7
Influence of mixing entropy on the nucleation of CoSi 2 C. Detavernier, R. L. Van Meirhaeghe, and F. Cardon Vakgroep Vaste-stofwetenschappen, Universiteit Gent, Krijgslaan 281/S1, B-9000 Gent, Belgium K. Maex IMEC, Kapeldreef 75, B-3001 Leuven, Belgium and E. E. Department, K. U. Leuven, B-3001 Leuven, Belgium ~Received 7 March 2000; revised manuscript received 24 May 2000! It is generally known that nucleation effects strongly influence the CoSi to CoSi 2 phase transition. The small difference in Gibbs free energy between the CoSi and CoSi 2 phase is responsible for the nucleation barrier. In this work, it is shown that the addition of elements that are soluble in CoSi and insoluble in CoSi 2 or vice versa influences the entropy of mixing and thus changes D G. In this way, the height of the nucleation barrier may be controlled, thus controlling the temperature of formation of the CoSi 2 phase in a thin film system. The influence of mixing entropy on silicide nucleation is illustrated by the effect of Fe, Ge, and Ni on CoSi 2 formation. It is found that Fe has a higher solubility in CoSi than in CoSi 2 , causing an increase of the nucleation barrier. The presence of Ge increases the nucleation temperature, similar to what was observed for Fe, while the presence of Ni lowers the nucleation temperature. Based on the crystallographic structure of their respective monosilicides and disilicides, a list is given of other metals that are also expected to influence the nucleation temperature. I. INTRODUCTION In thin film reactions, many silicides are formed by a nucleation-controlled reaction. A typical example is the for- mation of NiSi 2 at the NiSi/Si interface. A review paper on nucleation-controlled growth of silicides has been written by d’Heurle. 1 Although in most cases there is a lack of knowl- edge of the material parameters to allow for a quantitative description, it is shown that the classical theory of nucleation allows for a good qualitative description of the processes involved. As a reminder, we will briefly summarize classical nucle- ation theory. Consider the general case of a phase AB that is formed at the interface between two phases A and B. The driving force for this reaction is the difference in free energy D G between A 1B and AB . However, because of the forma- tion of AB , the system evolves from a situation with one interface A / B into a system with two interfaces A / AB and AB / B . This will usually result in an increase of the interfa- cial energy D s . For such a system, there is a competition between two mechanisms: on one hand, transformation of a volume of A 1B into a nucleus AB with radius r results in an energy ‘‘gain’’ D G V ;r 3 D G , on the other hand the addi- tional interfaces result in a surface energy ‘‘cost’’ D s ;r 2 s . The free energy of the nucleus is thus given by 2 D G N ~ r ! 5ar 2 s 2br 3 D G , ~1! with a and b depending on the exact geometry of the nucleus. D G N has a maximum value D G * for a critical ra- dius r * : r * s D G , ~2! D G * s 3 D G 2 5 s 3 ~ D H 2T D S ! 2 . ~3! Nuclei smaller than r * will exist in some equilibrium con- centration, due to random thermal fluctuations, but are intrin- sically not stable. Only nuclei with a radius larger than r * are able to grow. D G * can be regarded as the activation energy necessary for the nucleation of AB . From the for- mula, it is clear that nucleation phenomena will only be im- portant if D G , the free energy of formation of AB , is small. The rate of nucleation r * is given by the product of the concentration of nuclei with a critical size and some kinetic term Q, taking into account the local atomic rearrangement needed to form the nucleus: r * exp~ 2D G * / kT ! exp~ 2Q / kT ! . ~4! It is known from literature that when a film of Co is depos- ited onto a Si substrate, annealing results in a sequential growth of Co 2 Si, CoSi, and CoSi 2 . It has been reported that the formation of CoSi 2 is both nucleation and diffusion controlled. 3,4 The fact that nucleation effects are important may be derived from the rough appearance of the CoSi 2 layer and the ‘unusual’ kinetics of the CoSiCoSi 2 transi- tion. It may be expected that nucleation is the rate controlling process, because of the small difference in formation en- thalpy between CoSi 2 and CoSi. In case of NiSi 2 , the nucle- ation barrier is very high, resulting in a high nucleation tem- perature, and once the nucleus is formed, growth by diffusion may be regarded as an immediate process. In case of CoSi 2 , the nucleation temperature is rather low ~about 540 °C) and once a stable nucleus is formed, one still ob- serves rather slow diffusional kinetics. It is clear from formula ~3! that nucleation will only be rate limiting if D H is small. This is the case if CoSi 2 is PHYSICAL REVIEW B 1 NOVEMBER 2000-II VOLUME 62, NUMBER 18 PRB 62 0163-1829/2000/62~18!/12045~7!/$15.00 12 045 ©2000 The American Physical Society

