Neutron scattering measurements of interdiffusion in amorphous Si/Ge multilayers

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Neutron scattering measurements of interdiffusion in amorphous 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�

Neutron scattering measurements of interdiffusion in amorphous ^Si/Ge multilayers

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 et de germanium amorphes, ^{avec des} périodes allant de 80 à 100 Å. Le coefficient d’interdiffusion

D de Si/Ge a été déterminé en mesurant, ^en fonction des températures ^{et des} temps ^de recuit, l’intensité des réflexions satellites d’un faisceau de neutrons, liées ^à la modulation périodique ^du contraste. Dans l’intervalle T

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 been}

obtained using ^UHV evaporation techniques. The interdiffusion coefficient D of this system ^{was determined} by measuring ^the intensity ^{of the neutron} (000) ^forward scattering satellites arising ^{from the} modulation, ^{as a} function of annealing temperature ^{and time. The} temperature dependence ^{of D in the} range 620-710 ^{K is} described by D

^{6.34 x 10-3} exp (- ^2.35 eV/kT ) ^{cm2 s-1.}

Classification

Physics ^Abstracts

66.30

61.40

64.75

81.15

1. Introduction.

Atomic diffusion in amorphous semiconductors has

only been studied very recently. This includes impu- rity ^diffusion [1] and the diffusion of the covalent random network formers themselves [2, 3]. ^{In the}

latter case the main problem ^{to be overcome arises}

from unfavourable competition ^between diffusivity

and 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 crystalline

materials [4-6] has also been applied successfully ^to

measure diffusivities in amorphous alloys [7-11]. ^The multilayered samples ^{are made} by depositing ^thin

films of two materials in an alternating ^{sequence on}

a glass substrate. This makes ^a multilayer periodic ⁱⁿ

a 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 ^incident

on a multilayer ^{are reflected at} angles 0 given by ^the Bragg relation 2 d sin 0

nA where n is the order of reflection. Annealing ^the multilayers ^{at different} temperatures for different times results in the layers flowing into each other thus relieving ^{contrast effects}

and producing ^a decay of the reflection intensity.

The decay ^{of the} intensity I is related to the interdiffusion coefficient 15 by [5] :

Reported data have been mainly ^obtained through X-ray approaches ^{so far,} which limits the repeat length ^{of the} multilayered ^{films to a few nm in order}

to have acceptable 0 reflection angles ^{with the}

available X-ray wavelength ^as obtained from anode tubes. This technique has been used to measure

diffusivities in the Si/Ge amorphous system [2] ⁱⁿ

which the interdiffusion was found to be relatively rapid, ⁱⁿ complete disagreement with Raman ^measu- rements on hydrogenated multilayered ^films [12]. ^In

the Raman alternative the diffusion mixing ^{of the} layers is determined by the relative contributions to the spectra ^{of the} remaining pure amorphous ^{Si and}

Ge and of the diffusion induced Si-Ge mixture. In

special ^{cases, the diffusion} mixing ^{can also be}

measured 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} composition

modulation. To avoid, ^{or at least} minimize, spurious

effects due to very sharp composition gradients ^{it is}

advisable to measure b with relatively ^thick layers ;

cold neutrons with longer wavelenghts ^{than the}

usual X-ray radiations have to be thought ^{of as an} interesting alternative to obtain the diffusion decay

of 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

1752

range (400-600 K) ^the diffusivity happened ^{to be too}

slow to be observed. However, ^{evidence was obtai-} ned for a structural relaxation mechanism probably

related 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 diffusion of the intensity decay ^I ( t ) has been increased with respect ^{to our} preliminary study by reducing ^{d to}

about 80 A. The annealing temperature range has also 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} by depositing ^thin films of pure Si and pure Ge ^on flat

glass substrate, kept ^{at the} liquid nitrogen tempera- ture, by ^{the vacuum} deposition technique. ^Germa-

nium and silicon were placed ⁱⁿ graphite ^{boats and}

were evaporated in succession by electron beam guns. The pressure during ^the evaporation ^process

was about 2 x 10-8 torr. The thickness of the films

was measured and monitored with two independent quartz oscillators (The frequency ^{of the} crystals changes linearly ^{with the mass} deposited ^{on the}

