Studies of surface and interface phenomena by grazing angle neutron reflectometry

Applied Surface Scleuc¢ 6a/gl (1~92)573-579 North-Holland

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SUF[-~CI~ Science

Studies of surface and interface phenomena by grazing angle neutron reflectometry M . M ~ a z a a,b, C. S e n a e a n d M . K~.abouchi ¢ a Llzboratoire Lt:on Brdloum, CF~I-CNRS, Bt~timent 503, ('entre d'Et.des Niicl~airt,sde Sat'lay, 91191 Gif-aur-Ycela,, Frant~, ~' C~mzllvgttic hulustriell¢ de,~Laser* CIIAS, Route tit' Nozay, B.P 27. 9146(I ~tlrcoll~si& I:r~nc¢ " Laht~luloirc dr' Ph)'~ique des Matt;rialto, CNRS de Me.dan-Bl,llet ue, 02105 Meudo~t Priltctpa~ l'~ance

Received 2e November 1991; accepled filr publicalinn 12 December ItJal

Grazing-angle neutron reflcctomeu3' has been developed recently as a technique Io study roughness, interracial diffusion and chemical contamination at surfaces allfi interfaces of both liquid and stdid samples. Many of the classical phenomena in optics have been demonstrated with thermal and cold neutrtms such as tolal reflecann, refraction, diffraction and interference. Tile interaction between the de nroglie neulron waves and Ihe condensed manet is descrihed by an index of refraction which has the same mathematical expression as far X-rays, Taking into accotmt lhe intrinsic characteristics of Ihe neutron wave, the information obtained by this new leehnique can be uniqpe. In this paper, we give some examples which illustrate the possibilities a[ this technique to study thin films and slratified media.

~-. Theory of neulron reflection G r a z i n g - a n g l e neutron reflectometry ( G A N R ) provides a novel tool for investigating a wide range of surface and interracial p h e n o m e n a in thin films and stratified m e d i a with a spatial resolution t h a t is of t h e n a n o m e t e r scale [1]. A range of p h e n o m e n a similar to that o f classical optics is exhibited ~oy cold neutrons such as reflection, refraction and interference [2]. From the optical point of view, the neutron-condensed m a t t e r interaction can be described by a refractive index n which possesses t h e same m a t h e m a t ical expression as for X-rays [3]. For a nonmagnetic and non-absorbant material, this refractive index is related to the chemical composition by t h e following expression: n ~ l -d/bA2/2v;,

(1)

where A is t h e associated de Broglie neutron wavelength, J ' is the number of scatterer a t o m s per unit volume and b is the coherent nuclea~ scattering length [4]. The magnitude of thc last p a r a m e t e r varies irregularly with atomic number

Z and may be positive or negative particularly for nickel and titanium: bNi -~ + 1.03 X 10- i., cm and bTi = - 0 . 3 4 × 10 -I'- cm. Let us take the z-axis perpendicular to t h e reflecting surface, the par a m e t e r . z Y b ( z ) is called the nuclear scattering length density, and is of o r d c r o f l 0 t'/~ 2, so the total external refleclion phenomenOnoCan occur at a weak grazing angle (0.7 m i n / A for bulk nickel). T h e critical m o m e n t u m is given by applying the S n e l l i u s - D e s c a r t e s law at total reflection condition: K~ = (2~r sin g / A ) = ( ~ ¢ b / ~ ) ~/~.

(2)

In gencral, it was shown tha: the propagation o f the de Broglie qeutron waves acts in the condcnscd m a t t e r as an electromagnetic X-ray wave in the S polarization state [5]. In thin films and stratified media, an inhomogeneous neutron scattering length density J Y b ( z ) at surfaces a n d / o r interfaces is described by a series of discrete uniform layers. W e may assign a neutron scattering length density ./Yb~ and a thickness dj to each layer and use the iterative matrix method to d e t e r m i n e the reflection and the transmission

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M. Mffaza t't al / Grazing ang&"m',lron rc'lTt'cto#wtO'

