Characterizing Optical Thin Films (I)

Transcription

1 Chaaczg Opcal Th Flms (I) Physcal vapo dposo s h mos commo chqu usd o dpos opcal h lms o a lag vay o applcaos. Ths qus h ably o g a sold maal o a vapo (gasous) om, o aspo o a suac oo whch h lm s o b dposd, ad o b abl o cool h physcal ad opcal pops o h sula lm. Spug ad vapoao a vacuum a h pval chqus usd o g sold maals o a vapo om. Rgadlss o h dposo chqu usd, s cssay h dvlopm o coag qupm ad coag pocsss o hav h ably o dm h physcal ad opcal pops o h sula lms. Th s a cosdabl ag o qupm avalabl o do hs. Howv, all lm Opcal h lm mauacus hav o hav h ably o masu h pomac o shd dvcs. A codg spcophoom s h wokhos sum o do hs. Spcal masums o sgl lay coags ad ca mul-lays sucus ca b usd o ac opcal pops o h lms Calculag h spcal pomac o opcal h lms o a suac s a vy mau chology ad has b wdly publshd (,). I s h possbl o ak daa om h spcal masums o lms ad ac opcal pops. I s h pupos o hs acl o dscuss how hs ca b do, h valdy o h suls ad h o dscuss wha w ca uh la abou h lms om h suls. To do so, w s look a usg h opcal pops o h lm maals o calcula h spcal pomac. Wha w wa o do s o dm h ampluds ad ss o lgh cd o a h lm ad/o h lm sysm dposd o a suac. To do so s aly saghowad howv compl. O oly has o s up Mawll s quaos, apply h appopa bouday codos o av a a soluo. Th a a vay o appoachs ha hav b usd basd o hs appoach ad, alhough smgly d, vually av a h sam sul. Fo hs acl I choos o us a covo as pvously publshd by Havs (). Also, o smplcy I choos o pck up h calculaos a h wav quaos hav b solvd ad w a a a poso wh h calculaos hav bcom lavly smpl. Tha s, w assum all o h plmay mssy wok has b do appopaly ad w ca go owad a lavly asy ma. Also, w wll duc h comply uh by oly cosdg lgh ha s omally cd o h suac. Ths assumpo s vald sc oblqu cdc s o dd h ampls ha w wll b cosdg la. Fuhmo, w a gog o assum ha h maals a o-absobg. Ths s o ssal. Howv, h maals w absobg, h acv d () would hav o b placd by h compl acv d (-k). Oc w hav dmd how o hadl h oabsobg suao, w wll h allow o slghly absobg lms. Th ollowg dvao s also basd o pvously publshd maal ppad by h auho (3). Cosd lgh cd o a maal wh a smooh polshd suac o acv d (s Fgu ). Som o h lgh wll b lcd a h suac ad som o h lgh wll b asmd o h maal. Th Fsl cocs o h ampluds o h lcd ad asmd lgh avlg om (h suoudg mdum) o a gv quaos ad ad o lgh avlg om o a gv by quaos 3 ad.

2 () () (3) () Icd lgh R T Fgu. R ad T o lgh cd o a suac. As dcad pvously, h abov laoshps a vald o lgh cd a omal cdcs. Fo lgh oblquly cd o h suac s cssay o cosd h s ad p polazaos, calcula R ad T spaaly o ach polazao ad avag hm ogh. Alhough asy o do, hs s a complcao byod wha w d o cosd a hs po. Th amou o lcd ad asmd lgh a h ac a gv quaos 5 ad 6 ms o h Fsl cocs ad h acv ds (wh - ): ( ) ( ) ( ) ) ( R (5) ( ) T (6) I a h lm s dposd ov h suac o h maal h a ow acs wh h lgh ca b lcd ad asmd. Also, h wll ssally b a umb o mulpl lco ad asmssos ha d o b summd o gv h al amou o lcd ad asmd lgh. Ths sum s lad o h opcal pops o h lm, h opcal pops o h subsa, h lav valus ad h phas hckss o h lm. Cosd h suao show Fgu o lgh cd a omal cdc o a coad suac (No: alhough I had cludd oblqu cdc, a agl s cludd h gu so ha h lcd ad asmd bams would b spaad ou ad could b labld. Th calculaos a o omal cdc.):

