gratings for metrology and process control. 2: thin...

Gratings for metrology and process control. 2: Thin filmthickness measurement

Geraldo F. Mendes, Lucila Cescato, and Jaime Frejlich

A method of measuring thin film thickness is described, based on a previous paper where the authors ana-lyzed a graphical means for grating modulation calculation. Metallic or dielectric films on any substratemay be measured, and precision was shown to be comparable with that achieved ellipsometrically at leastin the 300-1500-A thickness range. The method is non-contact and destructive: the grating is recordedon the film. Measurements are simple, requiring a low-power He-Ne laser and a photodetector, and maybe carried out at a distance from the sample. Experimental results are presented for three types of sample,including measurements by reflection and transmission.

1. Introduction

In Part 1 we described a simple graphical method ofmeasuring the modulation of a shallow lamellar grating,whatever its nature (grating and substrate absorbing ornot, dielectric or metallic).1 This paper is concernedwith using this method to measure thin film thickness.The results confirm experimentally both the methodand its application to thin film measurement. Com-pared with other thin film methods, this may be clas-sified as destructive and noncontact. It is particularlysuitable for very thin films, up to 1000 or 1500 A, forwhich range its precision is comparable with thatachieved with simple ellipsometry.

II. Theory

The thickness of a thin film is measured by recordinga lamellar grating in its full depth. The problem of filmthickness measurement is then converted into one ofgrating modulation. In Part 1 we showed that the lattermay be easily done with a nomogram. 1 The latterprovides the grating modulation h (which actuallyrepresents the film thickness), its bar-to-period widthratio aid (not relevant for our present purpose), and acriterion for checking whether the grating on the samplefulfils the required theoretical conditions.1 Figure 1 isa schematic description of a rectangular grating re-

The authors are with Universidade Estadual de Campinas, Labo-ratorio de Optica (Instituto de Fisica), 13100 Campinas-SP, Brazil.

Received 27 October 198:3.000'3-6935/84/040576-08$02.00/0.(c) 1984 Optical Society of America.

corded on the full depth of the film (thickness h, com-plex index nl). The bar, groove, and period dimensionsare a, b, and d, respectively. The substrate is assumedto be homogeneous with refractive index 2. For amonochromatic, normally incident light beam (wave-length ), the Nth to zero diffracted intensity ordersratio was shown to be1

IN Io 1P-rbj 2 (a/d) 2 2Nl)

IrP + ( - b)( /d)12 (1)

for a reflecting grating where a and b are the complexreflectivities on the bar and grooves, respectively, andsinc(x) sin(7rx)/(7rx). Referring to Fig. 1 thereflectivities are written as2

P I + P2 exp(i2)

1 + PIP2 exp(i23)

Pb = .j exp(i2y),

where 2 - 47rhhi/X,

where 2y 47rhno/X. J(2)

For normal incidence of light we have2

P, = (no - )/(no + A),

P2 = (n - n2)/(nl + n2), (3)P3 = (no - 2 )/(no + 2).

Substituting Eqs. (2) and (3) into Eq. (1) we get afunctional relation between variables aid and h, whichmay be plotted for different ratios InIo as the param-eters, one plot for each diffracted order (N = 1, 2, 3, etc).For our purpose it is necessary to superimpose the firstthree plots (for I/Io, I2/1IO, and 3/10) in a single com-pound nomogram. All three measured I1/Io, I2/o, andI3/10 ratios for a particular sample should simulta-neously intersect in this compound nomogram thusproviding its aid and h values (the film thickness).

576 APPLIED OPTICS / Vol. 23, No. 4 / 15 February 1984

y

no

a] . MSh

a b _ , /do /

/ l /

Substrt

__x

Fig. 1. Schematic description of a rectangular grating recorded onthe full depth of a film of thickness h and complex index n1, on asubstrate of index h 2. Bar and groove widths and period are a, b, and

d, respectively.

a /d

no

Fig. 3. Schematic description of a nonabsorbing transmitting la-mellar grating of groove depth H, substrate thickness H2, and indexn1 with negligible optical interface between them. Parameters a, b,

and d are defined in Fig. 1.

1, /Io ~- If yo is a solution of Eq. (5), y should also be, providedI2 10 - that

2-y = K27r i 2

yo

or

h = KX/2 ho

with K an integer 1

500 1000 1500

h (A)

Fig. 2. Nomogram for a metallic lamellar reflecting grating in air;aid is shown vs h for different values of I/Io, I2/10, and I3/1I asthe parameters, corresponding to the example depicted in Fig. 6(c).The nomogram is symmetric both through ad = 0.5 and

h = X/4 = 1582 A.

