Optical constants and Drudeanalysis of sputtered zirconium nitride films

Monica Veszelei, Kent Andersson, C.-G. Ribbing, Kenneth Jarrendahl, and Hans Arwin

Opaque and semitransparent dc magnetron-sputtered ZrN films on glass and silicon have been optically

characterized with spectral reflectance measurements and ellipsometry. High rate sputtered ZrN hasgood optical selectivity, i.e., higher than 90% infrared reflectance and a pronounced reflectance step in thevisible to a reflectance minimum of less than 10% at 350 nm. The results are comparable with thoseobtained for single crystalline samples and those prepared by chemical vapor deposition. The complexoptical constant (N = n + ik) for opaque films has been determined in the 0.23-25-pum wavelength rangewith Kramers-Kronig integration of bulk reflectance combined with oblique incidence reflectance forp-polarized light. A variable angle of incidence spectroscopic ellipsometer has been used for determina-tion of the optical constants in the 0.28-1.0-pm wavelength region. The results of the two methods showexcellent agreement. The results indicate that ZrN is free electronlike and the Drude model can beapplied. The best opaque films had Drude plasma energies (hwop) between 6.6 and 7.5 eV and relaxationenergies (h/T) between 0.29 and 0.36 eV. Ellipsometer data for the semitransparent films show that therefractive index (n) in the visible increases with decreasing film thickness whereas the extinctioncoefficient (k) is essentially unchanged. The optical properties are improved by deposition upon a heatedsubstrate.

Key words: Sputtered zirconium nitride, optical constants, Kramers-Kronig, variable angle ofincidence, spectroscopic ellipsometry, Drude model.

1. Introduction

Zirconium nitride is one of several compounds withina group of related materials having a combination ofextreme physical and chemical properties. The car-bides and the nitrides of the transition metals, tita-nium, zirconium, and hafnium, are all stable withhigh melting points, hardness, and corrosion resis-tance.' The underlying cause for these properties isthe high cohesive energy, which in turn is determinedby a combination of ionic, metallic, and valencebonding between pd hybrids. In atomic form allthree metals have two s electrons outside and anunfilled d shell, whereas the metalloids have a 2s2pconfiguration. The details of the bonding, theamount, and even the direction of the charge transferhave been the subject of some controversy.2 Duringthe last two decades, however, reliable band structure

M. Veszelei, K. Andersson and C.-G. Ribbing are with theDepartment of Technology, Uppsala University, Box 534, S-751 21

Uppsala, Sweden. K. Jirrendahl and H. Arwin are with theDepartment of Physics, Link6ping University, S-581 83 Linkbping,

Sweden.Received 19 October 1992.0003-6935/94/101993-09$06.00/0.o 1994 Optical Society of America.

calculations have been published that describe thebonding properties and trends within the group.In particular, the augmented-plane-wave and linear-combination of atomic-orbitals (LCAO) calculationsfrom the Vienna group3-6 have been successfully usedto explain the similarities and differences among thevarious compounds. The relation between the cohe-sive and thermodynamic properties has been studiedfor a range of 3d compounds in recent studies.7 8

There is a vast amount of literature concerning thetechnical applications of these compounds, primarilybased on their hardness and stability. In particularthe use of protective coatings, e.g., in the tool indus-try, has motivated a multitude of studies concerningdifferent deposition techniques and the influence ofdeposition parameters on the strength and adhesionof the protective layer.9 The tool industry is by farthe biggest consumer of protective transition metalcompound coatings, but in the context of this study itis also interesting to note the smaller but related useof TiN in cosmetic coatings, e.g., on watch casings.In this case the strength of the material is exploited incombination with its attractive goldlike appearance,and attention is also given to the optical properties ofthe coating. The change of color with stoichiometryhas been studied.' 0

