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OPTICAL CHARACTERIZATION BY
ELLIPSOMETRY – A PROSPECTIVE
D. Aspnes
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D. Aspnes.
OPTICAL CHARACTERIZATION BY ELLIPSOMETRY – A
PROSPECTIVE. Journal de Physique Colloques, 1983, 44 (C10), pp.C10-3-C10-12.
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J O U R N A L DE PHYSIQUE
Colloque CIO,suppl6rnent a u n012, Tome 44, dkcernbre 1983
OPTICAL CHARACTERIZATION BY ELLIPSOMETRY
D.E.
-
page CIO-3
A PROSPECTIVE
Aspnes
3eZL L a b o r a - t c e e s , Murray iliLZ, New J e r s e y 07974, U.S.P..
R6sum6 - L e s c a r a c t 6 r i s t i q u e s s u i v a n t e s r e n d e n t l ' B l l i p s o m 6 t r i e u t i l e p o u r r 6 s o u d r e
d e nombreux p r o b l s m e s c o n c e r n a n t l e s c o r p s s o l i d e s , l e s i n t e r f a c e s e t l e s c o u c h e s
m i n c e s : s e n s i b i l i t 6 a u x m o n o c o u c h e s e t m i c r o s t r u c t u r e s , precision i n t r i n s s q u e ,
g r a n d e r E s o l u t i o n e n 6 n e r g i e et p o s s i b i l i t 6 d ' e f f e c t u e r d e s mesures s u r d e s c o r p s
t r a n s p a r e n t s . C e t a r t i c l e e s t c o n s a c r c a u x p r o b l e m e s p o s g s p a r l c s deviations p a r
r a p p o r . a u x B c h a n t i l l o n s p a r f a i t s : t h B o r i e d u champ moyen, t h B o r 2 m e s s u r les l i m i t e s .
m6thodes pour d f t e r m i n e r a v e c p r 6 c i s i o n l e s s p e c t r e s d e l a f o n c t i o n d i e l e c t r i q u e d e
c o r p s s o l i d e s r B e l s e t d e couches minces, e t e f f e t s d e l a t e x t u r e microscopique s u r
c e s s p e c t r e s . On d o n n e d e s e x e m p l e s d e c a r a c t 6 r i s a t i o n in situ p e n d a n t l e d z c a p a g e ,
l e n e t t o y a g e , l a c r o i s s a n c e e t l e d B p 6 t d e c o u c h e s m i n c e s , e t o n d i s c u t e l e s relat i o n s e n t r e l'611ipsomBtrie spectroscopique e t l e s a u t r e s m6thodes d e c a r a c t s r i s a tion.
Abslrncr - Submonolayer and ~nicrostructuralsensitivity, Intrinsic accuracy, high energy resolution, and the capability of obtaining data in any transparent ambicnt make ellipsometry a useful technique for addressing a number of
problems in solids. interfaces, and thin films. This paper covers topics concerned with deviations from sample perfcction: eti'ective medium theory, limit theorems, methods of obtaining accurate dielectric function spectra on real bulk
and thin lilm samples, and the cflects of mlcrostructurc on thcse spectra. Examples of in situ characterization of
etching, cleaning, growth. and sample deposition arc given. and the relation of bpectroscopic ellipsolnetry to other
characteriza~ionmethods is discussed.
I. IN'I'RODLJCTION
The vigorous devclc~p~nent
of photometric designs / I / in the last decadc has added a spcctroscopic di~ncnslonto cllipsometry while retaining the usual advantages of submonolayer sensitivity and the capability of making nondestructive
me;isure~nentsin any transparent ambient. The instrun~entationproblems in the visible-near utr spectral range havc
largely becn solved, and intcrest has shifted to the quantitat~veinterpretation of dielectric response spectra, analysis
of materials and interfaces, and other practical applications. Today one need no longer work with nearly ideal samples: meaningful measurements can be madu on bulk or thin-film specimens that may be anisotropic, inhomogeneous.
microscopically rough, covered with adsorbed layers, or havc finite interface widths.
Optical characteriration requires accurate data, or rnore przcisely, accurate spectral data. This is thc province of
spectroscopic ellipsomctry (SE), and most of the paper will deal with S E and the type of information that we can
lcarn from the dielectric function (1 = c , + lt2) data obtainable with automatic spcctroscopic instruments. Length
lim~tationsrequlrc con~promises,so I shall assume that topics associated with ideal sarnplcs -- the propagation of
clcctromicgnetic radiation in homogeneous media, reflection at mathematically sharp boundaries, n-phase models -arc famlliar sincc they are thoroughly discussed elsewhere /2/. 1 shall concentrate on topics designed to deal with
deviations from sample perfection: cffcctive medium theory, limit theorems, methods of obtaining accurate t spectra
of real samples, and the erects of microstructure on t spectra. Examples include sample cleatling and film dcposition, where such devlations are thc norm. The readcr interested in further details and applications is dirccted to previous rc>iews by J . Theeten and me /3,4/, to a previous review of ellipsometry by Neal / 5 / , and to a series of articles
on optical methods of thin film analysis in two recent issues of Acta Electronics / 6 / .
