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Neutron scattering measurements of interdiffusion inamorphous Si/Ge multilayers

Chr. Janot, A. Bruson, G. Marchal

To cite this version:Chr. Janot, A. Bruson, G. Marchal. Neutron scattering measurements of interdiffu-sion in amorphous Si/Ge multilayers. Journal de Physique, 1986, 47 (10), pp.1751-1756.�10.1051/jphys:0198600470100175100�. �jpa-00210370�

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Neutron scattering measurements of interdiffusion in amorphous Si/Gemultilayers

Chr. Janot (+ ), A. Bruson (+ + ) and G. Marchal (+ + )

(+ ) Institut Laue-Langevin, 156 X, 38042 Grenoble Cedex, France(+ + ) Physique du Solide, BP 239, 54506 Vand0153uvre Cedex, France

(Requ le 3 avril 1986, accept6 le 13 juin 1986)

Résumé. - Des structures multicouches ont été obtenues en évaporant successivement des films de silicium etde germanium amorphes, avec des périodes allant de 80 à 100 Å. Le coefficient d’interdiffusionD de Si/Ge a été déterminé en mesurant, en fonction des températures et des temps de recuit, l’intensité desréflexions satellites d’un faisceau de neutrons, liées à la modulation périodique du contraste. Dans l’intervalleT = 620 - 720 K, D varie comme 6,34 x 10-3 exp (- 2,35 eV/kT) cm2 s-1.

Abstract. - Multilayered amorphous Si/amorphous Ge films with a periodicity of 80 to 100 Å have beenobtained using UHV evaporation techniques. The interdiffusion coefficient D of this system was determinedby measuring the intensity of the neutron (000) forward scattering satellites arising from the modulation, as afunction of annealing temperature and time. The temperature dependence of D in the range 620-710 K isdescribed by D = 6.34 x 10-3 exp (- 2.35 eV/kT ) cm2 s-1.

J. Physique 47 (1986) 1751-1756 OCTOBRE 1986,

ClassificationPhysics Abstracts66.30 - 61.40 - 64.75 - 81.15

1. Introduction.

Atomic diffusion in amorphous semiconductors hasonly been studied very recently. This includes impu-rity diffusion [1] and the diffusion of the covalentrandom network formers themselves [2, 3]. In thelatter case the main problem to be overcome arisesfrom unfavourable competition between diffusivityand the thermal stability of the amorphous phase.The most sensitive technique available for measu-

ring diffusivities makes use of multilayered films.This technique, originally developed for crystallinematerials [4-6] has also been applied successfully tomeasure diffusivities in amorphous alloys [7-11]. Themultilayered samples are made by depositing thinfilms of two materials in an alternating sequence ona glass substrate. This makes a multilayer periodic ina direction perpendicular to the plane of the films,with a d-spacing equal to the thickness of one

bilayer. Neutrons or X-rays of wavelength A incidenton a multilayer are reflected at angles 0 given by theBragg relation 2 d sin 0 = nA where n is the order ofreflection. Annealing the multilayers at differenttemperatures for different times results in the layersflowing into each other thus relieving contrast effectsand producing a decay of the reflection intensity.The decay of the intensity I is related to theinterdiffusion coefficient 15 by [5] :

Reported data have been mainly obtained throughX-ray approaches so far, which limits the repeatlength of the multilayered films to a few nm in orderto have acceptable 0 reflection angles with theavailable X-ray wavelength as obtained from anodetubes. This technique has been used to measurediffusivities in the Si/Ge amorphous system [2] inwhich the interdiffusion was found to be relativelyrapid, in complete disagreement with Raman measu-rements on hydrogenated multilayered films [12]. Inthe Raman alternative the diffusion mixing of thelayers is determined by the relative contributions tothe spectra of the remaining pure amorphous Si andGe and of the diffusion induced Si-Ge mixture. In

special cases, the diffusion mixing can also bemeasured via Mossbauer spectroscopy [13].However, as shown by Cook et al. [5], when

measuring interdiffusion coefficients in multilayers,one has also to cope with the dependence of

diffusivity on the repeat length of the compositionmodulation. To avoid, or at least minimize, spuriouseffects due to very sharp composition gradients it isadvisable to measure b with relatively thick layers ;cold neutrons with longer wavelenghts than theusual X-ray radiations have to be thought of as aninteresting alternative to obtain the diffusion decayof the reflection intensity.The neutron technique has been previously used

[3] with amorphous Si-Ge multilayers having a d-spacing of 200 A. In the investigated temperature

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198600470100175100

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range (400-600 K) the diffusivity happened to be tooslow to be observed. However, evidence was obtai-ned for a structural relaxation mechanism probablyrelated to a redistribution of compressed and expan-ded small volumes resulting in an overall densitica-tion of the near interface regions of the materials.