1 April 1994 / Vol. 33, No. 10 / APPLIED OPTICS 1993

The interest in optical properties of transitionmetal nitrides was stimulated by the statement ofKarlsson" that thin films of transition metal ni-trides-in contrast to carbides-should be selectivelytransmitting in much the same way as are noblemetal films. This is not trivial-the similarity inappearance of bulk gold and titanium nitride does notimply that thin films of these materials have similartransmittance spectra. The visual impression of thelight transmitted through TiN is neutral gray, whereasa Au film is green in transmission. The basic reasonfor transparent heat mirror properties of a single thinfilm is the combination of low n values in the visiblepart of the spectrum and strongly increasing k valuesin the near infrared, i.e., the behavior that is typicalfor free electronlike metals as described by the Drudemodel. A practical criterion is that the presence of astrong edge in the bulk reflectance spectrum favorsheat mirror selectivity.'2 The bulk reflectivities forchemical-vapor-deposited (CVD) coatings of TiN, ZrN,and HfN were analyzed and contrasted to the other-wise closely related carbides of the same metals.'3The small shift in the position of the reflectance edgeof ZrN in comparison with that of TiN implies thatwhile the latter is absorption limited the former isreflectance limited. It has been predicted that thinfilms of transition metal nitrides should exhibit heatmirror behavior, and the bulk optical constants wereused to calculate the transmittance and reflectancespectra for 10-50-nm nitride films on glass andembedded between antireflecting dielectric layers.'4The predictions were experimentally verified in thecase of reactively, magnetron-sputtered, semitranspar-ent TiN films, albeit a certain discrepancy remainedbetween the thin-film optical constants and thoseobserved for bulk samples. Sputtering upon heatedglass substrates reduced the difference, although itwas not completely eliminated.'5 From these stud-ies it was concluded that nitride-based multilayerswould not reach as low a level of thermal emittance asthe noble metal based but have an advantage in theirsuperior stability. The performance limit is set bytransition metal nitride single crystals, and it istherefore obvious that the nitride films shall not giveas low emittance values as the noble metal films.However the transition metal compounds are notprone to diffuse as are the noble metals. The excel-lent thermal and chemical stability of TiN-basedmultilayers was recently demonstrated, and the differ-ence in breakdown mechanisms in comparison withsilver-based coatings was analyzed.'6"17

The first calculations'4 based on bulk optical con-stants predicted marginally better optical selectivityfor ZrN than for TiN. An attempt to verify thisfailed: the semitransparent, sputtered ZrN filmswere found to be severely oxidized with much lowerinfrared reflectance than predicted.'8 In this paperwe report new experimental results for sputtered ZrNfilms with significantly improved heat mirror proper-ties. The optical constants for these sputtered filmshave been determined with Kramers-Kronig integra-

tion as well as ellipsometry and were found to fulfillthe conditions mentioned above. In order to under-line and analyze the free-electron character of theoptical behavior, the intraband part of the complexdielectric function has been parameterized and sub-tracted from the experimental function in order toobtain the interband contribution. Our results re-semble, and in terms of selectivity surpass, someearlier studies on single crystalline and CVD ZrN.'3,19

2. Experimental

A. Sample Preparation

The ZrN films were grown reactively in a dc magne-tron-sputtered system from a pure Zr target and abase pressure in the 10-7-hPa (1 mbar = 1 hPa)range. The sputtering system has been describedelsewhere.20 The opaque films were sputtered onCorning glass 7059, whereas the semitransparentfilms were grown on silicon wafers. Before deposi-tion, the glass substrates and the silicon wafers werecleaned ultrasonically with a detergent solution, andafter rinsing in deionized water the substrates weredried in nitrogen gas. In the reactive sputteringprocess an argon gas flow of 100 sccm (cubic centime-ter per minute at STP) and a nitrogen gas flow of 15,20, or 25 sccm were used, resulting in depositionpressure in the 3-4 x 10-3-hPa range. Prior todeposition, the target was sputter cleaned with argon.The opaque films were sputtered with two differentplasma currents, 4 and 6 A, for 5 and 3 min, respec-tively. Table 1 lists the deposition parameters forthe investigated films. A resistive pyrolytic carbonand boron nitride heater21 was used for substrateheating, and the deposition temperatures were con-trolled to 150 and 300 C. We also deposited filmswithout substrate heating. The semitransparent

Table 1. Process Parameters for the Reactively, dcMagnetron-Sputtered ZrN Filmsa

Substrate Plasma Deposition Nitrogen TargetSample Temperature Current Time Gas Flow Voltage

No. (0 C) (A) (s) (sccm) (V)

I 150 4 300 15 364II 20 365III 25 357IV 6 180 15 378V 20 393VI 25 392VII 300 4 300 15 361VIII 20 359IX 25 355X 6 180 15 377XI 20 392XII 25 390ib 300 4 15 15 339iib 30 339iiib 45 341

"Samples I-XII are opaque and i-iii are semitransparent. Theargon gas flow was 100 scem, and the deposition pressure rangewas 3-4 x 10-1 hPa for all settings.

bOn silicon substrate.

