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

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considered to be fast diffusion paths. Across the linewidth, polycrys-

talline grains intermixed with single-crystal grain segments were

observed for the 3- and 2-mm-wide lines, while bamboo-like grain struc-

tures were observed in the submicron Cu lines and vias. The microstruc-

ture of the 5-mm-wide line was very similar to that observed in Fig.

9.4(a). The bamboo-like and polycrystalline grain structures are defined

as single grain per linewidth or per via and two or more grains per

linewidth, respectively. All Cu grains in the Cu lines analyzed occupied

the entire line thickness. The initial fine-grain structure of the Cu seed

and electroplated Cu layers as shown in Fig. 9.5 are converted to large

grains during abnormal grain growth, which can occur at room tempera-

ture or by annealing.

[61–63]

Figure 9.5 shows a STEM cross-section of an

as-plated, 0.7-mm-thick plated Cu film.

[64]

The sample was prepared

within 1.5 hours of warming to room temperature, and the grains did not

recrystallize during FIB milling. Once the sample was prepared, the grain

structure did not undergo any change over time. The cross section in Fig.

9.5 shows that the plated film has multiple small grains stacked in the

film thickness. Amean grain size and standard distribution of 0.05 ± 0.03

mm was calculated from a Gaussian fit to a log-normal distribution of

grain areas assuming circular-shaped grains. Both twins and dislocations

412 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Figure 9.4 FIB images of Cu lines. (a) through (d) Plan view of 3-, 2-, 1-, and

0.18-mm-wide Cu lines taken at an ion beam angle of 10 degrees; (e) cross-sec-

tion of a 0.18-mm-wide line taken at an ion beam angle of 45 degrees.

Chapter-09 11/29/04 6:50 PM Page 412

ELECTROMIGRATION IN CU THIN FILMS, HUETAL. 413

are visible in the as-plated grains. The barrier layer can be seen as the

dark contrast material underneath the Cu film. However, the PVD Cu

seed layer is not distinguishable from the plated Cu film. The transfor-

mation time from fine Cu grains to large grains is strongly dependent on

deposition parameters such as plating current, bath chemistry, and layer

thickness. It has been reported that plating Cu on a 0.15-mm-thick PVD

Cu seed has to be larger than the critical thickness of 0.25 to 0.35 mm for

the abnormal grain growth to occur.

[29, 65]

The large Cu grain sizes in the

damascene lines and vias are due to the dual-damascene process which

has a thick Cu film (overburden) over the trenches before CMP and thus

abnormal grain growth in the electroplated Cu. The bamboo-like struc-

ture in damascene lines and the single crystal nature of Cu in vias are

shown in Fig. 9.4(c) to (e).

Figure 9.6 shows TEM cross sections of V1/M1 and V2M2 interfaces.

[38]

These images show a thin liner at the interface. The thicknesses of the lin-

ers at the bottom of the V1 and V2 vias for these samples measured 3 and

10 nm, respectively. The variation in the liner thickness is due to the vari-

ation of the deposited film thickness and the PVD step coverage in the

various structures.

Figure 9.5 STEM cross section of an as-plated Cu microstructure. The sample

was prepared by FIB and liftoff within 1.5 hours of warming to room temperature.

Chapter-09 11/29/04 6:50 PM Page 413

9.5 Theory

9.5.1 Drift Velocity

The observations of mass transport under an electric field in lead-tin

and mercury-sodium condensed phases was first recorded in 1861.

[66]

The

414 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Figure 9.6 TEM cross-section micrographs of V1/M1 and V2/M2. (a) Thin, 3.1-nm

liner between V1 and M1; (b) 10-nm-thick liner at V2/M2.

Chapter-09 11/29/04 6:50 PM Page 414

ELECTROMIGRATION IN CU THIN FILMS, HUETAL. 415

atom flux produced by an electromigration driving force F

is given

by J

 n v

, where n and v

are the atomic density and drift velocity,

respectively. The drift velocity is expressed by the Nernst-Einstein relation,

 (D

eff

kT)F

(1)

where F

 Z

eE  Z

erj, E is the electric field, e is the absolute value of

the electronic charge, Z

is the apparent effective charge number, r is the

metallic resistivity, D

eff

is the effective diffusivity of atoms diffusing

through a metal line, Tis the absolute temperature, and k is the Boltzmann

constant. The quantity of Z

represents the strength of the electromigration

effect and ranges in value from 10

2

to 10

[67]

It is customary to divide Z

into two parts, Z

 Z

 Z

, where Z

arises from the direct force of

the pure electrostatic nature and Z

is the contribution from the so-called

“electron wind” force that arises from the momentum exchange between

charge carriers and the diffusing atom. The wind force suggested by

Skaupy

[68]

can usually be expressed by A/r(T)

[69]

or n

 n

[70, 71]

where Ais a constant; n

and n

are the electron and hole densities, respec-

tively;l

and l

are the mean free paths of the electrons and holes, respec-

tively; and s

and s

are the atom’s intrinsic cross section for collision

with the electrons and holes, respectively.