In the present study, the sensitiveness to diffusionof the intensity decay I ( t ) has been increased withrespect to our preliminary study by reducing d toabout 80 A. The annealing temperature range hasalso been moved to higher values (620-710 K) at

which measurable V coefficients were anticipated.

2. Sample preparation, experiments and results.

The amorphous Si-Ge multilayers were made bydepositing thin films of pure Si and pure Ge on flatglass substrate, kept at the liquid nitrogen tempera-ture, by the vacuum deposition technique. Germa-nium and silicon were placed in graphite boats andwere evaporated in succession by electron beamguns. The pressure during the evaporation processwas about 2 x 10-8 torr. The thickness of the filmswas measured and monitored with two independentquartz oscillators (The frequency of the crystalschanges linearly with the mass deposited on the

, transducer). The oscillators actuated also a shutterthrough an automatic control unit, thereby closingand opening it between crucibles and substrates atpreset values. The quartz crystals were calibrated,with respect to film thickness, using a Tolanskymultiple beam interferometer. A good reproducibi-lity in the layer thickness was achieved within a fewpercent by keeping the evaporation rate fairly low, atypical value being 1 Á s- 1. At low evaporationrates the films can be contaminated with some

oxygen and carbon. The composition of differentsections of a multilayer were determined by Augerspectroscopy and the contamination was, in general,found to be less than 1 %. A slight distribution ofthicknesses of the bilayers is thus unavoidable butlimited to about 2 to 3 A for an average thickness of100 A. These distribution in anyway out of thedetection limits of most of the microanalyticalmethods currently used for thin films and/or depthprofile analysis [14] : Rutherford BackscatteringSpectrometry gives information over 30 to 104 A,Secondary Ion Mass Spectrometry is reliable downto 5 A, etc... In fact, there is not too much inconve-nience in that since the chemical state of the as

prepared samples is well defined (pure layers of Siand Ge in succession) and the initial diffractionproperties of the multilayer are taken as a referencestate for any changes induced by thermal treatments.Each sample consists of 50 identical bilayers, eachbilayer being made of one Ge and one Si amorphousfilm of different thickness, in order to open the

possibility of measuring the second order along withthe first order satellites about the (000) neutronscattered beam. It is indeed worth remembering thatfor perfect multilayered material with equalthickness of the Ge and Si films all even orders ofreflection would be absent, as indeed observed in

our previous work [3] and which may be a furthertest for the reliability of the deposition parameters.Neutron scattering from these samples was perfor-

med using the small angle neutron scattering diffrac-tometer D17 at the Institut Laue-Langevin (Greno-ble), with a cold neutron beam monochromatized ata wavelength of 10 A. The scattered neutrons arecollected on a large two dimensional multidetector(64 x 64 cm) , with an angular resolution of 1/10deg., which allows 0-2 0 measurements to be carriedout by simply rotating the sample with respect to theincident beam. A typical « 0-2 0 scan » is shown infigure 1 for the first order reflection on a samplewhich was supposed to be made of 60 A Si/20 A Gebilayers. The total accumulation time correspondingto the picture is of the order of one hour. The displaygives a view of the 2D-multidetector with the thirddimension used for intensity in each counting cell.Remnants of the direct beam can be seen on the

right-hand side of the picture.The main experimental parameters which are

obtained here are :

- a signal to background ratio of 1W at themaximum of the reflection ;- a measured reflectivity in the first order satel-

lite equal to about 6 % ;- the angular position of the maximum reflection

which, in the present example of figure 1, has beenfound at 2 0 = 6.04 ° ( 6 = 3.02 ° ) corresponding toa d-spacing of 94.7 A ;

Fig. 1. - Typical ( 0 - 2 8 » neutron scan of the firstorder reflection on a Si/Ge amorphous multilayer sample.a) 3D representation of intensities measured on the 2Dmultidetector of D17 (ILL). b) Regrouped data andGaussian fit used to calculate the integrated intensity.