Lack of simultaneous intersection (account must betaken of experimental uncertainties in I/Io) indicatesthat the sample does not fulfill the required theoreticalconditions1 so that the results, although not necessarilyerroneous, should be considered with some restric-tions.

Three particularly useful examples will be considered:metallic films, transparent films on transparent sub-strates, and transparent films on absorbing substrates.For this purpose, theoretical models of three corre-sponding gratings will now be described. The testwavelength will be -y = 6328 A of the He-Ne laser.

A. Metallic grating

This is a particularly interesting example for whichEq. (1) becomes quite simple. It may be characterizedby the fact that there is no second interface (2 = 0) andlight is equally reflected from the bars and grooves ofthe grating ( = '). Equation (2) then becomes

a =P (4)

Pb = r1 exp(i2y) where 2-y = 4rh/J

which, substituted into Eq. (1) and rearranging theterms, gives

cos(2y) = 1 - IN__________ + (IIO I0)2(1-a/d )ald2(a/d)2 sinC2(Na/d) + (INIo)2(l - a/d)a/d.(5

This means that h is determined unambiguously but inthe range from h = 0 to h = /4. (It is easy to see thatIN/IO is symmetric through h = /4 and has a period ofX/2.)

Equation (5) is plotted in Fig. 2 for N = 1, 2, and 3,assuming that grating is in air (no = 1) and for h rangingfrom 0 to 1500 A (X/4).

B. Transmitting Lamellar Gratings

Figure 3 illustrates a nonabsorbing transmitting la-mellar grating with negligible grating-substrate inter-face. Diffraction may be accounted for by substitutingtransmittances (a and tb) instead of reflectivities (aand rb) into Eq. (1), so that

.1/0°= ji tb 1(/d2sinc2(Na/d). (7)

Transmittances are described by2

t t01t1 exp(i/3) with - 2r(H + H2)n,/X,1 + r 0 1r 10 exp(i2/)

th = toltlo expWy) with - 2r(H.n1 + Hno)/I1 + rr 10 exp(i2-y)

(8)

with to1 = tlo and ro = -r1 o, which, substituted into Eq.(7), assuming that r 1<< 1 and rearranging, leads to

cos(o - y) = 1 -2(a/d)2 sinc2(Na/d) + 2IN/10(1 - a/d)a/d

(9)

This is formally identical with Eq. (5) (which was de-veloped for the metallic grating) by substituting 2-y for

- y, which means that we may also use the nomogramin Fig. 2 for transmitting gratings by converting the hinto the H grating modulation:

H = h2no/(n, - no). (10)

C. SiO 2 Lamellar Grating on Si Substrate

This is a particularly interesting situation from atechnological point of view, for it should allow mea-

15 February 1984 / Vol. 23, No. 4 / APPLIED OPTICS 577

Ino

(6)

1/lo --

no5i02

h >2:.::

fl ubstratet/s//X~~~~~~~~~~ Si //

Fig. 4. SiO2 lamellar grating on Si substrate. The refractive indicesare nl = 1.46 for the SiO2 and h2 = 3.85 + iO.02 for the Si, both for the

6328-A wavelength. Other dimensions are defined in Fig. 1.

surement of very thin SiO2 film over a Si wafer. Thesituation is depicted in Fig. 4. The refractive indicesof SiO2 and Si are nj = 1.46 and h 2 = 3.85 + i.02, re-spectively 3 (for X = 6328 A), which when substitutedinto Eqs. (3) with no = 1 (air) results in

= -0.1870,P2 = -0.4501 - i.0021, (11)

P3 = -0.5876 - iO.0017.

Substituting into Eq. (2) we get

-0.1870 -0.4501 exp[i(20 + 0.0047)]r = 1 + 0.0842 exp[i(2 + 0.0046)]

Pb = -0.5876 exp[i(2y + 0.0029)]. '1

For 2 >> 0.0047 and 2y >> 0.0029 (i.e., h >> 3A) theseequations simplify to

-0.1870 - 0.4501 exp(i2o) ,-1 + 0.0842 exp(i2) I (13)

Pb -0.5876 exp(i2,y),

which, when substituted into Eq. (1), leads to a func-tional relation among ad, INi, and h. Numerical

computation allows plotting aid as a function of h forfixed IN1i1 ratios as the parameters. Figure 5 shows thesuperimposition of all three such plots (N = 1, 2, and 3)for no = 1 (air). This nomogram is no longer symmetricthrough h = X/4 or through aid = 0.5 as it was for themetallic case in Fig. 2.