1994 APPLIED OPTICS / Vol. 33, No. 10 / 1 April 1994

films were sputtered on silicon for 15, 30, and 45 swith the same parameters as sample VII (see Table 1).

B. Optical Instrumentation

Reflectance measurements were carried out on aBeckman UV5240 spectrophotometer in the 0.23-2.50-,um wavelength region. Near-normal-incidenceabsolute reflectance was measured by use of a V-Wattachment, permitting the registration of signalintensity after two reflections from the sample andone from a reference mirror (W), as well as onereflection from the reference mirror alone with thepath length (V). The reflectance ofp-polarized lightat an angle of incidence of 60° was measured between0.30 and 0.80 p1m. In the infrared region, from 2.5to 25 lm, we used a Perkin-Elmer spectrophotom-eter Model 983 for reflectance measurements. Inthe latter two cases a freshly evaporated aluminummirror was used as reference. Measurements werealso made on a variable angle of incidence spectro-scopic ellipsometer 2 2 23 at photon wavelengths be-tween 0.28 and 1.0 pum, operated at an angle ofincidence of 70".

3. Determination of Optical Constants

A. Reflectometry

Applying the Kramers-Kronig dispersion relation tonormal-incidence reflectance data is a common proce-dure for determining the complex optical constants(N = n + ik) and associated optical parameters. 24-26

The disadvantage with this method is that the reflec-tance is required from zero to infinite frequencies inorder to determine n and k even in a limited experi-mental frequency interval.

The Kramers-Kronig dispersion relation betweenthe phase shift at a particular frequency wo and thereflectance spectrum is often written2 6 as

J = ln[R(j)/R( o)] dw.O~~(O)o= - 2 2 '

7T Wo Wo(1)

a) 2 3

R

0.8

0.6

0.4

0.2

00.01 0.1 1

Energy (eV)10 100

Fig. 1. To perform Kramers-Kronig analysis one needs the film'snormal-incidence reflectance at all wavelengths. We have dividedthe reflectance spectrum into four regions. Region B is ourexperimental photon energy range. The data in region C are fromthe Schlegel et al. experiments'9 and to higher, region D, and lowerenergies, region A, the reflectance is extrapolated.

experimental region with energies ranging from 0.05to 5.4 eV (25-0.23 lm). The integral in this energyrange, B, is evaluated with the trapezoidal rule. Inthe low-frequency region, A, we extrapolated thereflectance by using the Hagen-Rubens relation:

R(w) = 1 - (2°Ow\ 1/2 =1 - 03+/k0 (3)

The constant E is adjusted so that RI = 1 - Avm,where RI and ol are defined in Fig. 1. It is thenpossible to integrate A analytically, which is pre-ferred from an efficiency point of view. We extendedthe range of experimental data to higher frequencies,region C, by using the results of Schlegel et al. 19 frommeasurements on ZrN CVD samples. A small correc-tion factor, 0.8-1.2, was used to match the Schlegel etal. results with our measured reflectance at 5.4 eV.In region D, for frequencies above 12 eV, we approxi-mate the reflectance by

R(w) = R2(W3/W)P

Note that an experimental error in reflectance thatyields the same percentage error at all frequenciesdoes not affect the phase. Some characteristics areeasier to demonstrate if we express Eq. (1) as24

O(o) = - ln[R(w))ln(K±) dwo. (2)

The major contributions to O(wo) come from frequen-cies near wo, since the weight functionln(I wo - / I o + I ) has a logarithmic infinity atwo, and from regions with a rapidly varying reflec-tance spectrum, i.e., where the function (d/dw)ln[R(w)]is large. Still a significant contribution to the inte-gral comes from frequencies far from wo. Thus theextrapolation to regions outside the interval of mea-sured reflectance must be done with care.

We have chosen to divide the spectrum into fourfrequency regions as shown in Fig. 1. B is our

(4)

Determination of parameter p is described below.The contribution to the phase shift from region D iscalculated analytically.

Figure 2 shows the contributions to the phase shiftfrom the different frequency regions. The part ofthe phase shift that originates from experimentalregion B has a peak at the steepest part of thereflectance spectrum. The contribution from higherenergies, region D, is a significant part of 0(oo) at allwavelengths. A, the contribution from the infrared,is invariably small.

