Philips J. Res. 47 (1993) 347-360

NON-DESTRUCTIVE ANALYSIS BYSPECTROSCOPIC ELLIPSOMETRY

by J.C. JANS

Philips Research Laboratories, PiO, Box 80000,5600 JA Eindhoven, The Netherlands

AbstractA concise review on the basic principles and methodology used inspectroscopie ellipsometry analysis is presented. The technique is trulynon-destructive and allows optical and structural parameters to be ac-cessed in a wide range of problems in materials research. Several recentexamples are presented. These include the structural analysis of high-doseoxygen-implanted silicon substrates, the determination of the opticalconstants of thin ZnSe films on c-GaAs grown by molecular beam epitaxyand the determination of the Ge content in Si,_.,Gex alloy films on c-Sigrown by chemical vapour deposition.Keywords: film thickness, multilayer optical modelling, non-destructive

testing, optical constants, spectroscopie ellipsometry.

1. Introduetion

Developments in materials research and technology have led to the rapidimprovement of a wide number of analytical methods'), There is a generaltrend towards more fast and often in-line, non-destructive testing.Spectroscopie ellipsometry is a gradually maturing relatively low-cost opticaltechnique which can satisfy such needs in a wide range ofproblems in materialsresearch. Whereas until recently spectroscopie ellipsometry has been almostexclusively used in advanced research laboratories, several commercial set-upshave now become available'"). In this paper I will review some of thebasic principles of the technique and I will give some recent examples ofapplications.

When a polarized beam of light is reflected at oblique incidence from asample surface, generally a change in polarization state is observed. In anellipsometric experiment this change in polarization state is analyzed. Thisinvolves the analysis ofthe change in both the amplitude and the phase oflightpolarized parallel and perpendicular to the plane of incidence").

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J.C. Jans

medium 1

p Erefl.

Eo

ë1medium 0

Fig. I. Oblique reflection from a planar interface, where <1>0 and <1>1 denote the angles of incidenceand refraction at the interface from medium 0 to medium I, while Êo and ÊI represent the complexdielectric constants of the media.

Traditionally, monochromatic ellipsometry is much used in thin filmanalysis. Here it will enable the measurement of film thickness down to thesub-nanometre range. The reason for this sensitivity is the fact that ellip-sometry is able to analyse a change in phase of two polarization directionsrelative to each other. This means that ellipsometry is basically an inter-ferometric method. The measurement of phase change makes the techniquevery sensitive to the presence of even extremely thin overlayers.

A distinct advantage of ellipsometry over conventional intensity-relatedphotometric measurements is the fact that ellipsometry deals with intensity-independent parameters. Furthermore, as it will allow two parameters (i.e.amplitude ratio and phase change) to be accessed from one observation, it willprovide more information from one single experiment which is of great advan-tage in optical modelling.

2. Theory

2.1. Definition of ellipsometric parameters

Ellipsometry deals with the analysis of polarized light. To understand thebasic principles of ellipsometric analysis it is necessary to concentrate on theinteraction of an electromagnetic plane wave with an interface. Consider aplane wave reflecting at oblique incidence from a planar interface as shown inFig. 1. The incident electric field vector E(inc) can be decomposed into acomponent polarized parallel (p) and a component polarized perpendicular (s,senkrecht in German) to the plane of incidence as:

E = E(inc) = Ep(inc)+Es(inc) (1).

348 Philips Journalof Research Vol.47 Nos. 3-5 1993

andEs (refl)Es (inc)

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Non-destructive analysis by spectroscopie ellipsometry

The amplitude reflection coefficients for pand s polarization directions aredefined as:

By matching the E and H fields of the electromagnetic wave across the.interface between two media 0 and 1 the complex Fresnel amplitude reflectioncoefficients'" ") are obtained:

ft;cos <1>0 - Jfo cos Cl>

ft;cos <1>0 + Jfocos <1>,(3a)

and

fto cos <1>0 - A cos <1>,

ftocos <1>0 + A cos <1>,

Here <1>0 and <1>, represent the angles of incidence and refraction at theinterface, whereas Êo and Ê, represent the complex dielectric constants of themedia j generally given by: Êj = Elj+iE2j' It should be realized that forabsorbing media the angles <1>0 and <1>, are also complex quantities.