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Page 1: Influence of mixing entropy on the nucleation of

PHYSICAL REVIEW B 1 NOVEMBER 2000-IIVOLUME 62, NUMBER 18

Influence of mixing entropy on the nucleation of CoSi2

C. Detavernier, R. L. Van Meirhaeghe, and F. CardonVakgroep Vaste-stofwetenschappen, Universiteit Gent, Krijgslaan 281/S1, B-9000 Gent, Belgium

K. MaexIMEC, Kapeldreef 75, B-3001 Leuven, Belgium

and E. E. Department, K. U. Leuven, B-3001 Leuven, Belgium~Received 7 March 2000; revised manuscript received 24 May 2000!

It is generally known that nucleation effects strongly influence the CoSi to CoSi2 phase transition. The smalldifference in Gibbs free energy between the CoSi and CoSi2 phase is responsible for the nucleation barrier. Inthis work, it is shown that the addition of elements that are soluble in CoSi and insoluble in CoSi2 or vice versainfluences the entropy of mixing and thus changesDG. In this way, the height of the nucleation barrier may becontrolled, thus controlling the temperature of formation of the CoSi2 phase in a thin film system. Theinfluence of mixing entropy on silicide nucleation is illustrated by the effect of Fe, Ge, and Ni on CoSi2

formation. It is found that Fe has a higher solubility in CoSi than in CoSi2, causing an increase of thenucleation barrier. The presence of Ge increases the nucleation temperature, similar to what was observed forFe, while the presence of Ni lowers the nucleation temperature. Based on the crystallographic structure of theirrespective monosilicides and disilicides, a list is given of other metals that are also expected to influence thenucleation temperature.

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I. INTRODUCTION

In thin film reactions, many silicides are formed bynucleation-controlled reaction. A typical example is the fomation of NiSi2 at the NiSi/Si interface. A review paper onucleation-controlled growth of silicides has been writtend’Heurle.1 Although in most cases there is a lack of knowedge of the material parameters to allow for a quantitadescription, it is shown that the classical theory of nucleatallows for a good qualitative description of the procesinvolved.

As a reminder, we will briefly summarize classical nucation theory. Consider the general case of a phaseAB that isformed at the interface between two phasesA and B. Thedriving force for this reaction is the difference in free enerDG betweenA1B andAB. However, because of the formation of AB, the system evolves from a situation with oninterfaceA/B into a system with two interfacesA/AB andAB/B. This will usually result in an increase of the interfcial energyDs. For such a system, there is a competitibetween two mechanisms: on one hand, transformationvolume ofA1B into a nucleusAB with radiusr results in anenergy ‘‘gain’’ DGV;r 3DG, on the other hand the addtional interfaces result in a surface energy ‘‘cost’’Ds;r 2s. The free energy of the nucleus is thus given by2

DGN~r !5ar2s2br3DG, ~1!

with a and b depending on the exact geometry of tnucleus.DGN has a maximum valueDG* for a critical ra-dius r * :

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DG, ~2!

PRB 620163-1829/2000/62~18!/12045~7!/$15.00

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Nuclei smaller thanr * will exist in some equilibrium con-centration, due to random thermal fluctuations, but are intsically not stable. Only nuclei with a radius larger thanr *are able to grow.DG* can be regarded as the activatioenergy necessary for the nucleation ofAB. From the for-mula, it is clear that nucleation phenomena will only be important if DG, the free energy of formation ofAB, is small.The rate of nucleationr* is given by the product of theconcentration of nuclei with a critical size and some kineterm Q, taking into account the local atomic rearrangemeneeded to form the nucleus:

r* 'exp~2DG* /kT!exp~2Q/kT!. ~4!

It is known from literature that when a film of Co is depoited onto a Si substrate, annealing results in a sequegrowth of Co2Si, CoSi, and CoSi2. It has been reported thathe formation of CoSi2 is both nucleation and diffusioncontrolled.3,4 The fact that nucleation effects are importamay be derived from the rough appearance of the Co2layer and the ‘unusual’ kinetics of the CoSi→CoSi2 transi-tion. It may be expected that nucleation is the rate controllprocess, because of the small difference in formationthalpy between CoSi2 and CoSi. In case of NiSi2, the nucle-ation barrier is very high, resulting in a high nucleation teperature, and once the nucleus is formed, growthdiffusion may be regarded as an immediate process. In cof CoSi2, the nucleation temperature is rather low~about540 °C) and once a stable nucleus is formed, one stillserves rather slow diffusional kinetics.