As a complement to the Kramers-Kronig analysiswe used a technique described by Nestell andChristy.27 At a particular wavelength, the opticalconstants are found as the intersection betweencontours of constant reflectances, i.e., the reflectanceat normal incidence and at a 60" angle of incidence, inthe n-k plane. A limitation of this method is thelarge absolute errors that appear in n and k when the

1 April 1994 / Vol. 33, No. 10 / APPLIED OPTICS 1995

(OI

R

0.8

0.6

0.4

0.2

0

o (rad)

1.2

0.8

0.6

0.4

0.2

00 1 2 3 4 5 6

Energy (eV)

Fig. 2. Contributions to phase shift 0 from the different spectralregions; see Fig. 1. The reflectance spectrum of the same film isalso presented.

two curves intersect at small angles. In practice, theoptical constants can therefore be determined only ina small interval of short wavelengths with this method.The procedure is started at some wavelength with no,ko that are good estimates of the intersection. Wethen find the intersection by using a Newton-Raphson iteration technique. The number of itera-tions needed is a measure of the accuracy; the fewerthe better. For successive steps in wavelength onecan use the optical constants determined in thepreceding step as initial values. We started at 300-nmwavelength and observed that beyond 400 nm thesolutions of n and k were not reliable; see Fig. 3. Thecontours intersect at too small an angle for longerwavelengths as illustrated by the insets in Fig. 3.The Kramers-Kronig curve was then fitted to theoptical constants obtained by the Nestell and Christymethod by varying parameterp in Eq. (4), thus givingn and k over the entire experimental region.

B. Ellipsometry

Ellipsometry is a nondestructive but indirect tech-nique to measure optical properties of bulk andthin-film samples.2 8 In the latter case determina-tion of the film thickness is also possible. In anellipsometric measurement, monochromatic polar-ized light is reflected at oblique incidence from asample. The reflected light will then, in general, beelliptically polarized. If the opaque samples in thisstudy are treated as a semi-infinite bulk material witha perfectly smooth surface, the measured quantity isthe complex reflectance ratio p defined as

p = r/rSX (5)

where rp and r are the complex Fresnel reflectioncoefficients for light polarized parallel and perpendicu-lar, respectively, to the plane of incidence. TheFresnel reflection coefficients are written as

N, cos (4 a-Na cos (8' N, cos (a + Na cos (to

Na cos (4a - Ns cos cf,= N, cos (rh±+N, co rh

(6)

(7)

The angle of incidence 4)a, wavelength , and thecomplex optical constants of the ambient medium Naare known parameters in an ellipsometric experiment.The angle of refraction +5 is a function of Na, N8, and(4)a and is obtained from Snell's law. By solving Eq.(5) for the optical constants of opaque sample N8 , thefollowing expression is obtained 2 8 :

N.(X) = Na sin fall + ( + P tan2 ha1 (8)

# ofIterations

1ooh

80

60

40

20

0280 300 320 340 360 380 400 420

Wavelength (nm)

Thus it is possible to obtain N, from the experimen-tally determined p. The situation becomes morecomplex with a multilayer sample. This is the casefor the thin-film samples in this study. Thesesamples can simply be described as two films (semi-transparent ZrN and native SiO2) on top of a semi-infinite opaque bulk (Si substrate) where all theinterfaces are smooth. The expression for the com-plex reflectance ratio is more complicated because ofmultiple reflections at the three interfaces. Theratio can still however be formally written as

p = R/Rs,

440

Fig. 3. Optical constants at a particular wavelength are found atthe intersection between constant reflectance contours in the n-kplane. The reflectance is measured at near-normal incidence andat a 60° angle of incidence. A Newton-Raphson iteration methodis used to find the intersection, and the number of iterationsneeded is a measure of the accuracy. As we can see, the intersect-ing contours are almost parallel at longer wavelengths; conse-quently the number of iterations increases.

where Rp and R, are functions of the Fresnel reflec-tion coefficients at the three interfaces and the thick-nesses of the two layers.28

The parameters in Eq. (9) are the optical constantsof the ZrN layer Nfl, the SiO2 layer Nf 2, and thesubstrate N 8, but they are also the thicknesses of thetwo layers df, and df 2. Reference data exist for bothSi and SiO2, and the oxide thickness can be obtainedby measurements on a substrate, the number ofunknown parameters is reduced to three, that is, Nfl,and dfl. The measured values are only two (p is a

1996 APPLIED OPTICS / Vol. 33, No. 10 / 1 April 1994

k I .