By writing the complex Fresnel amplitude reflection coefficients rp and rs as

(3b)

and I I i~srs = rs e , (4)

the convenient introduetion of a complex reflection ratio p is allowed as:

_ rp _ Irpl i(~p-~s) _ t ./, ill.P - - - -:-'--:-e . - an 'I' e .r, Irsl

In this notation the ellipsometric parameters tan Ijl and A represent theamplitude ratio and the phase change for pand s polarized light upon reflec-tion. Figure 2 shows a visualization of these parameters which are accessed inan ellipsometric experiment. In the following I will briefly review some of themost common optical models used in the analysis of ellipsometric data.

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2.2. Modelling the optical properties of bulk materials

For an optically isotropic bulk material the complex dielectric constant Ê, isdirectly related to the complex reflection ratio p by:

~, = sin 2<1>0[1 + (1- p)2 tan 2<1>OJ. (6)Eo l:+p

Strictly speaking this relation") is valid only for a smooth interface. Real

Philips Journal of Research Vo'.47 Nos.3-5 1993 349- ._-~~. - ~~~~~~~~~~__.

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J.C. Jans

Sample

incident:Iin. pol. light

", reflected:

"'::::::'" " I el~~t. pol. light

'-,)11;"---- ------'"' -, , 1 "., Es refl

., ~E,refl

Fig. 2. An illustration of the meaning of ellipsometric parameters i/J and 11.The pand s com-ponents of the incident linearly polarized beam of light generally obtain different phase andamplitude after reflection. The relative phase change is denoted as 11while the amplitude ratio isdenoted as tan i/J.

physical interfaces often will not follow such idealization, but even in this casethe equation can be useful since it eliminates the dependence of the angle ofincidence <Do and it expresses é and ~ in a more direct physical quantity ofinterest. When the equation is applied to non-ideal surfaces the result obtainedis commonly referred to as the pseudodielectric constant <E).

2.3. Modelling of thinfilms

Consider a homogeneous isotropic film with parallel-plane boundaries inbetween a homogeneous isotropic semi-infinite ambient and substrate asshown in Fig. 3. Here the complex reflection ratio p can be derived using theFresnel reflection coefficients at all interfaces and taking into account themultiple reflections in the film"), By taking Êj to be the complex dielectricconstants of the appropriate materials, we will find that:

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Non-destructive analysis by spectroscopie ellipsometry

substrate

ambient

film

Fig. 3. Oblique reflection from an ambient-film-substrate system with multiple reflections in thefilm. Here d represents the film thickness whereas Êo, ÊI and Ê2 represent the complex dielectricconstants of the media.

Extension of such modelling to multilayer media is straightforward"),

2.4. Modelling of inhomogeneous materials

Apart from multilayer modelling using stratified layers one of the mainmathematical instruments is effective medium modelling. Inhomogeneity in afilm, which can be the effect of, for example, interface roughness is commonlymodelled by such approach. The theory is based on the assumption thatoptical properties of a mixture can be described by a combination of theoptical properties of its constituents. For this assumption to hold, the mixtureshould be on an atomic scale, that is on a scale which is small compared withthe wavelength of the incident light. The theory connects microscopie (local)and macroscopie (average) electric fields. The underlying idea is thatpolarizabilities of the materials involved can be added".

One of the most widely used effective medium theories is the Bruggemaneffective medium approximation? given by

Here Ea and Eb are the complex dielectric constants of components a and b,J. is the volume fraction of component a, while EelT represents the complexeffective dielectric constant of the mixture. The Bruggeman effective mediummodel is well suited for modelling random configurations'") and will mix theoptical constants of components a and b in an effective background consistingof a mix of components a and b.

2.5. Computational analysis of ellipsometric data

As was shown (eq. 6) the analysis of bulk optical properties is quite straight-forward. The analysis of thin (single or multilayer) film specimens, however,is more intricate. For analysis ofthe experimental complex reflection ratio Pcxp

J.e. Jans

as a function of photon energy by means of a (multi)layered model as givene.g. by eq. 7 generally a regression analysis is used" 11. Here the aim is tominimize the fitting error a, where:

a = IPmodel - Pexp 12• (9)

From a single ellipsometric measurement two independent parameters Ij!and A are obtained. This means that basically it is possible to obtain an exactsolution for up to two unknowns in the model at the same time. In practice,however, problems are often more intricate. Here it should be realized thatmathematical/physical modelling is a substantial and also crucial part of theellipsometric analysis. A thorough discussion on the treatment involved isbeyond the scope of this paper. Further details on actual algorithms forproblems as stated above are readily available in ellipsometric literature".

