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FORMATION OF A NEW PHASE FROM CHEMICAL INTERACTIONS AT AN INTERFACE :
NUCLEATION CONTROL
F. d’ Heurle
To cite this version:
F. d’ Heurle. FORMATION OF A NEW PHASE FROM CHEMICAL INTERACTIONS AT AN
INTERFACE : NUCLEATION CONTROL. Journal de Physique Colloques, 1990, 51 (C1), pp.C1-
803-C1-808. �10.1051/jphyscol:19901125�. �jpa-00230034�
COLLOQUE DE PHYSIQUE
Colloque Cl, supplirment, au n o l , Tome 51, janvier 1990
FORMATION OF A NEW PHASE FROM CHEMICAL INTERACTIONS AT AN INTERFACE : NUCLEATION CONTROL
F.M. D' HEURLE
IBM T.J. Watson Research Center, PO. 218, Yorktown Heights, NY 10598, U.S.A. and Fasta Tillstandets Elektronik, K.T.H.-Electrum, Box 1298,
164 28 Kista, Sweden
Rdsumd
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Le phenomene considere constitue un cas particutier de formation d'une nouvelle phase solide ii partir d'une interaction d'origine chimique entre deux phases juxtaposees, dont I'une servant de substrat est elle-aussi solide, mais dont I'autre peut etre dans n'importe quel etat physique, solide, liquide ou gazeux (oxydation par exemple). Les conditions sous lesquelles la germination detient le rBle preponderant dans ces reactions sont examinees B I'aide de la thBorie classique de la germination. Alors qu'assez souvent le mode de croissance de la nouvelle phase est determinee par la diffusion, I'epaisseur de la couche e t a t alors proportionelle B la racine carrke du temps, la germination devient dominate lorsque le changement d'energie libre est suffisamment faible.A la limite dans le cas oh la germination est tres diificile celle-ci ne peut avoir lieu qu'B des temperatures elevees oh la diffusion est extr8mement rapide; la reaction prend alors un caractkre quasiment explosif. Si I'existence d'un point d'equilibre, eutectoide ou point de decomposition d'un oxide, permet de choisir des conditions oh AG peut devenir arbitrairement petit, l'existence de tels points d'equilibre n'est pas necessaire pour que la germination contr6le la reaction. Pour celA il suffit que AG soit suffiiamment petit. Quelques considerations d'ordre pratique terminent cet expose
Abstract
-
The phenomena to be considered here constitute a particular case of the general question of the for- mation of a new solid phase from a chemical interaction between two adjoining phases, one of which acting as a substrate should be solid also, while the second one can indifferently assume any physical state, solid, liquid or gaseous (as in oxidation). The conditions under which nucleation becomes the rate-determining process in such reactions are analyzed in terms of the classical theory of nucleation. Quite often the growth of the new phase is proportional to the square-root of time indicating diffusion control; germination comes to play the preponderant role when the change in free energy AG is sufficiently small. When germination becomes very difficult, it may take place only at such high temperatures that diffusion ceases to play any significant role and the reaction as- sumes a quasi explosive character. While the presence of equilibrium points, eutectoid or oxide decomposition, provides the possibility of making AG arbitrarily as small as desired, nucleation-control does not depend on such equilibrium points, the one necessary condition is that AG be small. Some practical aspects are considered.INTRODUCTION
The question of the formation of a new phase from a chemical interaction at an interface between two other phases has received relatively little attention in view of the general importance of the subject. Certainly one finds treatises about oxide formation on the surface of metals (nowadays largely concerned with the problem of charge transfer accompanying ionic diffusion) and the question of silicon oxide growth is the object /1,2/ of constant attention. Because of the current importance of the silicon device technology there exists a large literature on metal-silicon interactions. Yet there are very few publications that treat such reactions from the point of view of their common features. The present paper constitutes a brief attempt at considering the problem of the nucleation of a new phase at an interface in those cases where the driving force is the free energy change resulting from the reaction between the two adjoining initial phases. Besides the case of oxidation this condition occurs also in the case of eutectoid recombination, for example the formation of f.c.c. solid sol- ution of Fe-C (austenite) from the reaction of Fe$ (cementite) with b.c.c. iron (a Fe). This latter case illustrates fit- tingly the neglect that those reactions