm; lengthsim

Fig. 4. Resubstrate (GaLx = 30, 100,

The same stive substratedepicted in Fi

B. EM SimulThe exact a

substrates is fundamental meffect mode” a

w - more enwill be enclosector and refere

ultilayer dielecelectromagne

eters: a) semi-b) conductive

ctive dielectrisubstrate (Gah Lx = 30, 100mulations of s

eal part of ZC aAs); width W, 150, 300 μm

structure

simulations hae as SiGe shig. 5 and Fig.

lations of Conanalysis of migiven in [3]

modes i.e. “dieand “slow-wav

nergy from thed within the ence ground p

ctric/semicondtic simulator finsulating sube substrate - S

ic constant εeffaAs); width W0, 150, 300 μmstructure on Fi

for MSL on nWx = 5, 10, 15, m @ each Wx. E

e on Fig. 2.a).

ave been perfhown in Fig. 6.

nductive Substicrostrip line b, where the electric quasi-Tve mode” is de

he electromagsubstrate bet

lane.

ductor substratfor extraction bstrate – GaAsSiGe.

f of MSL on nWx = 5, 10, 15,

m @ each Wxig. 2.a).

non-conductiv 30, 60 μm; leEM simulatio

formed for con2.b). Result

trate SiGe build on conduexistence of

TEM mode”, “emonstrated, an

gnetic tween

tes of

s.

non-

30, . EM

ve ength ns of

nduc-ts are

uctive three

“skin-nd the

condbulk produenouacts the plow into lossy(met“grouthe scurrefrequmode“slowa husever

Fig(SiG

100,

cond

Fo

effecwithsuchthe t“grodielesubsvarie40 –smal-30 t

ditions for appresistivity of uct of frequenc

ugh to producelike an isolatinproduct of theenough to yiesilicon, the sem

y conductor wal-insulator-mund plane”. Hsilicon and onent – “skin-efuencies whicherate, the subsw-surface wavuge increase oral tens or hun

g. 5. Real partGe); width W 150, 300 μm

Fig. 6. Effectiductive substrlength Lx = 30

simula

or lower frequctive dielectri a slightly con

h a case this itransmission und plane”.

ectric loss-angtrate acts likes between

–110 Ω. For boll and the to 10 Ω in the

Telfor J

earance of eacsubstrate/frequcy and resistiv

e a small dielecng dielectric ane frequency aneld a small demiconductor sall, and the lin

metal) microstrence EM-fieldnly a thin "skffect mode” ph are not so strate acts like ve” propagates of the effectiv

ndreds.

t of ZC for MSWx = 5, 10, 15,

@ each Wx. Eon Fig. 2

ive dielectric rate (SiGe); w0, 100, 150, 3

ations of struct

uencies and wic constant lonductive dieleis reasonable line acts likeFor higher f

gle and substrke isolating d6-18 and thoth substrates

simulated frequency ran

Journal, Vol. 4

ch mode are cuency dependevity of the Si-suctric loss anglnd TEM modend the substratepth of EM-fiesubstrate wouldne may be trearip line onto ds don't penetkin" layer carpropagation tahigh and thenone of the abalong the line

ve dielectric

SL on conduct30, 60 μm; lenEM simulation2.b).

constant εeff oidth = 5, 10, 100 μm @ eachture on Fig. 2.

wider transmisooks like εeff ectric betweenfor “skin-effe

e a microstripfrequencies thrate is large endielectric. In he real part s the imaginar

impedances nge.