3. Instrumentation

As a rather extensive review on ellipsometric instrumentation has onlyrecently been published'? covering most of the developments since around1960, I will only briefly discuss some of the instrumental problems andprinciples involved. The photometric rotating analyser ellipsometer in itsoriginal automated concept developed around 197513,14 is one of the mostwidespread instrument types and still can be considered to be the "workhorse"in ellipsometric research.

Fig. 4. Schematic representation of a rotating analyzer spectroscopie ellipsometer.

Figure 4 shows a schematic representation of such a set-up as used to obtainthe examples presented in this paper. The set-up basically consists of a lightsource L, monochromator M, polarizer P, sample under measurement S,analyzer A rotating with constant angular speed WA and detector D. Light isincident at angle of incidence <1>0' The direction of polarization of polarizer andanalyzer, also labelled P and A are defined relative to the plane of incidence.

In a rotating analyzer ellipsometer the ellipticity of the light reflected by thesample under measurement is analyzed by monitoring the intensity of the

352 Philips Journalof Research Vol. 47 Nos. 3-S 1993

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Non-destructive analysis by spectroscopie ellipsometry

reflected light in relation to the angular rotation speed of the analyzer. Thedetected intensity is a sinewave function of the analyzer angle WA given by

By sampling the detector signal as a function of analyzer angle position WA

and subsequent Fourier analysis of this data the Fourier coefficients a, bandc of the signal are obtained. It can be shown'r " that these coefficients arerelated to the ellipsometric parameters l/J and ~ by the following relations:

[c+a]I!2

tanl/J = tanP -- ,c-a

(I la)

bcos à = [2 _a2]1!2'

Before each actual ellipsometric measurement a calibration procedure'< 15)has to be carried out to establish the exact position of the plane of incidence.This is necessary as both the polarizer and analyzer reference azimuths arerelated to this plane and sample exchange will affect the position of the planeof incidence. Furthermore the procedure is used to correct for the additionalphase shift and amplification factor in the detected sinewave rising from theelectronics in the detection circuit.

The calibration consists of evaluating the Fourier coefficients a, band c forvarious polarizer settings in relation to the plane of incidence. The main ideais that, with a polarizer P exactly in the plane of incidence, only linearlypolarized light will be reflected from the specimen under test. This fact can beexploited to establish both the polarizer reference position with respect to theplane of incidence and the phase shift induced by the electronics involved.There is an extensive literature concerning accuracy and instrumental errorsinvolved in the procedures for measurement and calibration as indicatedabove":"). Further discussion is beyond the scope of this paper.

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4. Applications

4.1. Structural analysis of high-dose oxygen-implanted silicon

Silicon-on-insulator (SOl) structures are of potential interest for the fabri-cation of integrated circuits"), One possibility of creating SOl structures ishigh dose implantation of oxygen in crystalline Si. Subsequent high tem-perature annealing produces a buried oxide layer, showing more or less sharpinterfaces with a thin crystalline Si layer on top. Possible application of theseso-called SIMOX (Separation by IMplanted OXygen) structures, in very large

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J.C. Jans

1.50

I 1.00'00c.c

'" 0.50I-

0.00200 300 400 500 600 700 800Wavelength (nm)

1.00

I 0.50gID 0.00"0III0 -0.50o

-1.00200 300 400 500 600 800Wavelength (nm)

Fig. 5. Experimental spectroscopie ellipsometry spectra (solid lines) obtained for a SIMOX wafer.The dotted lines are calculated with the use of a 5-layer model, which takes into account theinterfaces on both sides of the buried oxide layer.

scale integrated circuit (VLSI) design, is extensively discussed in literature'":").For characterization of these structures several well-established techniques arecommonly used":"). For example, transmission electron microscopy (TEM)will provide structural details and information on the buried oxide layer, whileRutherford backscattering speetrometry (RBS) and also secondary ion massspectroscopy (SIMS) provide depth-selective information on the distributionof elements. While yielding valuable information these techniques (and mostothers) are, however, destructive. Ellipsometric analysis has proven to be apowerful non-destructive method for characterizing SIMOX structures"). Itwill provide information on the thickness and composition of the layersinvolved, as well as on the presence of interface roughness.