11. DASIC PRINCIPLES
-- INSTRUMENTATION
An ellipsometer dctcrmines thc conlplcx reflectance ratio, p = rJr$, of a rellccting sample, where rp and r, are the
complex reflectances of p- and s-polari~edlight, respectively. The older null designs obtained p by establishing polarization states that extinguished the flux reaching the detector. The quadratic dependence of the intensity on instrumcnt settings near null and the necessity of operating the detector at very low light levels limited null cllipsometers
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19831001
JOURNAL DE PHYSIQUE
to very intense spectral line sources. SE is dominated b y photornctric instruments, where one of the elements is
rotated or otherwise modulated to systematically vary the flux reaching the detector / I / . I n addition to being readily
automated, photometric instruments operate a t high optical cficiency and are ideally suited for usc with the weak
continuum source, o f optical spectroscopy.
The approximately 30 groups that havc built or are building their own SEs have cast their economic ballots almost
exclusively for three configuration. These are the rotating analyzer, rotating p o l a r i ~ e r ,and phase modulated ellipsometers, or RAE. RPL, and P M E for short. T h e R A E and RI'E have certain advantages o f simplicity because the
only wavelength-dependent element is the sample itself. Systematic errors are less likely with a R A E than with a
RPE because polarization-insensitive detectors arc available while polarization-free sources are not. However, a
R A E cannot be used i f the sample or its environment are themselves appreciable sources o f light. The P.ME is not
affected by source polarization or detector polarization sensitivity. is capable o f high-speed operation, has no mechanically moving parts, and is a truc Stokes polarimcter that can distinguish circular from unpolarized light. However,
the modulation amplitude o f the dynamic conipensator is another free parameter that must be varied with
wavelength and which should be measured independently. The ~nventiono f a truly achrom;itic compensator would
make both R A E and R P E configurations instantly obsolete, since a rotating-compcnsalor ellipsometer would eliminate the major disadvantages o f both while losing none o f the advantages.
111. BASIC PRINCIPLES -- THEORY
A . I>ielectric Kesponse
M u c h present optic;~l characterization work concerns hcterogeneous materrals, where on ;i sufiiciently fine length
scale the dielectric function is itself a function o f position. Unfortunately, the standard solutions o f Maxwell's equations for ho~nogeneousmedia provide no insight into t h ~ sproblem, and more fundamental approach is necessary. The
key to understanding the optical properties o f heterogeneous materials is l o r e c o g n i x that ( for any material must be
calculated via a two-step process. A n externally applred electric field causes displ;icenients A< o f discrete charges q,
or charge densities p 0 . Thcse screening charges give rise to corrections to the field on a rnicroscoplc scale. The
first step is l o solve this local-field problem self-consistently for the microscopic lield Z ( 3 and polarization
p(T) = p ( 3 1 F a t every point i n space. But because the wavcle_ngth o f light, A, is far greater than the microstructural
dimensions, only the macroscopic averages E =
and P = <pG?> can actually be observed. Consequently,
the second step is to calculate thcse averages. I f the material is isotropic, then < is given by
<to>
-
where 6
<2(3>= < F O
volume V, Fqs. (1) become
+ 4rrp(T)>
is the macroscopic displacement ficld.
For a set o f discrete charges i n a
I n Eqs. (2) displacements clearly depcnd on thc h n d i n g properties and the local lields, whrle the averaging process IS
represented by the surn and volume normalization. The normalilation suggests that optical nieasurerncnts can be a
contactless means o f determining sample density.
c
makcs sense depends on whether the
Thus, t is a macroscopic average quantity. Whether a d ~ c l e c t r ~description
averaging process itself makes sense. I n some s~tuations, as for example submonolayer distributions o f adsorbed
:{toms on a substrate. a formulation i n ternis o f atomic polari7abilitics may be rnorc realistic. The solve-average procedure is routlne i n many areas o f physics, e.g., in quzintum mechanics, but because classical electrodynamics -- like
classical ther~ncdynamics-- sceks to describe extrcrnely cornplicatcd sybterns in terms o f ;I few macroscopic observa b l e ~ ,the microscopic orrgin o f these equations is often forgotten.