suffer: while the very voluminous literature on the metallurgy of steel may be said to be almost exclusively a very careful study of the modalities of austenite decomposition (eutectoid decomposition) only a few articles are devoted to the reverse process leading to the formation of austenite (e.g. refs. 3 and 4). This question of nucleation has been considered in a few previous articles /S-7/ the first of which is the most detailed and contains an extensive bibliography. In some respects the subject of nucleation at an interface between two reacting phases shares common aspects with the precipitation of a new phase from a supersaturated solution which is reviewed in ref. 8. Solid state reactions are not necessarily dominated by nucleation phenomena; readers interested in other aspects (e.g. dif- fusion) of the formation of new solid phases should turn to other sources of information /9-12/. The subject will- be considered in its generality, however, the focus will be limited to those reactions where nucleation is the rate controlling process. Although stresses will not be discussed one should remember that any precise investigation of transformations with small free energy changes are likely to be affected by the stored elastic energy /13/. This is presumed to play a major role in the formation of the rare-earth silicides /S/.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19901125
COLLOQUE DE PHYSIQUE
CLASSICAL THEORY O F NUCLEATION
Some results of the classical theory of nucleation will be briefly recalled to throw some light upon what follows. Initially nucleation has been analyzed in the case of a phase transition, e.g. melting or boiling, for either a pure element or a well defined compound, e.g. H,O, in the vicinity of some temperature equilibrium point, for the examples given O°C or 100°C. Such transitions occur without any change in composition. At the equilibrium point, T,, the free energy change, AG, between one phase and the other is identically zero, so that no change can occur. At any temperature T away from T,, AG assumes a finite value AG, which will drive the system to its state with minimum free energy, as the case might be, depending on whether one is above or below T,. The quantity AGT is equal to the product, AS X (T
-
T,), where AS is the difference in entropy between the two phases. In the actual transition in an homogeneous medium the transition is opposed by the necessity to create a new surface between the forming nucleus of the new phase and the preexisting phase; this "consumes" energy. The nucleation process is modulated by the competition between the decrease in free energy which varies as AGT X r3 and the accompanying increase which varies as a X r2 (where a is the specific surface energy, and r the radius of the nucleus). It is easy to show that as a function of r the total free energy passes through a maximum AG*, proportional to o3/AG% , for a value of the radius r*(critical radius) proportional to a/AGT (here AG, must be expressed per unit volume). For crystals with anisotropic surface energies it is clear that the matter becomes a little more complex, but the details need not concern us. Nuclei with a radius smaller than r* are subcritical in size since a decrease in their size will cause a decrease in the free energy of the system while the growth of nuclei with a radius greater than r* leads to the same result. One assumes a Boltzman's distribution of nuclei with the critical size and the rate of nucleation is evaluated therefrom. Since nucleation involves some diffusion of the element (or component) that enters in the nuclei the actual activation energy for nucleation AG* is the sum of two terms, the first of these is of the form a3/AG$ and the second AE is the activation energy for diffusion. Evaluation of the preexponential terms has been the object of several refinements that need not concern us. The theory as presented relates to homogeneous nucleation, al- though quite often nucleation is heterogeneous. In the results presented below a qualitative understanding of the nucleation effects is reached entirely on the basis of energy considerations, with but passing references to surface energy terms and specific effects due to heterogeneous nucleation.Some remarks of a general nature are needed at this point.
a) The calculation of the rate of nucleation at any temperature away from T, depends entirely on the "isothermal" value of AGT, and is really totally independent of the existence or non existence of any T, in the vicinity of T. That is, the nucleation rate at the temperature T is a function only of the value of AG at that temperature.