,

transducer). The oscillators actuated also a shutter

through ^an automatic control unit, thereby closing

and opening it between crucibles and substrates at

preset values. The quartz crystals ^were calibrated,

with respect ^{to film} thickness, using ^a Tolansky multiple ^beam interferometer. A good reproducibi- lity ^{in the} layer ^{thickness was} achieved within a few percent by keeping ^the evaporation ^rate fairly low, ^a typical ^value being 1 Á s- 1. ^{At low} evaporation

rates the films can be contaminated with some

oxygen and carbon. The composition of different sections of a multilayer ^were determined by Auger spectroscopy and the contamination _was, in general,

found to be less than 1 %. A slight distribution of thicknesses of the bilayers is thus unavoidable but limited to about 2 to 3 A for an average thickness of 100 A. These distribution in anyway ^out of the detection limits of most of the microanalytical

methods currently ^{used for thin films and/or} depth profile analysis [14] : Rutherford Backscattering Spectrometry gives information over 30 to 104 A, Secondary ^{Ion Mass} Spectrometry is reliable down to 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 Si}

and Ge in succession) ^{and the} initial diffraction

properties ^{of the} multilayer ^{are taken as a reference}

state for any changes ^induced by ^thermal treatments.

Each sample consists of 50 identical bilayers, ^each bilayer being ^{made of one Ge and one Si} amorphous

film of different thickness, ^{in order to} open the

possibility ^of measuring the second order along ^with

the first order satellites about the (000) ^neutron

scattered beam. It is indeed worth remembering ^that

for perfect multilayered material with equal

thickness of the Ge and Si films all ^even orders of reflection would be absent, ^as indeed observed in

our previous ^work [3] and which may be ^a further

test 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 at a wavelength ^{of 10} A. The scattered neutrons are

collected on a large ^two dimensional multidetector

(64 ^{x 64} cm) , ^{with an} angular resolution of 1/10 deg., which allows 0-2 0 measurements to be carried

out by simply rotating ^the sample ^with respect ^{to the} incident beam. A typical ^{« 0-2 0 scan » is shown in} figure 1 for the first order reflection on a sample

which was supposed ^to be made of 60 A Si/20 ^{A Ge} bilayers. The total accumulation time corresponding

to the picture is of the order of one hour. The display gives ^a view of the 2D-multidetector with the third dimension 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 the}

maximum 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 been}

found at 2 0 ⁼ 6.04 ° ( 6 ⁼ 3.02 ° ) corresponding ^to

a d-spacing ^{of 94.7} A ;

Fig. ^1.

Typical ^{( 0 - 2 8 » neutron scan of the first}

order reflection on a Si/Ge amorphous multilayer sample.

a) ^3D representation of intensities measured on the 2D multidetector of D17 (ILL). b) Regrouped ^{data and}

Gaussian fit used to calculate the integrated intensity.

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

^which

could 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 which}

shows the result of _{a 0 scan,} including ^{a small} part ^of

the large angle side of the first order reflection. The

noisy background ^now amounts to about 1/50 ^{of the}

reflection signal. The measured reflectivity ^{in this}

second order satellite is only ^{0.03 %} (the intensity

scale of the Figs. 1 ^{and 2 are in a ratio of} 200).

Fig. ^2.

Typical ^{« 0 - 2} 0 >> neutron scan of the second order reflection. Same representation ^{as in} figure ^{la but}

with an intensity ^scale expanded by ^a factor of 200 and a

different position of the detector (distance ^to sample ^and angular position).

As the geometrical reproducibility ^{of the measure-}

ment lay-out happened ^to be very critical, ^the decay

of the integrated intensity of the first order satellite

as a function of annealing time for different tempera-

tures was measured in situ by keeping ^the sample ⁱⁿ

a furnace ^on the diffractometer during ^{the whole}

time of the experiment. ^{Once the} temperature ^had been set at the desired value by ^a controller system, spectra accumulated over 5 min were then recorded every hour ^{or so at a} fixed 0 position corresponding

to the maximum reflectivity ^{and with a resolution} AA/A ^{limited to} 10 %. The weak point ^{of these}

neutron 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)] for _81T

two different samples ^{annealed at 410 °C and 400 °C} respectively. Very partial ^data corresponding ^{to a}

second order peak ^are also shown. Then the sample

first annealed at 410 ’C-was successively ^submitted

Fig. ^3.

Example ^{of time} dependence of the diffusion

mixing during ^{the first} annealing ^of multilayers.

to diffusion treatments at 418 °C, ^{436 °C and} finally

at 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 in

figure ^{3 for the} early part (2 ^{to 4} hours) of the first anneal after which the behaviour becomes linear.