It is clear from formula~3! that nucleation will only berate limiting if DH is small. This is the case if CoSi2 is

12 045 ©2000 The American Physical Society

Page 2: Influence of mixing entropy on the nucleation of

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12 046 PRB 62DETAVERNIER, Van MEIRHAEGHE, CARDON, AND MAEX

formed from CoSi, because the difference in heat of formtion is very small between these two phases. If one wouldable to form CoSi2 in a direct reaction between Co and Si,very low activation energy for nucleation would result, sintheDH for this reaction would be much larger. MBE expements have shown that this is possible if there is a very ssupply of Co atoms towards a heated Si substrate.5 In solid-state reactions, the same effect may be obtained by adddiffusion mediating layer in between the Co layer andsilicon substrate. In the case of a thin SiO2 interlayer, it hasbeen reported that CoSi2 is the first phase to form, skippinthe intermediary phases Co2Si and CoSi.6,7 Analogous re-sults are obtained for interlayers of some refractory me~e.g., Ti, Ta, Zr, and Hf!.8

Another way to influenceDH is to usea-Si as a substrateIn the case of an amorphous substrate, there is an additcrystallization energy, which causesDH to increase. Indeedit has been found experimentally that nucleation is no lona rate controlling process for CoSi2 formation ona-Si ~asevidenced by the reaction kinetics and the flat appearancthe disilicide!.1 However, not only the difference in formation enthalpyDH influences the nucleation reaction@see Eq.~3!#. If DH is very small, the term containingDS may alsobecome important. d’Heurleet al.have studied disilicide for-mation in the Ni/Co/Si system and found that the disiliciformation temperature is lowered as compared to the Csystem.9 This was explained by the influence of mixing etropy effects on the nucleation process. More recently, Mgelinck et al. studied the effect of the addition of Pt, Au, aCo on NiSi2 formation and also reported effects of mixinentropy.10,11 In general, it follows that the presence of ‘‘foreign elements’’ that have a different solubility in CoSi aCoSi2 may influence the nucleation process.

In this work, bilayers of Co/Fe~interlayer! or Fe/Co~cap-ping layer! were deposited on Si~100! and after annealingphase formation was studied. It will be shown that addingto the silicidation reaction, strongly influences the nucleatof CoSi2. We shall show that Fe has a higher solubilityCoSi than in CoSi2, causing an increase of the nucleatibarrier DG* due to an effect of mixing entropy. It will beshown that this influences both the reaction kinetics~nucle-ation temperature, rate of growth of the nuclei! and the crys-tallographic properties of the CoSi2 ~grain size!. Althoughthe paper mainly focuses on the Co-Fe-Si system, somesults on the effect of adding Ge and Ni to the Co/Si reactare also included, for comparison with the case of Fe ancorroborate the reaction model.

II. EXPERIMENTAL

The cleanliness of the interface is very important dursilicide formation.12 The substrates@p-type Si~100!, Na51013–1014 cm23# were cleaned using standard RCcleaning, followed by a HF dip. The HF dip is knownpassivate the Si surface, resulting in an oxide free interfbetween the deposited metal and the substrate. Layers oGe, Ni, and Co were deposited bye-beam evaporation in avacuum of 1026 mbar. For all the experiments mentionedthis paper, the Co film thickness is 10 nm, with a Fe, GeNi layer thickness varying between 0 and 10 nm. A Ti sulimation pump was used just prior to evaporation, result

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in a sharp decrease of the oxygen partial pressure. The lof oxygen in the as deposited films was below the deteclimit of x-ray photoelectron spectroscopy~XPS!.

To study the silicidation reaction, isochronal anneali~30 sec.! was done at various temperatures. Annealing wcarried out in a rapid thermal processing~RTP! system, in N2ambient. The sheet resistance of the film was measured ua four point probe. Because of the large difference in retivity between CoSi and CoSi2, sheet resistance measurments provide a fast means of obtaining information abphase formation. Grazing incidence x-ray diffraction~GI-XRD, u51°) was used for detailed phase identificatioStandard XRD (u/2u) was used to measure preferentcrystallographic orientation. XPS depth profiling was aplied to study the chemical composition of the layers afannealing.

