Scripta METALLURGICA Vol. 27, pp. 285-290, 1992 Pergamon Press Ltd. et MATERIALIA Printed in the U.S.A. All rights reserved

EFFECTS OF GRAIN ORIENTATION ON HILLOCK FORMATION AND GRAIN GROWTH IN ALUMINUM FILMS ON SILICON SUBSTRATES

J. E. Sanchez, Jr., E. Arzt Max-Planck-Institut fur Metallforschung

Seestrasse 92, D-7000 Stuttgart, Germany

( R e c e i v e d A p r i l 23, 1992) ( R e v i s e d May 27, 1992)

Inlroduction

Metallization interconnects in integrated circuit devices are typically patterned from thin films of aluminum alloys deposited onto oxidized silicon single crystal substrates. However, because of the large difference in the thermal expansion coefficients (ct) between aluminum and silicon (ctAl = 24 10-6/*C and txSi = 3 10"6/*C, respectively) and the large difference in thickness (h) between the film and substrate (hsi/hAl = 500) large biaxial stresses are generated in the aluminum films during the thermal treatments required for device fabrication. Film stresses as large as ~ 400 MPa (compressive) during heating and ~ 350 MPa (tensile) at room temperature have been measured (1). These large stresses may produce changes in the film and interconnect morphologies which are deleterious to device manufacturing yield and ultimate circuit reliability. The large compressive stresses produce hillocks (2) on the film surface which lead to interlevel short circuiting between metallization layers. Tensile stresses produce grain collapse (3) or holes (4) in the film which locally reduce the film cross section and current carrying capability of interconnects. While it is generally agreed that these morphological changes are due to the film stresses, detailed understanding of the mechanisms which produce these changes in films and interconnects is lacking. However recent results (5) have characterized the effect of film thickness and grain size on average film stresses during annealing. The purpose of the present note is to extend those results by considering the effect of grain crystallographic orientation, with respect to the direction of the applied biaxial strains, on film stresses. We then calculate probable stress gradients and elastic strain energy densities between adjacent grains of different texture orientations. These results are 1) applied to possible mechanisms for hillock formation by grain boundary diffusion, and 2) compared to the driving forces for abnormal grain growth. The analysis suggests that the compressive stress gradients between (110) and (111) grains lead to hillock formation by preferred growth of (110) grains out of the film plane. The resuks also suggest that, under certain conditions of film alloying and layering, the elastic strain energy densities between the typical (111) and (110) oriented grains provide a sufficient driving force advantage for the preferred abnormal growth of the (110) grains in the film plane. We conclude that these results help to explain recent experimental results of others which show 1) hillock grains are (110) fiber textured in a matrix of principally (111) textured grains (6), and 2) a change in film texture from a nominally (111) texture to principally (110) texture as a result of abnormal grain growth (7).

Film Thermal Stresses: Deoendence on Grain Orientation

The film stress (Gel) at temperature O') induced by thermal expansion mismatch is given by

ael = M As AT = M Act (T - To), (I),

where M is the biaxial elastic modulus for aluminum given by (E/l-v), where E is Young's modulus, v is Poisson's ratio, Act = ctAl - ctSi, and To is the temperature at which Ctel = 0 on heating. The subscript (el) is chosen to emphasize that this is the stress prior to yielding. Since M is ideally isotropic in A1 for (111) texture and nearly isotropic for other orientations, and ctAl and ¢tSi are essentially isotropic, ael is uniform

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286 GRAIN ORIENTATION IN A1 FILMS Vol . 27, No. 3

fox each grain in the film. However during typical thermal cycles films undergo sufficient straining to induce yielding. The film yield stress at temperature 03 has been shown (5) to be of the form

Oy 03 = Oh + Ogs, (2),

where Oh and Ogs are the thickness (h) and grain size (d) dependent contributions to Oy, respectively. There it was shown that (5)

oh 03 = m 03/.h, (3a),

ogs 03 = k 03 / d", (3b),

where n is a constant in the range 1/2 < n < 1, and the weak (5) temperature dependence of oy is indicated by the dependence of m and k on temperature. Here k is of the form of a Hall-Perch constant, and we note that grain size dependent flow stresses in aluminum thin films have been observed by a number of workers (8,9).

