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CHARACTERIZATION OF DIELECTRIC FILMS ON SEMICONDUCTOR SUBSTRATES BY
LEAKY-MODES MEASUREMENT
J.-P. Gruson, P.-J. Goirand, F. Cochet, O. Parriaux
To cite this version:
J.-P. Gruson, P.-J. Goirand, F. Cochet, O. Parriaux. CHARACTERIZATION OF DIELECTRIC
FILMS ON SEMICONDUCTOR SUBSTRATES BY LEAKY-MODES MEASUREMENT. Journal
de Physique Colloques, 1983, 44 (C10), pp.C10-131-C10-134. �10.1051/jphyscol:19831028�. �jpa-
00223485�
JOURNAL DE PHYSIQUE
Colloque CIO, supplement au n°12, Tome kH, decembre 1983 page C10-131
CHARACTERIZATION OF DIELECTRIC FILMS ON SEMICONDUCTOR SUBSTRATES BY LEAKY-MODES MEASUREMENT
J.-P. Gruson*, P.-J. Goirand*, F. Cochet and 0. Parriaux
Fondation Suisse pour la Recherche en Microtechnique, CH-2000 Neuchâtel, Switzerland
Résumé - Le concept et la technique de mesure des modes à fuite en optique in- tégrée sont utilisés pour la caractérisation de films diélectriques déposés sur des substrats absorbants et de Haut indice de réfraction.
Abstract - The concept and measurement technique of leaky modes in integrated optics are applied to the characterization of dielectric films on lossy and high index substrates.
The problem of optical wave propagation in a planar structure consisting of a homoge- neous dielectric slab sandwitched between a half-space of lower refractive index and a substrate of higher index has hot received much attention in integrated optics as the leakage of the optical field into the substrate during propagation makes such structures unsuitable for guided optics. However the concepts and measurement tech- niques developed in integrated optics can be of interest when film characterization is concerned, even though the leakage might be important, as it is in thin films on high index and lossy semiconductor substrates.
The main contribution on that problem was given by 111 rich and Prettl / I / , who derived approximate formulae for the complex propagation constant of the leaky modes
in such lossless pseudo-waveguides. Kersten / 2 / applied these expressions for the thickness measurement of low index films. More recently the same kind of approach was proposed for the characterization of polymer films / 3 / . A simple method is presented here that allows the complete characterization of a film on a high index substrate, that may be lossy, from the exact electromagnetic expression of the problem, by the use of a simple programmable calculator. Normalized charts corresponding to a silicon substrate will be given for the characterization of the index and thickness of a silica film from the measurement of the effective index of two leaky modes.
I - THEORY
F i g . 1 shows a l o s s l e s s d i e l e c t r i c slab of thickness w and index n2 deposited on a planar substrate of highercomplex index j nx, w i t h a l o s s l e s s s u p e r s t r a t e of index n3 < n2. A l l f i e l d components have a space and time dependence i n the form
exp (jcot - k0( r x - K - J Z ) ) w i t h * - , - = j / n ^ + rz. to i s the angular frequency, k0 = 2TT/A is the wave number i n vacuum, x the wavelength,
r = nr + jri-j (1) i s the normalized propagation F i g . 1 - Leaky waveguide on a c o n s t a n t , < ^ i s the transverse propagation high-index s u b s t r a t e . constant i n region i .
A leaky mode i n the f i l m i s c h a r a c t e r i z e d by an evanescent f i e l d i n region 3 , Re ( K i) < 0 , and an outgoing f i e l d i n the lossy s u b s t r a t e 1 , Im ( K I ) > 0. There i s a transverse p a r t i a l l y standing wave i n region 2. Maxwell's equations and theboundary
* Foot-note : On a B.Sc. stay from Institut National Polytechnique de Grenoble, France
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19831028
C10-132 JOURNAL DE PHYSIQUE
conditions define a complex transcendental dispersion equation /4/
where
ci
= l / n $ f o r Ttl modes and 1 f o r T E modes.For a given s t r u c t u r e , t h e zeros of ( 2 ) must be searched f o r with t h e corplex Fropa- gation constant r as the variable. In the inverse problem, n2 and w must be found from the measurement of the imaginary part n j of r. Experiment does not allow an easy and accurate estimate of the real part nr a s t h e l a t t e r i s associated with t h e l i n e width of t h e measured "m-lines" /5/ (see below and f i g u r e s ) . This l i n e broadeninn, as the mode order increases, i s due t o the increase o f the leakage i n t o the s u b s t r a t e t h a t reduces the transverse standing wave r a t i o in t h e film. If :I i s the number of measurable modes, t h e r e a r e 211 equations f o r F1+2 real unknowns and two modes a r e therefore required t o completely characterize layer 2. These modes can e i t h e r be of the same polarization but d i f f e r e n t order, or of the same order but TE and TI1 pola- r i z a t i o n s , depending on the sharpness of the a v a i l a b l e l i n e s .
