J O U R NA L O F M AT E R I A L S S C I E N C E L E T T E R S 1 8 ( 1 9 9 9 ) 4 7 1 ± 4 7 3

Effects of grain orientation on preferred abnormal grain growth in

copper ®lms on silicon substrates

JIANMIN ZHANG, KEWEI XU, JIAWEN HEState Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710 049, People'sRepublic of China

Aluminum and its alloys are the major materialsused for interconnects in integrated circuits. How-ever, their resistivities are not low enough to operateultra-large-scale integration (ULSI) circuits at ultra-high speeds because the parasitic capacitances ofinterconnects increase according to the scaling downof their physical dimensions. Furthermore, aluminumand its alloys are liable to show poor reliabilityagainst failures caused by elecromigration and stressmigration. Copper (Cu) is an attractive alternative tothese materials and has been investigated forapplications in interconnect formation [1, 2]. Theobvious advantage for using copper stems from itslow resistivity (1.72 ìÙcm) leading to low R±Cdelays, where R and C, respectively, represent theresistance and capacitance associated with intercon-nect architecture, and expected higher electromigra-tion resistance. The lower resistivity of copper willalso act to prevent Joule heating that should aid inthis regard, as well. However, because of thedifference in the thermal expansion coef®cients (á)between the copper ®lm and the silicon substrate(áCu � 17 3 10ÿ6 8Cÿ1 and áSi � 33 10ÿ6 8Cÿ1,respectively), the larger Young's modulus thanaluminum (ECu � 12:98 3 1011 dyn cmÿ2, EAl �7:06 3 1011 dyn cmÿ2) and the large difference inthickness (h) between the ®lm and substrate(hSi=hCu � 400 � 500), large biaxial stresses aregenerated in the copper ®lms during the thermaltreatments required for device fabrication. Filmstresses as large as 210 MPa (compressive) duringheating and 400 MPa (tensile) at room temperaturehave been measured [3]. These large stresses mayproduce changes in the ®lm and interconnectmorphologies that are deleterious to device manu-facturing yield and ultimate circuit reliability. Thelarge compressive stresses produce hillocks [4] onthe ®lm surface that lead to interlevel shortcircuiting between metallization layers. Tensilestresses produce voids [5, 6] in passivated ®lm thatlocally reduce the ®lm cross-section and current-carrying capability of the interconnects. Mechanical,physical and chemical properties of thin ®lms areaffected by microstructural attributes such as grainsize, grain size distribution, defect density andtexture. Film texture is of particular interest owingto the anisotropic property variations observed incopper. For example, the texture of electrolesscopper ®lm has been shown to affect the resultingoxidation behavior [7]. The correlation of room-

temperature stress with texture and the subsequentin¯uence on ®lm resistivity has also been noted [8].Ohmi et al. found that (1 0 0) and (1 1 1) preferredorientation Cu ®lms were grown on Si substrates bya low kinetic energy particle process, and (1 1 1)-oriented ®lms thus created on SiO2 were metastableand easily transformed by thermal annealing intocompletely (1 0 0)-oriented ®lms with large grains ofabout 100 ìm [9]. A recent paper discussed theobserved texture responses of copper thin ®lmsdeposited by a variety of techniques [10], in general,(1 0 0)-, (1 1 0)-, (1 1 1)- and (5 1 1)-oriented ®lmsdominated the response. From surface energy con-siderations, the close-packed (1 1 1)-oriented grainsshould be favored. An understanding of thesepreferred abnormal orientation grain growths hasremained elusive [11]. The purpose of this letter is toexplain the often extensive fraction of (1 0 0), (1 1 0),(1 1 1) and (5 1 1) texture component during thermalannealing by considering the effect of grain crystal-lographic orientation, with respect to the direction ofthe applied biaxial strains, on ®lm stresses. Weassume that the polycrystalline ®lms with a face-centered cubic (f.c.c.) structure (for example, Cu orAl) are deposited on rigid silicon substrates and thatthe grain structure is columnar in the ®lm, that is,the grain height is equal to the ®lm thickness.

The ®lm thermal stress (óe) at temperature (T )induced by thermal expansion mismatch is given by

óe � ÿ E

1ÿ v(áf ÿ ás)(T ÿ T0) (1)

where E is Young's modulus, v is Poisson's ratio, áf

and ás are thermal expansion coef®cients of the ®lmand substrate, respectively, T is the heating tempera-ture and T0 is the temperature at which óe � 0 onheating. The subscript `̀ e'' was chosen to emphasizethat this is the stress prior to yielding.

