光學薄膜的堆積密度及密度均勻性的分析與計算

1、An Ana lysis and Ca lcula tion of the Optica l Th i n F il m Pack i n g D en sity and D en sity Un iform ityTA N G Q i K IKU CH I K az uo(Sh incron Co . , L td , Tokyo 14028540 Abstract :T he p ack ing den sity of depo sited op tical th in fil m s is u sually cal 2cu lated by the variati on of index

2、 values in vacuum and in atm o sp heric hum idity .In ou r I AD exp eri m en ts , w e found that the p ack ing den sity of som e fil m s calcu 2lated by th is m ethod is larger than 1. 0. T h is m ean s its structu re is den ser thanthat of am o rp hou s natu re . T he reason fo r th is is it has a

3、strong com p ressivestress in fil m . W e also found that the w avelength sh ifts of som e fil m s depo sitedby I AD don t have a dep endence upon the p ack ing den sity becau se they have dif 2feren t m icro structu ral un ifo rm ity under differen t p rocess p aram eters. T he p ack 2ing den sity

4、and den sity un ifo rm ity coefficien t depo sited by EB and I AD w ith dif 2feren t p rocess p aram eters are calcu lated and analyzed . T he m icro structu res ofthe fil m w ere investigated by m ean s of SE M .Key W ords :O p tical T h in F il m , Pack ing D en sity , D en sity U n ifo rm ity , M

5、 i 2cro structu re .光學薄膜的堆積密度及密度均勻性的分析與計算唐騏菊池和夫(新科隆株式會社 , 東京 14028540摘要 :光學薄膜的堆積密度通常是利用薄膜在真空及大氣中折射率的變化來計算 , 在 I AD 實驗中 , 我們發(fā)現(xiàn)有些薄膜的堆積密度大于 110, 這意味著薄膜的密度比自然界中的材料 密度還要密積 , 原因是薄膜具有較大的內(nèi)壓應力 , 我們還發(fā)現(xiàn)了薄膜的波漂不依從于堆積密 度 。 這是因為它們在不同的蒸發(fā)條件下具有不同的密度均勻性 , 在用 EB 及不同條件的 I AD 的 情況下 , 我們計算并分析了堆積密度及密度均勻系數(shù) , 并用 SE M 觀察了薄膜的微

6、結構 。關鍵詞 :光學薄膜 , 堆積密度 , 密度均勻性 , 微結構 。1 I n troductionA w ater so rp ti on p henom enon in op tical coatings has been understood . T he p ack ing den 2sity of depo sited op tical coatings is greatly affected by the m icro structu re . Since i on 2beam techn iques w ere app lied in op tical coatings ,

7、a den se fil m can be ob tained to i m p rove the第 21卷第 425期 1999年 10月 光學儀器 O PT I CAL I N STRUM EN T S V o l . 21,N o. 425 O ctober, 1999environm en tal stab ility . To distingu ish these p rop erties , the p ack ing den sity P is u suallyadop ted1, 2. T he depo sited op tical th in fil m can be di

8、vide in to tw o p arts , one , the i m p enetra 2b le skeleton (so lid p art of the fil m con sisting of the depo sited fil m m aterial , and the o ther the po re (vo id p art . T hen , the p ack ing den sity is defined as :P =(volum e of the solid p a rt of the f il m (tota l volum e of the f il m

9、1(1T he theo ry and resu lts of exp eri m en t show the fo llow ing m odel :In the fil m grow th du r 2ing depo siti on w ithou t the i on 2beam bom bardm en t , s m all structu ral nuclei such as the nucle 2u s fo r later grow ing dendrites are fo rm ed at first and then the vo ids app ear in the f

10、il m s a 2m ong these nuclei of app rop riate size . D u ring fu rther fil m th ickness grow th , the structu ral u 2n its tend to clu ster in to larger group s. T he vo ids in the group are clo sed , such that larger vo ids app ear am ong the group s rather than the dendrites , and these group s of

11、 dendrites fo rmthe ob served co lum n s. In the fil m grow th du ring depo siti on w ith the i on 2beam bom bardm en t , since bom bardm en t of the energetic i on acts as the disp lacem en t effect and the p rom o ti on ef 2fect of m igrati on fo r adheren t atom s o r m o lecu les , the fil m m i