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coefficients at each interface j - l / j and the characteristic matrix of the jth layer which is given by [6]:

(

cos(,~,k,,d,)

[M,] = t - f i : sin(h+,kiid,)

'V' sin(,V<,,
'

]3) where /ell= 2 r / ~ and ~ i = n s sin ¢~j is the effeelive refraction lades, 0.; is the grazing angle at the j - l / j interface. The resultant muhilaycr matrix [Mtot] is obtained by multiplying the matrices of all the layers up to the final layer. The overall re,qeetivity of the multilayer is given by R = rr*, where r is [7]: ho(Mli + h~Mi: ) - (M2i + h,M22 )

,

hi)( M l l + fl,Ml2 ) + ( M,. 1 + fi~M.~2) '

(4)

where the index 0 refers to the vacuum and s to the substrate, M o are the elements of the matrix [M] given by the Abel&s formalism. The variation of the Fresnel neutron reflecfivity RF(K) with the momentum K = 2rr sin 0/A where 0 is the grazing angle is then related to the neutron scattering length density profile ~ t b ( z ). The characteristics of _J'b(z) profile are determined by the simulation of the experimental neutron reflectivity curve RF(K). The simulation procedure is highly constrained by: the total reflection limit, the resolution effect, the number of interference fringes, the positions of interference fringes and their intensities, The simulation , t ' b ( z ) profile yields information about the thickness of films and the degree of their homogeneity, interfacial diffusion and interf,~cial roughness in the multilayers, the concentration profile of adsorbed polymers in the s~iution, etc. [8]. Nevertheless. the neutron particle possesses a spin ½ and a magnetic dipolar moment p. = 1.913; its interaction with the electronic shell of the scatterer atoms described by a magnetic scattering length b' leads to a magnetic moment. Thus, in lhe general case, the neutron scattering length density ,~Fb can be represented as [9]: -

.#'b = h L r ' ( b + b' + i I b" I )/2,n-m~,

(5)

where b' is the magnetic scattering length and b"

is the abserption scattering factor which is related to the absorption cross section [10]. The term b" is generally ve~' weak. If the magnetic material is submitted to a magnetic field, the neutrons of an unpolarized beam of spin up and spin down see a medium with 2 refractive indices n~~(A) and n~(a), respectively, whose expressions are [11]:

,,;0[x] = 1 - ~ r A - ~ [ b - b ' ] 1 2 = , . . ~ [ a ] ~ l - . ra-'[b + b ' ] / 2 ~ .

(6)

In this case, the medium reacts like a birefringent crystal in ordinary optics. This effect results in a shift between the spin between the spin up and down reflectivities R+(A) and R (A). This important property is !argcly cxplohed in the investigation of magnetism of suriaees. It allowed the determination of the magnetic depth profile of superconductor thin films [12]. Other key properties of the de Broglie neutron waves, such as contrast variation, weak absorption and isotopic [13] effect give the G A N R technique some advantagos over other surface investigation techniques. In this paper, we present some experimental results of G A N R obtained on bulk substrate, thin films and multilaycrs.

2. Instrumentation Technically, the neutron reflec.io~3 experiment is very simple. "I"ner¢ are two ways of performing the experiment: (a) the reflectivity of a monochromatic neutron beam is measured as a function of the incidence angle 0el, (b) the reflectivity of a fixed incidence angle beam is measured as a function of the neutron wavelength, this method is called th~ time-of-flight technique. Our neutron reflectivity measurements were performed with the latter technique. Fig. 1 shows schematically the experimental set-up of the neutron reflectometer DESIR located at the ORP H E E reactor at the Atomi,: Energy Center of Saclay [14.15]. Accurately, it consists of a sing!e chopper with a wavelength band from 3 to 30 A. Its angular speed defines the repetition rate. The deflection of the polychromatic incident neutron beam is obtained by using four SSNi mirrors in-

M. M~azuet uL / Grazing angle neutron reflectomelt~,

575

Neutron

guide

Chgpper

mental neutron refiectivity curve, one has to consider an anti-reflection homogeneous thin layer at the top of the bulk glass. This surface layer is characterized by an index of refraction n~L (or neutron scattering length density P b ~ l - 1 . 1 × 10 -6 , ~ -z) and a thickness d~l = 50 A. For the bulk substrale the refractive index is n~ (or a neutron scattering length density J~'bsuh = 4.2 × 10-~ ~ - z ) . This surface layer is due to mechanical polishing [16]. T h e high difference between H b , i and .,-]~b,,h indicates that the surface layer is very hydrated [16].