As already explained, this nomogram allows a/d andthe grating modulation h (that is, the SiO2 film thick-ness) to be calculated from the experimentally mea-sured diffraction intensity ratios I1/10, I2/IO, and I3/IO.

Ill. Experimental Results

Some thin film samples were prepared for experi-mental analysis of all three theoretical models describedin Sec. II. Lamellar gratings were recorded on thesefilms and the diffraction studied to calculate the filmthickness. Our results support both the nomographicmethod for grating modulation calculation' and its usein thin film thickness measurement as described in thispaper.

All gratings (100-,um period and approximately equalbar and groove widths) were recorded on the film sam-ples by conventional contact-printing photolithographyusing a positive photoresist Shipley (AZ-1350B) and ahigh resolution emulsion mask (mechanically cut Ru-bylite pattern reduced 100 times on a Kodak high res-olution plate type 1A). A large grating period waschosen to minimize the edge-rounding effects, so thata better approach to the ideal lamellar shape could bereached.

As we are primarily interested in measuring thegrating modulation (or film thickness), we chose ad 0.5 because near this value the I1/Io ratio is almost in-dependent of aid. This means that the h value couldbe, if necessary, calculated exclusively from experi-

II /10

12 /Io

-1- 11 , - r--T- - r-- I I I l l l l500 1000 1500

h(A)

Fig. 5. Nomogram for SiO2 lamellar grating on Sisubstrate; aid is shown vs h for different values ofI1/8o, 12/I0, and 3/IJo as the parameters, corre-sponding to the grating described in Fig. 4 for no =1. As expected, this nomogram is no longer sym-metric either through ad = 0.5 or through

h = A/4.


LhF

Si / /1SAt

L A

b.

Fig. 6. Measurement of a thin aluminum film thickness: (a) a thinaluminum film coated on a Si substrate; (b) for measuring its thicknessa lamellar grating is photolithographed on it; (c) the whole is covered

again with an evaporated-aluminum film.

mental I/Io ratios without any higher diffraction orderswhich are more dependent on noise and grating shapedistortion.1

The diffraction of these gratings can be measuredwith a He-Ne nonexpanded laser beam (X = 6328 A)either by reflection or transmission at near-normal in-cidence. The diffracted intensity orders IN(N =0,1,2,3) were measured with a simple silicon photode-tector and digital multimeter. No appreciable differ-ence was detected when reducing the sensitive area,indicating that no relevant uniform noise was presenton the grating (see the Appendix to Ref. 1). Once cal-culated the IN/IO(N = 1, 2, and 3) ratios using the ap-

wa.0U)0

0

zww

z

Fig. 7. The sample depicted in Fig. 6(c) is seen in an interferentialmicroscope (Leitz Linnik) in white light (X = 6000 A). This pictureallows the good quality rectangular sample shape to be checked andthe depth of the grating groove to be measured by interferometric-

fringe displacement. 4

propriate nomogram, the grating modulation h (or filmthickness) was calculated as described in Sec. II.

A thin metallic aluminum layer was evaporated on aSi wafer, a lamellar grating was wet-etched on it, andagain covered with evaporated aluminum as describedin Fig. 6. The film thickness h was calculated fromdiffraction measurements and using the nomogram inFig. 2.

For comparison purposes the grating modulation wasalso measured with an interferential microscope4 (seeFig. 7). Both measurements are plotted in Fig. 8. Agood coincidence is apparent for very thin films (h <2000 A). For thicker films, probable distortion in thegrating rectangular shape may strongly influence theresults.

t

1000

I I 33 000

h (A) DIFFRACTION BY REFLECTION

Fig. 8. Thickness h of the aluminum film in Fig.6(c) is measured using an interferential microscope(Fig. 7) and our diffraction technique. Both mea-surements are plotted in this figure. The continu-ous line represents the ideal result. For largethickness values (h > 2000 A) experimental pointsdeviate from ideal, presumably because of the

stronger influence of grating shape distortion.


,~ - ./, l/ Glass

IAZ 1350 B

X (a)/

Ct | , AZ 1 350 B

Glass

Fig. 9. (a) A thin Shipley AZ-1350B photoresist coated on a glasssubstrate. Refractive indices were measured to be 1.64 and 1.51,respectively, for X = 6328 A. (b) A lamellar grating is photolitho-graphed on the resist film, which may be considered as an approachto the transmission grating in Fig. 3. Diffraction by transmission ismeasured on these samples and H is calculated in the text. If thephotoresist film thickness is to be measured the grating must beetched to the full depth of the film (i.e., H should be the actual film

thickness).