1.8 60'

1.6

1.4-

1.2

k . . . I 10 0.2 0.4 0.6 0.8 n

0.8 60'-

0.6 mS0.4

0' S.~~~00.2 0

0 01 1.2 1.4 1.6 1.8 n 0

S(9)

complex quantity). In a simple approach the opticalproperties of the ZrN film can be assumed to be thesame as those measured on a thick opaque ZrNsample. The only remaining unknown parameter isthen dfl. However in this study it cannot be as-sumed that the thin ZrN films have the same opticalproperties as the opaque ZrN samples. A largereffort had to be made to solve the unknown param-eters of the ZrN films.

4. Results and Discussion

A. Reflectance

Three deposition parameters were varied for thesputtered films: substrate temperature, nitrogen gasflow, and plasma current (see Table 1), resulting infilms with different optical properties. The processparameters were altered in order to find the optimumsettings for high-quality ZrN films. The influence ofthe parameters on the quality of the films can be seenin Table 2, where results from the reflectance mea-surements for the opaque films are listed. In Table 2the reflectance at 2-jim wavelength, the reflectanceminimum, and the position of the minimum arepresented for each sample. Note that some of thesamples have a reflectance higher than 90% in theinfrared wavelength region. An elevated substratetemperature results in a film with high optical qual-ity, i.e., high infrared reflectance and a deep mini-mum in the visible. This can be seen by comparingsamples I and VII or V and XI, all of which areprepared in the same way except for the substratetemperature. Samples I and V are prepared at 150"C and samples VII and XI at 300 C. Initially wesputtered opaque ZrN films without heating thesubstrate. Films prepared under these conditionstended to crack and peel off, probably because ofinternal stress. At higher substrate temperaturesthis problem is eliminated.

Figure 4 shows the reflectance spectra for threesamples prepared with the same substrate tempera-ture (300 "C) and plasma current (6 A) but with threedifferent nitrogen gas flows. The film produced at a

Table 2. Near-Normal-Incidence Reflectance at 2 g±m and atReflectance Minimum for Sputtered ZrN Films,

Sample Reflectance at Reflectance Position ofNo. 2-lm Wavelength at Minimum Minimum (nm)

I 0.90 0.09 355II 0.85 0.13 370III 0.80 0.15 390IV 0.82 0.15 320V 0.90 0.10 350VI 0.89 0.12 355VII 0.92 0.08 350VIII 0.91 0.07 360IX 0.88 0.09 365X 0.77 0.18 305XI 0.91 0.08 355XII 0.90 0.09 355

aThe position of the reflectance minimum is also presented.

R

0.8

0.6 _ '

25 sccm nitrogen0.4 l

0.4 *. - 20 sccm nitrogen

0.2 > - 15 sccm nitrogen

00.25 1.0 10 25

Wavelength (m)

Fig. 4. Experimental reflectance spectra for films prepared withdifferent nitrogen gas flows, 15, 20, and 25 sccm, and a plasmacurrent of 6 A (samples X, XI, and XII). As we can see, thespectral appearance of the reflectance changes with gas flow. Forthese settings, 20 secm is optimum.

nitrogen gas flow of 20 secm, sample XI, has thehighest infrared reflectance and the deepest reflec-tance minimum. A too small flow of nitrogen gas (15sccm) results in an understoichiometric film (sampleX), i.e., more Zr-like, with low infrared reflectance.A too high gas flow (25 sccm) has less effect on theoptical performance but results in a small decrease inthe infrared reflectance (sample XII). The mobilityof the molecules on the surface of the growing film isenhanced by increased substrate temperature andlower deposition rate. A high mobility results inlarger grains and lower density of crystal defects, i.e.,better quality. When decreasing the plasma cur-rent, the deposition rate is decreased accordingly, andless nitrogen is consumed in the process. At acurrent of 4 A, the optimum gas flow was found to be15 sccm. A study was made of the film thicknessversus deposition time for glass and silicon substratesat 150 and 300 "C. The relationship was in all casesclose to linear with a slope corresponding to 1.3 nm/s.The opaque films grown at these settings and at asubstrate temperature of 300 C exhibited the bestoptical performance in our study (sample VII). Therelatively high deposition rate is likely to reduce theproblem with oxidation during deposition, a problemthat we have encountered previously with ZrN.18It is however not obvious that an even higher deposi-tion rate would improve the film quality. As men-tioned above, the reconstruction of the surface layerunder growth is important, and the time required forthis process might imply that a higher rate may bedetrimental for film quality. Likewise, higher sub-strate temperatures can cause problems when sputter-ing thin films, since the oxidation process is acceler-ated with increased temperature.29

