Fullwave Analysis of Thickness and Conductivity Effects in Coupled Multilayered Hybrid and Monolithic Circuits

Size: px

Start display at page:

Download "Fullwave Analysis of Thickness and Conductivity Effects in Coupled Multilayered Hybrid and Monolithic Circuits"

Donald Barnett
5 years ago
Views:

1 Poceedings of he 4h WSAS In. Confeence on lecomagneics, Wieless and Opical Communicaions, Venice, Ialy, Novembe -, 6 76 Fullwave Analysis of Thickness and Conduciviy ffecs in Coupled Mulilayeed Hybid and Monolihic Cicuis M.L. TOUNSI, R. TOUHAMI, and M.C.. YAOUB Insumenaion Laboaoy, Faculy of leconics and Infomaics U.S.T.H.B Univesiy P.O Box, l-alia, Bab-zzoua, 6, Algies ALRIA School of Infomaion Technology and ngineeing Univesiy of Oawa 8 ing dwad, Oawa, Onaio, N 6N5 CANADA Absac: - In his pape, he hybid-mode specal domain appoach is genealized o descibe he dispesion popeies of coupled micowave cicuis wih any abiay meallizaion hickness and finie conduciviy in mulilaye configuaion. The influence of finie meallizaion hickness on he fequency dependen modal popagaion chaaceisics is shown fo boh suspended and inveed coupled sucues and can be easily exended o any mulilayeed cicui. The phase consan and effecive pemiiviy wih finie sip hickness and finie conduciviy ae discussed fo hybid and monolihic cicuis. ey-wods: - Hybid Mode, lecomagneic Field, Inegaed Cicuis, Meallizaion Thickness, Numeical Mehods, Specal Domain Appoach. Inoducion Any micowave inegaed cicui esponse like losses, dispesion, noise, ec., depends closely on how he implemened miniauized devices ae modeled. To be efficien, his aspec equies he esoluion of many issues elaed o he complexiy of he inegaed sucue such as he hybid naue of he elecomagneic (M) fields. Among hese feaues, edge effecs can significanly modify he disibuion of he M fields because of he influence of he meallizaion hicknesses which ole becomes moe and moe significan as he fequency inceases. Finie meallizaion hickness is one of he main facos ha affec he popagaion and aenuaion chaaceisics of plana waveguides, especially in high densiy miniauized monolihic micowave inegaed cicuis (MMICs) used in modeae powe pupose o in highe micowave and millimeewave fequency bands. As a esul of impovemens in fabicaing high pefomance complex componens in hese fequency bands, he design of MMICs equies efficien simulaion ools wih moe accuacy fo finie hickness plana ansmission lines []. This effec can be negligible fo single cicui lines even if he cicuis ae caied ou in hick film echnology. Neveheless, his ole becomes consideable when he cicuis ae designed o suppo high powes, o when he conduco exhibis high losses as in anenna newoks, o when he cicuis ae fabicaed in MMIC echnology. This is because he sip hickness may be compaable o he sip widh. The chaaceisics of plana cicuis wih finie sip hickness and conduciviy wee discussed using vaious echniques such as he peubaion echnique [], he fullwave mode-maching mehods [], and he mehod of lines [4]. Howeve, he peubaion appoach is no suiable fo MMICs since he skin deph and he sip hickness ae in he same ode, and he above full-wave mehods echniques ae ime consuming. Theefoe, an easie and fase mehod should be developed o mee he evoluion of MMICs. This aspec is paiculaly cucial fo mulilaye configuaions including MIS sucues (mealinsulao-semi-conduco) on aas o silicon when he loss faco of he layes needs o be aking ino accoun.