Figure 5 shows the measured (solid line) and calculated (dotted line) ellip-sometric data tan tjland cos 11as a function ofwavelength for a typical SIMOXstructure. Owing to the marked change in absorption of the Si top layer,different parts in the SIMOX structure are probed with variation of wave-length. In the region from 230 to 390 nm the absorption is so great that onlythe top Si layer with its native oxide is probed. In this wavelength intervalanalysis can be done by using a single-layer model, with c-Si as a "bulk"-likesubstrate and a transparent Si02 oxide overlayer on top. The structures

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Non-destructive analysis by spectroscopie ellipsometry

Structure Thickness Fraction ofI (nm) Si02(-)i

72° !~----Si02 1.6

c-Si 222.8

c-Si/Si02 3.1 0.50

Si02 371.0

c-Si/Si02 20.7 0.50

~j;Jf~Fig. 6. Thickness results obtained for the 5-layer model used in Fig. 5.

observed in the spectra (see Fig. 5) originate from the El and E2 opticaltransitions of c-Si and clearly reflects the crystalline character of the c-Si toplayer. In fact the El and E2 transitions are a sensitive monitor for the crystallinequality ofthe silicon layer"). From a fit ofthe ellipsometric parameters in thiswavelength region the presence of a 20 Á native oxide overlayer is deduced").The spectral region above 390 nm, where the c-Si top layer is much lessabsorbing, provides information on the thickness of both the top layer and theburied oxide layer. In this wavelength region the multilayer structure gives riseto interference effects, which are used in the fit of the multilayer model to theexperimental data. Using a 3-layer model (native oxide, c-Si top layer, buriedoxide) on ac-Si substrate, reasonably good agreement between calculated andexperimental curves is obtained. This model can be further improved by takinginto account the interface regions on both sides of the buried oxide. Thenecessity for such extension has been extensively discussed in literature":").The result of this 5-layer simulation is shown by the dotted lines in Fig. 5,where interfacial regions are modelled by mixing c-Si with Si02 with equalvolume fractions. Introducing a variable volume fraction or even a polysiliconJSi02 interface") did not result in a significant improvement of the fit. Thethicknesses obtained from the 5-layer model are summarized in Fig. 6. Fromthe example given it is clear that spectroscopie ellipsometry can be quite apowerful tool for non-destructive structural analysis with nanometre resolution.

4.2. Optical constants of ZnSe thin films

Developments in the use of wide-gap U-VI semiconductor materials haverecently led to the demonstration of blue-green diode laser action in ZnSe-based heterostructures= 27). Considerable basic research and development willbe needed to attain practical continuous-wave room-temperature laser opera-

J.C. Jans

Is 0.50Qi

1-05: 11I1~lt~--j----------_7"-1.00 L_____ll _...l' _ __!.._ __l__ _J____l _ __!..---:-'

1.50 2.50 3.50 4.50 5.50Photon energy (eV)

Fig. 7. As-measured ellipsometric spectrum for a 1J1m MBE-grown ZnSe film on c-GaAs.

tion. Apart from problems such as the development of ohmic or equivalent lowresistance contacts and controlling doping levels"), knowledge of the opticalconstants of the materials involved will be indispensable for optimization ofthe laser geometry.Up to now very little has been known about the optical constants of most

of the thin film materials involved. Figure 7 shows an as-measured ellip-sometric spectrum for a 1 f1m ZnSe film on c-GaAs grown by molecular beamepitaxy (MBE). Two regimes can clearly be observed. Below the bandgap ofthe ZnSe (approx. 2.68 eV) pronounced interference fringes can be observed.In this region the ZnSe is fully transparent. Above the bandgap a reiativelyfeatureless region can be observed. Here the ZnSe is strongly absorbing. Withincreasing absorbance in the ZnSe the incident light is gradually probing onlythe very surface region of the film. Ellipsometric modelling will allow access tothe above- and below-bandgap optical constants of the ZnSe in a convenientway. Figure 8 shows the result of such analysis"). Here the optical constantsfor the ZnSe thin film are compared with a simplified model of interbandtransitions given by Adachi and Taguchi" for single-crystalline non-dopedZnSe bulk material. As can be seen fairly good agreement is obtained. Theposition and presence of optical transitions Eo, Eo+~o and EI' El +~I in themeasured data is in good agreement with data available on bulk material").Fitting of our data to a model similar to that of Adachi and Taguchi will allowa parametrization of the measured optical response, which will be convenientin the analysis of e.g. ZnSSe compound films. From this example it is quiteclear that spectroscopie ellipsometry plays an important role in studyingchanges in band structure and electronic properties of U-VI semiconductorsas it has done in the analysis of various other materials"),