12、cro structu re w ill be i m p roved , and the p ack ing den sity w ill be h igher .How ever , the p ack ing den sity calcu lated by equati on (1 is difficu lt to so lve . In case of the op tical th in fil m s igno ring the ab so rp ti on , it is u sually calcu lated by the fil m index in vac 2uum an

13、d in atm o sp heric hum idity . In th is exp eri m en t , w e found that som e fil m s depo sited by I AD are w ith a p ack ing den sity larger than 1. 0, and som e do no t show a dep endence of w ave 2length sh ift upon p ack ing den sity . T hese p henom ena w ill be exp lained , and the new defin

14、 i 2ti on s of relative p ack ing den sity and den sity un ifo rm ity w ill be in troduced in th is p ap er . 2 An Ana lysis and Ca lcula tion of the Optica l Th i n F il m Pack i ng D en sityTo ob tain the value of the p ack ing den sity , tw o m ethods have been in troduced 1. O ne is by a scann i

15、ng sp ectrom eter , and the o ther by a quartz crystal m icrobalance . T he scann ing sp ectrom eter has been ex ten sively in u se recen tly . Som e calcu lati on m odels are described by K ino sh ita and N ish ibo ri 3adop ting a non 2structu ral m odel w here the fil m w ill be com po sedof the s

16、keleton , i. e . so lid p art and vo ids , Chop ra et al . 4, B ragg and Popp ard 5, and resp ec 2tively show ing the fo llow ing :P =(n -n v (n b -n v (2P =(n b 2+2 (n 2-n v 2 (n 2+2 (n b 2-n v 2 (3P =(n v 2+n b 2 (n 2-n v 2 (n b 2-n v 2 (n 2+n v 2 (4 w here n b , n v , and n are bu lk , vo id , an

17、d fil m refractive index , resp ectively . In vacuum , n v =1and n can be calcu lated u tilizing the data ob tained by a sp ectrom eter . Fo r the p ack ing den sity ,V ari ou s k inds of m aterial by changing five differen t p aram eters w ere calcu lated by O gu ra 1.A ll the resu lts of p ack ing

18、 den sity are less than that of un ity . How ever , in case of a p rocess w ith the p resence of energetic i on s , there are som e un so lved p rob lem s in equati on s (2 (4 1Fo r exam p le , in the I AD p rocess w ith oxygen i on bom bardm en t exp eri m en ts , an index of am o rp hou s Si o 2fi

19、l m w ith excellen t sto ich i om etry can be ob tained at h igh values of abou t 421 光學儀器 第 21卷第 425期 TAN G Q i et al : A n A nalysis and Calculati o n of the Optical Thin Fil m Packing Density and Density U niform ity 1. 476at 550nm than w ith the bu lk index value of Si O 2, 1. 460at 550nm , give

20、n by J . R .P ili pp 6. In serting the th in fil m index and bu lk index of Si O 2in to equati on s (2 (4 yields values of P at 1. 035, 1. 030, and 1. 026, resp ectively . A ll the resu lts of p ack ing den sity are larger than un ity . T h is p henom enon does no t on ly app ear in the case of Si O

21、 2fil m , bu t also in al m o st all dielectric fil m s , p articu larly tho se ob tained by i on 2beam o r p las m a assisted depo si 2ti on . A po ssib le exp lanati on is that the fil m is very den se w ith a larger in ternal com p ressive stress .A no ther p rob lem is how to determ ine the bu l

22、k index n fo r an am o rp hou s m aterial that does no t ex ist in natu re o r never investigated befo re . Fo r exam p le , in the case of T i O 2fil m , its bu lk index is very difficu lt to determ ine . O n the o ther hand , T i O 2fil m is po ssib le of the indexvalues from 2. 18to 2. 65at the w

23、 avelength of 550nm depo sited by vari ou s m ethods79. Fo r calcu lating the p ack ing den sity in th is case , an arb itrary bu lk index value is suppo sed and de 2fined as the related bu lk index . If setting the related bu lk index value of T i O 2to 2. 50o r 2. 70at a w avelength of 550nm , the

