Gupta D. (Ed.). Diffusion Processes in Advanced Technological Materials

Подождите немного. Документ загружается.

312 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

point of about 1500°C is quite high. So, not trusting the computer fitting

of a large quantity of data, the value of ∆G

mot

was obtained by direct

observation of the evolution of the largest grain size as a function of time

and temperature. The activation energy thus obtained was the same: about

4 eV.

[96]

In a pure material, the activation energy for the motion of the

C49C54 boundary should be defined, as in recrystallization or grain

growth, by the grain boundary diffusion of the slow element; here, the

slow element was Ti. In a recent paper,

[97]

a maximum value of about 3 eV

was estimated for such a process. The key to this discrepancy between

anticipated and experimentally derived activation energies would be that

the material is not pure.

Some investigators

[98]

observing the motion of the C49C54 bound-

aries in an electron microscope equipped with a residual gas analyzer dis-

covered a quite strong hydrogen signal occurring simultaneously with the

growth. It too had an apparent activation energy of about 4 eV, the same

as the other(s). This cannot be the activation energy for the evolution of

hydrogen from the grain boundaries of TiSi

, which is most probably of

the order of 1 eV, half of which would be for diffusion and the other half

for desorption (perhaps 1.5 eV if we assume hydrogen traps with a trap-

ping energy of 1 eV). It is hard to guess, but for diffusion of hydrogen in

Ni (with a melting point close to that of TiSi

), the activation energy is

0.4 eV.

[99]

That value is for lattice diffusion, but it seems that the grain

boundary diffusion of hydrogen is hardly any larger than that in the

lattice.

[100]

The analysis of boundary motion during recrystallization

[101]

impure materials (with impurity contents in the range of parts per million)

depends on the impurity drag effect.

[102]

At low temperatures, the segrega-

tion of impurities to the boundaries and the attraction between these impu-

rities and a moving boundary cause the activation energy to have a higher

value, equal to that for lattice diffusion plus the energy of segregation

(or rather desegregation) of the impurities. At high temperatures, where

entropy dictates that the impurities should “evaporate” from the bound-

aries, the activation energy equals the value for grain boundary diffusion.

In an intermediate temperature region between “low and high,” the appar-

ent activation energy assumes meaninglessly very high values that cannot

be defined analytically.

[103]

In the present case of the C49 to C54 transfor-

mation of TiSi

in thin films, available data are unfortunately limited to a

very narrow range of temperatures (30 K in the most extensive study

[92]

so that we do not have any knowledge of its behavior in low, high, or

intermediate temperatures. Thus, the apparent activation energy value of

4 eV could be meaningless (intermediate range) or correspond to the sum

of the activation energy for the lattice diffusion of Ti (not measured, but

probably about 3 eV) plus those for the desorption and diffusion of hydro-

gen. The effect of hydrogen has been discussed as an example of the

Ch_06.qxd 11/12/04 4:06 PM Page 312

REACTIVE PHASE FORMATION, D’HEURLE ET AL. 313

impurity drag effect;

[102]

yet it may also result from the hindering effect of

impurities on grain boundary diffusion,

[71]

usually thought of as occurring

in fixed grain boundaries, although the two effects should not be consid-

ered to be exclusive of one another. Support for such a view is found in

the important retardation of electromigration failure in Al thin-film con-

ductors in the presence of hydrogen.

[104]

Furthermore, it was observed that

the formation of purple plague (Au

Al) at Al-Au contacts was almost

completely suppressed in samples annealed in hydrogen,

[103]

and similar

results were obtained in the reactions of Cu, Ag, and Ni with Sn.

[105]

This

impurity effect on grain boundary diffusion is also illustrated in the self-

aligned technology, where the goal is to obtain a Ti disilicide over source,

drain, and gate, but not over the short spaces that separate source and

drain from the gate. With a continuous Ti film annealed in a vacuum or an

inert atmosphere, a most unwanted bridging occurs via the diffusion of Si

either in Ti itself or in one of the precursor phases to C49 TiSi

. That phe-

nomenon is prevented

[106]

by annealing in nitrogen, seemingly because the

small interstitial nitrogen atoms diffuse rapidly in the grain boundaries

where they successfully block any subsequent diffusion of Si atoms.

