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

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342 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

reactions with polymers, involving the formation of new compounds, at

coverages of about one monolayer and higher. It has been argued that the

data for polyimide do not imply reactive metals like Cr and Ti to be

bonded directly to the polymer, but rather suggest a disruption of the poly-

imide and the formation of oxidic, nitridic, and carbidic compounds.

[28, 47]

Co was also found to react strongly with PMDA-ODA.

[68]

Ni appears to

be much less reactive, but more reactive than Cu.

[19, 58, 69]

The alkali met-

als K

[28]

and Cs

[29]

have been demonstrated to reduce PMDA-ODA by

transferring an electron to the PMDAunit of the polymer. Dianion forma-

tion was also observed at high alkali metal concentrations.

The high reactivity of Cr, Ti, Al, and Co in the high-coverage regime

does not necessarily imply that individual metal atoms are strongly bound

to polymer chains. Based on measurements of the near-edge x-ray absorp-

tion fine structure in the very early stages of interface formation,

Strunskus et al.

[28]

ruled out purely physical interactions between Cr and

polyimide and discussed p-complex formation

[17, 48]

as one possible inter-

action mechanism. On the other hand, the fact that an intermixing layer

was observed at the Al-polyimide interface in cross-sectional TEM

studies

[17, 19]

points to relatively weak interactions of this reactive metal at

very low coverages. Our XPS and TEM experiments carried out in the Cr-

polyimide system at very low Cr coverages also show short-range inter-

mixing at the interface. However, the absence of long-range diffusion

even after very slow deposition at elevated temperatures in conjunction

with the lack of any influence of the deposition rate on the extent of inter-

mixing (compare Sec. 7.4) clearly points to strong chemical interactions.

[70]

7.4 Diffusion in the Polymer Bulk

Surface spectroscopy experiments indeed confirmed a strong correla-

tion between reactivity and mobility of metal atoms. In these experiments,

the metal was deposited at room temperature, and the drop of the metal

intensity was measured after annealing. While substantial intensity drops

were observed for noble metals,

[50, 69, 71–73]

reflecting appreciable metal

mobility, interfaces of polymers with Cr and Ti proved to be thermally

stable.

[17, 60, 69]

Al showed features of some mobility,

[17, 65]

and the mobility

of Ni turned out to be somewhere between that of Al and Cu. Note that the

metal mobility reflected in a drop of the metal intensity in surface analyt-

ical techniques cannot necessarily be taken as evidence of metal diffusion

into the polymer bulk; it is often caused by metal clustering at the surface,

as discussed below.

The ability of K and Cs to reduce polymers proved to have drastic

consequences on the diffusion behavior. Since positive ions repel each

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other, their diffusion is not impeded by the formation of immobile clus-

ters. Moreover, positive ions are much smaller than the neutral atoms. As

a result, these ions were found to be highly mobile in polymers, and

almost uniform K and Cs distributions were observed by means of angular-

resolved XPS

[29]

and Fourier-transform infrared reflection-absorption

spectroscopy

[28]

in polyimide films of appreciable thickness. A similar

behavior was seen for In in films of the organic semiconductor perylenete-

tracarboxylic dianhydride (PTCDA).

[30]

Here even Al was seen to diffuse

into the organic film quite extensively, which was attributed to the rela-

tively low ionization energy. In contrast, Ti, Sn, Ag, and Au turned out to

form interfaces that display evidence of overlayer metallicity at coverages

as small as 5 to 10 nm.

The first direct evidence of noble metal diffusion and aggregation in

the polymer bulk has been provided by cross-sectional TEM studies of

interface formation between Cu and polyimide (PMDA-ODA). In these

studies, LeGoues et al.

[19]

observed marked clustering of Cu at consider-

able distances below the polyimide surface after metal deposition at ele-

vated temperatures (but still well below T

) and low deposition rates.

However, no clustering in the bulk was observed at high deposition rates

and even elevated temperatures. After room-temperature deposition and

subsequent annealing, no metal particles were detected either. Investigations

carried out by Kiene et al.

[22]

have essentially confirmed these early results

and have shown that other noble metal-polymer systems, for example,

Ag/PMDA-ODA polyimide

[21, 74, 75]

and Au/TMC polycarbonate,

[32, 76]

exhibit a similar behavior.

