光学薄膜的堆积密度及密度均匀性的分析与计算

第21卷　第425期　1999年10月

　　光　学　仪　器O PT I CAL I N STRUM EN T S

V o l . 21,N o. 425

　O ctober, 1999

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 ity

TA 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 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 than that of am o rp hou s natu re . T he reason fo r th is is it has a strong com p ressive stress in fil m . W e also found that the w avelength sh ifts of som e fil m s depo sited by I AD don ′t have a dep endence upon the p ack ing den sity becau se they have dif 2. T he p ack 2feren t m icro structu ral un ifo rm ity under differen t p rocess p aram eters

ing den sity 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 of the 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 i 2cro structu re .

光学薄膜的堆积密度及密度均匀性的分析与计算

唐　骐　菊池和夫

(新科隆株式会社, 东京　14028540)

　　摘要:光学薄膜的堆积密度通常是利用薄膜在真空及大气中折射率的变化来计算, 在I AD 实验中, 我们发现有些薄膜的堆积密度大于110, 这意味着薄膜的密度比自然界中的材料密度还要密积, 原因是薄膜具有较大的内压应力, 我们还发现了薄膜的波漂不依从于堆积密度。这是因为它们在不同的蒸发条件下具有不同的密度均匀性, 在用EB 及不同条件的I AD 的情况下, 我们计算并分析了堆积密度及密度均匀系数, 并用SE M 观察了薄膜的微结构。

关键词:光学薄膜, 堆积密度, 密度均匀性, 微结构。

1　I n troduction

A 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 , a den se fil m can be ob tained to i m p rove the

　124・・光　学　仪　器第21卷

environm en tal stab ility . To distingu ish these p rop erties , the p ack ing den sity P is u sually . T he depo sited op tical th in fil m can be divide 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 :adop ted

(tota l volum e of the f il m ) 1P =(volum e of the solid p a rt of the f il m )

(1)

T 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 fil 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 2. T he vo ids in the group are clo sed , such that larger n its tend to clu ster in to larger group s

vo ids app ear am ong the group s rather than the dendrites , and these group s of dendrites fo rm . In the fil m grow th du ring depo siti on w ith the i on 2beam bom bardm en t , the ob served co lum n s

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 icro 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 and 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 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 sity

[1]

To ob tain the value of the p ack ing den sity , tw o m ethods have been in troduced . O ne is [1, 2]

by a scann ing 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

[3]

adop ting a non 2structu ral m odel w here the fil m w ill be com po sed

[4]

. e . so lid p art and vo ids , Chop ra et al . of the skeleton , i

tively show ing the fo llow ing :

, B ragg and Popp ard [5], and resp ec 2

(2) (3) (4)

(n b -n v ) P =(n -n v )

222

[(n 2+2) (n b 2-n v 2) ]P =[(n b +2) (n -n v ) ]

2222

[(n b 2-n v 2) (n 2+n v 2) ]P =[(n v +n b ) (n -n v ) ]

w here n b , n v , and n are bu lk , vo id , and 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 ,

[1]

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 .

A ll the resu lts of p ack ing 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 2fil m w ith excellen t sto ich i om etry can be ob tained at h igh values of abou t

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 ・125　・

1. 476at 550nm than w ith the bu lk index value of Si O 2, 1. 460at 550nm , given by J . R .

[6]

P ili pp . 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 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 lk 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 index

[7～9]

. Fo r values from 2. 18to 2. 65at the w avelength of 550nm depo sited by vari ou s m ethods

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 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 ectively . 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. 9280:0. 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 Ana lysis and Ca lcula tion of the Optica l Th i n F il m D en sity Un ifor m ity

In 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 2. m en ts

T he calcu 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 , the refractive index n v is a functi on of relative hum idity , w ith

1. 0≤n v (r . h . ) ≤1133

(5)

In 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 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 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 . If

　126・・光　学　仪　器第21卷

relative 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 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 the . T h is can be exp lained by un ifo rm ity of vo ids are no t com p letely filled w ith w ater m o lecu les

the m icro structu re . It is difficu lt to calcu late the p ack ing den 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 equati on s (2) ～(4) to

′

n b =(n i -n v i +p n v i ) p w

′222222

(p w n i 2+2p w -n i 2+n v i 2) n b =(2n i -2nv i +p w n v i n i +2p w n v i )

′2224

[(1+p w ) n v i 2-(1-p w ) n i 2]n b =[(1+p w ) n v i n i -(1-p w ) n v i ]

(6) (7) (8)

′

w 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 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 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 , equati on s (6) ～(8) can be resp ectively exp ressed as

p w =1-n v 2-n v 1

(9) (10) (11)

2222222222

+p w =

(n v 12-n v 22) (4+n 12n 22+2n 12+2n 22) 4+n 12n 22+2n 12+2n 22

p w =

A 1

2

222222

w here 　A 1=(n v 1-n v 2) (n v 2+n 2) (n 1+n v 1) ,

222222

A 2=(n v 1+n v 2) (n v 1n 2-n 1n v 2) ,

222222

A 3=(n v 1-n v 2) (n v 2-n 2) (n 1-n v 1) 1

4　Exper i m en ta l , Results and D iscussion

Sh 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 is 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 ito 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 . Its starting m aterial is T i 3O 5and the p rocess p aram eters are summ arized

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 ・127　・

in T ab le 1

.