P r a c t i c a l l y the user will mainly be concerned with a s p e c i f i c s u b s t r a t e f o r which normalized charts can be drawn. Each c h a r t bears in abscissa and ordinate the
measured value of n j ( c a l l e d the e f f e c t i v e index) of the modes considered, T E o and TE, o r T E , and THO. A mesh i s drawn on the c h a r t with two s e t s of curves: one with w =
const. and n2 a s a parameter, the other with n2 = const and w as the parameter. Each curve i s obtained by solving ( 2 ) f o r the Ts of the two chosen modes. The complex transcendental equation i s solved on an elementary computer by searchino the zeros of i t s modulus with the he1 p of i t s p a r t i a l d e r i v a t i v e s with respect t o nr and n j , written explici t e l y from ( 2 ) . The s t a r t i n g values in t h e search procedure a r e taken from t h e approximate expressions (23) and ( 2 4 ) i n / I / , t h a t allow a f a s t convergence.
I1 - EXPERI!IEP!T
The example of a s i l i c a film on a <loo> Si s i n g l e c r y s t a l a t 0.633 micron HeF!e wave- length i s considered here. From /6/ one takes n, = 3.85 (1 - j0.052). The c h a r t s cor- responding t o the f i r s t two TE modes and the two f i r s t TE and TH modes a r e given in Fig. 2 and 3. I t i s remarkable t h a t the mesh l i n e s very closely agree with t h e s t r a i g h t l i n e s given by the approximate expressions in / I / , departing s i ~ n i f i c a n t l y only i n t h e case of very thin layers. The agreement i s the best f o r TE modes; f o r n2=1.45 and w=1.5 pm, the e r r o r on the e f f e c t i v e index of the T E o and TE, i s 5.10-5 and 8-10-'resp.; f o r w=0.8 um, i t i s 3.10-4 and 8.10-3 resp. Therefore the expressions in / 1 / a r e s u f f i c i e n t l y accurate f o r film c h a r a c t e r i z a t i o n when w i s about 1.2 pm and above. For thinner f i l m s , t h e TE, l i n e s become very broad. The use of the TE, and TM, i s preferable, but the formulae i n / I / a r e l e s s accurate f o r TI1 modes; the exact resolution of ( 2 ) i s here necessary.
In the prism coupling technique / 5 / , described schematically i n Fig. A , a l i g h t beam i s focused on the contact region between t h e high-index prism and t h e film. The reflected beam projected on a screen e x h i b i t s dark
"m-lines" a t those values of the angle 8 corresponding t o the e x c i t a t i o n of a leaky mode. Fig. 5a) shows such a f i g u r e obtained with unpolarized l i g h t . When a p o l a r i z e r i s inserted in the incoming beam, two s e t s of rn:lines can be distinguished, TE-lines in Fig. 5b) and TP1-lines in Fig. 5c). The broadening of the l i n e s with increasinp mode order appears c l e a r l y , recommending the use of the f i r s t orders f o r an accurate film characterization.
Fig. 4
-
Excitation of a leaky mode with the prism technique.As an example a thick s i l i c a layer on Si was measured. TE, and TE, modes are considered and y i e l d n,=-1.4626 and w=3.365 pm. Comparisons with an e l l ipsometer, then a P!anospec provide w=3.5018 and 3.5451~111, assuming n2=1.4Q. Finally. chemical etchinp followed by a thickness measurement with a t a l y s t e p yields w=3.570 urn. A b e t t e r accuracy can be obtained by using a well calibrated instrument such a s an Abbe refractorneter f o r the e f f e c t i v e index measurements. A t sodium lamp wavelength we got n2=1.4603 and w=3.558
urn.
This i s in good agreement with the t a l y s t e p measurement within about 100 Angstrom, which i s the expectable accuracy of t h e present technique.
111 - CONCLUSION
The measurement technique presented here allows the characterization of thick d i e l e c t r i c films on a semiconductor substrate. A1 though l e s s accurate than ellipsometric techniques f o r thin layers, t h i s approach gives a good accuracy on the index, an accuracy on the thickness within 100 Angstom; i t i s f l e x i b l e and does not require a s p e c i f i c and costly equipment.
1. ULRICH R., PRETTL W . , Appl. Phys. (Germany)
1
(1973) 55 2. KERSTEN R.T., Optica Acta 22 (1975) 5033. DING T.N., GARMIRE E . , ~ ~ ~ 0 ' 8 3 , Baltimore, May 17-20, 1983, TuM37 4. DECOTIGNIE J.D., PARRIAUX O . , GARDIOL F.E., A.E.U. - 35 (1981) 201 5. TIEN P.K., Appl. Opt. 10 (1971) 2395
6. KUTKO R.J., Solid StatFTechnology - 43 (1978) Feb.
Fig. 2
-
Chart of TEo and TE1 e f f e c t i v e i n d i c e s with mesh l i n e s1.400 f o r w and n equal t o const.
TE1 e f f e c t i v e index
CIO-134 JOURNAL DE PHYSIQUE
TEo e f f e c t i v e index
v
F i n ?. .=.
"-
r h n r t n f TF .,,,..," " ' U " " 2nd TM " ' n f f n r t i ~ r n . . " C . . l ' . Li n d i c e s . 0
425 1.427 1.429 1.431 1.433 1.435
TMo e f f e c t i v e index
F i g . 5