R. Effective Medium Thcory
F..Kective medium theory ( E M T I allows the dielectric response o f a heterogenrous material to be described by the
dielectric functions of its constituents and a few witvelength-independenr parameters and consequently is a basic tool
i n rnatcrial charactcri~ationby optical means. I f the scparatc regions are small compared to the wavelcngth o f light
but largc enough to retziin their own dielectric idcntity. thc local-tield problern can be solved by electrostatics. This
quasistatic approximation describes many common and important situations.
'l'hc derivation o f an EM?' expression begins with a model microstrugurc. For example, we suppose a microstructure
whereall boundaric\ are parallel to the applied field. Then X I = E is cverywherc constant and the spatial average
over d m reduces simply to ;I spatial averagc over r m . For a two-phase composite this lcads to
where t, and t b are the dielcctric-functions of the-constituents and f, and fb are the respective volume fractions. If all
boundaries are perpendicular to E, then
= D is everywhere constant and the spatial average over FCi) becomes
t-'
=
Taka+ fJtb, fa + fb = I.
(4a,b)
All EMTs in the quas~staticapproximation can be represented by /4/
<
where O
q ,< 1 is a screening parameter and th is the dielectric function of the background or "host" material.
l'he standard 1,orentz-Lorcn~and Maxwell Garnett (MG) expressions and the Bruggeman effective medium approximation (EMA) are obtained for q = 1/3 (spherical microstructure) and a h = I . th = c, or t b , and t h = f . respectively,
and thus d i r e r only in the choice of host medium. There is no "universal" E M T for the same reason that there is no
"universal" microstructure. Cermet (coated sphere) gconietries are more accurately describcd by MG or symmetrized M<;/7/ theories, while aggregates (collections of random particle shapes) are more accurately described by
the EMA. The EMA shows a percolation threshold whereas MG does not. Under certain conditions the MG theory
shows resonances which do not appear in the EMA. We have found the EMA to be generally applicable to thin
filrns /4/, but there are many examples in the literature of bulk campsites that are more accurately describcd by
EMTs of the MG type /8,9/.
C. Limit Theorems
Given that there is almost complete frccdoln to choose any composition or microstructure, it is not a t all obvious that
the quasistatic approxiliiation placcs well-defincd limits on c But consider the simple cases discussed above. Equation (3) wa, derived by assuming that all internal boundaries were parallel to the applied field. In this case, no
screening charge is developed. Since there can never be less screening than no screening. Eq. ( 3 ) must represent one
limit to possible values of t for a two-phase composite. Similarly, the maximum-screening situation occurs if all
boundaries are perpendicular to the applied field. Since there can never be more screening than maximum screening.
Eq. (4) must represent the other limit. Thus for any composition or microstructure, all values of r calculated in
quasistatic approxim;~tionmust lie between the boundaries defined by Eqs. (3) and (4). These liniits were established b) Wlener in 1912 / l o / and arc represented in Eq. ( 5 ) by q = 0 and q = 1. respectively.
More restrictive limits have also been derived. The Hashin-Shtrikrnan theorem / I I / defines the limits on t if fa is
known. Then t must lie within thc region defined by the MG liniits ch = t , and c, = t , for 0
q
I regardless of
microstructure. The Bergman-Milton theorem /12,13/ defines the limits if in addition the sample is known to be isotropic to two (q = I/2) or three (q
1/3) dimensions The Bergman- milto on limits a r e obtarned simply by placing
the Wiener bounds on t h . Because all limits can be expressed a s billnear transformations in the complex plane, all
arc easily constructed circular arcs /12/. An example for mixtures of hypothetical materials with t , -2 + i3 and
cb
I
il is given in Fig. I.
< <
-
-
+
-
'l'he limit thcorelns provide guidelines a s to what can and cannot i
x determined. They greatly simplify the entire
E.MT problem since all EMTs must conform to them /14/. They show further that composition is the more Important variable if t , and f b are similar, while microstructure dominates if the) are widely dln'erent. Also, while a
detailed knowledge of the microstructure of a composite is an admirable objective, an exact solution would be about
a s useful as knowing the motions of the individual molecules in a macroscopic sample of a gas. It is far more important to be able to summarize the full complexity of a heterogeneous material in a few simple parameters via an E M T
and to use the limit theorems to assess the reliability of these parameters. It should be obvious that a spectroscopic
capability is essential in dealing with this problem /15/.
1). Finite Wavelength Erects
If the m~crostructural dimensions, d, are comparable to the wavelength. A, scattering becornes important and the
quasistatic approximation breaks down. However. it is still possible to define an ercctive dielectric function in terms
of the wavevector for forward propagation of light /16/. The laminar microstructures giving the absolute Wiener
bounds can also be solved exactly for any d/A, giving some insight into the relative importance of this ratio /17/.