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- the measured full width at half maximum forthe first order satellite is A( 2 0 ) = 0. 17

*

whichcould correspond to d-spacing spread over

5 A (~ 5 %) between 92 and 97 A.The second order satellite is less easily measured

but still visible as examplified in figure 2 whichshows the result of a 0 scan, including a small part ofthe large angle side of the first order reflection. Thenoisy background now amounts to about 1/50 of thereflection signal. The measured reflectivity in thissecond order satellite is only 0.03 % (the intensityscale of the Figs. 1 and 2 are in a ratio of 200).

Fig. 2. - Typical « 0 - 2 0 >> neutron scan of the secondorder reflection. Same representation as in figure la butwith an intensity scale expanded by a factor of 200 and adifferent position of the detector (distance to sample andangular position).

As the geometrical reproducibility of the measure-ment lay-out happened to be very critical, the decayof the integrated intensity of the first order satelliteas a function of annealing time for different tempera-tures was measured in situ by keeping the sample ina furnace on the diffractometer during the wholetime of the experiment. Once the temperature hadbeen set at the desired value by a controller system,spectra accumulated over 5 min were then recordedevery hour or so at a fixed 0 position correspondingto the maximum reflectivity and with a resolutionAA/A limited to 10 %. The weak point of theseneutron in situ measurements is that in line characte-rization during thermal treatments are made impossi-ble.As already explained [3], the decay law is expected

to follow the equation

Figure 3 shows the time dependence of the « diffu-

sion mixing» 15t = - dB 1 n [I ( t ) / I (0)] for81Ttwo different samples annealed at 410 °C and 400 °Crespectively. Very partial data corresponding to asecond order peak are also shown. Then the samplefirst annealed at 410 ’C-was successively submitted

Fig. 3. - Example of time dependence of the diffusionmixing during the first annealing of multilayers.

to diffusion treatments at 418 °C, 436 °C and finallyat 447 °C. The corresponding « diffusion mixing »curves are shown in figure 4.A certain amount of non-linearity, most likely

caused by structural relaxation [3, 8] is observed infigure 3 for the early part (2 to 4 hours) of the firstanneal after which the behaviour becomes linear.Initial non-linearity is absent for the second, third,etc... anneals of a given sample (Fig. 4). Finally forannealing times between 10 and 20 hours, thediffusion mixing again departs drastically from linea-rity and saturates to values of the order of

20 - 30 x 10- 16 CM2 corresponding to diffusion pene-tration of about 10 A (given by(Z2) = 2 Dtmax [3]). It is finally worth mentioningthat the multilayer d-spacing significantly shrinks asdiffusion mixing proceeds. For example, sample 3

Fig. 4. - Time dependence of the diffusion mixing for thesame sample annealed successively at increasing tempera-tures.

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had an initial real d of 90.1 A which successivelyreduces to 88.6 A, 86.8 A, 85.2 A and 80.4 A afterdiffusion mixing at 410, 418, 436 and 447 °C respecti-vely. It is difficult to say if these shrinking effectsoccur progressively during the whole annealing treat-ment at a given temperature. As the total thicknessreductions observed are of the order of a few A only,partial reduction between two annealed states wouldbe anyhow beyond the detection limit of the measu-rement. As explained later, samples annealed at

447 °C are partially crystallized and thus it is reasona-ble to think that crystallization contributes to theshrinking effects observed at this temperature. Simi-lar partial crystallization contributions cannot be

completely ruled out for thermal treatments at lowertemperatures even if they have not been observed atsuch temperatures in preparatory studies to the

present neutron experiment, using resistivity measu-rements, high angle X-ray diffraction and electronmicroscopy. The weak point is obviously that

checking the absence of crystallization at a giventemperature on samples suitable for X-rays, electronmicroscopy or resistivity measurements in not anunquestionable proof for no crystallization in sam-ples made suitable for neutron scattering experi-ments (different thicknesses, geometries and subs-trate). But the problem cannot be easily bypassed.The interdiffusivities b were determined for each

temperature from the slopes of the intermediatelinear parts of the plots in figures 3 and 4. Theresults are listed in table I and illustrated by anArrhenius plot on figure 5 (continuous line).At 447 °C, the diffusion mixing is stopped very

quickly after only a very brief annealing time and themaximum atomic displacements remain short range.Thus the diffusion coefficient given in table I for thistemperature although quite consistent with the otherdata, should only be considered as a reasonableestimate, determined from a very reduced data set(see Fig. 4).The reported value of 1) at 350 °C might be also

questioned since it was not measured in situ. Indeeddiffusion is very slow at this temperature and signifi-cant decay of the reflection intensity requires verylong annealing times which are not compatible withallocated time on a neutron beam !. Again the1) value obtained is consistent with the whole data

set and also agrees very well with our previous X-raydetermination [3].