24、 co rresponding evapo rated fil m indices are set at 2. 180, 2. 285,2. 365, and 2. 650. In the case of the related bu lk index value of 2. 50and u sing equati on (4 , the p ack ing den sities w ith resp ect to the above T i O 2fil m indices are 0. 9008, 0. 9370, 0. 9621, 0. 9987, and 1. 0367, resp e

25、ctively . T he rati o s of their p ack ing den sities are 0. 8689:0. 9038:0. 9280:0. 9633:1. 0. In the case the bu lk index value is 2. 70, the p ack ing den sities of the above fil m indices are 0. 8597, 0. 8943, 0. 9182, 0. 9531, and 0. 9894, resp ectively w ith rati o s of 0. 8689:0. 9038:0. 9280

26、:0. 9633:1. 0. T hu s , they yield the sam e rati o s though they have dif 2feren t p ack ing den sities calcu lated by differen t bu lk indices . T he sam e resu lts can be ob tained by equati on s (2 and (3 . T herefo re , the p ack ing den sity can be defined as relative p ack ing den sity .3 An

27、Ana lysis and Ca lcula tion of the Optica l Th i n F il m D en sity Un ifor m ityIn acco rdance w ith the above resu lts of T i O 2fil m , does the w avelength sh ift po ssess a si m p le relati on to the related p ack ing den sity ? T h is w ill be show n by the fo llow ing exp eri 2m en ts. T he c

28、alcu lati on m ethod is si m ilar to equati on s (2 (4 . W hen the th in fil m are expo sed to a hum id atm o sp here , the w avelength sh ift of the th in fil m is related to its ow n m icro struc 2tu re . B ecau se the fil m index n in equati on s (2 (4 is m easu red in a hum id atm o sp here , th

29、e refractive index n v is a functi on of relative hum idity , w ith1. 0 n v (r . h . 1133(5In the exp eri m en t , the am o rp hou s T i O 2th in fil m s , depo sited by I AD u sing differen t de 2po siti on p aram eters , are investigated , and bo th of their indices are 2. 390m easu red in vacuum

30、at w avelength of 550nm . If giving a relative bu lk index value of 2. 50and u sing equati on (2 , the relative p ack ing den sities are all 0. 9267. W hen expo sing the th in fil m s to hum id atm o 2sp here , the m easu red drifted indices are 2. 390and 2. 399, resp ectively . It is reasonab le to

31、 as 2sum e the value of n v 2as 1. 33w hen the w ater m o lecu le p enetrates the vo ids in the fil m . If521relative p ack ing den sity is still calcu lated by equati on (2 , bo th of their relative p ack ing den 2sities are 0. 9060and 0. 9137, resp ectively . T h is resu lt show s that they have a

32、 differen t rela 2tive p ack ing den sity in vacuum and in hum id atm o sp here . T he reason fo r th is is that all thevo ids are no t com p letely filled w ith w ater m o lecu les. T h is can be exp lained by un ifo rm ity of the m icro structu re . It is difficu lt to calcu late the p ack ing den

33、 sity by the above equati on s be 2cau se the bu lk index value is assum ed , and the w ater m o lecu les canno t p enetrate in to som e of the m ocro 2vo ids . T hu s , it is necessary to analyze and induce a facto r relative to w ater so rp ti on by m ean s of equati on s (2 (4 . R earranging equa

34、ti on s (2 (4 ton b =(n i -n v i +p n v i p w(6 n b 2=(2n i 2-2nv i 2+p w n v i 2n i 2+2p w n v i 2(p w n i 2+2p w -n i 2+n v i 2 (7 n b 2=(1+p w n v i 2n i 2-(1-p w n v i 4 (1+p w n v i 2-(1-p w n i 2(8w here n b is the index of a p art of fil m w h ich has no t ab so rbed w ater yet ; i =1, n 1and

35、 n v 1are resp ectively the indices of the th in fil m and the vo id in vacuum ; i =2, n 2and n v 2are the indices of the th in fil m and vo id in a hum id atm o sp here resp ectively , and p w is defined as den sity un i 2fo rm ity coefficien t related to w ater . Fo r a m o re accu rate calcu lati

