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

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curvature of the resistance change curves shown in Fig. 9.7. Consequently,

we would expect the void growth rate for high current density test cases

not to be linearly proportional to the current density, which is in contrast

to Eq. (1). We can, of course, make the liner joule heating less of a factor

by increasing the liner thickness at the expense of the line conductivity.

9.7 Fast Diffusion Paths

9.7.1 Free Surface and Grain Boundary Diffusion

Asurprisingly wide range of activation energies, from 0.5 to 2 eV, for

electromigration in thin-film Cu lines has been reported,

[76–78, 87–97]

and

many diffusion mechanisms (bulk, grain boundary, surface, and interface)

have been proposed to explain these results. It is important to identify the

dominant diffusion paths in Cu lines. Once the fast diffusion path is iden-

tified, we may find a way to reduce the fast diffusivity therein and

increase the Cu reliability. This section discusses the electromigration

studies of liftoff, unpassivated Cu lines of widths varying from 0.15 mm

(bamboo) to 10 mm (polycrystalline), to differentiate the relative contri-

butions of surface from grain boundary transport.

[80]

The test structure

[98]

consisted of Cu lines connected to two sputtered

Ti (10 nm)W (200 nm) bar electrodes, the purpose of which was to sim-

ulate blocking contacts and to measure the drift velocity of Cu in the

tested lines. The Ti (10 nm)Ta (15 nm)Cu (300 nm) test lines were all

deposited by e-gun evaporation at a base pressure of 10

7

torr and fabri-

cated by a liftoff process using e-beam lithography.

[98]

The bottom Ti layer

in the TiW bar served as an adhesion layer to SiO

and in the TiTaCu

line was used to reduce the contact resistance between Ta and W. The Ta

film was a diffusion barrier layer between Ti and Cu. The Cu test lines

were 0.15 to 10 mm wide and overlapped the TiW bar by 0.85 and 1.0

mm for 0.15- to 0.25-mm-wide lines and 0.75- to 10-mm-wide lines,

respectively. The samples were annealed in helium at 400°C for 3 hours

before testing to stabilize the microstructure. Bamboo-like, near-bamboo,

and polycrystalline structures were found in the metal linewidths between

0.15 to 0.5 mm, 0.75 to 1 mm, and 2 to 10 mm, respectively. The samples

were tested in a vacuum furnace at temperatures ranging from 255 to

405°C with a current density of 15 mA/mm

in a chamber pressure of 15

torr of nitrogen. Mass transport of Cu in the Cu lines as a function of tem-

perature was measured using both drift-velocity (void growth rate) and

resistance measurements. Void size was measured by scanning electron

microscopy. For these test structures, complete blocking boundaries exist

at both ends of the line. Edge displacement void growth, ∆L, at the cathode

422 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Chapter-09 11/29/04 6:50 PM Page 422

ELECTROMIGRATION IN CU THIN FILMS, HUETAL. 423

end exposed the Ti/Ta underlayer and caused the conductor line resistance

to increase by∆R. The drift velocity of Cu was directly related to the rate

of edge displacement by Eq. (11b) as v

 ∆L∆t and can be estimated by

 ∆L

t, assuming a constant drift velocity, where t is the amount of

time required to grow a void to critical size ∆L

. (Incubation times were

considered negligible.)

Let us assume the Cu/Ta interface diffusion is significantly slower

than GB and surface diffusion. The evidence of the slow Cu/Ta diffusion

is given in Sec. 9.7.3. For the case of a bamboo-like grain structure, the

contribution of mass transport by electromigration along GBs is negligi-

ble because there is no continuous GB path and the electromigration driv-

ing force is perpendicular to the GBs. The surfaces at the sidewalls and on

top of the lines become the fast diffusion paths in liftoff structures. The

combination of Eqs. (1) and (3) can be written as:

 d

(2w  1h)D

erj(kT). (12a)

Equation (12a) states that the marker velocity (or void growth rate) in the

bamboo-like line structure will be increased as the metal linewidth or

thickness is decreased, at a fixed sample temperature and current density.