With very thin films (10 nm) in current devices, the question of the

roughness of the layers used becomes important, which led to the system-

atic study of that roughness by optical means,

[107]

used in situ during the

heating of samples at constant ramp rates. Such a study

[108]

reveals a

strong roughening at about 600°C (see Fig. 6.8), corresponding to the for-

mation of the C49 phase of TiSi

, and no roughening at the temperature of

the C49 to C54 transition. The latter should not be surprising. (The small

light-scattering peak for distances of 5 mm at about 800°C for that trans-

formation is undoubtedly due to the difference in refractive indices for the

two phases, not to topological irregularities.) The paramorphic transfor-

mation implies small changes in volume and therefore small changes in

the surface aspect of the film. The signal obtained at 600°C for lateral dis-

tances of the order of 5 mm reveals a nucleation-controlled reaction, with

bumps on the samples for each nucleation center. (A study as a function

of scattering angles or laser wavelengths would indicate the average dis-

tance between such sites.) As the film transforms completely, the bumps

disappear, and so does the scattering signal. With the new phase, C49

TiSi

grows in “cauliflower” fashion from the nucleation centers.

Scattering corresponding to short distances (0.5 mm) reveals the local

roughness at the surface of the cauliflowers, which does not change sig-

nificantly with the completion of the process.

Before we attempt to analyze a possible nucleation process in the ini-

tial formation of TiSi

, we should consider what happens before that stage

in Fig. 6.8. In the diffraction pattern, at low temperatures, the line at about

45 degrees is the (101) line of Ti and at 44 degrees is the (002) line. The

Ch_06.qxd 11/12/04 4:06 PM Page 313

314 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

latter reveals what may be assumed to be an abnormally high expansion

coefficient, but that would be incorrect. The somewhat surprising behav-

ior is due to the dissolution of oxygen, which increases the c axis of

hexagonal Ti without significantly affecting the other axis, a. Values

obtained by Villars and Calvert

[109]

are a  0.2951 nm and c  0.4685 nm

for Ti, a  0.296 nm and c  0.483 nm for Ti

O, and intermediate values

for lower oxygen content. The oxygen intake causes the corresponding

increase in resistivity (Fig. 6.8), an increase that does not occur if the film

is protected against possible oxidation.

[110]

Figure 6.8. (A) Simultaneous measurements of resistance and roughness at two

different lateral scales during heating at 3 K/sec of a Ti film (20 nm thick) on poly-

crystalline Si. (B) Partial x-ray diffraction diagrams showing distinctly the formation

of the C49 and C54 phases of TiSi

. Note the correspondence between the fea-

tures in the two sets of pictures.

Ch_06.qxd 11/12/04 4:06 PM Page 314

REACTIVE PHASE FORMATION, D’HEURLE ET AL. 315

It had long been known

[26]

that the so-called ill-behaved silicides,

including TiSi

, became rough in appearance (to the naked eye) during

preparation, and that this roughness implies some nucleation-controlled

reaction. However, while in the case of NiSi

, for example, the preceding

phase NiSi was clearly identified, and the small ∆G driving the reaction

was thereby identified also, the same has not been true of TiSi

, or MoSi

and so forth. It was thus difficult to know at what stage of the reaction the

samples became rough. With the help of Fig. 6.8, we now know that

roughness occurs simultaneously with the nucleation of the C49 phase. In

the continuous absence of firm information about what precedes the C49

phase, we hazard here some educated guesses. It is probable that the pre-

ceding phase or phases have not been clearly identified for a number of

reasons: Amorphous phases are not clearly seen in x-ray diffraction. In the

case of Ti-Si reactions, a number of phases exist (TiSi, Ti

, and Ti

)

that are hard to identify because they have somewhat similar x-ray dif-

fraction patterns, often very poorly displayed from thin-film samples.

Finally, while the rough appearance of the C49 phase is constantly annoy-

ing in all samples, it probably varies with the sample preparation such as

the mode of film deposition and the doping of the substrates. A possible

reaction would be:

TiSi  Si  TiSi

(C49). (23)

(Because the phase considered here is C49, we must take into account

the small enthalpy difference between C49 and C54.) According to

Hodaj and Dumas,

[28]

the standard enthalpy change for this reaction

would be 3.5 ± 36 kJ/mol, which is extremely small. Although crys-

talline TiSi does not seem to form during the reaction of Ti with Si, there

are reports of the formation of an amorphous phase with a composition

close to TiSi.