3.2. Thin films: penetralion depth Fig. I. Schematic diagram of the neutron reflectometer DESIR at L~on Brglouin Laboratory-ORPHEE reactor. The glancia~gangle is kepl conslanI (Oq~= 2.2 × l0 "~rad) and the incident neutron beam is !~olyenergetic(). - 3 lu 30 ~,).

eated just before the sample. T h e neutron b e - m reflected frdm the sample surface is detected using a 3He gas X - Y multidetector (128× 128 plxels with a plxel size 1.5 x 1.5 ram2). We use a H c - N e laser beam along the neutron flight path for the initial alignment of the sample (liquid or solid samples). Ex0crlments were performed at a grazing angle 0, of the order of 2.2 x 10 2 tad. The intensity of the specularly reflected beam is recorded versus neutron wavelength or montenrum K.

The absence of any charge or accompanying electric field enabler the neutron to penetrate most materials with relative ease. For illustrating the high penetration depth of neutron waves relative to the X-ray waves, a thila titanium film deposited by thermal evaporation on Borkron glass is studied. The aimed thickness was dTi = 500 A,. The G A N R experiment is carried out at On = 1.50× 10 2 rad. T h e theoretical value of the nuclear scattering length density J//bTi is - 1.95 × 10-0 ~ - z . The neutron reflectivity profile is given by fig. 3. At K < K:, the de Broglie neutron waves are totally reflected. This total reflection phenomenon is imposed by the Borkron substrate

3. Experimental results

3.1. ~ulkmaterial The neutron reflectivity curve of a polished borosilicate glass sample is shown in fig. 2 which represent a decimal logarithmic plot versus momentum K - 2~- gin 011/A. The grazing angle was 00 = 2.5 × 10 2 rad. We discern two regions: the total reflection plateau ( K < K~ = 2"n- sin Oo/,~ c) and the vitreous region (K>~K¢). In this latter region, the experimental reflectivity is always lower than the theoretical one which corresponds to the bulk substrate. For simulating the expert-

.,L

!,

'"-~ooo ,

]

.

g = / 2 ~ slnOolX] (10.2J.1) Fig. 2. Observed GANR profiles flog R) of a borosilieale glass t*) versus tile momentvm K - 2rr sin Or,/~ and the corresponding theoretical (0) and simu{ated ( ) neutron r~flectlvlty profiles. The models used to simulate the reflectivily profiles are shown in the inset.

,~.~. ~(~ltl,~tlt,f tll. / GYtt.7151~,"IIIl.~'/~"IlellttOIl rc]7~'t'lolllcll3'

whose neutron scattering length der, sity is positive (the t h a a i u m possesses a negative neutron scattering length density and thus it cannot satisfy the total reflection relation). For K > K e, fringes are observed. A compari.~on of the experimental data wi~h the theoretical fringes shows that a particular m n m u m at K , = 0.74 x 1 0 - : ,~-~ near the total reflection plateau does not figure in the theoretical profile. This is ~ttributcd to a layer situated between the titanium layer and the bulk glass substrate [17]. The simulation is done by taking a stack of nine layers deposited on the Borkron glass substratc. The top of the titanium layer (zone 1) is gradually contaminated and con.. rains both titanium and other elements whose scattering !cnglh dcnsiiy is positive. Its thickness is around 105 A. Zone 2 is composed of quasipure titanium whose thickness d , is of the orde r of 351) ,~. Zone 3 is a sublaycr less dense than the bulk substrate whose extension is d ~ = 6 3 1 ,~. One can note that the experimental thickness of the contaminated titanium layer found by simulation agrees with the theoretical value, being, respectively, d~!,~ = 455 A against d~th~~ = 500 A. The total probed thickness is then dk, ~= 1086 A. Neglecting the dispersion effect inside the layers, ~he penetration depth L~ is considerably greater than the thickness of the stack d~,,: which is given by L~, = 2 d J O . This gives 7.4 # m .