III. RESULTS

A. Monosilicide formation

From literature, it is known that pure CoSi forms at abo375 °C, while pure FeSi forms at about 450 °C.13 From XPSdepth profiling, we observed that Co and Fe intermix befthey start to react with the Si substrate to form a cubic mosilicide phase. Both for Fe capping layers and interlayers,mixed monosilicide already starts to form at about 420 °Cevidenced by XRD and XPS. On top of the monosilicidelayer of unreacted Co and Fe is present. Removal oflayer by chemical etching causes the sheet resistance tcrease. It is worth noticing that the resistivity of the mixemonosilicide does not seem to be very dependent on thelayer thickness.

B. Miscibility

To check the miscibility of FeSi and CoSi, the positionthe ~210! monosilicide XRD peak was measured as a funtion of the Fe interlayer thickness. In Fig. 1, the peak potion for samples annealed at 440 °C is plotted versusx5dFe/(dCo1dFe). In the case of complete solubility of Fe iCoSi,x can be regarded as the atomic percentage of Fe inCo12xFexSi ~neglecting the small difference in density anmolar weight between Fe and Co!. The straight line fit indi-

FIG. 1. Plot of the monosilicide~210! XRD peak position as afunction of x5Fe layer thickness/total layer thickness (Fe1Co).

Page 3: Influence of mixing entropy on the nucleation of

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PRB 62 12 047INFLUENCE OF MIXING ENTROPY ON THE . . .

cates that Co12xFexSi obeys Vegard’s law@Fig. 1~a!#. Theextrapolation of the data towards pure FeSi (x51) is quitegood. Similar measurements were performed for samplesnealed at different temperatures@Fig. 1~b!#. It was found thatthe shift in peak position decreased for increasing anneatemperature, indicating that Fe is gradually expelled fromCo12xFexSi. However, some Fe remains in the monosilicidbased on the CoSi peak shift, the monosilicide formed frthe Co~10 nm!/Fe~10 nm!/Si sample still contains abou10–15 % of Fe, even after annealing at 680 °C.

To determine the depth distribution of Co and Fe in tlayer, XPS depth profiling was done for a Co~10 nm!/Fe~10nm! structure annealed at 360, 440, 480 and 600 °C~Fig. 2!.The composition of the monosilicide is in agreement withvalues obtained by XRD measurements@Fig. 1~b!#. Theatomic concentration profile clearly shows a tendency foCo enriched region near the Si substrate and a Fe enriregion near the surface. For increasing annealing tempture, an increasing amount of Fe is expelled towardssurface region.

We also investigated the XRD peak shift for the disicides. For samples annealed at 900°C, no shift in the C2peak position could be observed. On XRD scans, both Co2and FeSi2 peaks were observed. From this we may concluthat CoSi2 and FeSi2 are not miscible, as may be expectbased on their different crystallographic structure.

C. Nucleation temperature

From the sheet resistance versus annealing temperplot ~Figs. 3 and 4!, it is clear that in the presence of Fe~bothinterlayer and capping layer! the formation of the low resistive CoSi2 phase is delayed. For Fe interlayers that are thner than 1 nm, the delay in nucleation temperature is vsmall ~less than 10 °C). However, for 2, 3.5, 5, 7, and 10 nof Fe there is a gradual increase of the CoSi2 nucleationtemperature. As will be shown in more detail in the discusion below, this delay in nucleation may be explained aconsequence of the difference in mixing entropy betweenCo12xFexSi mixed monosilicide and the immiscible disil

FIG. 2. Atomic concentration profile for Co (n), Fe (s) and Si(h) as determined by XPS for a Co~10 nm!/Fe~10 nm! structureannealed at 360, 440, 480, and 600 °C. For clarity, the oxyconcentration~which was only detectable in the surface region! isnot shown.

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cides. Moreover, once formed, the growth of the CoSi2 layeris slowed down. This may be explained by the expelledthat precipitates at the CoSi2 grain boundaries, thus slowindown diffusion@Eq. ~4!#.

For a selected number of samples, phase formationstudied in more detail using grazing incidence XRD~Fig. 5!.For a Co~10 nm!/Fe~10 nm!/Si structure, annealing at 520 °Cresulted only in monosilicide formation~as expected fromthe high sheet resistance!. For the same structure annealed680 °C, a small CoSi2 peak was detected. After annealing900 °C, CoSi2 anda-FeSi2 were detected. These results cofirm the sheet resistance measurements of Fig. 3.