Figure 7.3 gives a striking example that demonstrates the crucial role

of the metallization conditions on the interfacial structure. While deposi-

tion of Cu at a very low rate at 350°C produces a rather spread-out inter-

face, implying pronounced Cu diffusion (Fig. 7.3, bottom), deposition at

room temperature and subsequent annealing at the same temperature

results in a sharp interface without cluster formation inside the polyimide

(Fig. 7.3, top).

[22]

Note that the metal films in Fig. 7.3 are still not contin-

uous, despite the relatively large nominal metal coverage of about

30 monolayers. The impression of a continuous film is a consequence of the

finite thickness of the samples of 40 to 100 nm, depending on the cutting

procedure. Upon tilting, isolated and connected clusters are clearly visible.

The results depicted in Fig. 7.3 and corresponding results obtained for

other noble metal systems

[9]

show that metal clustering at the surface

effectively impedes metal diffusion into the bulk and strongly suggests

that no significant metal diffusion into the polymers is expected from a

continuous film or an arrangement of large clusters. This conclusion is

also corroborated by the pioneering medium-energy ion scattering exper-

iments of Cu diffusion in polyimide by Tromp et al.

[18]

On the other hand,

METAL DIFFUSION IN POLYMERS, FAUPEL ET AL. 343

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344 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

the absence of clusters in cross-sectional TEM images does not allow dif-

fusion of metal atoms into polymers and the formation of small clusters

that are not detectable in TEM to be ruled out.

We have used a very sensitive radiotracer technique to study atomic

diffusion. Diffusion profiles of the radiotracer atoms in the polymer films

Figure 7.3 Cross-sectional TEM micrographs showing the striking differences in

the copper diffusion characteristics between Cu deposition at room temperature

(8 nm at 0.16 nm/min.) followed by subsequent annealing at 350°C for 30 min.

(top) and very slow evaporation of Cu (4 nm at 0.16 nm/min.) at 350°C (bottom).

Ch_07.qxd 11/12/04 4:10 PM Page 344

are measured by means of ion-beam microsectioning in a high-vacuum

chamber. A very high depth resolution of typically 3 to 4 nm can be

achieved by use of argon or krypton ions of energies as low as 100 to

200 eV

[77]

(as opposed to several keV in secondary ion mass spectrome-

try). Surface charging of the insulating polymer film is avoided by use of

an electron-emitting neutralizer filament. The sputtered-off material of

each section is collected on a catcher foil, which is advanced like a film

in a camera. After sputtering, the catcher foil is cut into pieces correspon-

ding to the individual sections, and the radioactivity of each section,

which is proportional to the tracer concentration, is counted. After depth

calibration, a penetration profile is obtained by plotting the radioactivity

of the individual sections against the penetration depth. Using a calibrated

source, absolute metal concentrations can be determined.

Representative penetration profiles are shown in Fig. 7.4. Here the

logarithm of the activity of

110m

Ag is plotted versus the square of the pen-

etration depth x. The total amount of metal is extremely small. On this

scale, ordinary diffusion of the tracer according to the thin-film solution

of Fick’s second law,

c(x)  const. exp







, (5)

leads to a straight line of slope 1(4Dt). In Eq. (5), D is the tracer diffu-

sivity and t is the diffusion time. It is obvious from Fig. 7.4 that silver dif-

fuses deeply into polyimide during deposition at elevated temperatures.

However, only the upper profile, obtained after evaporation of silver onto

the hot polymer sample at an extremely low rate, is nearly Gaussian. At

high and moderate deposition rates, profiles often resemble the lower pro-

file in Fig. 7.4, where most of the metal deposit is located at or very close

to the polymer surface. The fraction of atoms that diffuse over large dis-

tances and contribute to the linear range is very small. (Note the logarith-

mic scale.) Metal diffusion into the bulk is only detectable because of the

high sensitivity of the radiotracer technique. Nevertheless, diffusion of

even trace amounts of Cu through the polymer into Si devices may cause

damage in ultra-large-scale integrated chips if it is not effectively blocked

by a barrier. Penetration profiles of a similar shape have been recorded in

various measurements for noble-metal tracers in polyimides

[9, 24, 78, 79]

and

polycarbonates.

[80, 81]

Only the ratio of metal in the near-surface region and

in the tail varied from case to case.

