The light scattering of dielectric films

l hin S , d i d l"ilm.s. 5 7 ( 19791185 I,R9 (' ElsexierSequoiaS.A..l.ausanne Prmted in the Netherlands

]85

T H E L I G H T S C A T T E R I N G OF" D I E I . E C T R I C I-.'II,MS* A. [.t~ 1IER AND K. I.I!RI!N('Z ("('nlral R('.~ea/ch IJt~tttUl(' /or tql)'~/( ~, B u d a p e s t , I I / i ~,,ar.v ,

(Recei'.ed ,lul.~ 31. 1978: accepted October 2. 197g)

The Rayleigh scattering of dielectric lilms was measured at 441.6 nm waxclcngtlL The total scattering losses of TiO_,. SiO z, ZnS and MgF e tilms show a close correlation with the evaporation parameters. The light scattering of the TiO e Si(), and ZnS Mgl-, film systerns can be explained by scattering at the interfaces. By comparing curves of the light scattering as a function of scattering angle with the results of a numerical computing method the statistical parameters of the interfaces were obtained and ~vere found to be in good agreement w.ith electron microscope results.

1. IN I R ( ) I ) t ' ( " I I O N

The optical losses caused by' elastic light scattering are the major limitation of optical thin lihns. They are connected with structural micro-inhomogencities (pores etc.). The structural characteristics of such tihns have been examined by a direct microscopy method ~ and by comparing the rneasured angular distribution of the scattered light intensity with various theoretical models 2""~. Many authors have used the Bcckmann theor 5 ~vhich assumes a random isotropic roughness of one conducting surface with a specific r.m.s, height and correlation length (c, ,~ ).. 7 > ),). Elson'* has recentl 5, published a suitable method for evaluating the light scattering of anv multilayer tilm s,vstcm, lie solved Maxwell's cqt,ations in the tirst order approximation of perturbation thcorv. The formalism makes it possible to separate the statistical properties of the interfaces, which arc indcpendent of the other construction parameters. 2. EXPI{RIMI!NIAI

ZnS. TiO e, ('cO,, MgF 2 and SiO e layers and tile ZnS Mgi- 2 and r i O e SiO, lilm systems ~vere deposited onto BK7 glass substrates by the resistance heating of Balzers source materials. The substrate was maintained at a constant temperature of 20 300 C during ex.aporation. The evaporation rates wcre evaluated from the dr.ration of deposition. The optical thicknesses of the monolayers were 1250 nm" the *Paper presented :it the f o u r t h Internatl~mal ('ongrcss ~m Thin Fihns. I,oughhorough. G[ Septmnbcr 11 15, 197Y.Papcr2B3

Britain.

186

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lihn s> s t e m s c o n s i s t e d of d i l l ' t r e n t n u m b e r s of q u a r t e r - w a v e a n d h a l t - w a ~ e l a y e r s o f t h e g i v e n i n a t c r i a l s t o t ). ~ 500 n m . T h e a n g u l a r d i s t r i b u t i o n of t h e s c a t t c r c d i n t c n s i t } was m e a s u r e d w i t h a c o n v e n t i o n a l a r r a n g e m c n t u s i n g a g o n i o m e t e r w i t h pin d i o d e d e t e c t o r . W e u s e d a 30 m W I t e C d " l a s e r o p e r a t i n g at 441.6 n m as t h e l i g h t s o u r c e . T h e solid a n g l e o f t h e d e t e c t o r w a s 2.31 x 1 0 4 sr. T h e n o i s e level was d u e to s c a t t e r i n g at d u s t p a r t i c l e s m t h e air. 3. I()TA[

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I , I G H T S C A T T E R I N G OF DIELI-CTRIC FII.MS

187

T A B I . E I1 LIGItT S('AI I E R I N G [.OSS[/S OF MUI.:III.AYER MIRRORS

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T h e residual gas p r e s s u r e d u r i n g d c p o s i t i o n was 5 x 10 e, T o r r . h T h e o x y g e n partial p r e s s u r e d u r i n g d e p o s i t i o n was 7 × 10 "~ T o r r .