Results for the special case discussed above are also shown in Fig. I. The Wiener bounds are no longer rigorously
valid, but the error is small for d/A ( 0.1. As d/A increases. t moves toward the value corresponding to that of the
optically more dense medium due to a wavcguiding phenomenon. In random colnposites the effects are more complicated, but the waveguiding interpretation seems to be a good first approximation /18/. The finite-wavelength solutions show that it is impossible for the macroscopic electromagnetic wave to conform to microstructural dimensions,
so propagation takes place in an average sense.
JOURNAL DE PHYSIQUE
C10-6
E. Microscopic Roughness
A very important and very general manifestation of inhomogeneity occurs as microscopic roughness at sample surfaces. The eye tends to judge surface quality by macroscopic defects, but optically resolvable artifacts are generally
not important in ellipson>ctry because they scatter light out of the field of the instrument. However, if the scale of
irregularities is much less than A, then the electromagnetic wave will neither scatter nor conform, and the surface
rcgian must bc represented as an effective medium consisting of part substrate matcr~aland part ambient 1151.
ROUGHNESS
{
MeoH.y
OXIDES
SlOzLlNE
ORGANICS
I
-
ICP-41
0
-
Fig. 1
Limits on c for a composite with t,
-2 + i3 and r ~ ,= I + il; for fa 0.6; for an isotropic sample with
q = 1/3; for finite dIA. In the finite-wavelength case the T E and T M modes correspond to propagation
with the electric field parallel and perpendicular, respectively, to the laminations. The closed and open
circles represent increments of 0.1 and 0.5. respectively, in d/A.
Fig. 2
Removal of an air-grown natural overlayer on a c-Si wafer measured a t 4.24 cV. Resulth of other trcatments are also shown.
Fig. 3
Representative S E spectra for c-Si:
Fig. 4
Parameters of an oxide film on Fc determined by simultaneous measurement of AR and Ap.
(2,
undoped; c-Si:
<t2>,
ovcrlaycr present; p s i :
t2,
heavily doped
Bccause the less polari7able species dominates, t for the rough surface region will be relatively low and will tend to
appear very similar to that of an oxide overlayer. In fact, much of what passed as rcsidual oxides in the early litcrature was unquestionably microscopic roughness because microscopic roughness can be positively identified only by its
spcctral dependence and lack of chemical reactivity.
A. Cleaning and Etching
Clean, smooth, and undamaged surfaces are essential starting points for many processes, but a continuing difficulty
has been the lack of techniques for unambiguously monitoring etching and cleaning in real time. The procedure discussed here is based on the dependence of the pseudodielectric function, <c>, on the thickness, d, and the dielectric
response, t,. of an overlaycr /19/. to and d may be average or etfectivc values if the surface is microscopically rough
or the overlaycr is gradcd. < t > is a derived quantity calculated within the two-phase model from a measured or
calculated value of p, and represents the dielectric response of a hypothetical homogeneous sample with a mathematically sharp interface. < c > approximates the true bulk value, t, only to the extent that overlaycrs can be removed
from the actual sample. To first order in dA, < t > , andt are related by
where 6 is the angle of incidence, s, = n: describes the ambient, and where Eq. (6b) follows if 161 >>
>> c,.
Although surface characterization is usually done at a single wavelength, a spectral capability is preferred because
It1 >> lbl must be valid to guarantee uniqueness; that is, that the overlayer material is actually being removed when
the data so indicate. This can be achieved for most materials only in certain wavelength ranges, for example, in the
vicinity of the E2 peak in c2 for crystalline semiconductors. Because Eiq. (6b) is independent of 6,overlayer removal
can be followed without having to identify the material. However, considerable information about the chemical identity of an ovcrlayer can be obtained from its measured optical spectrum or its chemical resistance to attack by
selected reagents. It is not necessary to know s accurately to use this procedure.
The specific example shown in Fig. 2 illustrates the removal of the ovcrlayer that resulted from a two-year exposure
of a crystalline Si(c-Si) wafer to air /19/. A theoretical < c > trajectory, calculated by assuming that the overlayer
was SiO2, is also shown. The marks indicate thickncss increments of 5A and show that a IA increase in film thickness results in about a 2% decrease in the value of < t 2 > at the characterization energy of 4.24 eV. Hence, the
preparation method that leaves the narrowest transition region between bulk and ambient can be identified by the
The initial overlayer was 27A thick. but 12A could be removed with water and methanol
highest value of <el>.
