ANALYSIS AND MODELING OF SURFACE-ACOUSTIC WAVE RESONATORS

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1 Helsinki University of Technology Publications in Engineering Physics Teknillisen korkeakoulun teknillisen fysiikan julkaisuja Espoo 2000 TKK-F-A804 ANALYSIS AND MODELING OF SURFACE-ACOUSTIC WAVE RESONATORS Julius Koskela Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics for public examination and debate in Auditorium F1 at Helsinki University of Technology (Espoo, Finland) on the 12th of January, 2001, at 12 o clock noon. Helsinki University of Technology Department of Engineering Physics and Mathematics Materials Physics Laboratory Teknillinen korkeakoulu Teknillisen fysiikan ja matematiikan osasto Materiaalifysiikan laboratorio

2 Distribution: Helsinki University of Technology Materials Physics Laboratory P.O. Box 2200 FIN HUT Tel Fax Julius Koskela ISBN ISSN Otamedia Oy Espoo 2000

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15 TT n i$b BZR 7$8Zjs$Bt qy } B} $ R BP RZ Ps{ Ts{BZR${ bs% I %${ R R Btjk I } ti Bt Y R j {$Bt BP Y RZAR s 8s $sj{ krsj {ZstI Y Y $Yb$IYstI RYs} BP Y j {T BI RstI sjrb Bt 8} sz * 8$ts$Bt BP Y 7VG {Ys s{ $R${R P B8 RTR Z{Z 8 srz 8 tr >;n;;h $R jsab BZR$8 T{BtRZ8$t sti$p s B tt $ jk t b RZAR s R s $t%bj% I% k -} tr$% 3B Y$R srbt IZ{$t Y tz8t A BP -} $8 tr %$s tz8 ${sj R$8Zjs$BtR R 8R s s{$% G Ys% $8}j 8 t I s R$8Zjs$Bt BBj PB $tht$ } $BI${ j { BI s skr sti 8}jBk I $ B RZIk Y 7VG {Ys s{ $R${R Bt %s $BZR RZAR s R!t }s ${Zjs jk $8}B st PB 8 BP R Z{T Z {Ys s{ $9s$Bt $R Y - s{$bt BP Y }s s8 R ZR I $t Y }Y tb8 tbjb${sj I R$t 8BI jr G Ys% I % jb} I st ^{$ t 8 YBI PB Y - s{$bt BP Y ]! }s s8 R P B8 Y $B BZRjk {B8}Z I Ys 8Bt${ si8$st{ nd 3$ jitqy B ${sj 3B 8Zjs$Bt _YkR${sjjkY R Z{Z $t 3$ 1d 8sk A s, t B {BtR$R BP Y }$ 9B j { ${ RZAR s { krsjy 8 sj j { BI R Bt Y { krsj RZ Ps{ sti Y RZ BZtI$t %s{zz8 VR R$8}j$Pk$t s}} B-$8s$BtRY RZAR s $R srrz8 I R 8$T$tht$ B PZjhjj Y jbb YsjPR}s{ F (sti Y j { BI R s srrz8 I $tht$ jk Y$t P B8 Y j { ${ }B$t BP Y %$ b qy RZAR s sti Y j { BI R 8sk A s I ZR$t Y Y B k BP jsr${$k >x(xdhy Y 8BIkts8${sj Y B k BP }$ 9B j { ${$k >x1h sti s-b jj:r JZs$BtRbY$j Btjk s-b jj:r JZs$BtR s JZ$ I PB Y %s{zz8 qy Y B k BP jsr${$k {BtR$I R s YB8B t BZR {Bt$tZBZR 8 I$Z8 qy h ji JZst$$ R BP $t R s Y 8 {Yst${sj I$R}js{ 8 t h ji ǹ Y j { ${h ji n o sti Y 8st ${ h ji n 4 yt j$t s }$ 9B j { ${ 8 I$sY R RR trb sti Y j { ${ I$R}js{ 8 t h ji n ; s j$t s jk {BZ}j I B Y R s$t trb sti B Y j { ${ h ji no *Z B Y jbb % jb{$k BP Y s{bzr${ bs% R$t {B8}s $RBt B Y R} I BP j$y Y 8st ${ h ji 8sk $t } s{${ A t j { I ]BtR JZ tjky j { ${ h ji 8sk A s}} B-$8s I sr Y si$ t BP st BR{$jjs$t j { ${ }B t$sj *U no ) n*3 wndd qy$r $R,tBbt sr Y JZsR$Rs${ s}} B-$8s$Bt G$Y$t Y JZsR$Rs${ s}} B-$8sT $BtY {BtR$Z$% js$btr s >x1h T z Z x 7i ) ; 7 ) n3 >,q)d n3 i,>)d o (`> 7i>q L (? q 7i> (`i (? > n3 >)d n3 C 7i i)d >7i (* (? >, (* 3 (? i wn1d <? d? 1? n I tb Y ]s R$st {BB I$ts R?, r, F R} {$% jkx 7i s Y {B8T }Bt tr BP Y R {BtIT st, R RR trb 7i>q s Y {B8}Bt tr BP Y PBZ YT st,