Fig. 10. Interferometric picture of the sample in Fig. 9(b) but cov-ered with aluminum (see Fig. 7 for comments).

4000

3000

2000-

F

_ I _ I- --I 1.- _ - -___1 - I l - L I --- L - I_1000 2000 3000h (A) DIFFRACTION BY REFLECTION

insparent films were prepared by coating a glassrate with the AZ-1350B photoresist. The reflec-es at all three interfaces are quite low compared tomitted light, as required by the theoretical modelII). Absorption at the thin resist layer is assumed;ible. The refractive index of the substrate wasured to be 1.51 and, for a thin photoresist filmd on glass (and measured by the Abeles method 5 ),Dund to be 1.64 (both for X = 6328 A). Figure 9rates the sample and the grating recorded on it.transmission diffraction data were handled withomogram in Fig. 2 as for the metallic case. The hnig was converted into the film thickness H through10), in view of the fact that the sample's refractiveis 1.64 for this wavelength. The grating on each

le was then covered with evaporated aluminum,rom the reflecting diffraction a new h value wason the same nomogram. Obviously both valuesd coincide as they correspond to the same filmniess. The aluminum-evaporated grating was alsoired with an interferential microscopy (Fig. 10).e 11 shows the latter vs the thickness measured bytion diffraction, and the good agreement between3ets is apparent. Figure 12 plots the thicknessired through transmission against reflection; agood linear correlation is seen here too.)ther sample was prepared which better approacheseal transmitting grating. A glass substrate waslithographed and wet-etched with diluted HFproducing a grating closely resembling that de-[in Fig. 3. The gratings thus etched on these.es were measured by transmission and then cov-

Fig. 11. Interferometric vs reflection diffractionmeasurements of samples shown in Fig. 10. The

continuous line shows the expected ideal result.


w00U

0

z

wa:

wU.

c)

w

I-

z

us

:

4000

3000 -

L

oJ O

1000 2000 3000h (A) DIFFRACTION BY REFLECTION

Fig. 13. Interferometric picture of a lamellar grating etched on a glasssubstrate (as shown in Fig. 3) and later covered with aluminum and

measured as described in Fig. 7.

ered with evaporated aluminum and again measured byreflection diffraction and with an interferential micro-scope (see Fig. 13). No film is concerned with thesesamples but they allow correlating all three measure-ments, carried out on a single grating. Figures 14 and15 show an acceptable agreement among all three setsof measurements.

Another particularly interesting sample (from atechnological point of view) was prepared by oxidizinga Si wafer, thus allowing the growth of a thin SiO2 filmon it. This thin oxide film was measured with an el-lipsometer (Gaertner model L-117) and afterward alamellar grating was photolithographed on it in theusual way (Fig. 4). These gratings were measured bydiffraction and their modulation calculated with thenomogram in Fig. 5. Then the gratings were covered

Fig. 12. Transmission vs reflection diffractionmeasurements of the thickness of the samples in Fig.9(b). For reflection measurements, the sampleswere covered with an evaporated-aluminum film.Good agreement can be observed between both sets

of measurements.

with evaporated aluminum (see Fig. 16) as for the othersamples, and the diffraction measured again. Thegrating modulation (film thickness) was then calculatedagain (now using the nomogram in Fig. 2). Both suchdiffraction measurements are plotted vs the ellipso-metrically measured values in Fig. 17. We see therethat the nonaluminized samples correspond quite wellwith ellipsometric values, but that the aluminum-cov-ered samples appear slightly thinner. We assume thisresult is because evaporation of aluminum over thesamples was carried out a few days after the first twosets of measurements; as samples were kept at roomtemperature during this time a naturally occurring SiO2film may have developed at the SiO2 grating grooves(bare Si substrate surface) thus lowering the measuredaluminized grating modulations. The difference be-tween both diffraction measured sets is always less than-50 A which is a reasonable thickness for naturallyoccurring SiO 2 film.

IV. Conclusions

We have shown that thin film thickness may bemeasured using a lamellar photolithographed gratingand an appropriate nomogram. Our results supportexperimentally both this method in particular and thenomographic method for grating modulation calculationin general.

The method was successfully used with differentsamples which should be considered as illustrative (notexhaustive) examples. The necessity of photolitho-graphing a grating on the film concerned characterizes


z0U)U)M

U)za:

zco0

I

U

ccU.U.

a



Fig. 14. Interferometric vs diffraction gratingmodulation measurements for the gratings described

in Fig. 13.