4, No. 2, 2012

clarified by thence. When thubstrate is large, the substratee occurs. Whente resistivity ield penetrationd behave like aated as a MIM

an imperfectrate deeply inrries the mainakes place. Ae resistivity ibove cases ande. This leads toconstant, even

tive substrate ngth Lx = 30, ns of structure

of MSL on 15, 30, 60 μm;h Wx. EM .b).

ssion lines, theof a capaciton the plates. Inect mode” andp line withouhe product onough and thethat case εefof ZC from

ry part of ZC ialter from

2.

e e e e n is n a

M ct n n

At is d o n

e

;

e or n d

ut of e ff

m s

m

Arnaudov and

C. VerificatiVerification

GaAs test strulay-out of sumethodology. transmission lanalyzer and carried out. Thof the structurfor the calibrafile and the ex(TRL) calibraresults and dgraphics are p

Fig. 7. Phoapplied in

Fig. 8. Compathis method e

Algorithm

1. Measureof microstrip 2. Place in 3. Use (1a) 4. Use (4) t 5. Measurepropagation c 6. Substituconstant εeff.

The algorimodified in twith: • One-por

d Borisov: On

ion Measuremn measuremenuctures were c

uch test structS-parameter

line by meansprobe station

he VNA calibrre and extractated bandwidthxtracted paramation data, a described methointed out in F

oto mask of min thru and refle

calibration in

arison of on-waextracted εeff o

GaAs subst

for extractione the scatteringTRL (Wx, Lx <circuit simulaand (1b) to finto find ZC of te the geometryconstant γ by mute γ in (5) an

ithm of the the following

rt measuremen

n-Wafer Measu

ments and Testnts using a netconducted. In tures, analyzedrs measurems of VNA “H“Cascade Mi

ration softwares the effectiveh in a single S

meters of transcomparison b

hodology wasFig. 8.

icrostrip linesect (open) stann 10-30 GHz b

afer measured f microstrip tratrate from Fig.

n of microstripg parameters S< λline/4); ator and find Snd Zinput short stub the transmissioy length of themeans of (6); d extract the

proposed exway. Item 1

nts of the “op

urements for E

t Set-up twork analyzeFig. 7 is give

d by the propments of saHP 8510C” net

crotech RF1” e makes the ane dielectric conS1P file. Usinsmission-reflecbetween the s carried out.

on GaAs wafndards for TRband.

(circle dots) anansmission lin. 7.

p TRL εeff: S11, S21, S12 an

Sii open and Sii sand Zinput open ston line (TRL)e TRL and fin

effective diel

xtraction coulcan be substi

en” stub by m

Extraction of

er and en the posed ample twork were

nalysis nstant

ng this ct-line VNA . The

fer,

RL

nd by e on

nd S22

hort; tub; ); nd the

ectric

ld be ituted

means

of th•

of “sthe simuthe tr

Uposswithmicrinforopenand Fig.

Fig

inveinve

str

Th

and the lmetawhitbackobtaigrou

Insectiof msubstμm, layer

Wintenpenemetarising20 GrespedepthPropGHz20-6propbulk

Effective Die

he set-up in FigThere is an

short” stub by“artificial” o

ulator from twransmission lising this algible to extractlengths Lx a

rostrip TRL srmation aboutn. Two-port m

“open”, lik9.c), provide

g. 9. Pictures oextraction of stigated “openestigated stub structure withructure with tw

de

he pictures ofdark-grey colight-grey colo

al on the intte spaces undek-side GND mined after c

und-signal-gron the followingons of HFSS m

microstrip linestrate conductivsubstrate heigr thickness dSiO

When taking ansity distributioetration into thal line), tends g. At 1 GHz tGHz the magectively (in onh of penetratio

per TEM-wavez, while below0 μm there eagation (see Fmaterial (SiO2

electric Consta

g. 9.a) or Fig.option to incly means of thobtaining of wo-port measine (Wx, Lx) is

gorithm and t εeff for trans

and widths Wstub. One-portt the input im

measurements uke those deus enough inf

of existing “onf εeff. a) One-pon” stub; b) Twas a transmiss

h two “open” swo “short” stuetermined by

f Fig. 9 are gour designate

our shows the terface dielecer the actual mmetal. Shiftingcalibration anound (G-S-G) g Fig. 10 a), bmodels for 3-Ds, built on Si-svity σ = 25 S/

ght h = dSi = 4O2 = 6-7 μm ana closer look on, it is obserhe depth of bto increase in

the intensity isgnitude increane and the saon along the ze properties are

w 1-7 GHz regiexists one tra

Fig. 12), where2/Si) combinat

ant

9.c). lude one-porthe set-up in F“short” stub

sured S-params omitted. calibration st

smission line Wx. In Fig. 9.a

t measuremenmpedances wh

using TRL staepicted in formation for e

n-wafer” test sort measurem

wo- port measusion line; c) Dstubs; d) De-eubs. Referenccalibration.