[111, 112]

With TiSi in an amorphous state, the enthalpy

change for Eq. (23) would be increased (in absolute value) by an amount

corresponding to the crystallization of that phase; that may not be

enough for the formation of the TiSi

to cease to be nucleation-controlled.

Since Ti

has been observed in some experiments,

[113, 114]

we can

consider:

15 Ti

 75 Si  TiSi

(C49). (24)

The standard enthalpy change

[28]

for this would be 13.5 ± 36 kJ/mol.

This seems bigger than the preceding value (as anticipated, considering

the greater change in composition), but could still be small enough to

cause the reaction to be nucleation-controlled. [Compare this with

Eq. (21).] According to a recent publication, the phases Si, Ti

, and the

Ch_06.qxd 11/12/04 4:06 PM Page 315

316 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

two forms of TiSi

can coexist, which implies some sort of equilibrium

among them.

[115]

Moreover, the phase Ti

, like other such transition

metal silicides with the same formula, should be stabilized by interstitial

impurities: oxygen, carbon, and nitrogen.

[116]

A considerable amount of

research

[117–119]

has been devoted to this subject. The impurity atoms,

including hydrogen, occupy the center of trigonal antiprisms, with binding

energies that can be high enough to decrease the overall lattice parame-

ters. At high temperatures, oxygen impurities in Zr

completely desta-

bilize adjacent phases such as Zr

Si, implying a considerable decrease in

the free energy of the 53 phase. Yet quantitative data for the low-

temperature reaction of interest here could not be found. In practice, with

unavoidable contamination, the ∆H and (∆G) for Eq. (24) could be con-

siderably smaller than evaluated here. Thus, whether considering Eq. (23)

or (24), we can find some theoretical justification for the nucleation-

controlled formation of the C49 phase of TiSi

. Nothing has been said

about interface energy and stress effects, although we know that these fac-

tors are very important physically. Experimentally, more effort should be

spent to identify the precursor phase in TiSi

formation, as well as for

other such phases, for example, MoSi

. We should note that in the reac-

tion of Ti with crystalline Ge, the reaction:

 Ge → TiGe

(C54) (25)

is clearly nucleation-controlled.

[61]

When considering small driving forces, as in any form of nucle-

ation-controlled reactions or transformations, remember that the ∆G’s

and the ∆H’s cease to be comparable. Moreover, we should not use the

table values for the stoichiometric compounds, but should operate from

the actual curves for the various ∆G

’s as a function of composition. So

the message is that the approach used here, based on table values of

∆H’s, provides a simple tool to differentiate diffusion-controlled from

nucleation-controlled reactions. Where possible, refer to tables that

give the free energies of compounds (and elements). According to the

most recent thermodynamic evaluation of the Ti-Si system,

[120]

the free

energy change at 900 K for Eq. (23) would be 20.8 kJ, including the

correction for the C49 to C54 transition.

[91]

The same reference explic-

itly mentions that the phase Ti

can contain significant amounts of

excess Si substitutionally located on one of the two different Ti sites, so

that for our purpose (in the presence of excess Si), its formula should

be (Ti,Si)

. For Eq. (24), assuming stoichiometric Ti

, ∆G

would be 53.5 kJ. This quantity would be much reduced, in absolute

value, for Ti

saturated with Si and/or contaminated with interstitial

impurities.

Ch_06.qxd 11/12/04 4:06 PM Page 316

REACTIVE PHASE FORMATION, D’HEURLE ET AL. 317

6.3.2 Cobalt Disilicide, Entropy of Mixing,

(Possible) Enthalpy and Density-of-State

Effects in Ternary Reactions

With conductor dimensions reduced below about 0.3 mm, the operat-

ing window between the temperatures necessary to nucleate the C54

form of TiSi

and that at which surface energy effects cause the films to

break into separate islands has become intolerably small. Thus attention

was turned to CoSi

, with a similar or even somewhat smaller resistivity,

which does not suffer from the kind of paramorphic transformation that

plagues users of TiSi

. Because f.c.c Co and Ni are so similar from a met-

allurgical point of view, it is not surprising that the sequence of metal-

silicon reactions is the same with both metals: first Co

Si, then CoSi and

CoSi

. Although it is not especially relevant to what follows, we should

note that the Co-Si phase diagram is much simpler than that of Ni-Si,

with no phase corresponding to Ni

, and without several metal-rich

phases. Although the phase sequences are similar with the two metals, on

a temperature scale the formation of CoSi

is not so distinct from that of

CoSi as the formation of NiSi

from that of NiSi. Yet early measurements

showed that during isothermal heat treatments, the growth of CoSi

ceased to be parabolic as the temperature was lowered towards 500°C,

[121]