D. Preferential orientation

To study the preferential orientation of the CoSi2 layers,we usedu/2u XRD and measured the intensity of the CoS2~111!, ~220!, and~400! diffraction peaks as a function of Flayer thickness. Both for a Fe interlayer and capping layan increase of the intensity of all the CoSi2 diffraction peaksis observed for increasing Fe thickness@Fig. 6~a!#. However,since the ratio of the peak intensities remains rather consthere is no strong preferential orientation of the CoSi2 layer.In view of the low ~400! intensity, we may conclude thathere is no epitaxial alignment of the CoSi2 layer with the~100! substrate. The increase in the peak intensity is acc

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FIG. 3. Sheet resistance versus annealing temperature fCo~10 nm!/Fe/Si structure for various values of the Fe interlaythickness.

FIG. 4. Sheet resistance versus annealing temperature for aCo~10 nm!/Si structure for various values of the Fe capping laythickness.

Page 4: Influence of mixing entropy on the nucleation of

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12 048 PRB 62DETAVERNIER, Van MEIRHAEGHE, CARDON, AND MAEX

panied by a decrease in peak width@Fig. 6~b!#, indicatinglarger CoSi2 grains in the presence of Fe. For thick Fe intelayers (.4 nm) the XRD peak width increases agaslightly, indicating decreasing grain size.

E. The addition of Ge

Since Fe is believed to substitute for Co in the CoSi ltice, we also studied the effect of Ge, which is able to sstitute for Si. The ternary Co-Si-Ge system was studieddetail by Waldet al.14 They found two large solid-solutionregions: up to 50% Si is soluble in Co2Ge and there is asolid-solution range of up to 67% of Ge in CoSi. More rcently, several authors have reported the formation of Co2on strained or unstrained layers of Si12xGex .15,16The forma-tion of a ternary CoSi12yGey compound was observed bseveral authors, for reaction of Co with Si12xGex layers ofdifferent thickness and composition.

To study the effect of Ge on the nucleation of CoS2,bilayers of Co/Ge/Si~interlayer! or Ge/Co/Si~capping layer!

FIG. 5. Grazing incidence XRD scan for Co~10 nm!/Fe~10nm!/Si structures annealed at different temperatures. The pcould be identified as Co12xFexSi (s),CoSi2 (¹), andFeSi2 (n).

FIG. 6. ~a! Intensity of the~111!, ~220!, and~400! CoSi2 XRDpeaks as a function of Fe interlayer thickness for a Co~10 nm!/Fe/Sistructure annealed at 800 °C.~b! Width of the ~220! CoSi2 XRDpeak as a function of Fe interlayer thickness for a Co~10 nm!/Fe/Sistructure annealed at 800 and 1000 °C.

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were deposited on Si~100! and after annealing, phase formtion was studied. A similar behavior was observed as forboth for Ge interlayers and capping layers. From the shresistance versus annealing temperature graph~Fig. 7!, it isclear that the low resistive disilicide phase forms at increingly higher temperature for increasing amounts of Ge.case of Ge, the delay in nucleation temperature saturateabout 750 °C for a Ge interlayer thickness larger thannm. For a Ge interlayer thickness smaller than 3.5 nm,increase in the CoSi2 grain size could be observed, similarwhat was observed for Fe. More detailed results will be psented in a separate publication.

F. The addition of Ni

NiSi2 and CoSi2 are expected to be miscible, since thboth have a CaF2-type structure with a lattice parameter5.406 and 5.364 Å, respectively. The monosilicides Coand NiSi are expected to be immiscible because of theirferent crystallographic structure. Bilayers of Co/Ni/Si~inter-layer! or Ni/Co/Si ~capping layer! were deposited on Si~100!and after annealing, phase formation was studied. Fromsheet resistance versus annealing temperature graph~Fig. 8!,it is clear that the low resistive disilicide phase formslower temperature for increasing thickness of the Ni int

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FIG. 7. Sheet resistance versus annealing temperature fCo~10 nm!/Ge/Si structure for various values of the Ge interlaythickness.

FIG. 8. Sheet resistance versus annealing temperature fCo~10 nm!/Ni/Si structure for various values of the Ni interlayethickness.