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26 T1(T ~ Y(γ = 0.499,f) [1/Ω] (a) Re Im f 2p/v B Re Im Y( f ) [1/Ω] (b) Im 0.4 Im 0.2 Re Re f [MHz] 3$Z ;nu ]B8}s $RBt BP Y 8BI j wisry I {Z % RD B wrbj$i {Z % RUD wyd Y Ys 8Bt${ si8$st{ K V w(3;,wd sti wkd Y 8 srz I R}BtR BP s R RBtsB < _b ( )M0 yb )(EstI Y RZAR s $R ;1 H O T{Z N$qs! n yt Y R RT BtsB ); 8 ] } )x ] )n sti G)dE ( V R$8Zjs I RBtsB R}BtR $R {B8}s I B s R R Z{Z 8 srz 8 t >;H $t 3$ ;nwkd _Y tb8 tbjb${sj s tzs$bts R $ R R$Rst{ BP d; sti RB8 sit I$$Btsj {s}s{$st{ b $t BIZ{ I B Y 8BI jaz BY b$r Y }s s8 R s YBR I IZ{ I P B8 Y 3e\ e R$8Zjs$Bt qy RBtst{ P JZ t{k $R Rj$Yjk RY$P I sti Y $R R8sjj B $t Y I$R} R$Bt {Ys s{ $R${R qy R & {R 8sk A -}js$t I Ak bs% Z$I$t sti I %$s$btr $t Y I %${ B8 k <Bb % Y s{y$ % I B% sjj s{{z s{k -{ IR Ys BP {Bt% t$btsj ]! Y B k R} {$sjjk {BtT { t$t Y RYs} BP Y RBtst{ VR -} { I AsR I Bt 3$ ;nwydy } I${ I jbrr R s Y RB}AstI s RB8 bys BB jbb sti Y VG si$s$bt s Y$Y P JZ tt {$ R $R B% R$8s I <Bb % Y -} $8 tsj {Z % sjrb P sz R st Zt -} { I $t{ sr $t Y {BtIZ{st{ $t Y YR BP Y RBtst{ qy 8 {Yst$R8 ZtI jk$t Y js I jbrr RvN7VG si$s$bt B Y AZRAs R BP Y RBtsB v$r Y B}${ BP _s} R z sti zyi$r{zrr I $t 7 { x