In view of the characteristic shape of the penetration profiles and the

well-known metal aggregation tendency, special attention was paid to

sputtering artifacts.

[9, 23, 80, 82]

For example, it was shown that the sputter



4Dt

METAL DIFFUSION IN POLYMERS, FAUPEL ET AL. 345

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346 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

rate of noble metals is even slightly higher than that of polycarbon-

ates.

[23, 82]

Hence retarded sputtering of metal clusters, which would mimic

metal diffusion, can be excluded. In all cases, a resolution function was

recorded by sputtering a very thin tracer layer on a polymer film without

diffusion annealing. Moreover, sputtering was performed not only in the

direction of diffusion but also in the opposite direction after removing the

polymer film from the substrate.

[23, 82]

Finally, at a given temperature, we

determined diffusivities from the Gaussian tails of the diffusion profiles

(see Fig. 7.5) and showed that the resulting diffusivities were independent

of the annealing time.

[75, 81]

Monte Carlo simulations have shown that the dominant role of the

deposition rate is a direct consequence of the interplay of atomic diffusion

Figure 7.4 Effect of the deposition rate on penetration profiles of

110m

Ag into

PMDA-ODA polyimide. The tracer was deposited continuously at a rate of about

0.1 ML/min. during annealing at 315°C and flash evaporated at the annealing tem-

perature of 328°C.

Ch_07.qxd 11/12/04 4:10 PM Page 346

and aggregation.

[9, 83, 84]

Such effects are not observed in ordinary diffu-

sion experiments. Simulated metal concentration profiles and simulated

TEM images were found to exhibit the characteristics observed in the

experiments if we incorporated the condition that stable clusters form

whenever metal atoms encounter each other on their diffusion path. This

condition is implied by our observation of a critical cluster size of i  1

(see Sec. 7.3).

An example is given in Fig. 7.5. The Monte Carlo simulations also

reflect the experimental observation that the total metal concentration

found at large concentration depth decreases strongly with increasing dep-

osition rate due to the metal immobilization through clustering.

[9]

This is

illustrated in Fig. 7.6, where the fraction of metal atoms at depths of

3 and 30 nm is plotted against the deposition time (1rate). We can

METAL DIFFUSION IN POLYMERS, FAUPEL ET AL. 347

Figure 7.5 Simulated penetration profiles for the total metal concentration and for

metal clusters of different size ranges, indicated by the number n of atoms, after

deposition during (a) 2,500 and (b) 50,000 jumps per free atom (jpa) and subse-

quent annealing. The total annealing time of 5  10

jpa, the nominal metal cov-

erage of 0.2 monolayer, and the ratio of surface and bulk diffusivity of D

D  60

are equal for both runs. Cross-sectional views at the bottom show clusters that

have formed in a section of the simulated volume. The calibration of the deposi-

tion rates depends on the experimental diffusion temperature. For diffusion of

noble metals in polyimides and polycarbonates, a deposition rate of the order of 1

ML/min. typically corresponds to 100 jpa in the vicinity of the glass transition

temperature.

[9]

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348 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

conclude that at industrial metallization rates, only traces of noble metal

are to be expected in the polymer bulk. Because trace amounts of metals

can cause device failures in chip interconnects involving organic low-k

dielectrics, diffusion barriers must be used.

Based on the notion that metal diffusion into polymers is an interplay

between atomic diffusion and aggregation, suggested by the Monte Carlo

simulations and the experiments described in this chapter, the extended

linear tails in the low-concentration range of the radiotracer profiles (see

Fig. 7.4) were attributed to diffusion of isolated metal atoms. Arrhenius

plots of the tracer diffusivities for Cu and Ag noble metals in polyimides

(PMDA-ODA and BPDA-BDA) and polycarbonates, determined from

the linear tails of penetration profiles similar to those in Fig. 7.4, are

shown in Fig. 7.7. Diffusivities of O

, CO

, and H

O are also shown. Our

results from ion-beam depth profiling in conjunction with x-ray photo-

electron spectroscopy on Cu diffusion in SiLK

indicate that Cu diffusion

is more than an order of magnitude slower in SiLK

than in the polyimide

PMDA-ODA at 315°C.

[39]

This is in accord with the higher adsorption

Figure 7.6 Total metal concentration found in the computer simulations at pene-

tration depths 3 and 30 nm, as a function of the metal deposition time in units

of jumps per free atom.

