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322 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

akin to a Jahn-Teller effect occurs that destroys the degeneracy of the

structure and opens an energy gap, making FeSi

a semiconductor with

zero states at the Fermi level. Christensen

[130]

does not give the curve for

CuSi

, but for such a compound the Fermi level would move toward

higher energies and higher density of states among the antibonding states;

such a structure would be highly unstable, so that the highest stable sili-

cide of Cu is CuSi. It is very likely therefore that for silicides with the

CaF

structure, the cohesive energies as a function of the number of elec-

trons are distributed along some parabolic curve, descending from FeSi

to CoSi

and then ascending again with NiSi

and CuSi

, with a minimum

for an alloy of (Co, Ni)Si

, for which the Fermi level falls at or near the

bottom of the pseudogap.

[131]

Experimentally, such a model would agree

with an increased value of ∆G and enhanced nucleation of CoSi

, even

with small alloying additions of Ni. Such considerations about DOS

curves and Fermi levels have a rather qualitative character because they

do not give a complete account of the total cohesive energy of a crystal.

However, they find strong support in the fact that Fe additions to Co have

precisely the opposite effect of Ni additions: With 2 at.% Fe, and a heat-

ing rate of 3 K/s, the temperature of nucleation of CoSi

is increased by

50 K. The monosilicides with the same structure are totally soluble, and

at the level of alloying, Fe is also soluble in CoSi

. This eliminates the

possibility of significant entropy of mixing effects, so that what is

observed must be due to enthalpy. Further confirmation of this DOS effect

is found in the ternary phase diagrams,

[132]

where it is seen that FeSi

more soluble (by a factor of 10 or more) in NiSi

than in CoSi

because,

in the first case, it lowers the density (of NiSi

) at the Fermi level, and in

the second case, it increases it. As a first approximation, we would have

expected the disilicides to behave like the monosilicides: The monosili-

cides of Fe and Co (near neighbors in the Periodic Table) have the same

structure and are totally soluble. However, in going over to Ni, there is a

change in structure and only limited solubility (of FeSi and NiSi). As in

many such considerations about nucleation, nothing has been said here

about surface energy. Considering the similarity between Co and Ni, seg-

regation effects would tend to be small, and almost nonexistent for the

solid solution NiSi

-CoSi

. Some interface segregation of Ni might be

expected in CoSi (because of the limited solubility), but if such segrega-

tion stabilized the monosilicide, because of a reduced surface energy, it

would result in an effect opposite to what is observed.

The concern with silicide contact is not so much the upper surface as

seen by elastic light scattering but the interface with Si. Epitaxy and

reduced interface roughness can be obtained by the initial intercalation of

some Ti

[133]

between the Si substrate and the Co film. Similar results have

been achieved with other transition metals,

[134]

where the effect of such

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REACTIVE PHASE FORMATION, D’HEURLE ET AL. 323

intercalated layers is attributed to kinetics: reduction in the rate of growth

of the disilicide would enhance epitaxy.

6.3.3 Nickel Monosilicide

Although CoSi

has been used with considerable success for self-

aligned silicide technology (usually misnamed “salicide,” which brings to

mind not Si technology but some form of aspirin), this compound suffers

from serious defects: The reaction between Co and Si is quite sensitive to

the presence of surface impurities, including oxide, that are difficult to

avoid in actual device fabrication. So attention has turned to studies of

NiSi, which presents a number of advantages. In the sequence of phase

formation, it follows after the formation of Ni

Si, but the transition does

not involve any nucleation-controlled step, so it is quite smooth. Because

of its low resistivity and composition for conductors of equal resistance,

it requires a reduced consumption of Si, which is important with ever

more shallow junctions (n/p or p/n at source and drains, for example).

This problem of shallow depth is emphasized further in the current sili-

con-on-insulator (SOI) technology. In classical studies, namely with Ni

films about 100 nm thick and isothermal annealing, NiSi forms after

Si, with the two reactions diffusion controlled and the layers remain-

ing extremely smooth. However, during rapid thermal processing of thin

layers, other nickel-rich silicides have been observed,

[135]

which will

require further investigations. In a recent publication,

[136]

NiSi is reported

to have a serious advantage over its competitors (TiSi

and CoSi

): lower

stresses, both in the silicide itself and in the adjacent Si. However low

these stresses might be, they have been the cause of a serious error; the

lattice parameters derived from diffraction measurements on thin films

[52]

and incorporated in the reference literature

[137]

are not equilibrium values,

but correspond to stressed films.