Initial non-linearity is absent for the second, third,

etc... anneals of ^a given sample (Fig. 4). Finally ^for annealing times between 10 and 20 hours, ^the

diffusion 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 mentioning}

that the multilayer d-spacing significantly ^{shrinks as}

diffusion mixing proceeds. ^For example, sample ³

Fig. ^4.

^Time dependence of the diffusion mixing ^{for the}

same sample ^annealed successively ^at increasing tempera-

tures.

1754

had an initial real d of 90.1 A which successively

reduces to 88.6 A, ^86.8 A, ^{85.2 A and 80.4 A after}

diffusion mixing ^at 410, 418, 436 ^{and 447 °C} respecti- vely. ^It is difficult to say if these shrinking ^effects

occur progressively during ^{the whole} annealing ^treat-

ment at a given temperature. As the total thickness reductions observed are of the order of ^a few A only, partial ^{reduction between two annealed states would}

be 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 the

shrinking ^{effects observed at this} temperature. ^Simi-

lar partial crystallization contributions cannot be

completely ^{ruled out} for thermal treatments at lower

temperatures ^{even if} they ^{have not been observed at}

such temperatures ⁱⁿ preparatory ^{studies to the} present ^neutron experiment, using resistivity ^measu-

rements, high angle X-ray diffraction and electron

microscopy. ^{The weak} point ^is obviously ^that checking the absence of crystallization ^{at a} given

temperature ^on samples ^{suitable for} X-rays, ^electron microscopy ^or resistivity measurements in not an

unquestionable 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} intermediate linear parts ^{of the} plots ⁱⁿ figures 3 and 4. The results are listed in table I and illustrated by ^an

Arrhenius plot ^on figure ⁵ (continuous line).

At 447 °C, ^{the diffusion} mixing ^is stopped very

quickly ^after only ^a very brief annealing time and the maximum atomic displacements remain short range.

Thus the diffusion coefficient given in table I for this temperature although quite consistent with the other

data, ^should only be considered as a reasonable

estimate, 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. Indeed diffusion is very ^{slow at this} temperature ^and signifi-

cant decay ^{of the} reflection intensity requires very

long annealing times which are not compatible ^with

allocated time on a neutron beam !. Again ^the 1) value obtained is consistent with the whole data

set and also agrees very well with ^our previous X-ray

determination [3].

3. Discussion and conclusion.

3.1 INITIAL REFLECTIVITY OF THE MULTILAYERS.

- According ^to the kinematical theory, ^{the neutron} reflectivity ^{of a} multilayer for odd order is given by [15]

where N is the total number of bilayers (here

N

50) ^and f l, f2 ^{are neutron} scattering amplitude

densities for the two materials (fsi ^{= 3.64 x}

1010 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 when the argument of tanh is small. When applied ^{to the} multilayers ^{of the} present study ^{the two} equations give 7? ⁼ 0.13 in the firs order reflection. Sinusoidal rather than square modulation results in different reflectivities given by

which would produce Rsin = 0.08 in the first order for 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 order

reflectivity (3 ^x 10- 4 ) is about 10 times smaller than the 0.06/16 ^value expected ^from 7? ^equati6nb.

Thus, despite of the fact that the d-spacing appears to be constant (within ^{about 5} %) through ^{the whole} sample, ^the layer profiles ^{have an obvious} tendency

to be sinusoidal rather than abruptly square. Irregu-

larities or « roughness ^» in the surface of the layers

may also be suspected since the first order reflectivity

is ^even below the lower theoretical estimation by

about 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 the}

table). The last column gives the nominal thickness of ^the Si/Ge films respectively (in A).

Finally ^{it seems} possible ^to make almost perfect

mirrors orland monochromators with amorphous

Si/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 the} order of 200 °C at which the intensity decay ^{in first}

order would be only ^{about 1 % for} annealing ^{time as} long ^{as 1013 seconds} (one million years !) according

to the diffusion law discussed below.