enerated fromes the top-leve

intermediate ctric-semicond

microstrip lineg of the refernd de-embedlaunchers.

b) and c) are dD full-wave Esubstrate. Basi/m, microstrip400 μm and εrnd εr = 4.

at the picturved that the

bulk silicon bon magnitude ws very weak, wases about 2 ame volume), z-axis (boundae demonstrateion and microansition zone e εeff is greatertion – equation

14

t measuremenFig. 9.d). Thu

by a circuimeters data o

tructures it iconfigurationa) is shown ant can give uen the TRL iandards “thru”Fig.9.b) and

extraction [5].

structures for ent of the urement of the

De-embeddingembedding e planes are

m mask designel metal, whilelayer of shieldductor. Blank

es are substrateence planes idding of the

depicted crossEM simulationic features are

p width w = 20r = 11.7, SiO2

ures of E-fieldelectrical field

ody (under thwith frequencywhile at 10 and

and 10 timeassuming 1-D

aries 0 and h)d at 10 and 20

ostrip widths oof slow-wave

r than εr of thens (9), (10).

1

nt s it

of

s s a s s ” d .

e g

n e d k e s e

s-s

e: 0 2-

d d e y d s

D ). 0

of e e

E

142

Fig. 10. I2-D wave p5).w and H′

a

If we appdistribution ρ the SiO2/Si-iapproach alonEmax=-Vmax/h athe following The substitutio

Double inte

and after the obtain a gener

The values

boundaries toground metal derived for ththe absolute inversely propas E decrease

Intensity distriport on the x-z p′ = (5-10).h a) Eat 10 GHz; c) E

proximate a = ρ0.z (ρ0 is a interface, 1-Dng the z-axis aat the boundarexpression, l

onE= -grad(Φ)

∂∂2

egration of thdeterminationral equation fo

=ρε

Emax

V

of the potentiop metal strip(z=0), respecti

hese boundary dielectric perm

portional to thees, ε increases

ibution of E-fieplane with dimE- vector at 1 GE-vector at 20

linear type constant of fu

D gradient and maximumry metal-dielecleaning on the) is applied:

ερ−=Φ

z22

e above expre

n of the integrfor E, from wh

)(6

)3( 220

hVE

hz

+

−ρ

hVh −=

ερ

3

20

ερ6

30h−=

ial function Φ

p-dielectric (z=ively. Equationconditions. It

mittivity ε=ε0.e applied electrs (in one and

eld, excitation mensions W′ = GHz; b) E-vecGHz.

of charge deunction slope) potential fun

m E-field magnctric, we can de Poisson equ

ession is perforation constanhich (8) follow

Φ are V and 0 =h) and dielens (8b) and (8t is easily seen.εr of the medric field. In our

the same con

by (3-

ctor

ensity under nction nitude derive uation.

(7)

ormed nts we ws:

(8a)

(8b)

(8c)

at the ectric- c) are n that dia is r case nstant

volum“slow

Fig.axi10.bthe i

D. DIt

and conncharathrouRi-LiTEMare btwo-Thusfall obtaidepedirecconsinto

Fig.

mec

Ho

propActusubsbetwby cfrequsilicocapaveryon tstrucdepemodthe eor m

a)

me) and at cerw” and “skin”

. 11. Illustratios of the HFSSb) and Fig. 10interface Si/Si

Discussion onis a well-knTelegrapher

nection line cacteristic impugh its equivi-Gi-Ci elemen

M-wave propabased on the -conductor tras microstrip ainto considerined results fo

endent on thction), substrstant εr [4]. Thconsideration

12. a) Illustraon the interfachanism as a f

owever, the perty to suppually from atrate acts li

ween the metacharge accumuencies of fewon). Hence, t

acitance per uslightly on d

he distance bcture, henceendencies Li ree, but Ci is m

effective dielemore, much

Telfor J

rtain conditionwave effects o

on of the E-fieS model cross-.c). PolarizatiiO2 is due to thGraphs are no

n Conductive Sown fact fromequations thacan be descripedance ZC avalent p.u.l. (nts. Equationsagation in suc