2 Poceedings of he 4h WSAS In. Confeence on lecomagneics, Wieless and Opical Communicaions, Venice, Ialy, Novembe -, 6 77 This pape deals wih he analysis of he influence of boh hickness and finie conduciviy in coupled mulilayeed hybid /monolihic cicuis using he specal domain mehod (SDA) hough he calculaion of he dispesion chaaceisics (phase consan, effecive pemiiviy and guided wavelengh) vesus fequency, hickness and finie conduciviy of he sips. Poblem Fomulaion Due o he ease of is fomulaion and is numeical efficiency, he specal domain appoach [5] is a well-known echnique fo he compuaion of plana ansmission line cicuis. The immiance concep [6] fuhe enhances he pepocessing and compuing woks fo mulilaye muliconduco sucues. This concep is genealized hee o geneae he complee expessions of een s funcions unde hei impedance and admiance fom. The sucue unde analysis is a geneal unilaeal micowave cicui pined on lossy mulilayeed isoopic layes whose ansvese secion is depiced in Figue. The conduco sips ae chaaceized by finie hickness and finie conduciviy σ m. The dielecic layes ae of loss faco gδ i = σ di /ωε i, whee σ di and ε i ae especively he conduciviy and pemiiviy of dielecic i. ach dielecic laye is chaaceized by a complex pemiiviy defined as ε i * = ε ε i ( j gδ i ). Meallized ineface ε N *, µ N ε N- *, µ N- ε m+ *, µ m+ ε m *, µ m ε *, µ ε *, µ Thick sip wih finie conduciviy σ m Lossy dielecic layes Fig. Secion view of a mulilaye micowave sucue wih finie hickness and conduciviy. The modificaions made o ake ino accoun he hickness effec and finie conduciviy of he sips, ae based on ceain coecive facos wih egad o he case of hin meallizaion ( = ) and infinie conduciviy (σ m ). In ode o obain he dyadic een s funcions of he sucue, he poposed pocess sas wih he decomposiion of he M field ino TM-o-y and T-o-y waves by inoducing coodinae ansfoms [6]. The applicaion of bounday condiions a all inefaces of he mulilayeed sucue yields o a se of maix equaions fo he impedance een s funcions [7] xm zm = ( ) x α n z ( α n ) () These funcions link he angenial componens of he elecic field o hose of he cuens on he meallized ineface. quivalen suface impedance Unil now, all sips ae consideed o be of infinie conduciviy and of infiniesimal hickness ( = ). In ode o use he same model fo hick plana sucues, a ansfomaion echnique is used o ansfom he hin conducing film ino infiniely hin sip. Since mos conducing films ae fabicaed o be vey hin, he widh-o-hickness aio of hese films is quie lage. As a esul, he angenial elecic o magneic field aio on he film suface is almos he same as he value of he suface impedance of he conducing film. This feaue allows he impedance bounday condiion o be used in solving fo he ansmission chaaceisics of he conducing micosip lines. When we apply he bounday condiions a he meallized ineface of he sucue in Figue, he conducing sip is eaed as an impedance shee, which is chaaceized by a jump disconinuiy in he values of he angenial magneic field, bu no in he elecic field. These bounday condiions ha exis on he suface of he sip ae wien as [8] n (H H m m+ ) = s = n (n ) Z s (m m ) = n + m () () whee n is he nomal o he meallized ineface. m and B m epesen especively he elecical and magneic fields below he impedance shee, while m+ and H m+ efe o he fields above he shee.

3 Poceedings of he 4h WSAS In. Confeence on lecomagneics, Wieless and Opical Communicaions, Venice, Ialy, Novembe -, 6 78 Z s is he unifom equivalen impedance of he shee. If he hickness of he sip is geae han hee peneaion dephs, he suface impedance Z s = ωµ / σ (4-a) will adequaely epesen he bounday condiions fo plane waves wih σ m he sip conduciviy. If is less han hee peneaion dephs, a bee bounday condiion makes use of Z s m m = σ. (4-b) 4 Modified bounday condiions The applicaion of hese new bounday condiions a y = H m in he Fouie ansfom domain esuls in some modificaions o he elemens of he een s impedance maix. Specifically, he diagonal elemens of maix () need o be modified o incopoae he complex suface esisance of he supeconducing sip as m = - Z s and m = - Z s (5) Thus, () becomes xm zm = m m x z (6) A numeical soluion o his maix equaion can be obained by using alekin mehod in he Fouie domain o eliminae he igh side. The cuen elemens ae expanded in a se of known basis funcions which ake he edge singulaiies ino consideaion leading o a pope cuen disibuion ove he sip. x = P p= c p xp and z = Q q= d q zq (7) 5 Applicaion of alekin echnique Afe subsiuing he Fouie ansfoms of (7) ino (6) and aking inne poducs of he esuling equaions wih he es funcions xp', zq' (chosen equal o he basis funcions), we obain a homogenous sysem of algebaic equaions wih he (P + Q) unknown coefficiens c p and d q. whee This sysem can be wien as P p= P p=, p, q', q, q' c c p p + + Q q= Q q=, p, p', q, p' d d q q = = (8) = * ( β ) i, j ( α n, β ) x zs, s = p o q (9) n i, j, s and n is he specal index. The homogeneous sysem (8) has been obained via he applicaion of Paseval's ideniy. I is solved fo he popagaion consan by seing he deeminan of he sysem equal o zeo and by evaluaing he oos of he esuling chaaceisic equaion. 6 Numeical esuls The dispesion cha is a necessay sep o fix he bandwidh of he dominan and highe ode modes which ae excied a high fequencies. These modes can ceae adiaion losses ha mus be avoided. Figue shows he vaiaion of he even and odd mode phase consans vesus fequency fo a coupled line on aas (ε = ) whee he conduco is gold (σ m = 4. 7 S/m) and of hickness =.6µm. Phase consan (d/m) Odd 4 5 Fequency (Hz) aas Fig.. ven and odd mode phase consan of a shielded coupled micosip on aas subsae; h = µm, h = 7µm, =.6µm, w = s = µm ε h h