B. Optical Constants of Opaque Films

The optical constants of opaque films obtained by thetwo independent methods, reflectometry and ellipsom-etry, show excellent agreement. At no wavelengthat which both methods were applied did the opticalconstants differ by more than 5%. Figure 5 shows

1 April 1994 / Vol. 33, No. 10 / APPLIED OPTICS 1997

nk

2

300 400 500 600 700 800 900 1000

Wavelength (mn)

Fig.5. Optical constants of sputtered ZrN (sample VII) derived byKramers-Kronig integration and ellipsometry. The resulting op-tical constants differ by less than 5% at any wavelength at whichboth methods were applied.

the real and imaginary parts of the refractive indexfor sample VII. A selection of the optical constantsobtained is also listed in Table 3. It can be noted inFig. 5 that the real part of refractive index n is below0.5 in a major part of the visible spectrum (450-690nm). An n value well below 1.0 is characteristic forthe noble metals. Figure 6 shows the real andimaginary parts of the dielectric function, determinedby reflectometry, as well as the reflectance of thesame film over the experimental photon energy inter-val.

C. Optical Constants of Thin Films

Thin semitransparent films of ZrN were prepared onSi substrates with a native SiO2 layer (Table 1). The

Table 3. Selection of Optical Constants for Sputtered ZrN (Sample VIl)Derived by Kramers-Kronig Analysis and Ellipsometry

n k

Wavelength Kramers- Kramers-(pm) Kronig Ellipsometry Kronig Ellipsometry

0.30 1.79 1.87 0.71 0.660.40 0.71 0.72 0.98 0.980.50 0.43 0.45 2.09 2.020.60 0.44 0.44 2.92 2.910.70 0.51 0.51 3.64 3.690.80 0.62 0.61 4.27 4.350.90 0.76 0.68 4.95 4.941.00 0.89 0.82 5.55 5.621.50 1.68 8.362.00 2.62 10.92.50 3.65 13.33.00 4.75 15.44.00 7.43 19.45.00 10.7 22.26.00 12.8 24.37.00 14.9 26.88.00 17.1 28.79.00 19.1 30.4

10.0 21.1 32.715.0 30.3 38.520.0 37.1 40.3

ee2

10

5

0

.5

-10

.150 1 2 3

Energy (eV)

R

0.8

0.6

0.4

0.2

04 5 6

Fig. 6. Dielectric function = + i 2 and reflectance ofsputtered ZrN film (sample VII) as a function of photon energy inthe experimental interval. The dielectric function has been de-rived by Kramers-Kronig integration.

deposition times were 15, 30, and 45 s. These filmsand a bare Si substrate were then analyzed withspectroscopic ellipsometry. By using reference datafor Si and SiO2 in a single-film model, we determinedthe SiO2 thickness to be 2 nm in a regression fitanalysis. This thickness was then used in a two-layer model (2-nm SiO2/ZrN).

In an initial analysis the optical properties of ZrNtaken from ellipsometric measurements on an opaquesample (VII) made with the same process parametersas the thin films were used in the two-film model.However rather poor fits to the model data in aregression analysis of the ZrN thicknesses were found.This indicates that the thin-film optical constantsdiffer from the bulk optical constants. The fact thatthe El peak of Si near 365 nm (Ref. 30) is positioned inthe transmitting regime of the ZrN spectra made itpromising to use a method from which both the filmthickness and the film optical constants can be de-rived.3 ' The basic procedure is to assume a thick-ness of the ZrN layer and then fit the model data tothe experimental thin-film data by solving for theoptical constants of the ZrN layer with numericalinversion. Candidates for the film optical constantsare in this way generated for every assumed thickness.In principle it is possible to obtain film thickness byrequiring that substrate-related structures from theEl peak in the film optical properties vanish at thecorrect thickness. It turned out that this methoddid not give reliable results for this set of films andsubstrate, probably because of the complicated behav-ior of the reflectance ratio, Eq. (5), in this wavelengthregion. Other possible explanations are model mis-match and surface or interface roughness effects.

An alternative approach was tried in which thereflecting region (500-1000 nm) of ZrN was utilized.The underlying assumption was that the opticalconstants should not differ significantly betweensamples i, ii, and iii and that there is no structure inthe substrate optical properties in this region. Notethat this assumption was made only to determine thefilm thickness. The actual optical constants of eachindividual sample were subsequently calculated.