27 T1dT x V{BZR${ NBRR R $t N s,k 7VG i RBtsB R Bt N$qs! n N s,k RZ Ps{ Ts{BZR${ bs% RBtsB R Bt Bs I OT{Z N$qs! n RZAR s R P sz R Btjk P JZ t{kti } ti t jbrr RsR {st A t R t $t 3$ ;n qy R j si B I $B s$bt $t Y hj } PB 8st{ sti JZ$ {B {$BtR $t I %${ I R$t >xh VjYBZY Y {Bt $AZ$BtR BP }Y tb8 ts RZ{Y sr Y As{,R{s $t $tb 37T VGR sti Y Rkt{Y BtBZR VG -{$s$bt B Y jbrr R Ys% A t RZI$ I >nhy j s,s 8 {Yst$R8R $t N7VG RBtsB R Ys% 8s$t I b s,jk ZtI RBBI i { tjkjsr T$t P B8 ${ 8 srz 8 tr Ak tzz$js sj % sj I Ys s{bzr${ bs% R s {s}saj BP R{s}$t Y RBtsB s s Y BZY Y AZRAs R >EH yt _s} z BP Y$R bb,y R{s}$t s{bzr${ A s8r Ys% A t $I t$h I sr N7VG si$s$bt sti Y $ {Ys s{ $R${ P sz R Ys% A t JZsj$s$% jk -}js$t I AsR I Bt Y { krsjj$t st$rb B}k BP Y j$y$z8 stsjs RZAR s 3Z Y 8B $t _s} zy b Ys% JZst$s$% jk stsjk9 I Y P JZ t{kti } ti t{ BP Y si$s$bt sti R$8s I Y s{bzr${ jbrr R IZ B Y & { sr b jj sr YBR IZ B N7VG } B}ss$Bt jbrr RN7VG As{,R{s $t $tb 37T VGRstI Y 37T VG -{$s$bt qy stsjkr$r $R AsR I Bt Y $tht$ } $BI${ s$t b$y s ht$ s} Z $jjzr s I $t 3$ xd *Z B Y Y$Y st$rb B}k BP Y N7VG RjBbt RR {Z % R Bt Bs I OT{Z N$qs! n RZAR s R{Bt% t$btsj R{sjs bs% Z$I Y B $ R AsR IPB -s8}j Bt Y }s s-t $sj s}} B-$8s$Bt >nmh s ZtRZ$sAj PB N7VG I %${ R yt _s} zys R 8$T }Y tb8 tbjb${sjr 8$T 8}$ ${sj 8BI j $R {BtR Z{ I PB Y Ys 8Bt${ si8$st{ BP Y $tht$ j { BI s sk b$y s ht$ s} Z qy 8BI j 8sk A {BtR$I I sr s bbti$8 tr$btsj - tr$bt BP Y 7<T7VG RBtsB 8BI j $t _s} yz Vt sj T A s${ p t:r PZt{$Bt tw?, rd $R 8}$ ${sjjk {BtR Z{ I RZ{Y Ys Y RjBbt RR {Z % R PB N7VGR ZtI Zt$PB 8 8 sjj$9s$bt Bt N$qs! n s } BIZ{ I Ak Y B k b$y s srbtsaj s{{z s{k qy -{$s$bt BP PsRTRY s VGR $R $ty tjk $t{jzi IAZ y W z X p W a 3$Z xdu _ $BI${ j { BI s sk b$y $tht$ AZRAs R