and hence could be attributed to organic contamination. A further reduction of 12A with H F showed this to be the
true limiting thickness of the oxide. The final 3 to 4 A could only be removed with chcmical polishing and preferential etching with the sequence buffered H F (BHF), bromine-methanol ( B R M ) . BHF, N H 4 0 H (AMH), and BHF,
indicating microscopic roughness or residual subsurface damage left over from the initial polish. Results for < 11 1>
surfaces treated with CP-4 and NaOH and for an atomically clean 7x7 reconstructed surface measured in ultrahigh
vacuum are also given. The narrowest transition regions were obtained with the five-step chemical etching sequence
shown. AMH was shown to improve < 11 1 > surfaces but to degrade < 100> and < 110> surfaces, indicating preferential etching of < 11 1> facets on an atomic scale. Similar etching and cleaning procedures have been developed
for G e and the major 111-V semiconducting compounds /20/.
H. Measurement of Diclcctric Propertres of Bulk Matcri:rls
"Bulk" material, as used here. means any thickness sullicient to eliminate back-surface reflection efects either by
absorption or spati;~lseparation. so that the optical properties must be determined by front-surface reflection alone.
Accurate t data arc necessary as reference spectra and a \ sample and constituent date for material and thin film
characterization by eH'ective medium calculations. Ellipsonietry has several advantages over rcflectornetry with
respect to accuracy, insensitivity to light scattering by n~acroscopicallyrough surfaces, and the amount of information obtainable in a single measurement, but the single most important factor for obtaining accuratc optical data (as
can be inferred from the previous section) is sample prcpararion. Figure 2 and Eqs. (6) shoic that even very thin
overlayers can have a large effect on apparent values of (. Figure 3 shows the represcl~tativespectral dependence of
overlayer-induced changes in i t , > , here measured on an atomically clean c-Si wafer that had been microscopically
roughened by heating it in
Torr of 02.The reference spectrum was measured on a similar sample that had
been chemically cleaned as discussed above. The largest relative changc occurs in the vrcinity of the E2 peak at 4.24
eV, but all rcglons of the spectrum arc aflectcd. Clearly, accuratc t data cannot be obtained unless some care is
taken lo remove surface ovcrlayers and to keep the a m p l e in an inert atmosphere to prevent overlaycrs from forming
JOURNAL DE PHYSIQUE
C 10-8
during ~ncasurcment. I n cases whcre this has been done, there is very little dilTerence between reflectance spectra for
a given material whether measured directly /21/ or computed from S E data /20/.
C . Mcasurcrnent o f the Dielectric Properties o f T h i n Films
"'fhin" films mean samples where back-reflection effects cannot be ignored. Such samples must be analyzed with nphasc laminar models. where n 2 3 depending on the sharpness o f the interfaccs. T o obtain thin-film spectra from
S E data, i t is necessary to solve an equation o f the form
p
=
p(t;cl,dl;t2,d2 ....,t.:$,h)
(7)
where t,.d, rcprescnt the dielectric response and thickness o f the i t h laycr. The substrate dielectric function, t. and d,
and A arc assumed known. Even i f the film is isotropic and the interfaces are sharp, a\ any h there arc three unknowns and only two constraints.
The most elegant solution to the problem ol' underdetermination is to use the reflectance-measuring capability o f photometric instruments to determine the retlectance K or the reflectance changc AR upon film growth and thereby
obtain the necessary thrrd constraint /22/. Figure 4 shows results obtained by this procedure for an oxide film on Fe
/23/. The values o f d provide an internal consistency check since d is a systern invariant.
A t present the above method is applicable only to films grown i n situ because absolutc values o f R cannot be measured to sufiicient accuracy. More generally, the add~tionalconstraint must come from varying a system parameter
other than d. One possibility is 6. but the sensitivity is low. A more useful approach is to take advantage o f
interference cfTects. the gcncrally widcly different optical propcrties o f c and ,t and the capabilities o f S E instrumcntatron o f varying A. Then t, can be obtained b y assuming a value <d> for d, solving Eq. (7) on a wavclength-bywavelength basis for <c,,>
= c,, and looking for substr:lte- or interference-related structure i n the result. The procedure can be represented formally as
only the term linear i n ( i d > - d ) contains the system parameters, and i t vanishes only i f <d> = d i n which case
<c,>
= c,.
Sensitivity can be enhanced by differentiating the various <to> spectra with respect to energy i f necessary. I f artifacts cannot be eliminated, the model for p is not applicable to thc salnplc usually because the film is
anisotropic or nonuniform or the interfaccs are graded.