A detailed model (10) for the glide of threading dislocations through capped (e.g. oxidized) thin films on rigid substrates suggests that Oh may be described by an analytical expression

oh = Cijk G* b / h (4),

where Cij~ = sin ~b/cos 0 cos ~ G* is the effective shear modulus of the capped fdm-substrate system, b is the Burgers vector, and 0 and X are the included angles between the glide plane normal direction and Burgers vector and the film normal direction, respectively, as shown in figure 1. G* is given by the term {(I/(2~[1- v] ) Of Its/(itf + Its) In (l~sh/b) + laf ~to/(itf + lao) In 13ot/b)}, where [~s and I~o are constants, t is the oxide capping layer thickness, and Itf, Its, and Ilo are the elastic shear moduli of the film, substrate and oxide capping layer, respectively (10). We assume that the grain structure is columnar in the film, that is, the grain height is equal to the film thickness. In layered f'dms, the grain structure may be such that the grain height is less than h (11). The effect of grain orientation in the film is to determine the factor Cij~, where the subscripts (ijk) denote a particular grain fiber orientation, that is, grains with (ijk) planes oriented parallel to the film plane. The Cijk have been calculated for several low index grain orientations, and the average

values Cijk are listed in table 1. Here the average C'ijk have been calculated from the 4 slip systems with the lowest Ci~ for the 7 lowest index grain fiber orientations. Grains with (1 10) orientation have the lowest

value, CII0 -- CI10 = 1.42, with (111) grains having a higher value, Cl l l = Cll l = 3.46, etc. The difference between CI 10 and CI 1 1 is most relevant since typical films are principally (1 1 1) textured and (1 10) grains have the lowest Cijk. Thus both oh and Oy are dependent on grain orientation, i.e., Oh,ijk and

oy,i~ through the factors Cijk. Here we have assumed that Ogs is independent of grain orientation, and is dependent only on the length of the glide plane in the grain, i.e., the grain size d.

TABLE 1. Average values of the orientation factor (~iik for the 7 lowest index grain fiber texture orientations in a thin film, calculated from the 4 lowest Cijk for the available slip systems.

Grain Orientation Average ~ijk (100) 2.00 (110) 1.42 (111) 3.46 (210) 1.94 (211) 1.73 (221) 1.60 (311) 1.62

Vol. 27, No. 3 GRAIN ORIENTATION IN A1 FILMS 287

Fig. 1. Model of dislocation motion in glide planes of type <111> due to biaxial stress o in a grain of orientation (ijk) in the film plane. Film is assumed to be capped with, for example, an oxidized layer. The motion lays down trailing dislocation segments where glide plane meets the substrate and the surface layer. (After Nix, ref. 10.)

Consider the increase in film strain and (compressive) stress above To as, for example, during the first heating after f'dm deposition. We make the critical and simplifying assumption that the flow stress level in each grain is determined individually by equation 2 above, independent of the stresses in adjacent grains, during thermal treatments or annealing. This is justified by several considerations. Firstly, each grain is rigidly adhered to the substrate, limiting the forces that adjacent grains may impose on each other. Secondly the deformation-dislocation processes implied by equations 3a, 3b arc particular to individual grains. We may then consider the relative stress and strain levels in grains of differing orientations as the polycrystailine film undergoes annealing. During heating but prior to yielding of any grain, the stress is uniform in the fdm and is given by equation (1). However, with increased applied swain as the temperature increases, those grains in the "weaker" orientations will yield and maintain their stress and elastic swain levels as determined by equation 2, while the stresses and elastic strains of grains in "stronger" orientations will continue to increase, until they individually reach their yield or flow stresses. The difference in stress levels between grains of differing texture will be a maximum when the grains in the strongest orientation have reached their yield stresses. We emphasize that these differences arise solely from the orientation dependence of flow

stress through the factor Cijk. We may then define the maximum difference in stress levels between grains of different f'dm texture orientations (ijk) and (abe) and sizes (dijk, etc.) as Aoij~-abc given by

AOijk-abc = Oy,ijk - Oy,abc

= Cijk I-I / h + k / dij~ n - Cabc F l /h - k / dabc n (5),

where the term rI is defined for simplicity as rl = G* b. We note that Ao is determined by film thickness, grain size, grain orientations and the material parameter N. If we assume that grain size is uniform for all orientations, dijk = dabc, etc., equation 5 reduces to