3 3 Fgu. Showg a ay o lgh avlg mdum o cd o lm dposd ov subsa. Th chag phas o h lgh avlg hough h lm s gv by: cos θ π d (7) Tho h sum o h lcd amplud s gv by: R (8) Ths psso ca b smpld uh by cosdg cosvao o gy ad h ac ha w a dalg wh o-absobg maals: so ha quao 8 bcoms: R (9) I also ollows ha h sum o h asmd amplud s gv by:

4 T () Th abov ms (R ad T) a h ampluds o h wavs. Wha w a lookg o s h ao o h lcd ad asmd gs (R ad T) o h cd gy. Ths a gv by h poduc o ach o h ampluds wh h compl cojuga o h ampluds. Wh hs s do, alog wh h appopa calculaos, h lcac ad asmac bcom: R ( ) ( ) cos cos RR () T ( ) cos TT () Th abov m o h lcac ca b w as: R C B D C B A cos cos (3) wh: A Assumg o (h mdum s a o vacuum) B D d C π Assumg h agl o cdc s dgs I w ow subsu h pssos o h Fsl coc a h mdum/lm ac [quao ] ad h lm subsa ac [( - s )/( s ) ad h phas hckss o quao 3 w hav h ollowg psso o h lcac o a sgl lay lm (o omal cdc ad o-absobg): R cos cos d d π π

5 Th abov psso ca b aagd o gv (wh ): ( )( ) ( )( ) R π ( )( ) ( )( ) cos d π cos d () Th abov psso s accua o calcula h lcac o a sgl lay lm o kow acv d ad hckss d wh s a vaabl. Uoualy au s o as kd as w mgh wsh. Tha s, s o a cosa bu vas as a uco o h wavlgh [ ( ) ] ad ho h appopa acv d mus b usd calculag R a ach wavlgh. Also s o asy o solv quao o as a uco o h masud lcac a ach wavlgh. Howv, h cos uco s cyclcal. Ths mas ha h valu o h lcac wll cas ad dcas a gula ma as h hckss o h lm cass. Cosd h lcac o lms o magsum luod (.38) ad alumum od (.63) o a glass subsa (.5). Tabl I shows h valus o h Fsl cocs ad h ms A, B ad D. Fgu 3 shows a plo o h cos uco ad h lco o h wo lms as h hckss cass om zo o a hckss ha cospods o a ull cos cycl o ach lm. Tabl I TERM A B D.59.8 R ma R m k o s,5 A zo hckss h lcac s jus ha o h ucoad subsa (sc s ucoad) ad h od s sad o b. As h lm gows, h lcac wll cas (lm d > ha o h subsa) o dcas (lm d < ha o h subsa) ul achg h s m, mamum ad mmum spcvly. Ths hckss cospods o a qua-wav opcal hckss (QWOT) ad s sad o hav a od o. As h lm hcksss cas uh h lcac o h lms wll h go h oppos dco, dcasg o h hgh d lm ad casg o h low d lm ul achg ha o h ba subsa. A hs po h hcksss cospod o a hal-wav opcal hckss (HWOT) ad sad o b abs (as h w o lm) ad a od o. Fuh cass hckss wll hav h lcac casg ad dcasg h sam pa. Each succssv m wll b h hgh odd 5

6 cos Fgu 3. Rlcac o MgF ad Al O 3 lms as h lm hcksss a casd. od (3, 5, 7 c.) ad ach succssv valu qual o ha o h ucoad subsa wll cospod o h hgh v od (, 6, 8 c.). A h QWOT h cos s ad h psso o h lcac bcoms: R ( )( ) ( )( ) ( )( ) ( )( ) whch ca h b ducd o: R ( ) ( ) whch s adly solvd o :.5 R R (5) Equao 5 s a lavly smpl ad cov psso ha ca b usd o calcula h acv d o ay sgl lay lm a QWOT lms o odd umbd ods. Uoualy h sam ca o b do a h HWOT lms o h v ods sc h cos uco s ad h psso ducs o o wh h s o m l o whch o solv. Th psso s oly ms o h subsa acv d ad suls h lcac o h ucoad subsa.