1998 APPLIED OPTICS / Vol. 33, No. 10 / 1 April 1994

0 X ~--Ce

-' 2\

In a semimanual iteration procedure the thicknessesof the three films were then sought under thiscriterion. The best fits were achieved for a thicknessof 18 ± 0.2, 38 ± 0.2, and 60 ± 0.5 nm for samples i, ii,and iii, respectively. After the thickness was ob-tained, the actual optical properties of each individualZrN film were calculated in the spectral range from400 to 1000 nm with numerical inversion of theexperimental thin-film data. At shorter wavelengths,less than 400 nm, the influence from the Si substrateis too strong.

The resulting optical constants of the three filmsare shown in Fig. 7 together with those of an opaquesample (VII). Figure 8 shows the correspondingdielectric functions. It can be seen in Fig. 7 thatrefractive index n increases with decreasing filmthickness whereas the changes in the coefficient ofextinction k are less pronounced. This has beenpreviously observed for thin TiN (Ref. 15) and Aufilms.32 There are several reasons for poor opticalbehavior of thin films compared to bulk properties.For example, thin films of some materials can besomewhat discontinuous to as much as tens of nanom-eters average thickness.3 3 Earlier investigations onTiN thin films have shown that they were sensitive tooxidation.1729 It is likely that the same problem ispresent when thin ZrN films are prepared.' 8 Otherexplanations should be considered, one of which issurface roughness. Effective medium model calcula-tions show however that, if a surface roughness ismodeled with a thin surface film composed of ZrN andvoids in a ratio of one to one, F2 will decrease and Elwill increase. In this study we used optical proper-ties calculated in the Bruggeman effective mediumapproximation.3 4 The results from the calculationwould imply that the bulk sample is considerablyrougher than the thin-film samples in our case. Weregard this as unlikely. Instead we suggest that theexplanation for higher n for thin films is that thesefilms have smaller grain sizes than the opaquesamples, which will lead to a decrease in the free-electron mean-free path.'5 The resulting shorterrelaxation time will broaden the Drude low-frequency

n,k

5

4

3

o L400 500 600 700 800 900 1000

Wavelength (mun)

Fig. 7. Optical constants (N= n + ik) for sputtered ZrN filmswith the thicknesses indicated. Measurements were made withthe variable angle of incidence spectroscopic ellipsometer.

el,2

15

10 .

5 *.2

0 - opaque

-5 -18nm

- -- 38 nm

-15

-201 1.5 2 2.5 3

Energy (eV)

Fig. 8. Dielectric function ( = El + ir 2) for sputtered ZrN filmswith the thicknesses indicated. Measurements were made withthe variable angle of incidence spectroscopic ellipsometer.

range into the near infrared, with an increase in E2 asthe result.

D. Drude Analysis

The calculated optical constants were analyzed withthe free-electron Drude model. The Drude param-eters, plasma energy hop and relaxation energy h/T,were calculated for the opaque films. The resultsare shown in Table 4, where T is equal to thefree-electron relaxation time. The dielectric func-tion E = 61 + i 2 is expressed in the Drude model bythe equation

(10)(1)27 + .

The real part, el, can then be written as

61= 61(X) -2(T.

When Eq. (11) was applied to 1 and E2 in therelaxation region from 600 to 2200 nm, we found therelaxation energy from the linear fit of the data thatare shown in Fig. 9. The excellent linearity of the

Table 4. Calculated Drude Parameters, Relaxation and Plasma Energy,for Sputtered ZrN Films

Relaxation Plasma Screened PlasmaSample Energy h/T Energy hwp Frequency

No. (eV) (eV) (eV)

I 0.32 6.86 3.13II 0.56 6.55 2.93III 0.85 7.16 2.74IV 0.71 6.62 3.38V 0.36 6.88 3.16VI 0.33 6.61 3.08VII 0.29 7.35 3.19VIII 0.34 7.47 3.15IX 0.52 7.99 3.07X 1.29 7.88 3.50XI 0.31 7.25 3.20XII 0.35 7.20 3.14

(11)

1 April 1994 / Vol. 33, No. 10 / APPLIED OPTICS 1999

e

-20

-40

-60

-80

-100

-120

-140

2 12 17 22 27 32 37 e2E (eV)

Fig. 9. Calculation of the Drude relaxation energy h/r for sput-tered ZrN (sample VII). The dielectric function = + i 2,obtained from Kramers-Kronig analysis, was used.