b) Thus, nucleation phenomena will be a function only of the magnitude of AG, whether or not the system is evolving in the vicinity of an equilibrium point or not.
c) Nucleation becomes difficult whenever AG becomes sufficiently small because then AG* becomes very big. In the vicinity of an equilibrium point one can make AG* arbitrarily big by placing the system sufficiently close to the equilib- rium point.
d) As a function of temperature below an equilibrium point the rate of nucleation increases at f i s t as AG becomes bigger and AG* becomes smaller, then 1/T becomes so big as to prevent any transformation. The nucleation rate passes through a maximum and then decreases to zero.
e) Above an equilibrium point the rate of nucleation varies as a function of exp (-1/T3), extremely rapidly. There cor- responds to this a sudden change in behavior with increasing temperature which is best illustrated by boiling. If boiling is not artificially stimulated (as it almost always is) it becomes possible to heat liquids far above their equilibrium point, then boiling occurs almost at a fixed temperature with a violence which reminds one of an explosion.
f) In many of the solid state reactions to be considered below, nucleation displays some of the characteristics seen in homogeneous boiling. If the nucleation barrier is high enough, which occurs when AG is sufficiently small, nucleation does not occur until the system is carried up to high temperatures where diffusion (on a small scale at least, some 100 nrn) ceases to be rate limiting. In such cases of thin films reacting with their substrates the samples may react almost instan- taneously.
SOLID STATE REACTIONS
When two phases A and B "welded" to one another across a planar interface react to form a third phase AmB, the driving force is the free energy of formation of the new phase, but the system evolves from a system with one interface A/B with specific energy a, to one with two interfaces A/A,,,B, and AmB,/B with respective surface energies a, and a,. As in the phase transitions considered previously there will generally be an increase in surface energy Aa which opposes the re- action. Neglecting specific aspects of the shape of the nuclei (see references 5 and 8) A a will assume the form (U,
+
a3)-
U,,
and AG* will vary as Aa3/AG2. Most often AG is sufficiently big, and AG* sufficiently small that nucleation is easy and plays no significant role as a rate limiting factor in the kinetics. This is the case for many oxidation reactions at atmospheric pressure, e.g. the formation of SiO, that has been studied in great detail /1,2/ without the intervention of any observable nucleation. In a different domain the same considerations apply to the reactions of metal thin films with silicon substrates resulting in the formation of silicides, according to diffusion controlled kinetics, without any interference from nucleation effects (e.g. NhSi and many others found listed in ref. 14). This will be true as long as AG is sufficiently big, AG* sufficiently small and consequently nucleation sufficiently easy.One may look a little more carefully at some thermodynamic aspects of the initial growth of the new layer. This can be done with reference to fig. 1 where the free energy conditions, at some fixed temperature T, for the reaction of A with B to give AmBn have been sketched. For the sake of simplicity it is assumed here that there is no solubility of A in B, and that the B atoms are mobile in both A and &Bn. The f i s t thing likely to happen in the A/B reaction couple at T, is the solution of B into A. In this process the free energy of the new solid solution would follow the corresponding curve po- tentially until reaching a pseudo equilibrium with B, namely up to the concentration c',. At this point the solid solution is supersaturated in B by a quantity represented on the one hand by the ratio c1,/c, or the difference c',
-
c,, and on the other hand by the free energy difference equal to the quantity MN. The compound A,Bn would then precipitate at the interface with a AG equal toIMN
(per gram atom of supersaturated solid solution of composition c', ) as the driving force.It is seen that the condition has much in common with that of a supersaturated solution of B in A, perhaps quenched from a temperature T, greater than T,, and with a concentration c,. Under these conditions precipitation of A,B, would occur, probably at some grain boundary, with a driving force equal to OP (per gram atom of solution with concentration c).