7 A h QWOT valu (w o hs as h s od o m) wh h cos s -, h phas hckss s π adas. Tho ollows ha w ca s h psso o h phas hckss qual o π ad solv o h physcal hckss o h lm as ollows: π π d o d A ach succssvly hgh od h phas hckss s π adas hck ha a h pvous od. Tho, a h s od h abov psso appls. A h scod od h phas hckss s π o π d/ ad a h hd od h phas hckss s 3π o π 3 d/ 3. Tho ollows ha a ay od m, h phas hckss s mπ o π m d/ m wh m ad m a h wavlgh ad acv d spcvly o h m h od ad d s h lm hckss. Tho: mπ π d o m m d mm (6) m Equao 6 s vald a all ods, odd ad v. Sc o ay spcc lm h s oly o lm hckss ollows ha a ay v od h acv d ca b calculad om a adjac odd od h c pa. O, s a v od (,, 6.. c.) h: ( ) ( ) ( ) ( ) d ( ) ( ) ad s h hgh odd od. wh - s h low odd od Tho ollows ha h abov psso ca b solvd o wo ways (wh s a v od) ÅÅas ollows: ( ) ( ) ( ) o ( ) ( ) ( ) (7) W ow hav all h ools cssay o ak lco scas o a sgl lay maal ad ac h acv d. As a s ampl, l us compu h hocal pomac o a hypohcal m TO lm. I h lm w o-absobg ad o-dspsv o a o-dspsv, w would hav a vally asy suao. Fo ampl cosd h plo o a m TO lm wh a acv d o. dposd o a glass subsa wh a acv d o.5 (s Fgu ). All o h lcac paks a o h sam valu 33.9% ad h mma a.58%. Th wavlghs o h mama ad mma a (Show Tabl II od o dcasg wavlgh us a m). Th od o h c pa s asly dmd. Sag a h log wavlgh, whch s a mmum ad ho has o b v, w mus dm a v umb whch mulpld by a v umb wll qual h poduc o h 7

8 No-dspsv TO Rlcac (%) Wavlgh (m) Fgu. Rlcac o a m o-dspsv TO lm o a o-dspsv glass subsa wh s.5. hgh g ms h low c wavlgh. I w sa by yg, w s ha 9 (38) dos dd qual 38 (38). Tabl II od poduc I w wa o calcula h acv d a h v ods, w ca us quao 7. Ls ak h 6 h ad 7 h ods as a ampl. ( ) ( ) ( ) 7 59 O cous w pcd ohg lss sc h ogal calculao was basd o a v acv d o.. Th slgh o s du o usg wavlgh daa oudd o o h as g. I w had usd ga pcso o h wavlghs, h acv d calculao would hav b v clos. L s ow cosd a mo complcad suao. W sll hav a m TO lm ov a glass subsa bu boh maals wll b dspsv. Tabl III coas h dspso daa o h wo maals ad Fgu 5 shows a compu gad lco plo o h lm (wavlgh us a m). 8