9.5.2 Diffusivity

The effective diffusivity in a given line at one cross section can be

written as:

eff

 n



, (2)

where the subscripts GB and i refer to the grain boundary and the i

interface (atom diffusion along metal/insulator or metal/metal inter-

faces), respectively. n

and D

, n

and D

are the fractions of atoms and

diffusivities in grain boundaries and the i

interface, respectively. The

diffusivity D is expressed in terms of D

exp(QkT), where D

and Q

are the pre-factor and activation energy, respectively. In Eq. (1), diffu-

sivity is the dominant factor for the mass transport. Only atoms diffus-

ing along the fast diffusion paths will control the atomic movement.

Several types of possible fast diffusion paths are considered: disloca-

tions, the Cu/dielectric interface, the Cu/metal liner interface, free sur-

faces, and grain boundaries. The Cu bulk diffusivity with a high activation

energy of 2.2 eV

[72]

is the slowest and is many orders of magnitude less

than the fast diffusion paths. For bulk diffusion, we can estimate that the

Chapter-09 11/29/04 6:50 PM Page 415

time to grow a 0.1-mm void at 300°C using Eq. (1) with j  2  10

Acm

and Z

5

[73, 74]

is about 50,000 years. Thus the contribution from the

Cu bulk diffusion is negligible. A range of activation energies for Cu

dislocation, Cu/SiN

interface, free surface, and grain boundary diffu-

sion have been reported as 1.53 eV,

[75]

0.8 to 1.1 eV,

[37, 76, 77]

0.5–2 eV,

[75, 78–80]

and 0.8–1 eV,

[81–84]

respectively. The grain boundary structure can vary

widely within a given line, which causes considerable variability in dif-

fusivity from boundary to boundary.

[84]

Impurities on or in the fast path

can also play an important role in determining the Cu diffusivity.

[82, 83]

Grain boundary diffusivity is often an average value of the meas-

urements taken over a large number of grains that have a variety of

orientations. Dislocation pipe diffusion refers to atomic motion along

dislocations. However, the cross-sectional area of a single dislocation is

small, and the net diffusivity depends on the density of dislocations.

Interfacial diffusion refers to atom motion along the interfaces such as

between the metal/insulator (CuSiN

) or the metal/metal (CuTa) and

is highly dependent on the chemistry, bonding, impurity, and structure at

the interfaces. The observations of a dominant fast diffusion path along

CuSiN

[10]

CuTaN,

[11]

CuTa,

[11, 12]

and CuTiN

[32]

interfaces have

been reported. These differences indicate that interface diffusion is

related to the interface property and materials, which are very sensitive

to the sample preparation, such as processing. The surface diffusion is

also strongly influenced by ambient. The surface diffusion on clean Cu

or in a Cl

ambient is faster than on air-exposed Cu surfaces or in a H

ambient.

[79]

9.5.3 Effective Diffusivity and Microstructure

Let us consider a polycrystalline line structure with a Cu grain across

the metal line thickness, h. The number of fast paths for grain boundary

are (wd  1) for w  2d, or 1 for 2d  w  d, where w is the

linewidth and d is the grain size. The fraction of atoms diffusing through

grain boundaries is n

≈

w)f

where d

denotes the width of the

grain boundary.

The effective diffusivity for the case of an unpassivated liftoff

CuTa line is the sum of the top and the two sidewalls of free Cu sur-

faces, the Cu/bottom Ta interface, and the Cu grain boundary diffu-

sion. Assuming transport paths are independent, the product of Z

eff

and

eff

along a thin-film line of a given cross section can be described

as:

[85]

eff

 Z

h  Z

(2w  1h)  Z

, (3)

416 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Chapter-09 11/29/04 6:50 PM Page 416

ELECTROMIGRATION IN CU THIN FILMS, HUETAL. 417

where the subscripts S, I, and GB refer to the uncoated, free Cu surface (at

two sidewalls plus top of the line), the TaCu interface, and the Cu grain

boundary, respectively; d

and d

denote the width of the interface,

surface and grain boundary, respectively. d

h, d

(2w  1h) and n

are the fractions of atoms diffusing through the interface , the surface and

the grain boundary in the line, respectively. Finally, d is the grain size of

the Cu line.