AOijk-abc = ( Cijk - (~abc) 1-I / h (6).

l:Iiilagg.E~aa~m

Values for n may be estimated from the measurements of o h for (111) textured films in recent experimental work (5). There m111 (= C111 n ) was found to be approximately 25 MPaop.m at 300"C for aluminum and aluminum-copper films in compression. Using C l l l = 3.46, FI is ~ 7.2 MPa-gm. Thus the

288 GRAIN ORIENTATION IN A1 FILMS Vol. 27, No. 3

maximum difference in biaxial stress on heating between (111) and (110) oriented grains for typical 1 ~tm aluminum or aluminum-copper films at 300"C is estimated to be AOl 11-110 = (3.46 - 1.42 ) 7.2 MPa-p.m / 1 ttm = 14 MPa. For 0.4 ~tm thick films under similar conditions, AOlII-I10 = 35 MPa. These Ao give rise to compressive stress gradients of the magnitude Ao / do = Ao / h / 2 = 30-70 MPa/~tm in the region of the (110) oriented grains, where we assume that the as-deposited grain size (do) is typically less than the film thickness by a factor of at least two. These large stress gradients may induce meehano-diffusional mass flux from the boundary regions surrounding (111) grains to (110) oriented grains. We suggest that the growth of the (110) grains out of the film plane producing hillocks is driven by this boundary flux and may thus partially relieve the film compressive stress. The compressive stress relief qualitatively described by such a process will occur principally along the network of boundaries surrounding the (110) grains and will not appreciably relieve stresses in grain interiors. A more comprehensive treatment of compressive stress relief by the hillock growth of (110) grains in nominally (111) oriented films is beyond the scope of this note. However recent results (6) have shown that hillock grains in annealed aluminum films on silicon substrates were principally (110) textured in a mairix of (111) grains. This analysis also suggests that hillock growth by the process proposed here will not occur in perfectly textured films. Further we note that grain growth, which may typically occur below 300"C, will not appreciably affect this process since Ao is independent of grain size in the film, equation 6. We assume only that (110) and (111) grains are nominally of the same diameter.

Under certain conditions of film alloying, grain growth may be retarded until higher temperatures are reached due to the presence of small second phase particles which pin boundary motion (7,11). In such cases large decreases in film stress may be observed due to the large increase in d (equation 3b) when growth does occur.

Effects of F i l l Stresses on Abnormal Grain Growth

We can identify the biaxial strain energy density (W) in thin films as

W = 1/2 (Ol El+ 0"2 £2) = 1/2 (OI2/MI + 022/M2) (7),

where the bilaxial moduli, stresses and strains (Mi, oi, and ei, respectively) are measured or resolved in orthogonal directions in the film plane. For the biaxial situation considered here, M is isotropic and Ol = 02 = Oel is uniform in each grain prior to any yielding, and o l = 02 = Oy,~k after yielding in grains of orientation (ijk). The W is given by (oel 2 / M) prior to yielding and by (Oydj~ / M) in yielding (ijk) oriented grains thereafter. The difference in biaxial swain energy density (AWijk-abc) between grains of differing texture orientations is a maximum when the strongest grains have yielded, and is given by

AWijk-abc = 1/M (Oydjk 2- Oy~abc 2)

= 1/M { ( Oh,0 k + Ogs) 2 - (Oh~ac +Ogs) 2 } (8).

If we compare stresses between grains of the same size (d) but differing orientations, this result reduces to

AWijk-abc = 1/M I (l]/h) 2 (Cijk 2 - (~alx 2) + (2k l ']/d n h) (Cijk - (~a~)} (9).

AW is in general determined by f i l l thickness, grain orientations and grain size as well as the material parameters M, 11, and k. We can compute AWijk-abc for thin films (h < 0.4 ~tm) and small uniform grain sizes (d = 0.2 ~tm). These conditions are interesting since abnormal grain growth (7) and compressive stresses as large ffi 350 MPa (1) have been observed in such films. Based on the analysis here, these large compressive stresses are explained by both grain size strengthening due to boundary pinning by small intermetallic phases (7,11), which prevent grain growth, and film thickness strengthening. Using I-I, Cl l l ,Cl l0 , h and d from above, M = 115 GPa, k = 60 MPa-~tm3/4 as determined elsewhere, and n = 3/4