A detailed model [12] for the glide of threadingdislocations through capped (e.g., oxidized) thin ®lmon rigid substrates suggests that the biaxial yieldstress is shown as

ó � sinÖ

cosÖ cos ë

b

2ð(1ÿ v)h

ìf ìs

ìf � ìln

âs h

b

� �"

� ìf ì0

ìf � ì0

lnâ0 t

b

� �#(2)

where Ö and ë are the included angles between the

0261-8028 # 1999 Kluwer Academic Publishers 471

glide plane normal direction and Burgers vector andthe ®lm normal direction, respectively, as shown inFig. 1, b is the Burgers vector, v is Poisson's ratio ofthe ®lm, h and t are the thicknesses of the ®lm andoxide, respectively, ìf , ìs and ì0 are the elasticshear moduli of the ®lm, substrate, and oxide,respectively, and âs and â0 are numerical constants.If an oxide is not present on the surface of the ®lm,the second term in the brackets should be deleted.The effect of grain orientation in the ®lm is todetermine the factor

chkl � sinÖ

cosÖ cos ë(3)

where the subscripts (hkl) denote a particular grain-®ber orientation, that is, grains with (hkl) planesoriented parallel to the ®lm plane.

From Nix [12] for simplicity, let

G � b

2ð(1ÿ v)

ìf ìs

ìf � ìln

âs h

b

� �� ìf ì0

ìf � ì0

lnâ0 t

b

� �" #(4)

chkl � sinÖ

cosÖ cos ë(5)

Equation 2 can be rewritten as

ó hkl � chkl

G

h(6)

In the f.c.c. lattice, plastic deformation occurs as slipon the {1 1 1} or octahedral planes along the close-packed k1 1 0l direction. There are four of theseequivalent octahedral planes with three k1 1 0l slipdirections, each giving 12 equivalent slip systems(Table I).

For thin ®lms, plastic deformation occurs whenthe thermal or intrinsic stress of the thin ®lmproduces a resolved shear stress (CRSS); crystal-lographic orientation determines the resolved shearstress for a given thin-®lm stress. The chkl valueshave been calculated for several low-index grainorientations, and the average values of Chkl are listedin Table II. Here, the average Chkl values have beencalculated from the 12 slip systems except forin®nite values for the 12 grain-®ber orientations.

Then, Equation 6 becomes

ó hkl � Chkl

G

h(7)

We can see that the three lower average values ofthe orientation factor Chkl are 1.414, 2.000 and 2.750for grain orientations (1 1 0), (1 0 0) and (5 1 1),respectively. Considering the relative stress levels incolumnar grains with the same size but differingorientations as the ®lm undergoes annealing, duringheating but prior to yielding of any grain, the stressis uniform in the ®lm and given by Equation 1. Withincreased applied strain as the temperature increases,however, those grains in the `̀ weaker'' orientations(with lower Chkl) will yield and maintain their stresslevels as determined by Equation 7. The stresses ofgrains in `̀ stronger'' orientation (with larger Chkl)will continue to increase until they individuallyreach their yield or ¯ow stresses. The difference instress levels between grains of differing texture willbe at maximum when the grains in the strongestorientation have reached their yield stresses.

We can identify the biaxial strain energy density(W hkl) in each grain, while the biaxial elasticmodulus of the ®lms is isotropic.

W hkl � 1

M

G2

h2C2

hkl (8)

We can see that strain energy density is determinedby ®lm thickness, grain orientation and the materialparameters. The difference in biaxial strain energydensity between grains of differing texture orienta-tions is at maximum when the strongest grain hasyield.

Consider two adjacent grains with average valuesof the orientation factor Chkl, Ch0 k0 l0

, respectively. If(hkl) grain-growth speed is faster than (h0 k0 l0) grain

<hkl> <111>

Oxide

Film

Substrate

h

b

λ σ

σ

φ

σ

σ

Figure 1 The model of dislocation motion in glide planes of type

{1 1 1} due to biaxial stress ó in a grain of orientation (hkl) in the ®lm

plane.