3. Discussion and conclusion.

3.1 INITIAL REFLECTIVITY OF THE MULTILAYERS.

- According to the kinematical theory, the neutronreflectivity of a multilayer for odd order is given by[15]

where N is the total number of bilayers (hereN = 50) and f l, f2 are neutron scattering amplitudedensities for the two materials (fsi = 3.64 x1010 cm- 2 and f Ge = 2.14 x 1010 cm- 2 in their crys-talline states).The above expression is valid only for low reflecti-

vity. For higher reflectivities one has to take dynami-cal effects into account to obtain

which reduces to the first equation in the limit whenthe argument of tanh is small. When applied to themultilayers of the present study the two equationsgive 7? = 0.13 in the firs order reflection. Sinusoidalrather than square modulation results in differentreflectivities given by

which would produce Rsin = 0.08 in the first orderfor the samples of the present work.As already said measured data are in the range of

ReXP = 0.06 for the first order and the second orderreflectivity (3 x 10- 4 ) is about 10 times smallerthan the 0.06/16 value expected from 7? equati6nb.

Thus, despite of the fact that the d-spacing appearsto be constant (within about 5 %) through the wholesample, the layer profiles have an obvious tendencyto be sinusoidal rather than abruptly square. Irregu-larities or « roughness » in the surface of the layersmay also be suspected since the first order reflectivityis even below the lower theoretical estimation byabout 2 % (6 % vs. 8 % for sinusoidal modulation)!

Table I. - Diffusion coefficients obtained from least-square fits on data shown on figures 3 and 4 (X2 given in thetable). The last column gives the nominal thickness of the Si/Ge films respectively (in A).

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Finally it seems possible to make almost perfectmirrors orland monochromators with amorphousSi/Ge multilayers since, after all, the first order

reflectivity would have reached unity with 200

bilayers instead of 50. Furthermore, these multi-layers are very stable even at temperatures of theorder of 200 °C at which the intensity decay in firstorder would be only about 1 % for annealing time aslong as 1013 seconds (one million years !) accordingto the diffusion law discussed below.

3.2 DIFFUSION PLATEAU. - As clearly shown infigures 3 and 4, diffusion stops after a certain

annealing time at any temperature. For diffusionmixing at 350, 400, 410 and 418° C the plateaucorresponds to Dt =:::: 20 x 10-16 cm2 and to

Dt =z 30 x 10-16 cm2 at 436 °C which can be expres-sed in terms of a mean square diffusion penetration9 (Z2) 1/2 : 11 A [3]. Remembering that, accor-ding to table I, the corresponding samples are madeof 20 A Ge films squeezed between significantlythicker Si films, such a 10 A limit for atomic

displacements suggests that a planar growth of a Ge-Si alloy proceeds from each interface, thus consu-ming the Ge layers. The true composition of thegenerated Ge-Si alloys depends slightly on the

annealing temperature and can be estimated, fromthe contrast loss/reflectivity decay relation, to corres-pond to Geo.9 Sio and Geo.83 Sio.17 after diffusion at400 °C and 436 °C respectively. Given that the

diffusivity in crystalline Si is many orders of magni-tude below that in crystalline Ge, it may be not sosurprising that diffusion of Si into Ge, even in theiramorphous states, results in D going to zero quiteabruptly. Again, as already mentioned, partial crys-tallization effect cannot be completely ruled out.The existence of linear parts in the diffusive beha-viour (Fig. 3 and 4) gives evidence that 1) remainsconstant for a certain time and suggests that there isa concentration threshhold for 1) starting to

decrease.The very low diffusion plateau observed at 447 °C

is obviously of a different nature and can easily beinterpreted as resulting from the crystallization ofthe Ge films. Amorphous germanium is known tocrystallize between 445 and 450 °C [16, 17] whileamorphous silicon is stable up to about 600 °C [17].Thus, annealing the multilayers at 447 °C transformsthe samples into amorphous Si/crystalline Ge filmsafter an ultimate very short diffusion stage (Fig. 4).As diffusivities of Si or Ge in crystalline Ge would beat least 100 times smaller than the one measured inthe present work a new strong stability of the

multilayer interfaces is induced by this crystallizationstage. Actually, the plateaus must be considered ascorresponding to diffusivities below the detectionlimit of the present method.