- ~ --"

~"-

~

plateau

,

•

ii ~25

Q'~O

K=I'2~

-

.......

~i~

]1s

160

20S

sineo/~] (Ig-2~.Z)

Fig. 3. Ofi~er*rcd GANR prPfilcs (Lug R) of qhc ~]~ Ti/fiorosific~lte glass 10) V C ~ I I S the momentum K = 2 ~ :~n Ol,/A and tlle corresponding theoretical (¢,) and simulated (--) neutron reflectivity profiles. The models used to simulate ~fierenecnvity profiles are shown in the inset.

K=[2rr

sinOol~,]

(10"2.,{'1)

Fig. 4. Observed GANR pr~lfiles tlog R) tit the It}all "l'i/bt~r~lsilicate gla~ (e) versus the mnmenlum K - 2~r SillOO/A tnld the corresptmding theoretical (r~} and simulaled ( ) neutron rcflectivity pr~ffiles.The models used lu ~imulalc the r~:fluctivilyprofiles are SfitIWIIill ale inseL 3.3. T h i n flints: o x i d a t i o n effect

The change in the sign of the neutron scattering length density makes the G A N R very sensilive to oxidation and hydrogePation effects. Fig. 4 illustrates this property. The sample studied consists of a thin film titanium layer deposited on to borosilicate glass,. The expected layer thickness is approximately d~" ~- ltl00 A. The corresponding GNI~. curve is given by fin. 4. The simulation shows that we are dealing with a stack on six layers laid down on the massive substrate. A s it is indicated in the inset of the fig, 4, the simulation .~b(z) profile is always positive, this indicated that the titanium is oxidized. Moreover, J b ( z ) decreases gradually from the thin-film-substrate interface to the air-thin-film interface. This suggests that the oxidation phenr.menon decreases when the titanium film grows. The small increase of J t " b ( z ) at the air-titanium-film interlace is due to an atmospheric alteration. The simulation gives a total thickness of 460 A which is less than the expected value, indicating a calibration error during the deposition process. 3.4. Multilayers: i n t e r f a c i a l d i f f u s i o n

We have seen that both the sign and the magnitude of the parameter b change in an irreg-

M. M~azu et aL / Grazing angle neutron rcflet'tometO'

~,ooo ?hdor

o

. . . . . Expdr

~o~o

o

~'2

~o

~.,

o o~O.,o': 06

"

19s

K=[2,'z

3.32

slnOol;t]

(10-2,~.1)

Fig. 5. Observt.d GANR profiles (log R) tit Ih,~ [e(7o ANi-TU ATi)/borosilicate glass multi-bilayer {~) ~ersu~ the momenlum K = 2~ sin 0~/~ and Ihe corresponding theorellcal (o) and simulated I - I tleU[l~ll refleetivity profiles.

ular fashion with the atomic number Z . This property of the neutron scattering amplitude is largely studied; especially in the case of two neighbouring e l e m e n t s such as nickel and titanium. Contrary to titanium, nickel possesses a positive nuclear scattering length density /~'b h~ = + 9 . 4 1 X 10 ~' ,~ 2. For illustrating this effect. a high-refleetivity seleeti,Te mirror bnih of 11) (Ni