For the Cu damascene test structures, the top surface of a line is cov-

ered by an insulator, typically silicon nitride, and the bottom and sides of

the line are covered with a liner, such as Ta. The fast-diffusion paths are

along grain boundaries, the Cu/silicon nitride, and the Cu/Ta interfaces.

The effective diffusivity can be written as:

eff

 Z

(2w  1h)  Z

(1h)  Z

, (4)

where Z

and D

are the effective charge number and diffusivity at the

Cu/silicon nitride interface, respectively, and d

denotes the effective

width of the Cu/silicon nitride interface. For the bamboo-like grain struc-

ture, the contribution of mass transport by electromigration along the

grain boundary (GB) is negligible because of the absence of a continuous

GB path and an electromigration driving force that is perpendicular to the

GBs. The drift velocity can be written as:

 d

(1h)D

erj(kT)  d

(2w  1h)D

erj(kT). (5)

Equation (5) states that the drift velocity in the bamboo-like grain dama-

scene line is a function of the metal line thickness if the Cu/silicon nitride

interface diffusion is dominant. The drift velocity is a function of metal

line thickness and width if the Cu/Ta interface diffusion is dominant.

For test structures with completely blocking boundaries at both ends

of the line, the boundary condition for the atomic Cu fluxes at the contact

interface is:

(Cu)  J

(Cu)  J

(Cu)  n v

, (6)

where J

(Cu) and J

(Cu) are the atomic Cu fluxes in the Cu lines and the

blocking boundary, respectively, and J

(Cu)  0 because no Cu can dif-

fuse through the blocking boundary. Edge displacement (void growth),

∆L, at the cathode end of the line causes the conductor line resistance to

increase by∆R. The void growth rate is directly related to electromigra-

tion drift velocity by:

∆L∆t  v

. (7)

Chapter-09 11/29/04 6:50 PM Page 417

For a constant drift velocity, the lifetime t can be obtained as follows:

t  ∆L

n

, (8)

where ∆L

is the critical void size for the lifetime t.

9.5.4 Electromigration-Induced Backflow

Under electromigration test conditions, two opposing transport mech-

anisms operate simultaneously: atom migration due to the electromigra-

tion force, and atom backflow due to an electromigration-induced stress

gradient.

[50]

The stress gradient occurs because atoms, which are driven

out of the cathode end of the conductor, causing tensile stresses, accumu-

late at the anode end, where the atomic density becomes higher, causing

compressive stresses. This gradient results in a backflow of material

(Blech effect).

[50]

Combining the electromigration force and backflow

effects produces a net drift velocity:

 v

 v

 (DkT)(Z

erj  ∆s Ω)∆x, (9)

where v

is the electromigration drift velocity and v

is the average

mechanical backflow velocity. An important implication of this effect

is that for sufficiently short lines or low current densities, stress can

completely suppress mass transport. We can define threshold values: a

given j and a critical linelength L

[∆x in Eq. (9)] below which net mass

transport vanishes (v

 0) and jL

∝∆s.The magnitude of the elec-

tromigration-induced stress ∆s is dependent on the electromigration

force. The electromigration-induced stress ∆s

in the linehas to beless

than the fracture strength∆s

of the passivation layer and has a maxi-

mum value of ∆s

. In addition to the mechanical strength of the dielec-

tric material, the anode end of the line has to connect to a complete

blocking boundary to generate the short-length effect. As will be dis-

cussed in Sec. 9.12, for Cu interconnections below 0.25-mm technol-

ogy, the thickness of the liner at the via and line interface is often less

than 10 nm and the Cu current density at the liner interface is often

more than 3 mA/mm

. Thin liners at the anode end may not withstand

the incoming Cu flux and the compressive stress is relieved. In addi-

tion, the critical current densities obtained by using a very wide under-

lying or overlying line connected to a fine test line will not be the same

as those from an interconnect structure with similar linewidth.

Therefore, applying the short-length effect in Cu interconnections

should be performed with caution.

418 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Chapter-09 11/29/04 6:50 PM Page 418

ELECTROMIGRATION IN CU THIN FILMS, HUETAL. 419

9.5.5 Partial Blocking Boundary

In the case of partial blocking boundaries, such as thin liner at the Cu

via/Cu line interface, voids and extrusions will not necessarily be formed

at the via/line interface but will occur whenever there is an imbalance of

Cu fluxes at a certain location, by the equation:

 , (10)

where J

and J

out

represent the Cu flux entering and leaving at that loca-

tion. The calculation of void or hillock growth rates related to drift veloc-

ity in the partial blocking boundary case becomes rather complicated

since it is difficult to estimate the drift velocity in this continuous equa-

tion. No void or extrusion can grow if J

and J

out

are equal.