9 Tabl III k glass Fgu 5. m dspsv TO lm ov a dspsv glass subsa. Th plo show gu 5 s sgcaly d ha h o show Fgu. I h s plac, h h mama o h mma a a h sam valu. Boh a casg as h plo gos om log o sho wavlghs. Ths s du o h ac ha h acv d o boh maals (lm ad subsa) cass as o gos om log o sho wavlghs. Th c s uh mgad by h ac ha h TO lm bcoms mo ad mo absobg sag a 5 m ad low. Assum ha h lm s acually ukow. I s o log as cla as o wha h od s ad w d o dm. Aga h od o h s mmum a 86 mus b a v od ( o o c.) I w y, h whch s o qu h sam as Howv, 8673 ad 5367 whch a v uh apa ad ho h s ampl s coc. As us ou, h al wold o dspsv maals, h poduc o h od ms h wavlgh wll b casg (slghly) as w go o sho wavlghs wh ga acv d. Tabl IV shows h wavlghs, ods ad h poducs o h wo o hs ampl. Also show Tabl IV a h lcac mama ad h calculao o h acv d o h lm usg quao 5. As a las sp w ca calcula h acv d a h v ods by usg quao 7. Ths s do om h h low odd od h ow makd (-) ad om h hgh od h ow makd (m). 9

10 Tabl IV od poduc ma (m-) (m) avag As pcd, h calculaos o h acv d a acly h sam as usd om Tabl III o mak h calculad plo wh h lm maal s o-absobg. Wh h lm s absobg, h calculad acv d s o h sam as h ampl sc quao 5 s basd o h assumpo ha h lm s o-absobg. Absopo h lm ducs h valu o h lcac mama ha suls a low ha al acv d. Ths s pcd sc h dvao o quao 5 w assumd ha h lm maal was o-absobg. As dcad pvously, h lm maal s absobg, s cssay o plac h acv d wh k wh s usually gadd as h al pa o h acv d ad h co coc k s h magay pa o h acv d. Obvously h calculao o h lm pomac s much mo complcad. Agus Maclod () has dvd h ollowg psso o h co coc: k πd s s R T T (8) Th abov psso s vald a h ug pos o h lm. O ds o kow h lco om a coag o a subsa, h asmsso hough h lm o h subsa, h acv d o h subsa h hckss o h lm ad h acv d o h lm. Th lcac o h lm ov h subsa ca b masud dcly om a sampl wh a osd back o a wdgd back ha h scas o lcs h back suac ou o h apu o h spcophoom. Fom hs masum h acv d o h lm ca b calculad ad h hckss o h lm ca b calculad (ou a log ough wavlghs wh h lm s o-absobg). Th acv d o h subsa s kow. Ths lavs h asmsso o h lm o h subsa. W ca masu h asmsso o a h paalll pla o glass coad o o sd. Th kowg h lcac o h ucoad sd ca calcula h asmsso o h lm o h subsa as ollows: T T u T T p p T T u p (9)

11 wh T p s h masud asmsso o h pla T u s h asmsso hough h ucoad sd o h pla T s h asmsso o h lm sd o h pla. Th hckss o h lm could b masud dcly o calculad usg quao 6. Equao 6 s vald a QWOT wh h lm s o-absobg. Thus a calculao o h hckss ou a o o h log wavlghs would b vald. I quao 6 s subsud o h hckss quao 8, h psso o h co coc bcoms: T R k.6366 () s T m s To s h abov quaos (9 ad ), cosd h pvous m TO lm. Th compud asmsso o a h glass pla coad o sd s show Fgu 6 (h oma o h plo s d appaac ha h pvous plos sc hy w copd ad pasd dcly om h sowa usd o ga hm). I hs cas h sowa was acually usd o calculad h asmsso hough h lm ad w usd Ecl o calcula back o h masud asmsso hough h pla coad o o sd. T o Dspsv IAD TO Tasmsso ucoad cla sld Wavlgh (m) Fgu 6.. m dspsv TO lm ov a dspsv glass subsa Th abov lm s o-absobg a h mama wh h asmsso s h sam as ha o h ucoad cla sld. Th lm s absobg wh h mama a lss ha ha o h ucoad cla sld. I od o calcula h co coc w mus ak h asmsso daa a h v ods (mama h asmsso pa ad mma h lcac pa) ad calcula h asmsso o h pla. Th abov daa ca