3.2 DIFFUSION PLATEAU.

As clearly ^{shown in} figures ^{3 and 4, diffusion} stops ^{after a certain} annealing ^{time at} any temperature. For diffusion

mixing ^at 350, 400, ^{410 and 418° C the} plateau corresponds ^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 penetration

9 (Z2) ^{1/2 : 11 A [3].} Remembering ^{that, accor-} ding ^{to table} I, ^the corresponding samples ^{are made}

of 20 A Ge films squeezed ^between significantly

thicker 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 the} generated ^Ge-Si alloys depends slightly ^{on the} annealing temperature ^{and can be} estimated, ^from

the contrast loss/reflectivity decay ^{relation, to corres-} pond ^to Geo.9 Sio and Geo.83 Sio.17 after diffusion at

400 °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 so}

surprising that diffusion of Si into Ge, ^{even in their} amorphous ^states, results in D going ^{to zero} quite abruptly. 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) remains constant for a certain time and suggests that there is

a 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 ^be interpreted ^as resulting ^{from the} crystallization ^of

the Ge films. Amorphous germanium ^{is known to} crystallize between 445 and 450 °C [16, 17] ^while amorphous silicon is stable up ^to about 600 °C [17].

Thus, annealing ^the multilayers ^{at 447 °C transforms}

the samples ^into amorphous Si/crystalline ^{Ge films}

after an ultimate very short diffusion stage (Fig. 4).

As diffusivities of Si or Ge in crystalline Ge would be at least 100 times smaller than the ^one measured in the present ^{work a new} strong stability ^{of the} multilayer interfaces is induced by ^this crystallization stage. Actually, ^the plateaus ^{must be} considered ^as

corresponding ^to diffusivities below the detection limit of the present ^method.

3.3 THE MEASURED DIFFUSION LAW.

The diffu- sion data listed in table I and illustrated by figure ⁵

can be described by ^an Arrhenius law with an

activation 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 than the one deduced from X-ray ^{data obtained} by

Prokes et al. [2] (Fig. 5). There is also a significant disagreement ^with Do ^and Ea ^values proposed by

Persans et al. [12] from Raman spectroscopy ^investi- gations, ^as clearly pictured ⁱⁿ figure ^{5. It is} probably significant that Prokes et al. prepared ^their samples using ^{an ion beam} sputtering system ^{instead of our} electron-gun ^crucible evaporation technique, ^while

the data of Persans et al. refer to hydrogenated multilayered films. In both cases residual _argon and/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-diffusion

or germanium diffusion in crystalline ^{silicon corres-} ponds ^-to Do :-- 1()3 CM2 s-1 ¹ and EA ^{= 5 eV which} gives very small diffusivities of the order of

10- 33 CM2 s-1 ¹ when extrapolated ^{down to}

T ⁼ 700 K. Self-diffusion in crystalline Ge is much

faster, ^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} magnitude

below the diffusivities measured in the present ^work

(see Fig. 5).

Fig. ^5.

Temperature dependence ^{of the} interdiffusivity 1) 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 crystalline

Ge (-.-) : Do =10 cm2 s-1, Ea = 3 eV.

Interstitial diffusion 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.

1756

A more fruitful comparison apparently ^involves

diffusion of ^« big » interstitials in a bond-centered

configuration [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 from the interdiffusion law measured in the present ^work

as evidenced in figure ^{5. The two} diffusion laws have in common a point corresponding ^{to 676 K and have} slightly ^different slopes.

It is probably ^{worth to} point ^out that the activation energy obtained in the present ^work might ^be suspected ^{to be some sort of a lowest limit, on the} ground ^{that the} composition dependance ^{of D is}

strong and that the same sample has been used to

successively ^{measure D at 410, 418 and 436 °C.}

In conclusion, ^{we observed :}

(i) saturation of the diffusion mixing ⁱⁿ plateau stages, (ii) stopping ^{of the diffusion} mixing ^after crystallization of the Ge films and (iii) ^{a diffusion}

law similar to that of big interstitials in crystalline

silicon. It is thus conceivable that the interdiffusion process in amorphous Ge/amorphous ^Si multilayers

is dominated by non-substitutional jumps ^{of Si}

atoms into the Ge films using ^the pre-existing locally expanded volumes which are normal features in the structure of a random continuous network. The diffusion of Si into Ge being non-substitutional has not to be compensated by jumps ^{of Ge atoms into}

the Si films. Thus the Ge layers ^are progressively

consumed by ^the previously ^invoked planar growth

of a Ge-Si alloy ^which proceeds ^from interfaces and

seems to stop when the available free volume has been filled up. It would be very interesting ^{indeed to}

confirm 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 ^number 6-14-90).

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