data over a large range confirms the applicability ofthe Drude model. The plasma energy is calculatedin Fig. 10 in which Eq. (10) has been applied to E byusing the value of the relaxation energy obtainedfrom Fig. 9. The best films in our study have plasmaenergies between 6.6 and 7.5 eV, and the relaxationenergies were calculated to be in the 0.29-0.36-eVrange; see Table 4. These values are in accordancewith earlier measurements on ZrN.'3 19 Even thoughthe plasma energy is calculated to be approximately 7eV, a screened plasma resonance occurs just above 3eV; see Table 4. This behavior can be explained withinterband transitions. 3 35 The partial LCAO density-of-states calculations36 for ZrN show that interbandtransitions from nitrogen p states below the Fermienergy to Zr d states just above the Fermi energy canoccur. The partial density of states for nitrogen pstates has a peak at approximately 5 eV below theFermi energy that would give rise to a maximum ofinterband transitions around this photon energy.

The dielectric function can be split into two parts,the free conduction electron and the bound electroncontribution:

gexp = Ef + Eb-

-20

-40

-60

-80

-100

-120

-140

0 0.5

(12)

1.5 2 [(rt)2 + E2] (eV2)

Fig. 10. Calculation of the Drude energy i/w, for sputtered ZrN(sample VII). The dielectric function = + i 2 , obtained fromKramers-Kronig analysis, was used.

5.

4 e2

3

2

0- I,..~~~~~........0 '.... I.., .. I ... I . ;:''.-. I .--. ,, ...

2 2.5 3 3.5 4 4.5 5 5.5 6Energy (eV)

Fig. 11. Free (E2f) and bound (F2b) electron contributions to E2 forsputtered ZrN (sample VII). The bound contribution arises frominterband transitions from nitrogen p states below the Fermienergy to zirconium d states just above the Fermi energy.

The free-electron contribution from intraband transi-tions was calculated from Eq. (10) by using the valuesof hp and h/r. The bound electron contributionarising from the above-mentioned interband transi-tions was obtained by deducting the free-electroncontribution from the experimental dielectric function.In Fig. 11 the free and bound electron contributionsto 2 are plotted for sample VII. The interbandtransitions exhibit a threshold at 3.5 eV and increaseat higher photon energies.

The relaxation energy is a measure of the filmpurity and perfection. A lower value corresponds toa higher optical quality. When we make the samecomparison as in Subsection 4.A of films preparedwith different substrate temperatures, i.e., samples Iand VII or V and XI, we observe that the highersubstrate temperature results in a lower value of therelaxation energy. Sample VII has the lowest valueof h/r and represents the optimum nitrogen gas flow,substrate temperature, and plasma current in thisstudy. A comparison between sputtered ZrN andTiN films shows that the former have better heatmirror selectivity.

6. Conclusions

Opaque and semitransparent films of ZrN have beenprepared with high rate reactive, magnetron dc sput-tering onto glass and silicon substrates. The filmsexhibit more than 90% infrared reflectance, a pro-nounced reflectance step in the visible to a reflectanceminimum of less than 10% at 350 nm. The opticalquality of the films can be compared with that fromearlier single crystalline and CVD samples. Theoptical constants of opaque films have been deter-mined in the 0.23-25-pm range with Kramers-Kronig integration of bulk reflectance combined withoblique incidence reflectance for p-polarized light.A variable angle of incidence spectroscopic ellipsom-eter has been used for determination of the opticalconstants in the 0.28-1.0-pm wavelength region.The optical constants obtained from the two indepen-dent methods used show excellent agreement. The

2000 APPLIED OPTICS / Vol. 33, No. 10 / 1 April 1994

= 029 eV

. . . I . . . .. .. . .. . .. . .. . ' '.

free-electron Drude model was applied, and the bestopaque films had plasma energies, hp, between 6.6and 7.5 eV and relaxation energies, h/T, between 0.29and 0.36 eV. The optical properties were improvedby deposition on a heated substrate (300 C).Comparisons of the optical constants for the semi-transmitting and the opaque films show that the realpart of refractive index n increases with decreasingfilm thickness whereas imaginary part k is unaltered.The results in this paper show that sputtered ZrN haspromising optical properties for heat mirror applica-tion.

We thank Bjbrn Karlsson of Vattenfall, Alvkarleby,and Arne Roos, Uppsala University, for their sugges-tions and comments concerning this manuscript.The work reported here has been sponsored by theSwedish Council for Building Research and the Swed-ish Research Council for Engineering Sciences.

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