Page 5: Influence of mixing entropy on the nucleation of

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PRB 62 12 049INFLUENCE OF MIXING ENTROPY ON THE . . .

layer. Previously, d’Heurleet al. also observed a decreaseCoSi2 formation temperature in the presence of Ni.9

IV. DISCUSSION

A. Entropy of mixing

From the sheet resistance measurements, it is clearthe addition of both Fe and Ge increases the nucleation tperature of CoSi2, while Ni decreases the nucleation temperature. Based on the classical theory of nucleation, smarized in Eq.~3!, this may be caused by either an increaof the numerator, containing the surface energy terms odecrease of the denominator, containingDG. In case of asurface energy effect, one would expect a saturation beior: since the presence of only a few percent of Fe, Ge, ocould already completely saturate the grain boundariesinterfaces, one would expect that for a very thin interlaythe nucleation temperature would increase strongly, andremain constant, independent of a further increase of theterlayer thickness. This is clearly not the case in our expments. Moreover, it was shown experimentally that Fe aGe are dissolved into the bulk of the monosilicide, thus ging rise to a volume effect. From this one may conclude thalthough surface energy effects may be important, theynot play a major role in increasing the nucleation tempeture.

In case of a compound crystal~e.g., Si12xGex), in theapproximation of an ideal mixture, the entropy of mixinggiven by

Smixing~x!52R@x ln~x!1~12x!ln~12x!#/mole. ~5!

In the standard reaction to form CoSi2 , CoSi1Si→CoSi2 ,DS is usually neglected, a common procedure for solid-sreactions. Suppose, however, that some elementA is com-pletely soluble in CoSi and insoluble in CoSi2. In this case,the reaction is given by

Co12xAxSi1~122x!Si→~12x!CoSi21xA ~6!

and there will be a difference in mixing entropy betweeninitial and final phases.

DS5R@x ln~x!1~12x!ln~12x!#,0. ~7!

Thus, the reaction will result in a decrease of entropy~theprecipitation of A results in a transition from disorder torder!. On the other hand, if an elementB is soluble in CoSi2and insoluble in CoSi, the reaction is given by

~12x!CoSi1xB1~11x!Si→Co12xBxSi2 ~8!

and in this case the difference in mixing entropyDS.0. Forthe intermediate case, in which some elementC is partlysoluble in CoSi and CoSi2 , DSÞ0 if the solubility of C isdifferent in CoSi and CoSi2. The difference in mixing en-tropy DS will influence the change in free energyDG5DH2TDS,0 @Eq. ~3!#, and this will influence the activation energy for nucleationDG* 's3/DG2 ~Table I!. SinceFe and Ge are more soluble in CoSi than in CoSi2, one canexpect that adding these elements to the silicidation reacwill heighten the nucleation barrier and thus increase

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temperature of nucleation. In case of Ni, which is mosoluble in CoSi2 than in CoSi, a decrease of the nucleatitemperature can be expected.

B. Nucleation in the CoÕFeÕSi system

In the case of Fe, the reaction can be modelled as folloat low temperature, Co and Fe intermix, and Co12xFexSistarts to form from the reaction of the CoFe alloy with thesubstrate. One may calculate the free energy of formationthe mixed monosilicideGf(x)5H f(x)2TSmixing(x). If oneassumes an ideal mixture, the entropy of mixing can beculated using Eq.~5!. It is further assumed that in the solisolution the enthalpy varies linearly with composition

HCo12xFexSif ~x!5HCoSi

f 1x~HFeSif 2HCoSi

f !. ~9!

After annealing at 440 °C, the mixed monosilicide hformed, and a shift in CoSi peak position is observed, incating that Fe is built into the monosilicide. For annealinghigher temperature (.440 °C), Fe is gradually expelledfrom the monosilicide. This may be explained based onlarger enthalpy of formation of FeSi~280.4 kJ/mole! ascompared to that of CoSi~2100.5 kJ/mole!.17 Thus, in thepresence of an infinite supply of Si, the formation of Co-bonds will be preferred. However, some Fe~of the order of10–15 %) remains incorporated in the monosilicide, becaof the energy gained by the mixing entropy effect. Thisillustrated by the minimum inGf(x) at x.0 in Fig. 9~a!.Recently, similar behavior was reported for Ti(SiGe)2 onSiGe by Aldrichet al.18

Co12xFexSi1nSi→nCoSi21~12n!Co12yFeySi. ~10!

TABLE I. Overview of the influence of mixing entropyDS on theactivation energy for nucleationDG* .