4 Poceedings of he 4h WSAS In. Confeence on lecomagneics, Wieless and Opical Communicaions, Venice, Ialy, Novembe -, 6 79 The losses ae essenially due o conducing sips, he even mode which popagaes beween he sips and gound plane is less aenuaed han he odd mode which popagaes beween he wo sips. The even mode is also less dispesive han he odd mode. The obained esuls agee well wih. Figues -a, -b, and -c, illusae he vaiaion of he even and odd modes phase consan of a coupled MIS (meal-insulao-semiconduco) sucue fo diffeen values of he silicon conduciviyσ Si. Conay o he sucues pined on aas, he odd and even mode phase consans ae diffeen due o he saified naue of he dielecic layes. When he conduco losses ae pedominan (fo low values of σ Si ), he even mode phase consan is geae han he once of he odd mode while fo he high values of σ Si (Figue.c) we noe ha beyond 5 Hz i exhibis he invese behavio and he esuls ae close o hose obained fo aas. The compued show good ageemen wih Figue 4 shows he vaiaion of even and odd modes effecive pemiiviy fo coupled plana sucues on Silicon fo diffeen values of he sip hickness. Noe he decease of ε eff when incease fo he wo popagaion modes. Also, we noe ha he even mode is less dispesive ha he odd one. The obained esuls agee well wih measued daa []. In Figue 5, he even and odd mode effecive pemiiviies ae shown fo diffeen combinaions of he hickness and slo widh s. In his case, he diffeence in popagaion speeds of he even and odd modes inceases as s decease and he incease is moe eviden when is finie, since he wo modes ae influenced in a diffeen way by. Figue 6 gives he chaaceisics of coupled plana sucues in mulilaye dielecic configuaion. On he conay, as s deceases, he diffeence beween he even and odd mode speed fis inceases (fo lage s) and hen deceases. This behavio can be obseved only when one akes meallizaion hickness ino accoun since when = hee is a monoone incease in diffeence of popagaion speed. The obained esuls agee well wih published daa []. Phase consan (d/m) Phase consane (d/m) Phase consan (d/m) 4 5 Fequency(Hz) (a) σ Si = S/m Od mode 4 5 Si O Si w Si O ε Si ε s w ε ε h h h Fequency (Hz) (b) σ Si = S/m h h h 4 5 Fequency (Hz) (c) σ Si = S/m Fig.. Phase consan of hee-layeed coupled plana sucues fo vaious values of silicon conduciviy (wih =.6µm, w = µm, a = h /, s = µm, h = µm, h =.6µm, h = (h +h ), ε =, and ε = 4): a) σ Si = S/m ; b) σ Si = S/m ; c) σ Si = S/m