577

Ti) bilayers deposited on a borosilicate. T h e expectedoPSeudo-period was A'h~ = 140 ,~ (d,i = dTi = 70 A). As in the previous samp!c~, the total reflection p h e n o m e n o n (fig. 5) occurs, T h e firstorder Bragg diffraction peak and Kiessig interference fringes are observed, T h e neutron specular reflectivity of this multi-bilayer performed at 0 . = 2.2 × l 0 ~" rad. "[he theoretical curve tor which the nickel and titanium layers are expected to be fully pure, dense' and homogeneous is described by a crenel refractive index profile which is very different from the experimental curve. Oscillations with a good contrast are observed in the neutron reflectivity spectrum. T h e simulation yields a pseudo-period A sire = 120 ,~ ,which is less than the theoretical one (A~h~ = 140 A). This difference can be due to errors during the sputtering process or to an interfacial diffusion phenomenon. T h e simulated scattering length densities of nickel and titanium layers are respectively ~ Y b ~~ = + 9 . 4 x 10 ~ ,~ -" and .deb~'~ ' ~ - l . 0 x 10~,~ 2. The simulated nickel neutron scattering density corresponds to that of pure nickel, the simulated titanium neutro~ scattering density is less negative than the pure titanium one. This indicates that there was diffusion of nickel in the titanium layers during t h e spnttering process. oJ

i

i

i

i

.....

'-,,

....

-

I • (b)

az8

K=[2~r sinOolZ] (10-2~-1)

~

a6~

~z

I

K=[21r sinO0/~] (10-2A'1) Fig, t:~.(at Ohsc~'ed GANR profiles (big RI of ale 10(400 ANi 400 .~Ti)/borozilieat e glil~ mulll-bihl!,er ( o ) I,'ersus t he I~lomentu m K = 2"n-sin Oo/~, and the corres~mding.~heorelical (o] and simulated ( ) neulron re flectivlt~,,profiles. (hi Obse r.,ed polarized GANR profiles (log R) of the 10(4~30ANi-40[) ATi)/4-horosillcate glass muhi-bilzycr versus the momentum K = 2~r sin 0JA: o: spin up; and •: spin down.

578

M, M~a~-ael ilL / Grazblg angl~, ncutron rcfleclometo,

3.5. M , Itiluyers: magnetic reflection

To illustrate this effect, a 1 0 ( N i - T i ) / l a y e r / horusilieate glass multilayer was studied. The expected thickness of nickel and titanium layers measured b v a crystal quartz oscillator are d , ~ = d~.m ~ 41~) A. To investigate the overall characteristics of this periodic stack, the monoehromator is first scanned on the onpolarized neutron reflectometer DESlR at 0 n = 2.4 x l0 -~" tad (fig. 6a), As shown in fig. 6a, many Bragg order= were deteeted. Assuming uniform densities and sharp boundaries, the nickel and titanium layers can be considered to be nominally about d ~ = d ~ n = 330 ,~. The simulated value of the mullibilayer period is then Asirn= 660 against Athe= 800 A which is the theoretical value. Taking into account the great difference between the simulated and the theoretical values, this suggests that diffusion has taken place during the sputtering as in the previous example. The simulated neutron scattering length densities are ~/~b~ = +9.4 × 10" ,~.-" and ./fb~[" = - 0 . 5 × 10~ ,~-", respectively. This confirms the diffusion of nickel into titanium. Second, l~ohlri2ed neutron measurements were carried out (fig. 6b). The [ + ] and [ - ] n~utron spin reflectivities are shown in fig. 6b. It should be noted that the [ + ] Bragg peaks are shifted relative to the [ - ] ones. Moreover. the [ + ] spin reflectiv!ty becomes larger than that of the [ - ] spin at the filth-order Bragg position at KB(/~ = 5 ) = 0.51 × 10 -2 ~ - ~ . This is most easily explained by assuming that some interdiffusion occurs between the nickel and titanium layers ~hich is in agreement with the previous unpolarized GANR results. As is indicated above, the critical parametcr~ Q~ = 2 r sin 0o/A~+ and Q~ = 2,,: ~in 0~)/A,~ are different; their "*veratre values are 0.3! × 10 2 .~-i and 0 . 2 7 × l0 -~ ,~-~, respectively. This indicates that ilickel is also magnetic in the thin film structure.