Fig. 15. Transmission vs reflection diffractionmeasurements for the samples in Fig. 13 before andafter being evaporated aluminum covered,

respectively.

it as a destructive method, but the simple equipmentrequired for measuring diffraction and the fact that thelatter may be carried out at a distance from the samplemay sufficiently compensate for that.

An appropriate nomogram is required for the opticalnature of the sample to be measured. All metallic films

or transparent nonabsorbing film-substrate combina-tions having almost equal refractive indices may becalculated using the same nomogram (Fig. 2). Othersamples (SiO2 film on Si substrate, for example) requirethe construction of a special nomogram (Fig. 5, for ex-ample). However, all films on whatever substrate may


1500k-wa.0UU)0

Uzw

IL

z

z0U)

z

0

U

CcU.

I

1500 F-

1000-

SO0r-

also be calculated with the same nomogram as for themetallic case (Fig. 2) if the grating photolithographedon them is aluminum covered as illustrated throughoutthe examples in this paper.

We should also point out that the latter metallizedsamples may be measured more effectively than thenonmetallized ones, as seen in the SiO2-Si example.Comparing nomograms in Figs. 2 and 5 we see that theI /Io ratio is more sensitive to film thickness variationsfor the metallized samples, a fact that was experimen-tally confirmed.

One of the limitations is that the grating closely ap-proach a rectangular shape for the results to be reliable.For very thin films (h < 1500 A) as shown for the SiO2film coated on Si, its precision is comparable to that ofsimple ellipsometry6 and much better than for inter-ference microscopy. 7

This research was supported by the Conselho Na-cional de Desenvolvimento Cientifico e Tecnol6gico(CNPq), Financiadora de Estudos e Projetos,Telecommunicacoes Brasileiras S/A and Fundacao de

Fig. 16. Interferometric picture of a lamellar grating of SiO2 overa Si substrate as described in Fig. 4 and covered with aluminum (see

Fig. 7 for comments).

0I_I

U)0.J-Jw

500 1000 1500h (A) DIFFRACTION

Amparo a Pesquisa do Estado de SAo Paulo. The au-thors acknowledge Claudio Loural from the ResearchCenter of TelebrAs (CPqD-Campinas) for ellipsometricmeasurements. We thank C. I. Z. Mammana, A. P.Mammana, E. Braga, and F. Damiani from the Labo-rat6rio de Electronica e Dispositivos for their help andsupport. We also acknowledge M. Barnett, L. Cardoso,Danilo Dini, Rogerio Suave, and Mauro Gibson for theirtechnical assistance.

Most of the experimental work was developed at theLaboratorio de Eletronica e Dispositivos (Faculdade deEngenharia) Universidade Estadual de Campinas.

Jaime Frejlich is also a fellow researcher of CNPq(Brazil).

References1. G. F. Mendes, L. Cescato, and J. Frejlich, Appl. Opt. 23, 571

(1984).2. M. Born and E. Wolf, Principles of Optics (Pergamon, New York,

1975), p. 62.3. Ellipsometric tables of ellipsometer model L-117 from

Gaertner.4. See, for example, M. Francon, Progress in Microscopy (Row, Pe-

terson, Elmsford, N.Y., 1961), Chap. 6.5. 0. S. Heavens, Optical Properties of Thin Solid Films (Dover, New

York, 1965), p. 119.6. Gaertner Bulletin EA-77 reports an accuracy of 2.5-10 A for the

L-117 ellipsometer (Gaertner Scientific Corp., 1201 WrightwoodAve., Chicago, Ill. 60614).

7. A. L. Gauler, Opt. Engl. 21, 991 (1982) reported a 500-A accuracy.We think 1/10 of a fringe (300-250 A) or even somewhat less maybe obtained depending on the particular sample. In this paperwe report t150-A accuracy.

8. A. L. Gauler, Opt. Engl. 21, 991 (1982) reported a 500-A accuracy.We think 1/10 of a fringe (300-250 A) or even somewhat less may

be obtained depending on the particular sample. In this paperwe report i150-A accuracy.

Fig. 17. Ellipsometric vs diffraction thicknessmeasurements for SiO 2 films coated on Si substrates.Ellipsometric measurements (Gaertner model L-117ellipsometer) were carried out for the SiO 2 film onthe Si substrate before the gratings were etched onthe samples. The crosses represent the diffractionmeasured once the lamellar gratings were etched on'the samples (Fig. 4); the circles show the samemeasurements carried out on the samples after being

evaporated-aluminum covered.


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