12 also b usd o calcula h acv d a h mma h asmsso pa, h lm s o-absobg, sc h lcac om h lm sd s jus -T. Daa a h ma o h abov asmsso sca ad calculaos mad om ha daa s summazd Tabl V. Icludd h abl s -T whch wll b h sam as h lcac Tabl IV wh h lm s o-absobg. Tho, h acv d w calculad om h asmsso daa wh h lm s o-absobg, would b h sam as h calculao om h masud lcac daa. Wh h lm Tabl V Od l T p Tu T T R o R k s absobg, h calculad acv d wll b d ha ha om h lcac daa, ypcally hgh wh calculad om h asmsso daa [compa ow -T (R h lm s o-absobg) ad R o R (lcac as masud)]. Th co coc k s calculad usg quao ad codd h boom ow o h abl. No ha hs daa s vy clos o h daa usd calculag h lco ad asmsso o h lms (s Tabl III). Th dc bw h valus usd o calcula h lm pomac ad h compud k om R ad T daa s du o oudg o h lco ad asmsso masums o 5 dcmal placs. Rmmb ha wh calculag h acv d h compud valus w o h sam as usd o calcula h asmsso ad lco o h lm. Sc w ow kow h co coc, s possbl o coc h acv d calculaos. A laoshp o do hs was pod by Maclod (s pag 373 o c ) who cds Hall ad Fguso () o ally publshg h psso. Th quao s: c.5 s( R ) πk d R s R R () I h abov quao, h s psso s jus h acv d as calculad om h lco mama ( o ho h acv d) ad h scod psso s a coco aco. Th hckss s h al hckss o h lm ad ca b dmd usg a dpd masum o calculad om h opcal daa a spcal go wh h lm s o-absobg. I od o apply quao o hs ampl, w mus s calcula h lm hckss om a odd od ad log wavlgh usg quao 6. Usg h hd od a 3 m wh a acv d o.3 w g m. Usg hs hckss ad h Rad T lm o subsa daa, w g h ollowg cocd acv ds:

13 Tabl VI Od dsg o R c Th dsg ow coas h acv d a h wavlgh o h spcd od whch was usd gag h lco ad asmsso daa. Th o R ow coas h acv d as calculad om h lco mama ( ow om Tabl VI) ad o h odd ods usg quao 7 (avag ow om Tabl VI). No aga ha wh h maal s absobg, h acv d s low ha h al dsg valu. Th c ow coas h cocd acv d usg quao. Noc ha hs las ow suls acv d valus vy clos o hos usd o ppa h ampl. Tho, w hav dmosad a chqu whch ca b usd o chaacz sgl lay opcal h lm ha a o-absobg o oly slghly absobg. Th laoshps dvlopd h a lavly smpl ad ld hmslvs o cluso vaous spadshs ha would smply aalyss o mulpl coag us o maals. Th laoshps could also b usd o sup wokshs ay o o may mah pogams o accomplsh h sam goal. Th auho ouly dos hs yp o wok usg boh a MahCad woksh ad a Ecl spadsh. I hs acl w hav dvlopd ad dmosad h ools cssay o ak masud lco ad asmsso daa ad ac h opcal pops o a sgl lay h lm maal. Th ampl usd h was om pcs compud daa o dmosa ha h chqu woks wll. I h al wold h accuacy ad pcso o masud daa s o as good as usd o h ampl. Also, al lms do o hav pc homogy as assumd ad usd hs ampl. I h acl hs ss, w wll dscuss spcal masum chqus, h au ad c o hogous lms ad apply hs laoshps o al l lm daa. Rcs: ) O. S. Havs, Opcal Pops o Th Sold Flms, Dov Publcaos, Ic ) H. A. Maclod, Th-Flm Opcal Fls, Isu o Physcs, 3d Edo,. 3) D.E. Moo, copyghd os o "Ppaao ad Pops o Opcal Th Flm Maals" - a sho cous ppad o h Socy o Vacuum Coas Educao Pogam,. ) J. F. Hall ad W. F. C. Fguso, Opcal pops o cadmum suld ad zc suld om.6 mco o mco, J. Op. Soc. Am., 9 pp. 7-78,