Ch_07.qxd 11/12/04 4:10 PM Page 348

energy of Cu on SiLK

, discussed in Sec. 7.2, which indicates stronger

interaction. Diffusivities for Au and Ag in polycarbonates are displayed

in Fig. 7.8.

Note in Fig. 7.7 that the diffusivities of noble-metal atoms in poly-

imide are many orders of magnitude smaller than those of simple gas mol-

ecules of comparable size. This was interpreted in terms of significant

contributions from metal interactions with the polymer even for noble

metals. Substantial interactions between noble metal atoms and polymers

are also reflected in the relatively high adsorption energies discussed in

Sec. 7.2 and listed in Table 7.1. Based on a detailed analysis of the metal

diffusion behavior in BPApolycarbonate,

[9]

which turned out to be completely

decoupled from the polymer dynamics, for example, we have attributed

the drastic slowing down of the atomic mobility of metals in compari-

son to noninteracting gas molecules to metal-atom-induced temporary

METAL DIFFUSION IN POLYMERS, FAUPEL ET AL. 349

Figure 7.7 Diffusion coefficients versus reciprocal temperature for diffusion of

and

110m

Ag in PMDA-ODA polyimide, Cu in Kapton

, and

Cu in BPDA-PDA poly-

imide. Arrhenius plots for diffusion of O

, CO

, and H

O in Kapton

®[85]

are shown

for comparison. Legend: open circles,

[75, 78]

open squares,

[79, 86]

solid squares,

[45]

solid circles,

[87]

open triangles from RBS combined with ion implantation,

[88]

and

crosses.

[79, 86]

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350 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

cross-linking.

[24, 80]

It was reported, for example, that polyimide-

polyamide copolymers could no longer be dissolved in typical solvents

after a fine dispersion of Ag and Pd had been incorporated (by reduction

of the corresponding metal salts).

[89]

Despite the available evidence of substantial interaction of noble

metal atoms with polymers, we cannot exclude the possibilty that the dif-

fusivities determined from the linear tails of the radiotracer profiles reflect

diffusion of small clusters rather than atomic diffusion. This particularly

holds for the measured Ag diffusivities because the tracer concentration in

Figure 7.8 Arrhenius plots for atomic diffusion of

198

Au (solid symbols) and

110m

(open symbols) in the polycarbonates BPA-PC and TMC-PC. The dashed lines

indicate the glass transition temperatures measured by means of DSC at a heat-

ing rate of 20°C/min. Diffusion in BPA-PC is well described by linear Arrhenius fits

with activation energies of Q  98 and 109 kJ/mole and pre-exponential factors of

 0.0016 and 0.022 cm

/s, respectively.

[9, 80, 87]

The data for TMC-PC exhibit a

downward curvature.

[81, 87]

Ch_07.qxd 11/12/04 4:10 PM Page 350

the experiments with Ag typically corresponds to several monolayers

(while only ≈14 monolayer was used in the Cu tracer studies). As dis-

cussed in Sec. 7.2, the differences in the ratios of D

D

for surface and

bulk diffusion also point to this possibility. Our recent radiotracer meas-

urements of

110m

Ag in TMC polycarbonate

[23]

indeed suggest that the dif-

fusivities reported by Willecke and Faupel

[81]

are those of small clusters

and that single Ag atoms, which are only present in trace amounts, are

mobile even at room temperature.

In these experiments, several diffusion profiles were measured in

samples where a thin layer of

110m

Ag was deposited at 35°C over periods

of 12 to 15 minutes, and annealing was performed for up to 11 days.

[82]

A representative

110m

Ag profile is shown in Fig. 7.9 (open squares). As

expected from the aggregation-induced immobilization, the Ag concen-

tration drops by several orders of magnitude over very short penetration

METAL DIFFUSION IN POLYMERS, FAUPEL ET AL. 351

Figure 7.9 Penetration profiles obtained after

110m

Ag deposition and annealing at

35°C, with a predeposited layer of 0.08 ML Cr, and with co-deposition of ≈3 ML

of nonradioactive silver after 3 min. of tracer evaporation (12 min. total deposi-

tion time). The resolution function, obtained from a thin layer of

110m

Ag evapo-

rated on a Fe-Si-B glass without annealing, is shown for comparison. The depth

scale is linear.

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