Certainly some aspects of the formation of a new phase at an interface will be more easily understood by one familiar with the phenomenon of precipitation at grain boundaries as analyzed e.g. in ref. 8. Some evidence for such a process of solution followed by precipitation has been obtained during the oxidation of tantalum /15/.
Again some observations seem warranted at this juncture:
a) In general MN will be larger than OP. (One must be careful here, the quantities MN and OP must be expressed per unit of A,Bn formed in order to be compared. However, once this is done the comparison as done here remains correct).
Since the activation energy varies as AG-z one anticipates that nucleation will be easier in the course of new phase for- mation (as understood here) than during precipitation. Another factor is that the a,, that enters into ha and thereby into AG* (in the third power), is likely to be larger for an A/B interface than at a grain boundary. Thus both the interface and the free energy terms would contribute to ease the formation of a new phase. This agrees with the general observa- tion that most phases form and grow without any evidence of a significant nucleation bamer.
b) In fig. 1 it is seen that MN increases with the free energy of formation of the new phase (given in fig. 1 by the depth of the well representing the free energy curve vs composition for the phase AmB, ). Indeed, one finds that most phases grow with simple diffusion-controlled kinetics, however, when the free energy change characteristic of the reaction AGO becomes small enough, nucleation becomes the overall control mechanism (see below). The quantity AGO may be the free energy of formation of the new phase when the reactants are elements (in their standard state), or some difference in free energies of formation when one (or both) of the reactant is already a compound.
c) It is seen from fig. 1 that AG for the precipitation of the new phase (per gram atom of this new phase) becomes nearly equal to its free energy of formation when the solid solubility the reactants in each other becomes very small.
d) It is clear that the picture presented up to now is greatly simplified. Keeping fig. 1 as it is, one could envision what would happen if B atoms were not mobile, or mobile only in either A or &B, One could then consider some solubility of A into B, the presence of several possible phases, stable as well as metastable, variations in the shape of the free energy curve for the solid solutions, etc
...
It may be that the pursuit of this approach would lead one to a general classification of the processes of phase formation. To the author's knowledge this has not been done for solid-solid reactions.I I 1
0 0
>
"
W Z W Y
E
I l l
A ce CS 2; AnBm B
COMPOSITION
Figure 1. Sketch illustrating the free energy relationships in the nucleation of a phase &B, at the interface between A and B.
cl-806 COLLOQUE DE PHYSIQUE
SYSTEMS WITH AN EQUILIBRIUM POINT
One may look first at examples of systems with an equilibrium point, and this for two different reasons. The f i s t is that eventhough one is dealing now with systems with several interfaces, the systems are thermodynamically close to those that are considered in the classical theory of nucleation. The second is that, even if one does not know exactly the position of the equilibrium on the temperature scale, one is assured that AG is zero at the equilibrium point, and that away from equilibrium AG remains sufficiently small.
One broad class of reactions with an equilibrium point is that of oxidation, where one may define an equilibrium tem- perature at constant pressure and an equilibrium pressure at constant temperature. The matter is discussed in some detail in ref. 7. It has been the object of many observations about a quarter of a century ago, and a beautiful example w n - cerning copper oxidation is provided in fig. 2 (from ref. 16, see also 17). One is placed below the equilibrium temperature so that the rate of nucleation decreases as the temperature increases because of the decrease in AG. The observed nuclei, not nuclei really but what grows after the nuclei are formed, become larger at higher temperature because of an increased rate of diffusion and growth, but that does not concern nucleation proper. The shape of the features observed in the microscope is also a function of preferential growth and cannot be assumed to provide a faithful account of the original shape of the nuclei. The substrate is polycrystalline; the density and rate of nucleation varies with the orientation of the grains as anticipated from theoretical considerations. In this case of copper oxidation one may eliminate the oxide by lowering the oxygen pressure. Upon a new increase in pressure new nuclei form at different locations implying that nucleation in this case is homogeneous, which appears to be in concordance with the absence of numerous nuclei on the grain boundaries. The same is not true of oxidation on other metals, e.g. iron, where, under certain conditions at least, the grain boundaries are heavily decorated with oxide /18/. What has been described here about oxidation is true also of other surface reactions, such as sulfidation /19/.