where 0 o is the angle of incidence and ,:.~is the wavelength of the scattered light. Ap.,~ is the construction function of the multilayer system normalized to the incident intensity: it contains the refractive indices, the thick nesses of the layers, the number of layers and the angles of incidence and scattering for p or s polarization, l-'or a system of identical films which contain perfectly correlated surfaces the scattered amplitudes from all the surfaces are summed in Ap. s. When the surfaces are independent but the surface statistics are the same (i.e. the surfaces are uncorrelated) the scattered intensities from all the surfaces are summed. The form factor I. of a gaussian stlrface is given by the formula F=

~

exp

-.--(sinO-sinOo)-'T-'

where 0 is the sum of the angle of incidence and the angle of scattering, o" is the r.m.s. height roughness and T is the correlation length of irregularities. It] the computation wc used the generally known refractive indices ( 1.38 for MgF 2, 2.3 for ZnS and TiO2 and 1.5 for the substrate) and the optically measured layer thicknesses. The results of the litting procedure for correlated surfaces are shown in detail in Figs. I 3. The correlation lengths obtained are in good agreement with the mean column diameters measured by using electron microscopy 3. 5. INTERFERliNCF, P I I E N O M E N O N

The intensity distribution of the scattered laser light can be deterrnined not only by the distribution of the speckle noise from surface irregularities but also by the tuning conditions of the layer system. For correlated surfaces peaks appear in the angular distribution of the scattered intensity of a detuned layer system. The differential scattering cross section at ). = 441.6 nm, normalized with the form factor, for a ZnS. M g F , laser rnirror having 12 layers and tuned to 500 nm wavelength was computed according to Elson's formulae: the results are shown in Fig. 4 for both correlated and uncorrelated surfaces. From the figure we can identify

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lhe cxtrema for the correlated surface, and on comparing this figure with the curves shown in F'igs. 1 and 2 we lind similar peaks. This effect is very important in investigations of multilaycr filters.

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Fig. 1. The m e a s u r e d b a c k s c a t t e r i n g inten,,it,, z,,. s c a t t e r i n g a n g l e for various Z n S M g F 2 m i r r o r s d e p o s i l e d at a s u b M r a l ¢ t e m p e r a t u r e of 20 (_'l l a n d for c o m p a r i s o n the b a c k s c a t t e r i n g intensit) c a l c u l a t e d a c c o r d i n g to Elson b.', a s s u m i n g perfectl~ c o r r e l a t e d interfaces w i t h given roughness, p a r a m e t e r s a a n d 71 1.

Fig. 2. T h e m e a s u r e d b a c k s c a t t e r i n g intenxit) t,,. s c a t t e r i n g a n g l e for ,,arlous XnS Mgl'., m i r r o r s d e p o s i l e d at a s u b s t r a t ¢ t e m p e r a t u r e o1"300 ('1 ) a n d the c o m p u t e d cur', es { I h~r c o m p a r b , on.

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I J G H T S ( ' A I 1ERING OF I)IliI.ECTRi(" FILMS

6.

189

('ONCLUSIONS

The computing method given by Elson "~seems to be suitable for the description of both correlated and uncorre[ated layer systems. The statistical parameters o- and T of the surface and interfaces were determined from light scattering measurements and agreed with the electron microscopy results and also with the predictions of condensation theories. The scattering losses of homogeneous fihns cot, ld be increased by increasing the substrate temperature except in the case of CeO 2 tilms. The light scattering measurements of multilayer structures gave similar results, and this effect could be quantitatively identified with the increase in surface roughness. The intensity maximum of the scattered light at small (or large) angles is caused not only by' volume or special surface effects but also by an interference phenomenon connected with the degree of cross-correlation of the interlaces. RI!FERt':N('ES I 2 3 4

K. tl. G u e n t h e r and |1. K. Pulker, .4ppl. Opt., 15 (12)(1976) 2992. D. H e i t m a n and V. Pcrmien, Opt. Commun., 23 ( I } (1977) 13 I. K. It. O u e n l h e r , H. L. G r u b e r and H. K. Pulker, Thin ,S'~did kThns, 34 (1976) 363. ,I. M. Elson, Appl. Opt., 16(ll)(1977}2872:Appl. Ph.r~. Lett..32(3)(1978) 158.