For the case of a polycrystalline line structure, the effective drift

velocity becomes:

 {(d

d)(1  dw)D

exp(Q

kT)Z

 d

(2w  1h)D

exp(Q

kT)Z

}erjkT, (12b)

where D

and D

are the pre-exponential factors, and Q

and Q

are the

activation energies for grain boundary and surface diffusion, respectively.

In this case, we would expect the drift velocity to be less sensitive to

linewidth for large w, because (1  dw)  1.

Surface and grain boundary diffusivities are known to be dependent

on purity, the orientation of the surface, and the plane of the grain bound-

aries;

[75, 79, 84, 99]

however, the measured values were generally average val-

ues obtained by sampling drift velocities along many fast paths. For

example, the number of grain surfaces sampled in a 0.25-mm-wide line for

a void size of 1 mm is estimated to be more than 300, using ∆Lhw(d

(2h  w)), where ∆L  1 mm, w  0.25 mm, h  0.3 mm, d

 0.5 nm,

and d  0.8 mm.

The size of the void ∆L

at the cathode end of the line (mass depletion)

was measured from SEM micrographs. Hillock growth at the anode end

of the line was also observed. Figure 9.9(a) to (c) shows the SEM micro-

graphs of Cu depletion at the cathode ends of 0.15-, 1-, and 5-mm-wide lines

for t  6.8, 30, and 18 hours, respectively, with j  15 mAmm

at 314°C.

Chapter-09 11/29/04 6:50 PM Page 423

424 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Figure 9.9 SEM microgaphs of tested Cu lines with j  15 mA/mm

at 314

C for

various linewidths. (a) 0.15-mm-wide line for t  6.8 hours; (b) 1-mm-wide line for

t  30 hours; (c) 5-mm-wide line for t  18 hours.

Chapter-09 11/29/04 6:50 PM Page 424

ELECTROMIGRATION IN CU THIN FILMS, HUETAL. 425

The Cu drift velocity was estimated by ∆Lt, where ∆L and

t are the mean void size and mean lifetime, respectively. Figure 9.10

shows the drift velocity v

 as a function of w. A careful inspection of

Fig. 9.10 shows that the velocity decreases monotonically with linewidth

w but goes through a minimum at w  1 mm and then increases to a con-

stant value. The lines are the least-squares fits of the data to Eq. (12a) for

w  1 mm and to Eq. (12b) for w  1 mm, respectively. In the case of the

bamboo grain structures for w  1 mm, grain boundary transport is elim-

inated and only surface diffusion of the Cu lines is considered. The film

thickness, the profiles of the cross-sectional area (trapezoid shape) of the

line, and the values of erjkT are known. The only adjustable parameters

in Eq. (12a) are d and d

. The best values of fitting parameters for the

data w  1 mm were used as the constrained values for analyzing the data

points for w  1 mm in Eq. (12b). The solid lines shown in Fig. 9.10 are

the least-squares fits. The contribution of Cu drift velocity in grain bound-

aries is also pointed out in Fig. 9.10. The ratio of v

to v

for a 10-mm-

wide line decreases from 2 to 1 as T increases from 255 to 405°C. This

indicates that major void growth is due to surface migration even in a

polycrystalline 10-mm-wide line for T  250°C. The activation energy of

grain boundary diffusion is 0.2 eV higher than that of surface diffusion,

and the ratio of (d

)(d

) is about 0.02. The extracted values

of fitting parameters from the data in Fig. 9.10, d

erj and

erj, as a function of 1T are plotted in Fig. 9.11. The activation

Figure 9.10 Plot of drift velocity as a function of linewidth stressed at sample tem-

peratures of (a) 405 and (b) 255

C. The lines are least-squares fits.

Chapter-09 11/29/04 6:50 PM Page 425

energies of surface and grain boundary diffusion are 0.9 and 1.1 eV,

respectively. The derived values of activation energies are in good agree-

ment with the reported values of 0.78 to 0.90 eV for the activation energy

of surface diffusion

[75, 99]

and 0.88 to 0.95 eV for grain boundary diffu-

sion.