4. Conclusion From a formal point of view, the de Brogiie cold neutron waves behave as electromagnetic waves in the S polarization state. It is then per-

mitted to apFly all the classical optics computation for S electromagnetic waves in neutron op, c s and particularly for stratified media. Due to some key properties of neutrons, the G A N R technique is sensitive to different feat~ es at solid surfaces and interfaces. The simple relation between the refractive index and the chemical composition means that neutron refleetivity profiles probe surface and interfacial structures more directly than light reflectivlty. The irregular variatint, of the neutron scattering amplitude with the atomic number allows the ident~flcatlon of light elements in some heavy compounds witl" much greater certainty. The variation of the neutron scattering amplitude with the mass number allows the identification of isotopes of a given element; especially in the case of hydrogen and deuterium. Then, the neutron refleetometrJ is an excellent probe tool in biology and polymer surface studies. The variation of the sign of the neutron scattering amplitude allows to determine easily the way of the interlaeiai diffusion and the degree of contamination in th~n films and stratified media. The neutron magnetic interaction is also a key property. The polarized neutron refleetometry i~ a good tool for magnetic surface studies in magnetic multilayers and superconductors. It is therefore fortunate that the absorption coefficient of the neutron beam is small and the neutrons are indeed able to penetrate larger samples. Finally, a few previous examples show clearly the capabilities of this new technique for the investigation of surface and interface phenomena.

Acknowledgements The financial support was provided in part by the Comissariat ~t I'Energie Atomique CEA and the Compagnie Industrielle des Lasers CILAS. The authors thank the following people: Dr. B. Farnoux from the Laboratoire Lgon Brillouin, Mr. F. Samuel from the Compagnie lodustrielle des Lasers, Dr. O. Schaerft from the Institut Laue Langevin, Dr. B. Mozer from the National Institute of Standard and Technology and Dr. Coddens from the Laboratoire L~on Brillouin for their invaluable assistance.

M. Mhaz:7 et aL / Grazing ungle net,tron r@qectomeo3,

RefereDe~'s [1] B. Farnoux, Mater, Res. Soc. Syrup. Prec. 166 (Igg0). [2] V.F, Sears, Neutron Optics (Oxford University Press, lY89). T31 M.L. Goldherg and B. Seitz, Phys. Bey. 71 (1947) 295. [41 G.E. Bacon, Neutron Diffract(on (Clarendon. Oxford, 1975). 15] L Lekner, Theory of Reflection (Nijhoff, Dordr¢cht, 1987}. [6] M. morn and E. Wolf, Principles c~f Optics (Pergamon. Oxford. 197(I). [7J F. Abeifis, Ann. Phys. 5 {1951)) 777. [8] M. M~aza, in: Fermi Schno[ Proc, 19Y0-91, Industrial Applicatiuns of Nculrons. to appear. [9] M. Mhaza. J. Opt. Commui~.. submitted. [101 L, Koester and H. Roach. Summary of Neutron Scariering Lengtlls. IAEA Contract 25171RB (191;I).

579

[I I] W.G. Williams. Polarized Neutroil (Clarendon. Oxfe-d. 1~70). [12] G.P, Feleher. B.T. Kampwirth. K.E. Gray and R. Felici. Phys. BeY. L¢lt. 52 (1984) 1539, [151 T.P. Russ¢I. A. Karim, A. Mansuur and G.P, Fclcher, Macromolecules 21 (1988} 1890. |14l B. Faraoux. Rapport d't~ti~it~ du Lahoratolre Ldon Briltouin, 11~88-1989. [15] M. M~aza, C, S¢lla, B. Famous. P. Samuel and P. Trocellier, Springer Series (Springer, Berlin, 1991-92), to he published, [lb] M M~a~a, C. Sell:,. F. Sgmuel, B. Farnoux and P. Tr~eelllar, L Opt. Commun., submitted, [17] M. M-~aza, C. Selia, F. Wahiing, F. Samuel. B. Famous. M. KfiabrJuzhi, M. Gnlo/i and G. FOUIeL J. Appl. Phys. ( [ 991 ), Io bU published.