Figure 2. Surface micrographs illustrating the nucleation of Cu,O at the surface of copper. Oxygen pressure 4 X 10-a Torr, time 10 minutes, magnification 350 X. The oxygen pressure has been deliberately kept low in order to obtain a small AG and a relatively slow observable rate of nucleation. From reference 16.
A second example is that of the growth of PdSi which is discussed in refs. 5 , 7 and 20. When a thin film of palladium is deposited upon a single crystal silicon suhstrate one observes upon heating the formation of Pd,Si at temperatures lower than 200°C. The growth is diffusion-limited with no rate-limiting nucleation effects. Above a eutectoid temperature T,, of the order of 600°C the equilibrium phase becomes PdSi, but that cannot form at T,, since at that temperature AGO is identically zero. Superheating by some 100' is required for any reaction to occur. It is interesting to note that over silicon (1 11) Pd,Si is epitactic with a small a, and a large Ao for the nucleation of PdSi, however, that is not true of Pd,Si over silicon (100). Consequently the nucleation of PdSi requires a superheating of some 200' in the f i s t case and only about half as much in the second one in qualitative agreeement with the classical theory of nucleation as described here. Upon nucleation the temperature is so high and diffusion so rapid that the growth of PdSi appears instantaneous, at least for films of the order of some 100 nm, for experimentalists in clear distinction from the tedious slowly varying diffusion-controlled growth of other phases.
GENERAL CASE OF NUCLEATION-CONTROLLED PHASE FORMATION
The cases considered above concerned systems where one can define equilibrium points but in solid state reactions such as the formation of PdSi, most of the reactions that display the characteristics of nucleation-control occur in systems with no known equilibrium points. (See the list in ref. 5, and for a more recent example, the formation of TiGe,, ref. 21. The reaction of ScSi with silicon to give Sc,Si, has also been found to be nucleation-controlled, ref. 22). The one thing that all of these reactions share in common is a small AGO. An example that has been analyzed in some detail in ref. 7 is that of Nisi, from the reaction of NiSi with silicon. In such cases AGO is the difference between the free energies of formation of NiSi, and NiSi. Thermodynamic data show no transitions from the "nucleation" temperature, about 800°C all the way down to 0 K, but a slowly increasing AGO with increasing temperature. As a matter of fact it is difficult to gauge accurately such small changes in free energies since the difference that one is interested in is likely to be smaller than the limit of accuracy of the values listed for the free energies of formation of the respective compounds. When a layer of Ni deposited over silicon is heated one observes in sequence the formation of Ni,Si and of Nisi below 500°C. Both re- actions are diffusion-controlled. Although the equilibrium phase in contact with silicon is NiS4, further heating causes no change in the samples until a temperature in the vicinity of 800°C is reached, when nearly at once the film is trans- formed into NiSi,. The nucleation barrier and the "nucleation" temperature are so high and diffusion so rapid that the reaction occurs nearly instantaneously. 'Slight modifications in AGO can alter significantly this mode of behavior. One can increase the driving force by chosing metastable reactants, either amorphous silicon or metastable (in very thin layers over (1 11) silicon) NiSi with the N i s structure /23,24/, in both cases the growth of NiSi, occurs then at much lower temperatures and with diffusion-controlled characteristics. The density of nuclei over single crystal silicon varies greatly from system to systems and can reach remarkably small densities, e.g. in the reaction of RhSi with silicon to give Rh&, individual nuclei are separated by distances of the order of a few millirneters, visible with the naked eye /5,6/. At the nucleation sites the new phase grows through the thickness of the films and then spreads laterally, often with a periodicity similar to what is observed in the explosive crystallization of amorphous films. In all cases where information could be obtained it is clear that nucleation is heterogeneous and does not occur at random on the silicon surface, but for example in the formation of CoSi, /25/ at CoSi grain boundaries.