and indeed the formation of CoSi

becomes practically impossible below

that temperature. By comparison with NiSi

, the effect was correctly

attributed to a difficult nucleation. Recent results give a ∆H

of 95 ± 4

kJ/mol for the formation of CoSi and 99 ± 6 kJ/mol for CoSi

[122]

resulting in a difference of 4 ± 10 kJ/mol for the nucleation of that

phase, a value commensurate with 5 ± 20 kJ/mol for the nucleation of

NiSi

[Eq. (21)]. The two values are nearly equal, as anticipated within

the limits of accuracy.

One problem with CoSi

is that on account of its nucleation-controlled

formation, its surface is rough. Attempts made to reduce the roughness by

alloying reveal some interesting aspects of the control of ∆G, the driving

force that enters into ∆G*

(∆s

∆G

) and thus controls the density of

critical nuclei. The effect is well illustrated in Fig. 6.9, where the nucle-

ation temperature for the formation of CoSi

is seen to increase when the

Co film is alloyed with different amounts of Ge. (See Lavoie et al.

[123]

for

this and other alloying elements.) An opposite effect had been observed

with the use of Co additions to Ni, where alloying with 50 at.% reduced

the nucleation temperature to about 350°C,

[124]

below what is required to

nucleate pure CoSi

. In that case, the two preceding phases, NiSi and

CoSi, with different structures (respectively, MnPtype: orthorhombic, and

FeSi type: cubic, complex) did not mix and were clearly separated. In

Ch_06.qxd 11/12/04 4:06 PM Page 317

318 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Fig. 6.10, the NiSi and CoSi monosilicides are seen to form in the same

sequence near the Si substrate and at the surface, regardless of the order

of the metal film depositions, Co then Ni, or vice versa, or alloyed solid

solution. The new solid solution (Co, Ni)Si

forms at the interface between

the two phases, clear evidence of the role of nucleation control. The key

Figure 6.9 Elastic scattering of light for two different lateral scales, (A) 5 mm and

(B) 0.5 mm, for a Co film with various amounts of Ge during heating on Si (100) at

3 K/s. The sharp features correspond to the nucleation and formation of CoSi

There is very little evolution of roughness below 600°C during the formation of

Si and then CoSi. Both of these reactions are diffusion-controlled.

Ch_06.qxd 11/12/04 4:06 PM Page 318

REACTIVE PHASE FORMATION, D’HEURLE ET AL. 319

point here is the new phase, a single-disilicide phase, made possible by the

nearly total similarity of NiSi

with CoSi

, which have the same structure

(CaF

) and the same lattice parameters; namely, a solid solution of the

two. The reaction then becomes:

12 CoSi  12 NiSi  Si  (Co, Ni)Si

. (26)

For such a reaction, in comparison with Eq. (21) for the formation of NiSi

and identically for CoSi

, the ∆G is increased by a quantity proportional

to the entropy of mixing. For one mole of (Co, Ni)Si

, that quantity would

be kT[xlnx  (1x)ln(1x)], where x is the metal composition [from

0 to 1, but 12 in Eq. (26)]. The increased ∆G increases the density of crit-

ical nuclei and thereby decreases the temperature at which nucleation is

observed. For the additions of Ge to Co (Fig. 6.9), the effect is opposite

Figure 6.10 Backscattering spectra showing the formation of (Ni, Co)Si

at the

interface between NiSi and CoSi, where entropy of mixing effects increase the

free-energy change for the formation of the disilicide solid solution. The position of

the initial transformation underlines the importance of nucleation in opposition to

diffusion as the controlling mechanism.

[91]

The spectra correspond to samples

(Si/Co/Ni) heated at 475°C for 1.5, 3, 7, 12, and 34 hours, respectively. Back-

scattering alone does not enable us to distinguish between Co and Ni; that was

done separately by means of Auger spectroscopy.