5 Poceedings of he 4h WSAS In. Confeence on lecomagneics, Wieless and Opical Communicaions, Venice, Ialy, Novembe -, 6 8 ffecive pemiiviy /h =. /h =.44 /h =. /h =.5 [] Fequency (Hz) Fig. 4. ffecive pemiiviy vesus fequency fo vaious values of sip hicknesses (wih ε =.5, w/h = s/h =.5, h =.6mm, h = mm, and =.8 mm). ffecive pemiiviy = mm =, mm =, mm [] 4,,5,,5, Slo widh (mm) Fig. 5. ffecive pemiiviy vesus slo widh fo diffeen values of sip hicknesses. Such behavio is hen confimed fo coupled suspended-inveed sucues (Figue 7). Howeve, he cuves of he effecive pemiiviy exhibi now an invesion of diffeence in he modal popagaion velociy fo smalle values of s wih espec o he pevious case. The obained esuls agee well wih []. Si ε Si ε h h h h ffecive pemiiviy ffecive pemiiviy,4,,,8,6,4,,5,,5 Slo widh (mm) = mm =. mm =. mm [] Fig. 6. ffecive pemiiviy vesus slo widh fo diffeen values of : case of suspended coupled plana sucues (wih = mm, w =.5mm, h = mm, h = h = mm, ε = 4, ε = ε = ).,5,,5 w w s h ε ε = mm =. mm =. mm [],,5,,5, Slo widh (mm) ε ε Fig. 7. ffecive pemiiviy vesus slo widh fo diffeen values of hicknesses : case of inveed coupled plana sucues (wih = mm, w =.5mm, h =.5mm, h = mm, h =.5mm, ε = 4, ε = ε = ). 7 Conclusion In his pape, we have poposed an efficien mehod o analyze he hickness and finie conduciviy effecs in coupled micowave cicuis. The advanage in he CPU ime is efleced by he fac ha he calculaion of phase consan pe fequency poin does no exceed s. h h h h h

6 Poceedings of he 4h WSAS In. Confeence on lecomagneics, Wieless and Opical Communicaions, Venice, Ialy, Novembe -, 6 8 The obained esuls show he necessiy o aking ino accoun boh hickness and finie conduciviy of he sips paiculaly in he case of he MIS lines (meal-insulao-semi-conduco) in he egion of slow-wave modes. The dependence of modal phase paallel coupled micosip on he meallizaion is significan, especially a highe millimee-wave fequencies, and fo elaively low dielecic consans. The poposed mehod can be exended o anisoopic sucues wih supeconduco signal sip. Besides, exension o he coplana sips and coplana waveguides is saighfowad. Refeences: [] Z. Ma,. Yamashia, and S. Xu, Hybid-mode analysis of plana ansmission lines wih abiay meallizaion coss secions, I Tans. Micowave Theoy Tech., vol. 4, pp , Ma. 99. [] R. A. Pucel, D.. Mas, and C. P. Hawig, Losses in micosip, I Tans. Micowave Theoy Tech., vol. 6, pp. 4-5, une 968. [] W. Heinich, Full-wave analysis of conduco losses on MMIC ansmission lines, I Tans. Micowave Theoy Tech., vol. 8, pp , Oc. 99. [4] F.. Schmuckle and R. Pegla, The mehod of lines fo he analysis of lossy plana waveguides, I Tans. Micowave Theoy Tech., vol. 8, pp , Oc. 99. [5] T. Ioh and R. Mia, A echnique fo compuing dispesion chaaceisics of shielded micosip lines, I Tans. Micowave Theoy Tech., vol., pp , Oc [6] T. Ioh, Specal domain immiance appoach fo dispesion chaaceisics of genealized pined ansmission lines, I Tans. Micowave Theoy Tech., vol. 8, pp. 7 76, uly 98. [7] M.L. Tounsi, M.C.. Yagoub, B. Haaoubia, "New design fomulas fo micosip ansmission lines using high-dielecic subsae," COMPL: In. fo Compuaion and Mahemaics in lecical and leconic ng., vol. 4, N o, pp. 5-4, an. 5. [8] A. I. Amoa, H. hali, Full wave analysis of HTS supeconducing micosip ansmission lines using specal-domain immiance appoach, Poc. of h Naional Radio Sci. Conf., Mach 9-996, Caio, gyp, pp H. ahomi Abii, Analyse dynamique des lignes miconiques pa la méhode specale, Ph.D. hesis, INP enoble, Fance, 984. [] R.T ollipaa, V.. Tipahi, Dispesion chaaceisics of modeaely hick micosip lines by he specal domain mehod, I Micowave uided Wave lees, vol., pp. -, Ma. 99. []. enili,. Macchiaella, Quasi-saic analysis of shielded plana ansmission lines wih finie meallizaion hickness by a mixed specal-space domain mehod, I Tans. Micowave Theoy Tech., vol. 4, N, Feb. 994.

, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t

, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t Lecue 6: Fiis Tansmission Equaion and Rada Range Equaion (Fiis equaion. Maximum ange of a wieless link. Rada coss secion. Rada equaion. Maximum ange of a ada. 1. Fiis ansmission equaion Fiis ansmission