A soluble in CoSi, insoluble in CoSi2 DS!0 uDGu↓↓ DG* ↑↑A more soluble in CoSi than in CoSi2 DS,0 uDGu↓ DG* ↑A less soluble in CoSi than in CoSi2 DS.0 uDGu↑ DG* ↓A insoluble in CoSi, soluble in CoSi2 DS@0 uDGu↑↑ DG* ↓↓

FIG. 9. ~a! The free energy of formation for the mixed monoslicide Gf(x). ~b! The change in free energy for forming CoSi2 fromthe mixed monosilicideDG(x). All calculations were done forT5600 °C.

Page 6: Influence of mixing entropy on the nucleation of

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12 050 PRB 62DETAVERNIER, Van MEIRHAEGHE, CARDON, AND MAEX

CoSi2 formation can occur by reaction~10!, with y5x/(12n) and n the number of mole CoSi2 that is formed forevery mole of Co12xFexSi that is consumed. For the standaCo/Si reaction,x5y50 andn51. In the presence of Fe inthe CoSi, Fe will have to be expelled from the reactiongion, since Fe is not soluble in the CoSi2 that is formed. Thiswill cause a Fe enrichment of the remaining Co12yFeySi (y.x). The larger the amount of Fe present in the monoscide, the more Fe-enriched monosilicide will remain afterreaction (n,1). One may then calculate the change in frenergy for forming CoSi2 from the mixed monosilicide:

DG5nGCoSi2f 1~12n!GCo12yFeySi

f 2GCo12yFeySif . ~11!

In Fig. 9~b!, DG is plotted as a function ofx for differentvalues ofn. The calculations were done using a value2107.5 kJ/mole for the free energy of formation for CoS2.It is clear that in the presence of Fe in the CoSi,uDGu willdecrease, thus the nucleation barrierDG* will increase,causing an increase of the nucleation temperature.

The increase in CoSi2 grain size with increasing Fe thickness may also be explained using the nucleation concepthe presence of Fe, the nucleation of CoSi2 is more difficultand is delayed to higher temperatures. At a certain tempture, a limited number of nuclei will reach the critical radiuand thus become stable. The density of nuclei with a radequal to the critical radius r * is proportional toexp(2DG* /kT). Since the presence of Fe increasesDG* , thedensity of nuclei will be smaller for increasing Fe thickneSince diffusion is faster at higher temperature, once a stnucleus is formed, it will grow very rapidly. Thus, due to thdelay in nucleation, there will be less nucleation centers tin the normal Co/Si reaction and once formed the nuclei mgrow much faster, resulting in larger CoSi2 grains. However,during the formation of the CoSi2 layer, Fe has to be expelled from the monosilicide. If a large amount of Fedissolved in the monosilicide, a high concentration of Fe wbe built up at the edge of the CoSi2 nucleus, and in this wayfurther growth of the CoSi2 nucleus will be inhibited. Thisexplains the decrease in grain size observed for thickeinterlayers: the growth of each nucleation center is hampeby the increased Fe concentration surrounding it. FoCo~10 nm!/Fe~10 nm! structure annealed at high temperture, a patchwork of CoSi2 grains surrounded by FeSi2 grainsis formed.

Recently, two papers were published concerning Coternary disilicides. Dezsiet al.19 studied bulk samples anthin films of Co12xFexSi2. It was found that up to 10% of Cowas soluble inb-FeSi2, while only 1.5% of Fe was solublein CoSi2. Honget al.20 studied epitaxial Co12xFexSi2 layerson Si~111!. The layers were formed by codeposition of CFe, and Si while the substrate was held at room temperaThey observed that the as-deposited films adopt a cstructure of CsCl-type with random vacancies, with an etaxial orientation with respect to the Si~111! substrate. Thisstructure was found to be stable up to 650 °C. At hightemperatures, Fe-rich films (x.0.85) converted into anorthorhombicb-FeSi2 structure, which is in agreement wita solubility of about 10% Co inb-FeSi2 found by Dezsiet al. However, Honget al. reported that forx,0.85 thecubic structure was preserved, although the initially ra

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domly distributed vacancies in the CsCl structure evolvtowards a partially ordered CaF2 structure. Their data indi-cated that Fe does not substitute for Co atoms in a perCaF2 structure. Instead, forx,0.5, Fe preferentially occupied the interstitial octahedral sites of the CaF2 structure,while for 0.75,x,0.85, the as deposited CsCl-structuremained stable up to at least 650 °C. The CsCl-type strucmentioned by Hong is not uncommon for disilicides. Itknown that when pure CoSi2 is formed by codeposition techniques at low deposition temperature, a metastable CsCl-structure is formed, and some CsCl-type grains rempresent even after annealing at 600 °C.21