[138]

The correct, equilibrium unit cell

dimensions should be close to a  0.5175 nm, b  0.3321 nm, and c 

0.5609 nm.

[139, 140]

The expansion coefficients along the a and c axes are

extremely large,

[138–140]

which would lead to high residual tensile stresses

in the films at room temperature; that this is not so implies low elastic

modulii. Curiously, however, the expansion coefficient along the b axis is

negative.

NiSi forms rather easily via two diffusion-controlled steps, and would

be quite satisfactory as such. However, NiSi reacts with Si to form NiSi

via a nucleation-controlled reaction that normally occurs at about 750 to

800°C. Such a step is definitely undesirable when working with NiSi. In

practical applications, with possibly strange topography and various

dopants and levels of doping, the danger exists that the disilicide would

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324 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

form at temperatures below 750°C. So with this compound, efforts are

directed toward making the nucleation of NiSi

more difficult. Considerable

success has been met in this regard by the addition of Pt to Ni.

[141]

It turns

out that PtSi, with the same structure as NiSi (MnP), is relatively soluble

in NiSi, but the solubility of Pt in NiSi

is almost nil. Thus with solubility

of Pt in the monosilicide and lack of solubility in the disilicide, the

entropy of mixing would increase the stability of NiSi with respect to

NiSi

. Addition to Ni of some 5 at.% Pt increases the nucleation tempera-

ture of NiSi

to above 900°C. The authors of the original article

[141]

are

careful to point out that surface effects can also enter into these consider-

ations. To this we can add that (1) entropy of mixing effects would appear

to be sufficient to explain the results observed, and (2) if there is surface

segregation of Pt, it is more likely to happen with the disilicide because of

the low solubility than in the monosilicide. As a first approximation we

can anticipate such an effect to stabilize the disilicide, in opposition to

what occurs. Be that as it may, experimental evidence that Pt additions

delay the agglomeration of NiSi implies that Pt is surface active in the sys-

tem Si-NiSi and presumably in NiSi

as well.

[142]

Yet NiSi is not entirely problem-free. It has been reported that films of

NiSi on (100)Si develop at the interface little pyramids of NiSi

with (111)

faces that penetrate into the substrate.

[143]

Assuming equality of the free

energies of formation of the monosilicides and disilicides, such a phenom-

enon will be energetically favored if the interface energy between NiSi and

(100)Si is greater than that of epitaxial NiSi

with (111)Si by a factor

greater than √3 (according to the ratio of areas). Dopants are likely to influ-

ence such pyramidal formations. We may be encountering here truly thin-

film effects (not operative in bulk samples): Differences in surface energy

may enhance the formation of a thin epitaxial film of NiSi

(not necessar-

ily smooth but faceted), under conditions that would cause the formation

of NiSi with thicker samples. NiSi suffers from another defect that almost

directly results from its own composition. The compound has been quite

elegantly shown to form via the diffusion of Ni atoms,

[144]

However,

because of the equiatomic composition, the less mobile Si atoms should

diffuse quite readily at temperatures not much higher than those required

for Ni motion. Such motion of Si makes it possible for films of NiSi to

agglomerate even before the formation of NiSi

, and that, more than the

nucleation of the disilicide, may limit the use of NiSi.

6.4 Conclusions

Phases formed as a result of reactive diffusion will grow according to

parabolic kinetics if the growth is controlled entirely by diffusion, or

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REACTIVE PHASE FORMATION, D’HEURLE ET AL. 325

according to linear parabolic kinetics if the initial stage of growth can be

expressed in the form L proportional to t

with n greater or equal to 1.

Mathematically, in the first case, if several phases should grow, they

would start to grow at time zero, although physically, things would be dif-

ferent with the phase characterized by the highest diffusion coefficient

growing first, followed by the others. In the other case, where growth can

be approximated by linear-parabolic kinetics, the phases should appear

sequentially. Ideally, the linear effect could be due to kinetics limited by

an interface reaction rate, but there is little experimental evidence to prove

that this is indeed physically correct.