9.6 Resistance and Void Growth

This section discusses the line resistance changes as a function of

current-stress time in metal lines connected to blocking boundaries,

such as W or thick diffusion barrier liners at a contact interface. Here

the local flux divergence at the contact interface is the dominant

failure mode. The diffusion flux of Cu atoms in the Cu line at the con-

tact interface is directly correlated to the electromigration drift veloc-

ity. Material depletion at the cathode end causes the conductor line

resistance to increase. For layered interconnections (such as TaN/Ta/Cu),

the relationship between the rates of material depletion and the line

resistance change, ∆L∆t and ∆R∆t, can be generally obtained as

follows:

∆R(t)  (r

∆L)A

 r

(L  ∆L)A

.(11a)

∆R∆t  (r

A

 r

A

)∆L∆t is proportional to v

, since ∆L∆t 

. The subscripts Ta and Cu refer to Ta liner and Cu conductor, respec-

tively; r is the electrical resistivity; A is the cross-sectional area of the

specific metal; Lis the initial conductor length; and ∆L is the void growth

length. The change in line resistance is simply a linear function of the

electromigration drift velocity. However, the joule heating generated from

the thin liner, the first item of the right-hand side of Eq. (11a), sometimes

cannot be neglected; a ∆T of 100°C,

[86]

or even melted TaN/Ta liner, have

been observed.

out

 J

)



∆x

∂h



∂t

Chapter-09 11/29/04 6:50 PM Page 419

The line resistance change curves as a function of time for a sample

temperature of 296°C are shown in Fig. 9.7. The void formation in a dam-

aged line is shown in Fig. 9.8, which is a cross-sectional view SEM micro-

graph of a 0.28-mm-wide line, illustrating the typical degradation mode of

void growth at the cathode end of the line. The lifetimes are rather uni-

form, varying within 30% sample-to-sample and illustrating that the mass

transport rate is an average measurement through a large number of grain

surfaces. Initially, the line resistance changes slowly, followed by an

abrupt step of resistance change and a period of rapid constant resistance

rise. We can take the data points with a dotted line as an example for cor-

relating void growth and line resistance change. The initial period of the

slow resistance change rate for the testing time 60 hours was caused by

void growth within the W/Cu overlap length (∆L

), because the large volt-

age change will be sensitive only to a void that grows beyond the Cu/W

overlap area. Therefore, ∆R(t) ∼ 0, if ∆L  (∆L

). The abrupt line resist-

ance step is believed to occur when the void grows just beyond the W

stud. It corresponds to a change in the contact resistance between

420 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS

Figure 9.7 Test line resistance vs. stressed time. ∆L

and ∆L

are the void growth

within and beyond the Cu/W overlapping area, respectively.

Chapter-09 11/29/04 6:50 PM Page 420

ELECTROMIGRATION IN CU THIN FILMS, HUETAL. 421

W studs/TaN/Ta liner/Cu and also to current flowing over a thinned liner

region covering a step between the end of the W stud and the line, as

shown in Fig. 9.8. The final period of resistance change is attributed to

void formation and growth where the current has to pass through the thin,

high-resistance liner underlayer to connect the remaining Cu line to the W

via. For this period, Eq. (11a) should be modified to:

∆R(t)  (r

∆L

)A

 r

[(L  ∆L

)  ∆L

]A

 ∼ (r

∆L

)A

(11b)

where ∆L

is the void length beyond ∆L

Equation (11b) shows the rela-

tionship between the edge displacement ∆L and line resistance change.

The resistance change rate in the final period should be a constant, if the

void growth rate ∆L

∆t is constant. However, a very high current density

of 10

Acm

will be applied to the liner with typical resistivity of

200 mΩ-cm in the 20-nm-thick Ta in the region of ∆L

. Joule heating

could be generated, especially in a defective liner. We can roughly esti-

mate a ∆R of 120 Ω for ∆L

 0.3 mm. Thus for a high current density

test, a faster void growth rate for ∆L  ∆L

is expected compared to the

region of ∆L  ∆L

. This explanation is in agreement with the upward

Figure 9.8 SEM micrograph of the electromigration damage in a 0.28-mm-wide

line. Arrows show the electron flow direction.

Chapter-09 11/29/04 6:50 PM Page 421