Telegrapher ansmission liand embeddedration by the

for εeff in (5) he width Wxate thickness

he effect of frin.

ation of polarice Si/SiO2; b)function of fre

resistiv

Si/SiO2-sandport propagata macroscopicke a condu

al layers, and mulation at thw GHz (depenthe distributedunit length, ddSi. In contrastbetween meta

on dox+dSi. emains roughl

much higher, eectric constant

higher tha

b)

Journal, Vol. 4

ns this value cooccur.

eld distributio-sections in Fion charge acche Maxwell-W

ot in scale.

Substrate Pecm transmissioat each parallibed fully by

and propagatio(per-unit-lengts (1)-(6) are cch a structure,equations solunes with a rd microstrip le presented may be deterx (perpendicu

s h and relatinging electric

zation charge ) EM-wave prequency and svity.

dwich does ntion of TEMc point of vctor for volthese changes

he Si/SiO2-intnding on the dd Ci is equal

depends mostt, the inductanal planes of t

Due to thly the same asespecially if dt can be as higan the relati

4, No. 2, 2012

ould exceed εr

on along the z-ig. 10.a), Fig. cumulation onWagner effect

uliarities on line theorylel-plate intery its complexon constant γth) distributedconsistent with, because theyution for longregular shapeline structurework. So thermined also aular to wavetive dielectricc field is taken

accumulationropagation substrate bulk

not obey theM-waves onlyview, the Siltage changes are followedterface, up to

doping level ol to the oxidely on dox andnce Li dependthe microstrip

hese differens for the TEMdox

Arnaudov and Borisov: On-Wafer Measurements for Extraction of Effective Dielectric Constant 143

permittivity of Si (11.7) and SiO2 (4). This effect is described by the so-called Maxwell-Wagner polarization mechanism, which results in much higher values of the effective dielectric constant for “slow-wave” propagation [3].

00

10 sri

i

n

ii

effSW d

dεεεεε ==′

=

(9)

∞

−

==

=

=′ s

n

i ri

in

iieffTEM

dd εεε

εε 01

110 )(

(10)

200

3 SiOSiox

chardd

εεμρ =

(11)

In equations (9) and (10) are given expressions for the absolute values of the effective dielectric constants, indexed SW – for “slow” and “skin-wave” propagation and TEM for TEM-wave, respectively. Here di is the thickness of each layer, εri relative constant of corresponding layer material. It can be proved that values from (9) can be much greater than the relative ones εri, while on the contrary in (10) εri is their upper limit. Equation (11) exhibits the so-called “characteristic” bulk resistivity of semiconductor, at which the maximum “slow-wave” frequency is reached (see Fig. 12. b)). In the literature εs0 is called static Maxwell-Wagner permittivity and εs∞ – optical value of it. The latter is easily developed from applying a series connection of capacitors with identical areas, different thicknesses and extracting their equivalent capacitance εreq. In summary, when TEM-wave propagates a displacement current in the structure prevails, while in the other modes conduction currents in metal and semiconductor skin-layers are predominant.

An important comment may be included here, a polarization effect takes place when the substrate does not possess properties of perfect insulator dielectric, on the contrary, there exists a certain amount of free carriers (holes or electrons), depending on the semiconductor doping level and type. From a microscopic point of view, some more explanation can be added to the above statements. Due to the field-effect of MOS/MIS/MESFET gate structures, when biased with DC potential + RF signal, regions with accumulated minor carriers (enhancement mode and inverse channel) or depleted major carriers (depletion mode) are formed [6]. The thickness of such a boundary region on dielectric-semiconductor interface varies according to the DC voltage value and polarity, magnitude of RF voltage swing, substrate doping level and channel modulation may occur. This could be the source for building of distributed microwave active devices as detectors, voltage-controlled filters and attenuators, etc.