It is indeed quite remarkable that in the course of a large number of investigations reactions seem to belong quite neatly to one or the other of the two categories considered here, namely either diffusion or nucleation controlled. This consti- tutes, however, a gross generalization; nature is not always so simple. Other phenomena, including effects known as re- action rate limitations, e.g. in the formation of SiO, / l / as well as in other reactions /9,10-12/, occur. Depending on the magnitude of AGO the nucleation "temperature" need not be so high as to render diffusion insignificant as a rate limiting mechanism. The formation /24/ of Cos4 (isostructural with Nisi,) offers a good example of a phase formation where nucleation and diffusion controls overlap. In comparison with Nisi, this indicates that AGO is slightly larger (making nucleation easier and lowering the "nucleation" temperature), which is in keeping with the observation that the stability of the disilicides increases, for metals belonging to the same period of the periodic table, as the number of electrons decreases.
EXTENSION AND CONSEQUENCES
Some aspects of phase nucleation at "high" temperatures can be qualitatively explained from the classical theory of nucleation which provides easy means of understanding the different roles played by free energy andsurface energy terms.
A more thorough understanding of themechanisms involved in phase formation should take into account such details microscopic and spectroscopic information as found, for example, in ref. 27. Moreover, while looking into details some limits of the classical theory become apparent, so that more sophisticated means must be used. The lead provided in ref.
28 towards using the Cahn-Hilliard theory of nucleation should be followed. The idea explored therein of a new phase spreading laterally at an interface may be supported by recent electron microscopic observations /29/. It is clear that the nucleation of a new phase at an interface can be difficult and interfere seriously with the character of an anticipated reaction. Occasionally, at low temperatures it may prevent the occurence of some phases / 5 / . Even when not so drastic a difficult nucleation process may have deleterious effects in preventing the formation of a very smooth, uniform surface layer. One may attempt to circumvent such difficulties by increasing the driving force, e.g. as already indicated in the case
Cl-808 COLLOQUE DE PHYSIQUE
of Nisi, by changing the nature of the reactants. One may also use ion bombardment at the reaction interface, which 1) by damage increases the energy level of the reactants, 2) affects the initial interface energy, and/or 3) by ion beam mixing effect nucleates the new phase. (It may also eliminate the retarding effect of an interference film, e.g. silicon oxide, but that is another matter). In some cases the use of rapid thermal annealing processes may force nucleation to occur at temperatures higher than those that obtain under more conventional heating, and thereby increase the density of nuclei and improve the uniformity of the reacted layer. The importance of difficult nucleation effects in dictating reaction paths has been sufficiently stressed here. This does not mean that all reactions observed to occur at discrete surface locations are regulated by nucleation. With thin oxide films it has been observed that the reaction of silicon with SiO, (solid) to form SiO (gas) occur at isolated locations /30/. From a thermodynamic point of view that reaction is similar to a sublimation; it can occur only at a free surface, not inside a solid. If it is shown to occur at discrete locations at an interface, it is only because the oxide film is already broken, or so weak as to be unable to sustain any pressure. That is a matter concerning the quality of the oxide film, and has nothing to do with interface nucleation, either homogeneous or heterogeneous. The report that the density of sites increases with decreasing oxide thickness supports this conclusion /31/.
ACKNOWLEDGEMENTS.
The author is particularly thankful to Prof. GrGnlund for the permission to reproduce fig. 2. It is also his pleasure to acknowledge his gratitude to many colleagues with whom he has had the privilege of discussing nucleation: P. Gas, R.
Ghez, P. Gordon, E. Irene, J. Oudar, J. Philibert, K. Russel, 0. Thomas, W. Tiller and many others too numerous to be mentioned here.
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