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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: [email protected]).
Radoslav B. Borisov is MMIC Designer at “RaySat BG” and currently making his Ph.D. in the field of Microeletronics (e-mail: [email protected]).
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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