IV. CONCLUSIONS A methodology for simple extraction of effective

dielectric constant in microstrip transmission lines on multilayer substrates, from measured or simulated S-parameters data, using on-chip test structures, has been demonstrated. The basic key to build successful models and perform genuine electromagnetic simulations of IC topology layout is the knowledge of complex

characteristic impedance and propagation constant. The effective dielectric constant is derived from the phase constant. This method is capable to be implemented in LTCC and LCP substrate material evaluation for IC packaging purposes, also.

Fundamentals of the presented method can be referred to the so-called “direct” ones as far as S-parameter measurements or simulations of the investigated structures are concerned. The chosen approach of “open” and “short” transmission line stubs, with length less than one quarter wavelength, is mandatory in order to mitigate resonance phenomena, where indefiniteness of the input line impedance exists and particularly tan(βl) is 0 or ∞. In such cases is recommended the implementation of “indirect” methods, which are based on inserting of sample material in bulk waveguide resonators or building transmission line resonators on the investigated material.

As far as “open” stubs are dealt with, a reasonable question about inserted equivalent electrical “elongation”, due to the fringing electrical field at the edges, may arise. The conducted experiments show that such phenomena in thin semiconductor substrates (100-400 µm) and relative dielectric constants in the range of (9-13), cannot cause considerable errors in the achieved data. Nevertheless, in order to eliminate such possibilities, we have the opportunity to omit one-port open-stub measurements and rely on the two-port measured S-parameters data of TRL (see Fig. 9.b)) with subsequent “artificial” conversion to “open” and “short” stub data in the circuit schematic simulator. This mathematical operation is absolutely free of errors, because of the implementation of ideal “open” (perfect magnetic wall) and “short” (perfect electrical wall).

A practical conclusion can be summarized from Fig. 11. When a true TEM-wave propagates in the structure, the value of E-vector magnitude is 0 exactly at the interface boundary of dielectric-GND metal plate, while if some other mixed modes exist there is a shift upwards into the dielectric body and physical substrate thickness h converts into heff, i.e. the graphs for 1 and 10 GHz. This effect is observed for dielectric substrates with some conductive features, where heff differs from h.

REFERENCES [1] W. R. Eisenstadt and Y. Eo, "S-Parameter-Based IC Interconnect Transmission Line Characterization," IEEE Trans. Comp. Hybrid, Manuf. Technol., vol. 15, no. 4, pp. 483-490, Aug. 1992. [2] Yungseon Eo and W. R. Eisenstadt, “High-Speed VLSI Interconnect Modeling Based on S-Parameter Measuraments,” IEEE Trans. Comp. Hybrid, Manuf. Technol., vol. 16, no. 5, pp. 555-562, Aug. 1993. [3] Hideki Hasegawa, M. Furukawa, and H. Yanai, “Properties of Microstrip Line on Si-SiO2 System,” IEEE Trans. Microwave Theory Tech., vol. MTT-19, no. 11, pp. 869-881, Nov. 1971. [4] R. Garg, P. Bhartia, I. Bahl, and A. Ittipiboon, Microstrip Antenna Design Handbook, Norwood, U.S.A.: Artech House Inc., 2001. [5] Ming-Hsiang Cho, Guo-Wei Huang, Chia-Sung Chiu, Kung-Ming Chen, An-Sam Peng, and Yu-Min Teng, “A Cascade Open-Short-Thru (COST) Method for Microwave On-Wafer Characterization and Automatic Measurements,” IEICE Trans. Electron., vol. E88-C, no. 5, pp. 845-850, May 2005. [6] M. Gospodinova, V. Mollov, and R. et al Arnaudov, “Study of the DC Biasing Effect on Insertion Losses in High-frequency Interconnections”, Elsevier Microelectronics Journal, Netherlands, vol. 31/11-12, Nov. 2000, pp. 1009-1014, ISSN 0026-2714.

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