Figure 5 shows an cxarnple where the sample consists o f a 5 4 0 0 ~thick large-grain polycrystallinc S i (p-Si) film Insitu doped with phosphorus and deposited on a c-Si wafer covered with 1000A o f thermally grown ox~de. A fourphasc model is rcquired, and f.'ig. 5 shows that the interference-related artifacts cannot be completely eliminated
unless a fifth phase representing microscopic roughness at the air-film interface is also added. The total elimination
of artifacts i n the p-Si spectrum shows that the model accurately represents the sample. 'The complete spectrum o f
this film is given i n Fig. 3.
D . Materlal Characterization: Long-Range Order. Doping, and Alloy Cornpos~tion
Visible-near uv dielectric propcrties are particularly sensitive to crystalline order i n the 1 0 - 1 0 0 ~range owing to a
corresponding sccsitivity o f the electronic wavcfunctions. The spectral variety obtained for a series o f S i samples, a l l
consisting almost exclusively o f S i arvms tetrahedrally bonded to four other S i atoms, is shown i n Figs. 3 and 6. The
(2 spectrum o f C-Si is characterized by two sharp structures at 3.4 and 4.2 eV with the latter having a peak value o f
47. For heavily doped p- (c-)Si, the lower structure 1s broadened subrtantially and both are shifted to lower energies. The shift is too small to be seen clearly i n Fig. 3, but i t is readily detected by Fourier or derivative methods.
Changes due to the complete loss o f long-range order are best represented by the amorphous S i (a-Si) spectrum i n
fig. 6 for the sample deposited at 571C. The sharp structures at 3.4 and 4.2 cV are completely absent, having been
rcpl;tccd by a broad peak near 3.7 cV. T h e spectrum for the a-Si sample deposited at 525C is slmilar i n shape but is
2 5 6 lower in amplitude. This suggests by Eq. (2) that the packrng is less cfieicnt i n this material, i.e., the sample is
less dense. A n expansion o f Eq. (5) for any o f the common E M T s for n two-phase composite consisting o f a-Si and
voidc (t,
I ) supports this conclusion and shows that the relative decrease i n amplrtude o f c2 is 3/2 the relative
decr~asei n density. Thus, the 525C sample is about 16% less dense than the 571C sample. The sample deposited at
625C shows poorly defined structure signaling the onset o f polycrystallinity, but the crystallitcs arc small. N o t e that
all spectral dependences are quite distinct and that they di1Tcr substantially from the overlayer-distorted < t 2 > spectrurn also shown i n Fig. 3.
-
Optlcal measurements can be used to determine the composition o f semiconductor alloys i n several ways, the most
accurate being the determination o f critical point energies i n optical spectra. These vary by as much as I eV across
a given series, so i n the absence o f significant nonlinearity a resolution o f 10 meV i n the threshold energy will therefore translate into :I compositional uncertainty o f about I%. Although sensitivity is generally enhanced by numeri-
cally dilferentiating ( spectra one or more times with respcct to energy to bring out weak structures and to suppress
baseline elTccts, we have recently shown that Fourier analysis can be used to advantage to optimize both noise and
baseline filtering and to eliminate distortion i n calculating numerical dcrivativcs. I f the critical point is isolated, the
threshold energy can be obtained without having to differentiate the data at all because the slopc o f the phases o f the
Fourier cceflicients plottcd against weflicient index gives the critical point energy directly. Figure 7 shows such a
plot for the c- and p-Si data o f Fig. 3 and indicates that to within about 10 meV the introduction o f 3.3 x 1 0 * ~ c m - '
charged impurities reduces the E2 critical point threshold from 4.29 to 4.21 eV. Application o f Fourier techniques to
ST: data for GaAsl-,P, givcn elsewhere i n the Proceedings /24/ illustrate further advantages o f this approach.
E. Dcpos~tionand Growth: Real-Time Characterization
We cite threc cxamplcs o f the use o f ellipsometry for real-time analysis o f deposition and growth. The emphasis here
is on the automatic capabilities o f modern instrumentarion rather than on thc spectroscopic.
for an a-Si film bcing deposired on a SilNI subFigure X shows ellipsometrically measured ($,A) values a t 5461i,
strate /25/. The initial segment is due to the change I n optical properties o f the substrate upon heating to 580C.
The dashed curve shows the prediction o f the three-phase niodel assuming uniform coverage for all thicknesses. l'he
dot-dashed curves show s i m ~ l a rpredictions but done via E M T assuming that growth occurs as hemispherical accumulations about nucleation centers. The data clearly demonstrate a nucleation growth mechanism. The spacing
between centers is also obtained because the separation dcrermines when the hemispheres will coalesce to form a continuous filnl. The remarkable feature o f thesc data is!hat the o p t ~ c a lmeasurements are sufficiently sensitive to ident i f y thc growth mechanism for thicknesses less than 2 A . far below the capabilities o f any other techniques.