[81–83]

The apparent effective charge number Z

can be estimated by

using the diffusivities and data in Fig. 9.11. From the above relationship,

after substituting the surface diffusivities

[79, 99]

computed either from D



0.15 cm

s and Q

 0.78 eV, or D

 0.26 cm

s and Q

 0.90 eV, at

400°C, r  5.0 mΩ-cm, and d

 0.5 nm, we obtain Z

0.1 or 0.8,

respectively. The negative sign in Z

means that Cu atoms drifted in the

direction of the electron wind force. Using the grain boundary diffusivi-

ties,

[83]

we obtain Z

14. The values of Z

estimated in this way

426 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Figure 9.11 Plot of d

and d

vs. 1/T.The straight lines are cal-

culated from the best-fitting values of Z

to the data using the known values of

and d

Chapter-09 11/29/04 6:50 PM Page 426

ELECTROMIGRATION IN CU THIN FILMS, HUETAL. 427

depend on the accuracy of published values of D

and Q. Although the

absolute value of Z

 Z

appears to be consistent with a theoretical pre-

diction, the electron wind force decreases as an atom moves from the bulk

to a grain boundary and to a surface.

[100]

In summary, a systematic study of Cu electromigration drift velocity

shows that the paths for fast migration are the surfaces in bamboo-like and

near-bamboo structures, and a mixture of surface and grain boundaries in

polycrystalline films. The activation energy for grain boundary diffusion

is approximately 0.2 eV higher than that of surface diffusion, and the ratio

of (d

)(d

) is approximately 0.02.

9.7.2 Ambient Effect

The effect of impurity on Cu surface diffusion has been reported.

[75, 79, 101, 102]

The measured surface diffusivities are strongly dependent on the atmos-

phere and absorbed impurity on the surface of the diffusion experiments.

The Cu surface self-diffusion increases with the vapors of solute Pb, Tl,

Bi, or Cl over the Cu surface

[75, 79]

and is reduced with the absorption of C,

Ca, Mn, or O

on the Cu surface.

[79, 101]

The kink and ledge sites of the Cu

surface can absorb impurities that reduce the concentration of diffusing

defects and thus suppress the rate of surface self-diffusion.

[75]

The Cu sur-

face diffusivity is higher in an oxygen atmosphere or vacuum than in a

hydrogen atmosphere.

[75, 79]

This result suggests that oxygen may remove

the inhibiting effect of surface impurities.

[75]

To this end, the electromi-

gration lifetime of unpassivated 0.18-mm-wide bamboo-like Cu lines with a

Fig. 9.3(e) structure was measured. The samples were tested in a vacuum

furnace with a chamber pressure of 10 to 30 torr of high-purity nitrogen

or forming gas (N

 5% H

) in the temperature range 180 to 362°C. The

total impurity concentration in the nitrogen gas was less than 1 ppm, with

O the major impurity at 0.5 ppm. The concentration of oxygen was

found to be less than 10

7

ppm from an oxygen detector. With a test struc-

ture shown in Fig. 9.3(e), the Cu void growth rate at the cathode end of

the line was the same as the Cu drift velocity because the end of the M1

line was connected to a completely blocking boundary of W M0. The

migration fast path is the top surface in the bamboo-like damascene line.

Thus the extracted activation energy from these samples is the electromi-

gration activation energy of Cu surface diffusion. The mean lifetime t

as a function of 1/T is plotted in Fig. 9.12. The electromigration activation

energies of Cu surface diffusion in nitrogen and forming gas are found to be

0.7 ± 0.1 and 0.9 ± 0.1 eV, respectively. The derived values of electromi-

gration activation energies are in good agreement with the reported values

of the activation energy of surface diffusion of 0.78 and 0.95 eV measured

Chapter-09 11/29/04 6:50 PM Page 427

in oxygen (10

5

torr) and hydrogen (760 torr) ambients, respectively.

[75, 79]

Higher values reflect the slowing of surface diffusion by the presence of

gases compared to the value of 0.5 eV measured in situ in ultrahigh vac-

uum on a clean Cu surface.

[103]

9.7.3 Alloying Effect

This section discusses the results of electromigration in pure Cu and

Cu alloys using standard drift velocity test structures [Fig. 9.3(a)]. The

tested samples were the Ta/Cu or Cu alloys/Ta line segments on top of a

W underlayer line. The Cu line segments were patterned by an ion milling

technique.