Vol. 27, No. 3 GRAIN ORIENTATION IN A1 FILMS 289

which is intermediate to the limits 1/2 < n < 1 proposed (5), we estimate AWIII-II0 = 1.7 10 5 J/m 3. We can compare this to the average driving force for grain growth (Fgg = Tgb/r*) where Tgb is the grain boundary energy and r* is the average in plane curvature of the boundaries. Since r* is = 5-6 d, r*= 1.0 gm (1.0 10 -6 m) for 0.2 ttm diameter grains. For Tgb = 0.3 J/m 2, Fgg ffi 3.0 10 5 J/m 3. The strain energy difference is thus of the same order of magnitude as the typical driving force for grain growth.

Recent simulations (12) of the effects of surface energy differences (Ays) in differently oriented grains in thin films demonstrate that abnormal grain growth may be driven by ATs as small as several percent of the average film Ts. Models for abnormal grain growth (13) predict that the resultant grains will have an orientation that minimizes Ts. However, in an exception notable for its technological importance, (111) textured aluminum alloy films interlayered with thin chromium and copper films undergo abnormal grain growth (7) resulting in large (110) grains of presumably higher surface energies. We propose that the swain energy difference between grains of varying orientations, which is a maximum between (111) and (110) oriented grains, provides sufficient driving force for the preferred abnormal growth of (110) grains. Equations 8,9 show that this AW is increased for thinner films and smaller grain sizes and can be an appreciable fraction of the driving force for grain growth due to boundary curvature. Indeed the texture changes away from (111) to (110) as a result of abnormal grain growth (7), opposite that which is predicted by current theory and simulation, occurs in multilayered aluminum films where the effective aluminum film thickness is below = 0.4 grn and the grain size is pinned by second phase particles which dissolve (14) only at high temperatures. The AWl 11-110 advantage of (110) grains is significant at the initial stages of abnormal grain growth, where we can assume dl 11 = d110 (equation 9), and where the compressive stresses arc at a maximum and the grain size is at a minimum. Note that the growth driving force advantage of the (110) grains increases as they grow larger relative to the (111) grains, since the (110) grains weaken as they become larger. This advantage works so that the (110) grains both initiate the abnormal growth process and maintain a growth advantage as they consume the principally (111) textured film. More detailed modelling of the effects of strain energy variations in differently textured grains on grain growth processes will be presented elsewhere.

Discussion

Several factors may affect the extent of the processes proposed here. Stress relaxation along the boundary regions may reduce the effect of strain energy density differences on boundary motion, limiting somewhat the growth advantage of grains with lower strain energy densities. In addition actual populations of grain sizes in thin films are approximately lognormally distributed. We can assume that the sizes of grains comprising the different texture components are randomly dispersed throughout this size distribution. Then, following the analyses above, the situation where (110) oriented grains are larger than adjacent (111) grains will lead to an enhancement of the effects described. Conversely, (110) grains smaller than adjacent (111) grains will lead to a reduction of these effects on film microstructure. Finally, we have assumed that the model for dislocation motion as described by equation 4 and figure 1 is valid for glide in grains of size (d) less than the film thickness (h). Careful characterizations of the texture components in deposited films, and correlations with measured hillock densities and abnormal grain populations, are required to more fully understand the extent of the stress gradient driven hillock formation and strain energy driven grain growth in actual thin fdm alloy systems.

Conclusions

In summary, we propose that during the annealing of thin aluminum films on silicon substrates the differences in flow stresses between differently textured grains can lead to stress gradients that prefer the hillock growth of (110) oriented grains. In a similar treatment we show that the preferred in plane growth of (110) grains may be due to the dependence of elastic strain energy densities on grain orientation. These results help to explain the experimental results of others which show the hillock growth (out of the film plane) and abnormal in plane growth of (110) oriented grains. Further work will provide more detailed analyses of these effects.

290 GRAIN ORIENTATION IN A1 FILMS Vol . 27, No. 3

We wish to thank A. Wanner for a critical reading of the manuscript, and O. Kraft for helpful suggestions. We wish to also acknowledge R. Venkatraman and H. Frost for providing copies of manuscripts in the press. One author (JES) would like to acknowledge the support of the Max Planck Society during his tenure in Stuttgart, Germany.

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