F ig . 1　Schem atic diagram of the i on 2beam assisted depo siti on 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 . 2

Starting m aterial :U lti m ate p ressure (Pa ) :Substrate temperature (℃) :O 2partial p ressure (Pa ) :D epo siti on rate (nm s ) :

I on energy (eV ) :I on current density (ΛA c m 2)

R ati o of A r :O 2:

016260

Αb , c d , e f , g h i , j

T i 3O 5

≤510×10-

4

b , d , f , h >150　　c , e , g , i , j

(113～210) ×10-011500

20A r only

201∶1

2

………

10, 201∶2

201∶5

20O 2only

　　In case of the relative bu lk index of 2. 50, the exp eri m en tal resu lts 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 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 atom 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 argon . Since the i on p enetrati on leads to differen t vo id sizes in the fil m , the p ack ing den sity is dep endence on the vo id size acco rding to equati on (1) . In is in troduced to the bom bardm en t

[8][10]

　128・・光　学　仪　器第21卷

　　　　　　　　F ig . 2　C ro ss 2secti onal mo rpho logies of T i O 2fil m depo sited by I AD (excep t F ig . 2(a )

depo sited by EB ) w ith different p rocess param eters show n in T able 21

　　Table 2　Calcu lati on of relative p ack ing den sities and den sity un ifo rm ity coefficien ts

related to w ater so rp ti on of T i O 2th in fil m , depo sited by conven ti onal EB (first row ) and I AD (after first row ) m ethods u sing differen t p rocess

p aram eters .

p

n 1

n 2

a

p w

. [1**********]070. 83400. 86670. 87270. 87870. 88130. 89470. 89930. 90070. 90670. 90870. 92670. 92670. 93270. 95730. 97330. 9967

. [1**********]930. 90430. 92480. 92840. 93200. 93370. 94160. 94440. 94510. 94860. 94980. 96010. 96010. 96350. 97730. 98590. 9983

. [1**********]370. 92570. 94190. 94470. 94760. 94880. 95510. 95720. 95780. 96060. 96150. 96950. 96050. 97210. 98260. 98930. 9987

. [1**********]940. 72120. 93330. 82120. 88491. 00000. 79090. 90611. 00000. 86360. 88181. 00000. 97270. 71821. 00000. 87881. 0000

. [**************]. 88260. 97230. 92730. 95311. 00000. 91750. 96261. 00000. 94650. 95361. 00000. 98940. 89501. 00000. 95611. 0000

. [**************]. 93540. 98460. 96030. 97431. 00000. 95570. 97971. 00000. 97120. 97501. 00000. 99430. 94511. 00000. 97711. 0000

[**************]. 3432. 3222. 3682. 3562. 3222. 4112. 3802. 3512. 4052. 4022. 3902. 3992. 4922. 4362. 5002. 495

[1**********]. 3002. 3092. 318b 2. 322c

2. 342

d

e 2. 3602. 363f 2. 390

g

2. 3902. 3992. 436

h

2. 460i j

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

・129　・

T ab le 2, the relative p ack ing den sity of the item w ith anno tati on from a to j increases w ith . T he den sity un ifo rm ity coefficien ts , how ever , are no t dep enden t the increase of their indices

. F rom their m icro structu res show n in F igu re 2, the cro ss 2secti onal m o rp ho lo 2on their indices

gies of 2(c ) , 2(e ) , 2(g ) , 2(h ) , and 2(j ) show am o rp hou s 2like , and their den sity un ifo rm ity coefficien ts equal 1. 0. O ther m o rp ho logies in F igu re 2have a co lum nar structu re , and their den sity un ifo rm ity coefficien ts are less than 1. 0becau se w ater vapo r p enetrates in to the vo ids betw een the co lum n s . T hu s , the den sity un ifo rm ity coefficien t is dep enden t on the num 2ber and the size of vo ids . If the size of the vo ids is less than that of w ater m o lecu les , the w ater p enetrati on p henom enon w ill no t occu r . Since the reso lu ti on pow er of SE M is no t enough to reveal the m icrstructu re dow n to a scale of several nanom eters , it is difficu lt to distingu ish the structu ral differences am ong F igu res 2(c ) , 2(e ) , 2(g ) , 2(h ) , and 2(j ) . T h is is w hy the fil m , w ith an index less than that of p w

T ab le 2show s the character that the relative p ack ing den sity of the th in fil m dep ends on its index and the w ater so rp ti on dep ends on the den sity un ifo rm ity coefficien t . Perm eati on of w ater is cau sed by som e m icro structu res in fil m , and it dep ends on the den sity un ifo rm ity co 2. Since there is a rela 2efficien t relative to w ater and no t on the p ack ing den sity in som e cases

ti on sh i p betw een structu re den sity and m icro structu ral p rop erty , the m o rp ho logy of th in fil m strongly affects bo th the p ack ing den sity and den sity un ifo rm ity coefficien t . T h is is esp ecially true fo r the relative p ack ing den sity and den sity un ifo rm ity coefficien t of the th in fil m s , fo r roughness , w ater so rp ti on and diffu si on behavi o r , op tical behavi o r such as drift of index , and . fo r m echan ical p rop erties such as relatively h igh stresses 6　References

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6　H 　R 　Ph ili pp. H andbook of Op tical Constants of So lids, Edt . E. D. Palik, A cadem ic P ress, Inc . 1985:749～76317　J 　. , A pp l . Op ts . 1989, 28(15) :3303～33171M 　Bennett et al 8　S 　O gura , Q 　T ang , P roceeding of SP IE , 1996, 2966:214～2241

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～6061Sputtering and P las m a P rocesses , 1997:601

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