TABLE I The twelve slip systems of the metals with f.c.c. lattice

[1 1 0](1 1 1) [1 1 0](1 1 1) [1 1 0](1 1 1) [1 1 0](1 1 1)

[1 0 1](1 1 1) [1 0 1](1 1 1) [1 0 1](1 1 1) [1 0 1](1 1 1)

[0 1 1](1 1 1) [0 1 1](1 1 1) [0 1 1](1 1 1) [0 1 1](1 1 1)

TABLE II Average values of the orientation factor Chkl for grain

®ber texture orientations in a thin ®lm

Grain orientation (hkl) Average Chkl

(1 0 0) 2.000

(1 1 0) 1.414

(1 1 1) 3.464

(2 1 0) 4.691

(2 1 1) 3.277

(2 2 1) 7.492

(3 1 0) 4.287

(3 1 1) 3.507

(3 2 0) 7.226

(3 2 1) 5.489

(3 3 1) 9.055

(5 1 1) 2.750

472

during thermal treatments or annealing, the changeof free energy can be shown as

ÄG � 1

M

G2

h2(C2

hkl ÿ C2h0 k0 l0

)� 2ã

d hkl

(9)

where ã is the grain boundary energy and dhkl is the(hkl) grain size in the ®lm plane. This movementcan take place only when ÄG , 0, that is

1

M

G2

h2C2

h0 k0 l0.

1

M

G2

h2C2

hkl �2ã

dhkl

(10)

It can be seen that only those grains with a loweraverage orientation factor Chkl can grow. The growthadvantage of the lower average Chkl grains increasesas they grow larger, relative to the higher averageorientation factor grains, because the second term ofthe right-hand side is inversely proportional to thegrain size dhkl. This advantage works so that thegrains with lower average values of the orientationfactor both initiate an abnormal growth process andmaintain a growth advantage as they consume thegrains with higher average values of the orientationfactor. We can predict that, for abnormal graingrowth, the resultant grains will have an orientationthat minimizes the average values of the orientationfactor. From Table II, we can see that three loweraverage values of the orientation factor (so that lowerstrain energy density) are 1.414, 2.000 and 2.750 for(1 1 0)-, (1 0 0)- and (5 1 1)-oriented grains, respec-tively. As to (1 1 1) texture, the average C1 1 1 � 3:464is slightly higher than C2 1 1 � 3:277, but fromsurface energy considerations the close-packed(1 1 1)-oriented grains should be favored. Consideringboth average values of the orientation factor (or strainenergy density) and surface energy, the stable texturesare successively (1 1 0), (1 0 0), (5 1 1) and (1 1 1).

In summary, we propose that during the annealingof thin copper ®lms on silicon substrates, thedifference in ¯ow stresses between differently

textured grains can lead to the preferred abnormalgrowth of the (1 0 0), (1 1 0), (5 1 1) and (1 1 1) grainsin the ®lm plane. Because the average values of theorientation factor, i.e., the strain energy density of(1 0 0), (1 1 0) and (5 1 1) grains are lower than(1 1 1) and the others, the latter are metastable andcan easily transform by thermal annealing into(1 1 0)-, (1 0 0)- and (5 1 1)-oriented ®lms. Theseresults help to explain the experimental results ofothers. The other factors, including the effects ofadjacent grains, deformation strengthening, grainsize, grain size distribution, defect density andsurface energy, are not considered in this letter.Further work will provide a more detailed analysis ofthese effects.

References1. G . H . TA K AO K A , J. I S H I K AWA and T. TA K AG I ,

J. Vac. Sic. Technol. A8 (1990) 840.

2. T. O H M I , T. S A I TO, T. S H I BATA and T. N I T TA , Appl.

Phys. Lett. 52 (1988) 2236.

3. P. A . F L I N N, J. Mater. Res. 6 (1991) 1498.

4. P. C H AU D H A R I , J. Appl. Phys. 45 (1974) 4339.

5. R . P. V I N C I , T. N. M A R I E B and J. C . B R AV M A N,

Mater. Res. Soc. Symp. Proc. 308 (1993) 297.

6. P. B é R G E N S E N, J. K . L E E , R . G L E I X N E R and C . Y.

L I , Appl. Phys. Lett. 60 (1992) 1706.

7. F. W. YO U N G , J. V. C AT H C A RT and A . T. G WAT H -

M E Y, Acta Metal. Metal. 4 (1956) 145.

8. A . F. B U R N E T T and J. M . C E C H , J. Vac. Sci. Technol.

A11 (1993) 2970.

9. T. O H M I , T. S A I TO, M . OT S U K I and T. S H I BATA ,

J. Electrochem. Soc. 138 (1991) 1089.

10. D. P. T R AC Y and D. B. K N O R R J. Elec. Mater. 22 (1993)

611.

11. S . P. M U R A R K A, Mater. Sci. Engng R19 (1997) 87.

12. W. D. N I X , Metall. Trans. A 22A (1989) 2217.

Received 30 Julyand accepted 8 October 1998

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