28 T11T Y RjBbTRY s VG {Bt $AZ$Bt $R s{{bzt I PB Btjk $t Y } B}ss$Bt jbrr BP Y N7VG 7Bj%$t Y 8BI j tz8 ${sjjk sti s}}jk$t Y stsjkr$r {Yt$JZ R %$ b I $t 7 { 1Y I$R}js{ 8 t h jir sti Y j { ${ si8$st{ $t st $tht$ RBtsB 8sk A {B8}Z I tsaj$t JZst$s$% stsjkr$r BP Y j s,s 8 {Yst$R8R xd V{BZR${ N s,s {Yst$R8R NsR T$t P B8 ${ R{stR BP Y s{bzr${ h ji $t Rkt{Y BtBZR RBtsB R Bt ne H O T N$qs! n % sj R Btjk P JZ t{kti } ti t s{bzr${ si$s$bt B Y AZRAs R BP Y R Z{Z sr RYBbt Ak Y R $ R BP $8s R $t 3$ x1 yt _s} z Y }Y tb8 tbt $R JZsj$s$% jk -}js$t I AsR I Bt Y RjBbt RR {Z % R sti Y }Bjs $9s$Bt PB N7VGR Bt Zt$PB 8jk 8 sjj$9 I N$qs! n RZ Ps{ yt Y RB}AstI Y s{bzr${ h ji $t Y s$t s s $R B% t I Ak Y s 4 {$BtR V { s$t P JZ t{$ R Y AZRAs R wby${y 8sk A {BtR$I I sr 8 sjj$9 I { krsj RZ Ps{ D RZ}}B N7VG $ t8bi R by${y s Rkt{Y BtBZRjk {BZ}j I B Y s{bzr${ h ji $t Y s$t N s,k bs% Z$I 8BI R Ys% A t RZI$ I s j$ Bt dd1 H TN$qs! n >MH stibt7qt{zjzs 9>d((H V I s$j I stsjkr$r BP 8sRRTjBsI I RjBbt RR {Z % R $t _s} zy {Bth 8R Ys Y } I${ I P JZ t{kti } ti t{ BP Y si$s$bt {jbr jk 8s{Y R ABY b$y Y jsr T$t P B8 ${ R{stR sti b$y Y j { ${sj 8 srz 8 tr 3Z Y 8B Y P JZ t{$ R 8BR } Bt B Y si$s$bt I } ti Btjk Bt Y js$% 8 sjj$9s$bt Y${,t RR *Z B Y st$rb B}k BP Y RZAR s { krsjy I { I si$s$bt $R R}s$sjjk srk88 ${ VjYBZY Y N7VG RjBbt RR {Z % R s Rk88 ${ sabz Y { krsj Ts-$RY }Bjs $9s$Bt $R tb qy srk88 k $R }s ${Zjs jk R Bt PB Y b s, RY s % ${sj {B8}Bt t by${y Y $t P B8 I {R yti I8 srz 8 tr Ys% {Bth 8 I Ys Y Ps%BZ I I$ {$Bt BP Y si$s$bt $R $ti } ti t BP Y }Bjs $k BP Y j { ${ I $% <Bb % s{{b I$t B BZ {B8}Zs$BtR Y IB8$tst RY s YB $9Btsj {B8}Bt t $R sj8br Rk88 ${ qy$r RZ RR YsI R}$ Y } BA $8s RN7VGR s s{zsjjk si$s I B Y AZRAs R sj8br Rk88 ${sjjk 3$Z xn $jjzr s R Y R$8Zjs I I$R}js{ 8 t } Bhj R BAs$t I P B8 Y $tht$ RBtsB 8BI j $t _s} zy yt {BtR sr B Y jsr T$t P B8 ${ R{stR 8 srz $t Y RY s % ${sj {B8}Bt ty R{sjs I$R}js{ 8 t h ji s I Ak Y 8BI j $R $t } I B I R{ $A Y IB8$tst RY s YB $9Btsj {B8}Bt t sti $ $R srrz8 I Rk88 ${ *Z B Y ht$ R$9 BP Y R RBtsB I$& t{ R s R t $t Y j s,s Y BZY Y 4 {B R <Bb % s {jbr R$8$js $k $R BAR % I A b t Y 8 srz I sti 8BI j I s8}j$zi I$R $AZ$BtR sti$t }s ${Zjs $t Y si$s$bt j s,$t B Y AZRAs R yt sii$$bt B N7VGRsjRB iskj $Y bs% R 8sk A si$s I Rkt{Y BtBZRjk B Y AZRAs R BY Rkt{Y BtBZR sti str% Rsjjk -{$ I iskj $Y bs% R s BAT R % I $t Y jsr T$t P B8 ${ R{stR }B I $t _s} zyaz Y k s j$, jk B A sy b s,!y s{bzr${ j s,s 8 {Yst$R8R $t{jzi Y si$s$bt BP AZj,T s{bzr${ bs% RbY${Y s $t } I B k$ ji Y b s, s{bzr${ As{, BZtI %$R$Aj $t Y R{stR

29 T 1n T (a) 891 MHz (b) 904 MHz (c) 907 MHz (d) 911 MHz (e) 917 MHz ( f ) 934 MHz (g) 949 MHz 3$ Z x 1U e-} $8 t sj RY s % ${sj I$R}js{ 8 t } Bhj R 8 srz I b$ Y s jsr } BA P s Z $t N7VG si$s $Bt B Y AZRAs R $t s R RBts B Bt neh O T{Z N$qs!n jbb Y RBtst{ P JZ t{k wy, KD Y si$s $Bt $R b s, AZ R Bt st I$s $Bt B{{Z R Rj$ Y jk sab% Y RBtst{ w, QD qbbs IR s JZ t{y$t P JZ t{k BP sabz d <9 Y si$s $Bt I$8$t$RY R w D sti %$ Zsjjk I$Rs}} s R ww, /D qy I$R}js{ 8 t $t Y 8 sjj$9 I sti P { kr sj RZ Ps{ R s tb $t R{sj ]BZ Rk BP FBZt$ tzz $js