Ch_06.qxd 11/12/04 4:06 PM Page 319

320 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

because, in that case, the monosilicide and monogermanide are soluble

(with the same structure and compatible lattice parameters). The diger-

manide and disilicide with different structures appear not to be very mis-

cible. The reaction has the form:

Co[Si

(1x)

, Ge

]  Si → (1x)CoSi

 12 xCoGe

. (27)

Compared to Eqs. (21) and (26), Eq. (27), going from left to right, entails

a decrease in entropy, a decrease in the absolute value of ∆G, a decrease

in the density of nuclei, and, as observed, an increase in the nucleation

temperature. A number of alloying additions are observed to behave

according to either Eq. (26) or (27); these are nicely systematized by

Detavernier et al.

[125]

If excess Si is present with the product phases in 27,

as is often the case, the digermanide can be reduced to CoSi

and Ge sub-

sequent to its formation. This is due to the higher stability of the silicides

in comparison to the germanides (higher heats of formation in absolute

values). The latter effect, however, is not germane to this discussion.

These qualitative considerations are fundamentally correct, and with

Co-Ni alloys, they apply fully with compositions near 50%. However, we

must be careful. Aternary section of the Co-Ni-Si equilibrium phase dia-

gram, with Si at the top, is dominated by two parallel (horizontal) domains

of complete solubilites for the dimetal silicides and the disilicides and in

the middle a third region for the monosilicides, with solid solution

domains extending to about 20% on each side separated by an immisci-

bility gap.

[126]

Between 500 and 800°C, where CoSi

or (Co, Ni)Si

nucle-

ates, no drastic change is anticipated. Then why should small amounts of

Ni additions, as low as 2%, cause detectable reduction in the nucleation

temperature? Inasmuch as both the parent monosilicide and the product

disilicide phases are solid solutions, an explanation based on the entropy

of mixing fails. It is probable that the effect is due to an additional

enthalpy effect in the disilicide. In general, phases are most stable when

the density of state (DOS) at the Fermi level is low. Other things being

equal, a structure with the Fermi level at a minimum in the DOS curve

implies a maximum in the number of bonding states below the Fermi

level, and low energy levels for those states. This is exemplified by semi-

conductors where the density of states falls to zero in the gap: Compare

diamond to nitrogen, adjacent in the Periodic Table, or Si to Al, or Ge to

Ga. More subtle examples can be found. For the transition metals with

BCC structure, the calculated density of states at the Fermi level is found

in a trough (referred to as pseudo gap) in the BCC but not in the FCC

structure. It is the BCC structure that is stable [127, p. 135]. For HCPmet-

als (Zr, Hf, Ru, and Os), the Fermi level is also found at troughs in the

DOS curves.

[128]

In the Hume-Rothery phases, the b and g brasses in the

Ch_06.qxd 11/12/04 4:06 PM Page 320

REACTIVE PHASE FORMATION, D’HEURLE ET AL. 321

Cu-Zn system, the density of states at the Fermi level is also at a minimum.

[129]

Figure 6.11 displays the DOS versus energy curve for CoSi

[130]

The

Fermi level is found with bonding states on the low-energy side of a

pseudogap. For NiSi

, with one more electron, and for FeSi

(in the CaF

structure), with one less electron, the curves are nearly identical although

somewhat shifted on the energy scale. However, the Fermi level for NiSi

is found on the high-energy side of the pseudogap, in the antibonding

states. For FeSi

, on the contrary, the Fermi level moves to low energies

and lies precisely at the peak found at about 0.5 eV in Fig. 6.11.

As a further illustration, the high density of states at the Fermi level

constitutes an unstable condition, so that in equilibrium FeSi

, a distortion

Figure 6.11 Density of states versus energy for CoSi

, with the Fermi level marked

by a vertical line near zero on the energy scale. The numbers on the vertical scale

are eV per formula unit. For silicides with the same CaF

structure, the Fermi lev-

els would be found in the antibonding states for NiSi

at the arrow on the right, and

among the bonding states for FeSi

at the arrow on the left. The density of states

curves are essentially the same for all three disilicides but would be slightly dis-

placed on the energy scale. Here the positions of the Fermi levels are given in

relation to that of CoSi

. According to Jepsen et al.

[128]

Ch_06.qxd 11/12/04 4:06 PM Page 321