356 Philips Journal of Research Vol.47 Nos. 3-S 1993

Non-destructive analysis by spectroscopie ellipsometry

12~--------------------~~~~108

1: 6w 4

2.........~~ /o

_2L_~ __ ~ __ _L__~ __L- __L_~ __ ~

1.50 2.50 3.50 4.50 5.50Photon energy (eV)

Fig. 8. Optical constants for the ZnSe thin film from Fig. 7 together with results for a simplifiedinterband transition model given by Adachi and Taguchi'") for bulk ZnSe.

4.3. The determination of the Ge content in SiJ_xGex alloys

The Si.; xGe; binary alloysystem has recently gained a widespread interestdue to its promising incorporation in Si-based semiconductor devices. One ofthe applications presently receiving much attention is the SiGe-base hetero-junction bipolar transistor (HBT)33). Spectroscopie ellipsometry has beenshown to be a suitable means for monitoring Si/Ge alloy ratio and determiningSi/Ge crystalline quality. Figure 9 shows the pseudodielectric optical constants<€) as a function of photon energy for a 380 ny thick Sio.87 GeO•13 alloy film onac-Si substrate. Deposition was carried out by chemical vapor deposition(CVD) at 625°C and atmospheric pressure using SiH2CI2 and GeH4 in a H2

ambient'"). Below 3.0 eV interference effects in the thin alloy film can beobserved in the pseudodielectric data. As the El type optical transition observed

40r---------------------------.

1: 10o20 I

JJJI

,/E2 _/,/

o =.::.::::::::::::------

30

-10

2.50 3.50 4.50 5.50Photon energy (eV)

Fig. 9. Pseudodielectric optical constants <e) for a 380 nm Sio.87Geo.J3alloy film on ac-Si substrate.

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J.C. Jans

1.0

I 0.9~QîE 0.80IJ),g-a; 0.7E.g

0.6x

• Our data--- Carrel. = 1

/,.,.-,,-

•»".".-,/,.-.-.-'

.-,.-.-'.'0.5 1L_..l......-l_.J..._....L_--l._.J.__L...-l_.J.__J

0.5 0.6 0.7 0.8 0.9 1.0Xfrom RBS H

Fig. 10. Correlation of Ge content for Sil_.,Gex alloys obtained from spectroscopie ellipsometrywith results from RBS.

in these alloys is known to be very sensitive to variation of the Ge content"),it can provide a sensitive monitor for accessing the Sil_xGex alloy com-position. The results for the optical constants shown in Fig. 9 are in goodagreement with recent-data for Czochralski-grown bulk material") as shownfrom a comparison of the maximum in <E2 > for the El transition as a functionof alloy composition". Figure 10 shows the correlation of the ellipsometricresults for alloy composition with results obtained from Rutherford back-scattering. The result illustrates that the ellipsometric method allows fastnon-destructive determination of the Ge content within about I at.% over awide composition range.

358 Philips Journal of Research Vol.47 Nos, 3-5 1993

5. Conclusions

Several examples on the application of spectroscopie ellipsometry inmaterials research have been given together with a concise review of theprinciples involved. Spectroscopie ellipsometry is a powerful truly non-destructive technique capable of structural analysis and determination ofoptical properties of a wide range of materials. Because it provides moreinformation from one single experiment than conventional spectrophotometryit enables the determination of the complex dielectric constants of materials ina more convenient way. As the technique is gradually maturing 38)_by nowseveral set-ups are commercially available-emphasis in ellipsometric researchhas shifted from instrumentation to ellipsometric methodology.

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Non-destructive analysis by spectroscopie ellipsometry

Acknowledgement

I would like to thank many of my colleagues at Philips Research forproviding and contributing to the examples given in this work.

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Thin Solid Films.

AuthorJan C. Jans: Ing. degree (Applied Physics), HTS Heerlen, The Netherlands, 1985; Philips ResearchLaboratories, Eindhoven, 1986-. He is involved in the optical characterization ofmaterials usingspectrophotometry ánd spectroscopie ellipsometry. He is registered as a European Engineer(Eur.lng.) and is a member of the Society of Photo-Optical Instrumentation Engineers (SPIE).

360 Philips Journal of Research Vol.47 Nos.3-5 .1993