30 T1;T (a) 891 MHz (b) 904 MHz (c) 907 MHz (d) 911 MHz (e) 917 MHz ( f ) 934 MHz (g) 949 MHz 3$Z xnu 7$8Zjs I RY s YB $9Btsj I$R}js{ 8 t } Bhj R PB Y R R Z{Z BP 3$ x1bas$t I b$y s }Y tb8 tbjb${sj 8BI j PB $tht$ RBtsB R

31 T1xT Y( f ) experiment theory 2D resonator 2D periodic 1D resonator [1/Ω] Y( f ) 10-2 Re Y( f ) f [MHz] 3$Z x;u srz I sti R$8Zjs I si8$st{ sti {BtIZ{st{ BP Y R R Z{T Z $t 3$R x1 sti xn 3B s P t{ sjrb Y R$8Zjs$BtR PB st $tht$ striz{ sti s RBtsB b$y st & {$% jk $tht$ s} Z s RYBbt x1 N s,s sti Y ej { ${ _ PB 8st{ qy 8BI j sjrb sjjbbr ZR sjrb B R$8s Y & { BP Y s{bzr${ si$s$bt Bt Y j { ${ R}BtR BP Y RBtsB 7$8Zjs$BtR {Bth 8 Ys Y N7VG AZRAs si$st $Bt $R $ti I R}BtR$Aj PB Y -} $8 tsjjk BAR % I $t{ sr $t Y {BtIZ{st{ $t Y %${$t$k BP Y RBtst{ R 3$ x; 3Z Y -} $8 tr sti R$8Zjs$BtR $t _s} zy $ti${s Ys Y R ty BP Y si$s$bt I } tir Btjk b s,jk Bt Y s{bzr${ s} Z ]BtR JZ tjky js$% jbrr R s } BtBZt{ I PB ts Bb s} T Z R Vt $t R$t P sz BP Y R{stt I $8s R sti Y R$8Zjs$BtR $R Y sj8br Bsj sar t{ BP str% Rsj RBtst{ R yt _s} zyy$r $R s $AZ I B Y Ps{ Ys PB ABY ne H sti ;1 H {Z N$qs! n Y N7VG s tzs$bt $t{ sr R I sr${sjjk b$y Y } B}ss$Bt stj B& Y { krsj Ts-$R ]BtR JZ tjky$y B I str% Rsj bs% Z$I 8BI R s j$, jk B I$R}jsk R Bt } B}ss$Bt jbrr R V{{B I$t B Y R$8Zjs$BtRY AZRAs si$s$bt sti Y N7VG s tzs$bt b jj -}js$t Y jbrr R {jbr B sti Rj$Yjk sab% Y RBtst{ qy R 8sk sjrb A R}BtR$Aj PB Y % k Y$Y %sjz R BP R $ R R$Rst{ JZ$ I $t Y 7<T7VG RBtsB 8BI j w_s} yzd V Y$Y P JZ t{$ RY -{$s$bt BP Y PsR RY s AZj,Ts{BZR${ bs% R $R Y IB8$ts$t jbrr 8 {Yst$R8 <Bb % Y R & {R {sttb -}js$t Y -} $8 tsjjk BAR % I jbrr R $t Y RB}AstI sti$t }s ${Zjs $t Y %${$t$k BP Y st$ RBtst{ qy R 8sk A IZ B Y I$ { -{$s$bt BP Y RjBb RY s AZj,Ts{BZR${ bs% R sti Y s{bzr${ jbrr R $t Y j { BI R B R s {Y $R JZ$ I Bt Y$R sr} {sr b jj sr B hti Y 8 str B B}$8$9 Y RBtsB B 8$t$8$9 Y jbrr R