A second example is shown i n Fig. 9, which gives the time dependence o f small changes i n the ellipsometric parameters measured for the growth o f the (0001) face o f a Cd crystal at various substrate temperatures /26/. Thc tempcratures are represented as a supersaturation parameter o. The ellipsometrlc data show oscillations that can bc
related to the spreading o f monoatomic steps by accretion or evaporation o f C d atoms at the edges o f the steps. The
equilibriun~ condition can be determined very accurately from thesc data. For temperatures such that
Ilnln,, (
0.12, the surfaces become rough on a larger scale. The results clearly allow conditions to be optimized
during the actual growth of the ~naterial.
<
A final examplc concerns thc epitaxial growth o f a AI,Ca,-,As
/27/.
layer of nominal composition x
-
0.25 by M O C V D
-
llere, the ellipsometric data were solved as a function o f time for the local refractive ~ n d e xn
-
=
n
+ ix
at
6 3 2 8 i n i t h the film thickness as a parameter. Values o f n for thickness increments o f 1 0 0 i are shown i n Fig. 10
after introducing the proper steady-state flow o f ( C H 3 ) l A I into t h r system. Instead o f immediately reaching the
composit~onx
0.25, the optical data show that thc film composition gradually evolved toward this value These
data were ~nterprctedas cvidence o f the loss o f (C1-II),AI at other surfaces within the chamber. A n increased i n ~ t i a l
flow o f (CH,),AI was clearly required to cornpensate this loss i n growing the composition x = 0.25 until the wall
sites were saturated.
-
The fact that the old Ellipsometry Conferences have cvolved into the more gencral theme o f optical characterization
is the most convincing evidence that ellipsometry is no longer perceived to be a fitting subject for study i n its own
right and that the emphasis has shifted to using ellipsometry to study physical systems o f interest. Where do we go
from here?
W i t h respect to other vis~ble-nearuv optical techniques, i t is clear that null ellipsornctry, even i f done at several cmission lines, is no longer a competitive analytic tool but is useful only for routine mcasuremcnts on elementary
configurations, e.g., for determining the thicknesses o f thermal oxides on single-crystal S i wafers. The amount o f
information obtainable at a few discrete wavelengths is severely limited no matter how clever the experimentalist.
Rcflectancc measurements have also become much less attractive because their historic advantage -- a spectral capability -- is no longer unique. I t is relatively difficult to measure reflcctances to the same levcl of accuracy routinely
attainable with complcx rellectance ratios and ,less information is obtained at each wavelength. Although work continues to be done with null ellipsometric or reflcctometric techniques, this is Inore a consequence o f the lack of availability o f conlmercial S E equipment. O n the other hand, transmission measuremcnts w i l l never lose their utility for
weakly absorbing samples simply becausc reflectance methods cannot determine absorption coeficients below 100
cm-' with any degree o f accuracy. Kaman scattering will providc extremely useful and complementary surface
information when the sensitivity problems are solved.
W i t h respect to other spectral ranges, ellipsometry has not yet been a significant factor i n either the infrared or
vacuum ultraviolet partly because o f the lack o f good optical components but also because the information here tends
to occur as individual structures relatively well l o c a l i ~ c di n energy. Questions there have concerned the presence or
absence o f structure rather than details o f the lineshapcs. The situation is quite different from that o f the visiblenear uv, where only the single bonding-antibonding transition "line" is available and the information is contained
almost entirely i n its shape.
DE PHYSIQUE
JOURNAL
1
1
1
1
,
1
1
1
1
~
1
p-si
Fig. 5
<e2>
Fig. 6
r2
spectra for a p-Si film showing error-induced interference artifacts.
spectra for Si with various microstructures.
COEFFICIENT INDEX n
9 ldegl
Fig. 7
Phases of the Fourier coefficients of the c- and p-Si spectra of Fig. 3 vs. coefficient index. The radial
lines indicate theoretical variations for ideal critical points with the threshold energies given.
Fig. 8
Nucleation and growth of a-Si on Si3N4.
With respect to non-optical techniques, ellipsometry cannot attain the spatial resolutions, atomic specificities, and
spectral ranges possible with electron spectroscopies, and for general analytic purposes if a given sample can survive
the transition to the ultrahigh vacuum environmcnt necessary to use these techniques one probably has no business
doing optical measurements. I\;evertheless, there are s~tuations,even in ultrahigh vacuum environments, where the
microstructural sensitivity and h ~ g henergy resolution of optical probes can provide useful complementary information.