In order to distinguish the CaF2 structure from a CsCl-type structure with random vacancies, we have calculatesimulated XRD pattern for both structures, indexing the Csstructure with a lattice parameter equal to two times the fdamental unit cell. In the case of CsCl, the~111! and ~311!reflections are very weak~for a perfect CsCl lattice they arforbidden!. Since we clearly observed~111! reflections, sincethe~111! intensity increases for increasing Fe layer thickneand since the~220!/~111! intensity ratio remains rather constant~between 2.5 and 3.5!, we may conclude that the CoS2that is formed has CaF2-type structure and that no evidencfor a CsCl-type CoSi2 structure was found for the samplediscussed in this paper. For the FeSi2 precipitates, XRD in-dicates that the high temperature (900 °C) phase is tetranal a-FeSi2. However, our XRD measurements cannot ruout the formation of metastable FeSi2 phases at lower temperature.

C. Mixing entropy effects for other elements

In binary alloys, an empirical rule by Hume-Rothestates that two elements are soluble if they have the scrystallographic structure and if their lattice parameter dfers by less than 15%. One may expect that for silicides,crystallographic structure will also be important in determing the solubility. However, although some results have bpublished concerning the solubility of possible doping ements, little is known about solubilities of metallic elemenin silicides. Some work has been reported regarding the sbility of Pt in NiSi,22 Au and Co in NiSi2,10 Ni in CoSi2,9

and various elements in MoSi2.23 Based on this work, onemay conclude that also in the case of silicides, tendenciessolubility may be predicted based on arguments concerncrystallographic structure.

Based on the crystallographic structure of CoSi, Co2and the structure of other mono- and disilicides, one cbuild a list of possible candidates that are expected tosoluble/insoluble in CoSi and CoSi2. An overview is given inTable II @the crystallographic data on which this table

TABLE II. Overview of elements that are expected to b~in!soluble in cobalt silicides.

Soluble in Co2Si Ni, Ru, Rh, IrSoluble in CoSi Ge, Fe, Cr, Mn, Ru, Rh, Re, OsSoluble in CoSi2 Ni, AuNot miscible with CoSi Sc, Ti, Cu, Y, Zr, Nb, Pd, Hf,

and CoSi2 Ta, W, Pt

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PRB 62 12 051INFLUENCE OF MIXING ENTROPY ON THE . . .

based were taken from Ref. 24, while Au is expected tosoluble in CoSi2 since it has been shown to be solubleNiSi2 ~Ref. 10!#.

Based on Table II, one can expect that Ni and Au wdecrease the formation temperature of CoSi2, while Ge, Fe,Cr, Mn, Ru, Rh, Re, and Os are expected to increasenucleation temperature. For Ti, Ta, Zr, and the other ements that are expected to be insoluble in both cobalt mocide and disilicide, no changes of the CoSi2 nucleation tem-perature can be expected caused by effects of mixentropy. However, since the presence of these elementschange the interfacial and/or grain boundary energy, chanin the nucleation barrier that are due to surface energy effremain possible.

V. CONCLUSION

It is shown that the addition of Fe, Ge, or Ni stronginfluences the nucleation of CoSi2. This can be explained bythe different solubility of Fe and Ge in CoSi and CoSi2: sinceFe is soluble in CoSi and insoluble in CoSi2, Fe has to beexpelled from the nucleus during CoSi2 nucleation. This

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causes a change in mixing entropy, which results in ancreased nucleation barrier. Since nucleation is more difficit will occur at higher temperature and the density of nucwill be smaller than for the normal Co/Si reaction, thus eplaining the delay in nucleation and increased grain sizeis observed experimentally. Since Ni is soluble in CoSi2 andinsoluble in CoSi, the opposite effect is observed. Basedthe crystallographic structure of their monocides and discides, a list is given of other elements that are expectedhave a similar behavior as Fe and Ge.

ACKNOWLEDGMENTS

The authors would like to thank L. Van Meirhaeghe ftechnical support during sample preparation and U. Demfor the XPS measurements. C.D. thanks the ‘‘Fonds vWetenschappelijk Onderzoek–Vlaanderen’’~FWO! for fi-nancial support. C.D. is grateful for interesting discussioand comments with/from F. d’Heurle, D. Mangelinck, S.-Zhang, C. S. Ho, and many others during the Erice sumschool on silicides~1999!.

, J.

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