36、 on of the den sity un ifo rm ity coefficien t , the index of the fil m in a hum id atm o sp here shou ld be m easu red after bo iling the th in fil m in w ater o r com p leting the hum idity test . Since a p art of fil m index is a con stan t val 2ue bo th in vacuum and hum id atm o sp here , equat

37、i on s (6 (8 can be resp ectively exp ressed asp w =1-n v 2-n v 1(9p w =22222222(n v 12-n v 22 (4+n 12n 22+2n 12+2n 22 +224+n 12n 22+2n 12+2n 22(10p w =2A 1(11 w here A 1=(n v 12-n v 22 (n v 22+n 22 (n 12+n v 12 ,A 2=(n v 12+n v 22 (n v 12n 22-n 12n v 22 ,A 3=(n v 12-n v 22 (n v 22-n 22 (n 12-n v 12

38、 14 Exper i m en ta l , Results and D iscussionSh incron SX 21100i on 2beam assisted depo siti on (I AD system w ith a diam eter of 120mm radi o frequency typ e i on sou rce w as u sed fo r th is exp eri m en t . A schem atic alignm en t of the cham ber is illu strated in F ig . 1. T he sub strate i

39、s B K 7, abou t 30mm in diam eter and 1mm th ick . T he p hysical and op tical th icknesses are con tro lled w ith a quartz crystal m on ito r and the op tical m on ito r of reflectance m ode , resp ectively . T he calcu lati on of index in vacuum and air is by m ean s of reflective op tical m on it

40、o r . D u ring the depo siton , R F i on sou rce p rovided an energetic i on beam of oxygen excep t the EB depo siti on . T he sub strates w ere p re 2cleaned w ith oxygen i on s of 500eV fo r 2m inu tes befo re fil m depo siti on . A s the calcu lati on m odel , the T i O 2th in fil m is adop ted .

41、 Its starting m aterial is T i 3O 5and the p rocess p aram eters are summ arized 621 光學儀器 第 21卷第 425期 TAN G Q i et al : A n A nalysis and Calculati o n of the Optical Thin Fil m Packing Density and Density U niform ity in T ab le 1 .F ig . 1 Schem atic diagram of the i on 2beam assisted depo siti on

42、 apparatus Table 1 T he p rocess p aram eters of T i O 2single layer fil m s depo sited by conven ti onal EB and I AD m ethods. A nno tati ons in T ab . 2&F ig . 2b , c d , e f , g h i , j Starting m aterial :T i 3O 5U lti m ate p ressure (Pa : 510×10-4Substrate temperature ( :260b , d , f

43、, h >150 c , e , g , i , j <150O 2partial p ressure (Pa :(113210 ×10-2D epo siti on rate (nm s :016011I on energy (eV : 500I on current density (A c m 2 202010, 202020R ati o of A r :O 2: A r only 1 11 21 5O 2only In case of the relative bu lk index of 2. 50, the exp eri m en tal resu lts

44、 of T i O 2th in fil m w ith indices n 1and n 2, depo sited by conven ti onal EB and I AD u sing differen t p aram eters , are in sert in equati on s (2 (4 and (9 (11 . T he resu lts of relative p ack ing den sity p and the den si 2ty un ifo rm ity coefficien t p w are listed in T ab le 2. T he anno

45、 tati on s on the n 1co lum n sign ify the resp ective cro ss 2secti onal m icro structu res , taken by scann ing electron m icro scop e (SE M , are show n in F ig . 2.V aop r depo sited fil m s have been found to have a co lum nar m icro structu re , show n in F ig . 2(a , resu lting from a low ato

46、m m ob ility . T he p resence of i on s has been found to increase the atom m ob ility , accelerate the nucleati on p rocess , thereby increasing the p ack ing den sity of the fil m s . Fo r p roving the i m po rtance of den sity un ifo rm ity , a m ix tu re of oxygen atom s and argonis in troduced

47、to the bom bardm en t810. Since the i on p enetrati on leads to differen t vo id sizesin the fil m , the p ack ing den sity is dep endence on the vo id size acco rding to equati on (1 . In 721 128 光學儀器 第 21 卷 F ig. 2C ro ss2sectional m o rp ho log ies of T iO 2 film depo sited by I AD ( excep t F ig