In metal-silicon reactions, at least, the kinetics clearly obey linear-

parabolic equations, even if it is difficult to obtain precise information

about any interface reaction.

In the reaction between A and B, where A and B are elements, the

driving force for the reaction will often be high enough to make nucle-

ation relatively easy, so that the kinetics are dominated by diffusion

phenomena.

Nucleation is characterized by an activation energy ∆G*, which is the

sum of two terms (∆G*  ∆G*

 ∆G*

kin

). The first of these, ∆G*

, pro-

portional to ∆s

∆G

eff

, provides the density of nuclei of critical size; the

second term, ∆G*

kin

, gives a measure of the rate at which these nuclei can

grow, which is necessary for nucleation to occur. ∆G

eff

is the sum (in

actual value difference) of the chemical driving force (negative) ∆G and

the elastic energy (positive) ∆H

elas

Diffusion-type phenomena will usually dictate what is the first phase

to form. In reactions between metallic elements that have different melt-

ing points, the first phase to form will usually be a phase richest in the ele-

ment with the lowest melting point. Si should be excluded from this

scheme as it undergoes a state transformation during a reaction with a

metal. However, nucleation phenomena dictated by interface energy and

elastic energy considerations (∆G*

) may account for a selection between

phases with close compositions, or stable and metastable forms of a phase

with a given composition. We usually lack sufficient information to even

offer plausible explanations for such natural choices; except in some

cases, for example, when a metastable phase is clearly the result of epi-

taxy between the phase and the substrate. Quite often, the selection of the

first phase to form will depend in some obscure way upon the mode of

sample preparation.

The change in free energy in going from one phase to the next may

become very small. This is because, given the fundamental chemical fact

that in the series such as AB

to AB

(with the subscripts increasing

monotonically from n to z), the gain in free energy for additional B’s

decreases continuously, consequently in going from one phase to the next

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326 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

the change in free energy becomes smaller. At some point, nucleation

becomes the rate-controlling mechanism for the formation of a new phase.

This effect will be most remarkable at low temperatures, for example, in

thin-film reactions, and may play only a minor role in bulk reactions at

high temperatures. It is easy to understand this qualitatively, but unfortu-

nately, we often lack sufficiently precise thermodynamic information to

make possible any significant quantitative evaluation.

One consequence of a difficult nucleation, and therefore a low density

of nucleation sites, is that the reaction products, in thin films at least, will

tend to display a very rough surface. That is quite undesirable from a prac-

tical point of view but provides means of pinpointing nucleation phenom-

ena by relatively simple optical means. Such means revealed that in the

formation of TiSi

, with the desired C54 structure, initially the C49 struc-

ture itself is nucleation-controlled. It is hoped that this recent work

(Sec. 6.3) will lead to a better understanding of the mechanisms of for-

mation of not only TiSi

, but of other transition metal silicides such as

VSi

or WSi

Even if the precise thermodynamic data about the nucleation of

phases such as CoSi

and NiSi

are not available, it is known that the free-

energy changes are small and can therefore be modified by alloy addi-

tions, altering the ∆G’s due to the entropy of mixing. Furthermore, in the

case of effects observed with small alloying additions, where mixing

effects would not be significant, we can tentatively explain observed

effects from an analysis of alloying effects on the density of state curves.

Acknowledgments

The authors wish to express their appreciation to a number of col-

leagues who contributed to this chapter in various ways: J. Tersoff,

D. Migas, and L. Miglio for discussions about density of state curves; and

R. Vandermeer for comments about phase boundary motion. Many people

contributed in some ways or another to our understanding of the phenom-

ena analyzed in this chapter: C. Cabral, Jr., J. Dempsey, V. Dybkov,

T. Finstad, R. Ghez, D. Gupta, A. Gusak, J. Harper, E. A. Irene, S. La

Placa, C. S. Petersson, S. Privitera, O. Thomas, S.-L. Zhang, and many

others too numerous to list here. Several friends read the manuscript in

various states of completion; we are grateful to them all for their kind

help. This chapter covers the work done by many investigators over a long

period of time; inevitably, some references that should have been given

were accidentally ignored. We offer our sincere apologies to all those who

should have been quoted but were not.

Ch_06.qxd 11/12/04 4:06 PM Page 326

REACTIVE PHASE FORMATION, D’HEURLE ET AL. 327

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