[28]

The top and bottom Ta layers served as an etch mask and

etch stop. The bottom Ta layer was removed by RIE using CF

chemistry.

During RIE processing, CuF

may have formed on the surfaces of two

sidewalls of the Cu lines. All the samples were annealed in He at 400°C

for 3 hours. The final metal structure is Ta (20 nm)/Cu or Cu alloys

(300 nm)Ta (20 nm). The top Ta layer thickness was estimated from

428 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Figure 9.12 Plot of mean lifetime t vs. 1/T. The straight lines are least-squares

fits.The data points are obtained from the samples using a Fig.9.3(e) test structure.

Chapter-09 11/29/04 6:50 PM Page 428

ELECTROMIGRATION IN CU THIN FILMS, HUETAL. 429

Augh electron spectroscope (AES) analysis with Ar



sputtering profiles.

The SEM micrographs in Figure 9.13 show the depleted cathode ends

after electromigration stressing of 5-mm-wide lines at 250°C for 55 hours

of a TaCu(Mg)Ta structure, and for 128 hours of a Ta/pure Cu/Ta struc-

ture and a Ta/Cu(Zr)/Ta structure. Voids developed under the top, immo-

bile Ta layer and along the sidewalls of the line in this sandwich structure.

The dominant Cu electromigration paths would be along the Cu grain

boundary plane and/or along the two Cu sidewalls. These Ta layers are not

seen in Fig. 9.13 because of the high penetration depth of the 30 KeV elec-

tron beam in the SEM. Many fine islands are seen in the depleted Cu(Mg)

sample. The edge displacement ∆L of TaCu(1 wt.% Mg), pure Cu, and

Cu(0.7 wt.% Zr)Ta isolated lines as a function of stress time is plotted in

Fig. 9.14.

[104]

The linear behavior of Cu(Mg) and pure Cu indicates that

drift velocities of Cu in Cu(Mg) and pure Cu are independent of time, with

little incubation time for a sample temperature of 250°C. In the case of

Cu(Zr), a nonlinear behavior was observed. The combination of a small

Figure 9.13 SEM micrographs of 5-mm-wide lines after electromigration stressing

with 2  10

A/cm

at 250°C for (a) 55 hours with Cu(Mg); (b) and (c) 128 hours

with pure Cu and Cu(Zr), respectively.

Chapter-09 11/29/04 6:50 PM Page 429

Cu grain size in Cu(Mg), the formation of fine Cu islands seen in Fig.

9.13, and the lack of a pinning effect of Cu by Mg along the fast diffusion

paths resulted in enhancing the Cu line damage. The void growth rate on

the Cu line in Cu(Mg) was found to be 5 and 35 times faster than in pure

Cu and Cu(Zr), respectively. This is partly due to the fine islands left

behind the depletion front. The islands can be formed if Cu on the trailing

surface of the grains has not been completely fed into grain boundary

depletion before the voids encircle the grain.

The activation energy for electromigration in pure multigrained Cu is

found to be 0.77 ± 0.04 eV, which is less than the Cu grain boundary

diffusion.

[80, 82]

The value of 0.77 eV should represent the surface diffusion

activation energy along the two sidewalls of the line.

430 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Figure 9.14 Edge displacement in Cu and various Cu alloys as a function of stress

time at 250°C.

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ELECTROMIGRATION IN CU THIN FILMS, HUETAL. 431

The time for an equivalent resistance change ∆R corresponding to

electromigration damage in pure Cu and Cu(Sn) alloys is progressively

increased as a function of Sn content in the Cu at 250 and 203°C for

2.0-mm-wide, 0.3-mm-thick lines, as shown in Fig. 9.15(a) and (b), respec-

tively. A deviation from linear behavior was observed in Cu(Sn). This

nonlinear behavior of the line resistance change is similar to that observed

during electromigration in Al(Cu),

[105]

in which Cu depletion precedes

Figure 9.15 Line resistance change vs. electromigration stressed time for Cu and

Cu(Sn) alloys with j  2.6  10

A/cm

at temperatures of (a) 250 and (b) 203°C.

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