3.3 THE MEASURED DIFFUSION LAW. - The diffu-sion data listed in table I and illustrated by figure 5can be described by an Arrhenius law with anactivation energy Ea = 2.35 eV and a pre-exponen-

tial factor Do = 6.34 x 10- 3 cm2 S- I (within

X 2 = 0.993 of a least square fit).The interdiffusivities measured in the present

work are about 3 orders of magnitude slower thanthe one deduced from X-ray data obtained byProkes et al. [2] (Fig. 5). There is also a significantdisagreement with Do and Ea values proposed byPersans et al. [12] from Raman spectroscopy investi-gations, as clearly pictured in figure 5. It is probablysignificant that Prokes et al. prepared their samplesusing an ion beam sputtering system instead of ourelectron-gun crucible evaporation technique, whilethe data of Persans et al. refer to hydrogenatedmultilayered films. In both cases residual argonand/or hydrogen might be responsible for the diffusi-vity enhancement.Comparison of the present data with diffusivities

in crystals is also very interesting [18]. Self-diffusionor germanium diffusion in crystalline silicon corres-ponds -to Do :-- 1()3 CM2 s-1

1 and EA = 5 eV whichgives very small diffusivities of the order of

10- 33 CM2 s-1 1 when extrapolated down toT = 700 K. Self-diffusion in crystalline Ge is muchfaster, with Do!= 10 cm2 s-1

1 and Ea 3 eV, and

diffusivities extrapolate down to 0.3 x 10- 20 CM2 s-1 1

at 700 K i.e. only one or two orders of magnitudebelow the diffusivities measured in the present work(see Fig. 5).

Fig. 5. - Temperature dependence of the interdiffusivity1) measured in the present work (-) :Do = 6.34 x 10- 3 cm2 s-1 and Ea = 2.35 eV. Other Arrhe-nius plots correspond to : - Self diffusion in crystallineGe (-.-) : Do =10 cm2 s-1, Ea = 3 eV. - Interstitialdiffusion of oxygen in crystalline Ge (......) :Do = 0.17 cm2 s-1, E. = 2.54 eV. - Interdiffusion mea-sured in multilayers Si/Ge using Raman spectroscopy [12](- - -) : Do = 106 cm2 s-1, E. = 3.3 eV. - Interdiffu-sion measured in Si-Ge amorphous multilayers using X-ray reflection (-----) [2] : Do = 1.07 x 10- 6 CM2,Ea =1.b eV.

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A more fruitful comparison apparently involvesdiffusion of « big » interstitials in a bond-centeredconfiguration [18]. The most famous example is

probably oxygen interstitially dissolved in silicon,which diffuses according to the law D (cm 2S- 1) =0.17 exp ( - 2.54 eV/kT ) not too far indeed fromthe interdiffusion law measured in the present workas evidenced in figure 5. The two diffusion laws havein common a point corresponding to 676 K and haveslightly different slopes.

It is probably worth to point out that the activationenergy obtained in the present work might be

suspected to be some sort of a lowest limit, on theground that the composition dependance of D is

strong and that the same sample has been used tosuccessively measure D at 410, 418 and 436 °C.

In conclusion, we observed :

(i) saturation of the diffusion mixing in plateaustages, (ii) stopping of the diffusion mixing aftercrystallization of the Ge films and (iii) a diffusionlaw similar to that of big interstitials in crystalline

silicon. It is thus conceivable that the interdiffusionprocess in amorphous Ge/amorphous Si multilayersis dominated by non-substitutional jumps of Siatoms into the Ge films using the pre-existing locallyexpanded volumes which are normal features in thestructure of a random continuous network. Thediffusion of Si into Ge being non-substitutional hasnot to be compensated by jumps of Ge atoms intothe Si films. Thus the Ge layers are progressivelyconsumed by the previously invoked planar growthof a Ge-Si alloy which proceeds from interfaces andseems to stop when the available free volume hasbeen filled up. It would be very interesting indeed toconfirm these assumptions through direct observa-tions using cross-sectional transmision electron

microscopy.

Acknowledgments.We gratefully acknowledge the Institut Laue-Lange-vin for allocation of beam time (experiment number6-14-90).

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