Spectroscopic ellipsometry is uniquely suited for nondestructive, real time, in situ studies of surfaces and interfaces in
physical systems involving reactive, liquid. or relatively high pressure ambients where submonolayer sensitivity is
required. Given that such information should be extremely useful for control purposes, it has always been somewhat
surprising that ellipsometry has not been used more widely in chemical, electrochemical, plasma, CVD, or M B E
processes involving cleaning and etching of surfaces and in plating, deposition. or other methods of growing thin
films. I expect that a large, and hopefully major, fraction of future S E work will be aimed in this direction. Specific
questions can also be raised. Does reactive ion etching disorder underlying substratc material. and if so, to how great
a depth? Do the initial stages of oxidation (plating, deposition, corrosion. passivation, etc.) take place uniformly over
a surface or proceed by spreading outward from nucleation sites'! What are the equilibrium thicknesses and compositions of adsorbed layers on heterogeneous catalyst surf;ices under operating conditions, and can poisoning of these
processes bc detected at an early stage? What is the nature of the oxide- or nitridc-semiconductor interface before
the details have been hopelessly destroyed by ion milling? As discussed above. even such mundane applications as
the accurate determination of optical parameters of simple materials can benefit greatly from ST: capabilities, and
much work also remains to be done in this area. At the next Optical Characterization conference I expect to see
considerable progress on all these topics.
VI. ACKSOWI.ED(;EMEhT
I am grateful to my co-authors for permiss~onto discuss work prior to journal acceptance: A . A. Studna and E.
Kinsbron for the niatcrial on heavily doped p-Si, and I f . Arwin for thin film analysis.
Fig. 9
Surface roughness fluctuations in growth and cvaporation of single-crystal Cd.
Fig. 10
Evolution of the complex refractive index n n i~ at 6 3 2 8 i for an epitaxial A1,Gal-,Asjlm
by MOCVD on GaAs. The composition reaches the steady-state value x 0.25 at about 700A.
-
-
+
-
grown
J O U R N A L DE P H Y S I Q U E
REFERENCES
[I1 HAUGE P.S., Surf. Sci 96 (1979) 803.
I21 AZZAM R.M.A and BASHARA N.M., Ellipsometry and Polarized Lighr (North-Holland, Amsterdam,
1976).
[31 THEETEN J.B. and ASPNES D.E., Ann. Rev. Matcr. Sci. 11 (1981) 97.
I41 ASPNES D.E., Thin Solid Films 89 (1982) 249.
[51 NEAL W.E.J., Appl. Surf. Sci. 2 (1979) 445.
[61 Acta Electronics 24 (198111982) Nos. 2 and 3.
[71 SHENG P., Phys. Rev. Lett. 45 (1980) 60.
181 GITTLEMAN J.I. and A B E L B B., Phys. Rev. B 15 (1977) 3273.
[91 GIBSON J.J. and BUHRMAN R.A., Phys. Rev. B 27 (1983) 5046.
[ l o ] WIENER 0.. Abh. Math. Phys. KI. Konigl. Sachs. Ges. 32 (1912) 509.
[I 11 HASHIN Z. and SHTRIKMAN S., J. Appl. Phys. 33 (1962) 3125.
I121 BEKGMAN D., Phys. Rev. Lett. 44 (1980) 1285.
[131 MILTON D.W., Appl. Phys. Lett. 37 (1980) 300.
[I41 NIKLASSEN G.A., GRANQVIST C.G., and HUNDERl 0.. Appl. Opt. 20 (1981) 26.
[I51 ASPNES D.E., THEETEN J.B., and HOTTIER F., Phys. Rev. B 20 (1979) 3292.
[I61 STKOUD D. and PAN F.P., Phys. Rev. B 17 (1978) 1502.
1171 ASPNES D.E., Phys. Rev. B 25 (1982) 1358.
[I81 EGAN W.G. and ASPNES D.E., Phys. Rev. B 26 (1982) 5313.
[I91 ASPNES D.E. and STUDNA A.A., SPIE Proc. 276 (1981) 227.
1201 ASPNES D.E. and STUDNA A.A., Phys. Rev. B 27 (1983) 985.
1211 DONOVAN T.M., ASHLEY E.J., and BENNETT H.E., J. Opt. Soc. Am. 53 (1963) 1403.
[221 CAHAN B.D., Surf. Sci. 56 (1976) 354.
[231 C H E N C.T. and CAHAN B.D.,J. Electrochem. Soc. 129 (1982) 17.
[241 KELSO S.M. and ASPNES D.E., these Proceedings.
[251 HOTTIER F. and THEETEN J.B., J. Cryst. Growth. 48 (1980) 644.
[261 GAUCH M. and QUENTEL G., Surf. Sci. 108 (1981) 617.
[271 LAURENCE G., HOTTIER F., and HALLAIS J., Revue Phys. Appl. 16, (1981) 579.