48、. 2 ( a Table 2Ca lcu la t ion of rela t ive p ack ing den sit ies and den sity un ifo rm ity coefficien t s rela ted to w a ter so rp t ion of T i 2 th in film , depo sited by conven t iona l EB O ( first row and I AD ( after first row m ethod s u sing d ifferen t p rocess p a ram eters. n2 p pw n1

49、 2. 349d 2. 360 2. 363f 2. 390g 2. 390 2. 399 2. 436h 2. 460 i 2. 495 j 21180a 2. 322c 2. 342 2. 351e 21216 21251 2. 300 2. 309 2. 318b © 1995-2006 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved. 21286 21302 2. 343 2. 322 2. 368 2. 356 2. 322 2. 411 2. 380 2. 351 2. 405 2. 402 2.

50、390 2. 399 2. 492 2. 436 2. 500 2. 495 depo sited by EB w ith d ifferen t p rocess p aram eters show n in T ab le 21 Eqn. 2 Eqn. 3 Eqn. 4 Eqn. 9 017867 018107 0. 8340 0. 8667 0. 8727 0. 8787 0. 8813 0. 8947 0. 8993 0. 9007 0. 9067 0. 9087 0. 9267 0. 9267 0. 9327 0. 9573 0. 9733 0. 9967 018733 018893

51、 0. 9043 0. 9248 0. 9284 0. 9320 0. 9337 0. 9416 0. 9444 0. 9451 0. 9486 0. 9498 0. 9601 0. 9601 0. 9635 0. 9773 0. 9859 0. 9983 019008 019137 0. 9257 0. 9419 0. 9447 0. 9476 0. 9488 0. 9551 0. 9572 0. 9578 0. 9606 0. 9615 0. 9695 0. 9605 0. 9721 0. 9826 0. 9893 0. 9987 016788 017394 0. 7212 0. 9333

52、 0. 8212 0. 8849 1. 0000 0. 7909 0. 9061 1. 0000 0. 8636 0. 8818 1. 0000 0. 9727 0. 7182 1. 0000 0. 8788 1. 0000 Eqn. 10 018573 018867 0. 8826 0. 9723 0. 9273 0. 9531 1. 0000 0. 9175 0. 9626 1. 0000 0. 9465 0. 9536 1. 0000 0. 9894 0. 8950 1. 0000 0. 9561 1. 0000 Eqn. 11 019198 019367 0. 9354 0. 9846

53、 0. 9603 0. 9743 1. 0000 0. 9557 0. 9797 1. 0000 0. 9712 0. 9750 1. 0000 0. 9943 0. 9451 1. 0000 0. 9771 1. 0000 T ab le 2, the rela t ive p ack ing den sity of the item w ith anno ta t ion from a to j increa ses w ith . the increa se of their ind ices T he den sity un ifo rm ity coefficien t s, how

54、 ever, a re no t dep enden t . on their ind ices F rom their m icro st ructu res show n in F igu re 2, the cro ss2sect iona l m o rp ho lo 2 g ies of 2 ( c , 2 ( e , 2 ( g , 2 ( h , and 2 ( j show am o rp hou s2like, and their den sity un ifo rm ity coefficien t s equa l 1. 0. O ther m o rp ho log i

55、es in F igu re 2 have a co lum na r st ructu re, and their den sity un ifo rm ity coefficien t s a re less than 1. 0 becau se w a ter vapo r p enet ra tes in to the ber and the size of vo id s. If the size of the vo id s is less than tha t of w a ter m o lecu les, the w a ter revea l the m icrst ruc

56、tu re dow n to a sca le of severa l nanom eters, it is d ifficu lt to d ist ingu ish the st ructu ra l d ifferences am ong F igu res 2 ( c , 2 ( e , 2 ( g , 2 ( h , and 2 ( j . T h is is w hy the to 1. 01 p enet ra t ion p henom enon w ill no t occu r. Since the reso lu t ion pow er of SEM is no t e

57、nough to . efficien t rela t ive to w a ter and no t on the p ack ing den sity in som e ca ses Since there is a rela 2 t ion sh ip betw een st ructu re den sity and m icro st ructu ra l p rop erty, the m o rp ho logy of th in film st rong ly affect s bo th the p ack ing den sity and den sity un ifo rm ity coefficien t. T h is is esp ecia lly roughn