EFFECTS OF LINE AND PASSIVATION GEOMETRY ON CURVATURE EVOLUTION DURING PROCESSING AND THERMAL CYCLING IN COPPER INTERCONNECT LINES

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1 Acta mater. 48 (000) 3169± EFFECTS OF LINE AND PASSIVATION GEOMETRY ON CURVATURE EVOLUTION DURING PROCESSING AND THERMAL CYCLING IN COPPER INTERCONNECT LINES T.-S. PARK and S. SURESH{ Department of Materials Science and Engineering, Massacusetts Institute of Tecnology, Cambridge, MA 0139, USA (Received 30 December 1999; accepted 17 April 000) AbstractÐA simple teoretical analysis for curvature evolution in unpassivated and passivated copper interconnect lines on a silicon substrate is proposed. A layer consisting of copper and oxide lines is modeled as a omogenized composite tat as di erent elastic moduli and termal expansion coe cients in two di erent directions, i.e. along and across te lines, due to te anisotropic line geometry. Tese e ective termoelastic properties of te composite layer are approximated in terms of volume fractions and termoelastic properties of eac line using standard composite teory. Tis analogy facilitates te calculation of curvature canges in Damascene-processed copper lines subjected to cemical±mecanical polising and/or termal cycling. Te e ects of line eigt, widt and spacing on curvature evolution along and across te lines are readily extracted from te analysis. In addition, tis teory is easily extended to passivated copper lines irrespective of passivation materials by superimposing te curvature cange resulting from an additional layer. Finite element analysis as been used to assess te validity of te teoretical predictions; suc comparisons sow tat te simple teory provides a reasonable matc wit numerical simulations of curvature evolution during te Damascene process in copper interconnects for a wide range of line and passivation geometry of practical interest Acta Metallurgica Inc. Publised by Elsevier Science Ltd. All rigts reserved. Keywords: Coating; Composite; Copper; Teory and simulation; Termal cycling 1. INTRODUCTION Te reliability of metal interconnect lines in integrated circuits is known to be in uenced by failure mecanisms suc as electromigration [1±3] and stress-induced voiding [4±6]. In ultra large scale integration (ULSI) devices, multilevel metallization is needed. Oxide passivation layer deposition usually involves eating up to 4008C so tat te interconnect lines undergo several termal cycles. Termal stresses are generated by te large di erence in expansion/contraction wic develops between te metal interconnect lines and surrounding materials during termal cycling. Tensile termal stresses formed during cooling from te oxide deposition temperature can cause voiding near te interface between an interconnect line and te surrounding passivation layer. Due to te di culty of etcing copper, a new fabrication tecnique called te Damascene process as been introduced in te semiconductor industry { To wom all correspondence sould be addressed. [7]. In tis metod, trences wose dimensions conform to te geometry of te copper interconnect lines in te circuit are dry-etced in an oxide layer wic is grown on te silicon substrate. Tese trences are ten plugged wit copper by recourse to cemical vapor deposition (CVD) or electroplating. Te extra copper above te trences is ten removed by cemical±mecanical polising (CMP), and ten a passivation or capping layer is deposited on top of te interconnect structure. As tis process involves polising, te control of curvature of te silicon wafer becomes critical for uniform polising over te entire wafer. Te canges in curvature induced during polising and subsequent passivation also provide valuable information about te evolution of internal stresses in te interconnect lines. Te objective of tis work was to develop a simple teoretical analysis of te evolution of curvature along and across copper interconnect lines on silicon substrates during various fabrication steps, as functions of te line and passivation geometry. Te analytical results are veri ed wit numerical simulation using te nite element metod /00/$ Acta Metallurgica Inc. Publised by Elsevier Science Ltd. All rigts reserved. PII: S (00)00114-

2 3170 PARK and SURESH: CURVATURE EVOLUTION IN INTERCONNECT LINES s (FEM) for a range of line geometry of practical interest. M x ˆs xx i ˆ n s k x n s k y 1. ANALYTICAL MODEL Figure 1(a) is a scematic of Cu interconnect lines on a Si substrate following te Damascene process. Assuming tat te aspect ratio (/w ) of te Cu and SiO lines is ig (typically equal to or greater tan unity), te structure can be omogenized into a composite layer as sown in Fig. 1(b). Due to te anisotropic line geometry, tis composite layer as di erent values of e ective elastic modulus and termal expansion coe cient along te lines, E x and a x, respectively, tan tose across te lines, E y and a y, respectively, even if Cu itself is modeled as elastically and termally isotropic. Using composite teory, tese e ective properties can be calculated in terms of te volume fraction, elastic modulus and termal expansion coe cient of Cu lines, f l ˆ w=p), E l and a l, and tose of SiO lines, f o ˆ 1 w=p), E o and a o. Considering a plate of an elastic material wic is subjected to bending moments, M x and M y, along te x- and y-directions, respectively, were x± y is te plane of te plate, te resulting non-equibiaxial stresses are generally expressed as [8] M y ˆs yy i s ˆ ns k y n s k x were s xx i and s yy i are te normal stresses in te plate along te x- and y-directions, respectively, k x and k y are te curvatures along te x- and y-directions, respectively, and and n s are te elastic modulus and Poisson ratio, respectively, of te Si substrate. Equations (1) and () can be rewritten as k x ˆ 6 k y ˆ 6 s xx i n s s yy iš s s yy i n s s xx iš: s 3 4 From equations (3) and (4), it is evident tat te curvature in one direction is expected to ave some contribution from te termal stress resulting from termal mismatc in te oter direction. Tis coupling term, owever, includes te Poisson ratio, wic makes tis contribution relatively small. In addition coupling can be taken into account by considering te e ective termal expansion coe cients of te omogenized composite layer, wic somewat compensates for te limitations of a onedimensional approac. It could, terefore, be postulated tat a simple uniaxial, anisotropic composite model for patterned elastic lines migt provide su ciently accurate predictions of curvature evolution in response to canges in geometry (suc as tat arising from cemical±mecanical polising) or to canges in internal stresses arising from termal cycling. A simple analytical model for curvature evolution, in unpassivated and passivated interconnect lines, is developed on te basis of tis premise. Te conditions of validity of suc a simple model are ten assessed using detailed nite element simulations. Te stresses are from termal mismatc in te uniaxial state is approximated as s xx iˆ E x a x a s DT, s yy iˆ E y a y a s DT: 5 Combining equation (5) wit equation (3) or (4), te curvature components are calculated to be Fig. 1. Scematic of unpassivated Cu interconnect lines on a Si substrate following te Damascene process: (a) individual Cu lines and SiO lines; (b) omogenized composite layer. k x ˆ 6 E x a x a s DT, s k y ˆ 6 s E y a y a s DT: 6 Equation (6), wic is valid only for uniaxial loading, is used for calculating curvature evolution of

3 PARK and SURESH: CURVATURE EVOLUTION IN INTERCONNECT LINES 3171 s l i a y DT ˆ f l n l a l DT f o te omogenized composite layer consisting of Cu and SiO lines wic is subjected to biaxial loading. Te volume-averaged stresses from termal mismatc in te equibiaxial state are expressed as E l n o s o i E o a o DT : 14 s xx iˆs yy iˆ E f a f a s DT 7 were E f and a f are te biaxial modulus E f = 1 n f Š and termal expansion coe cient, respectively, of a uniform lm. Combining equation (7) wit equations (3) and (4), te curvatures can be found as k x ˆ k y ˆ 6 s E f a f a s DT were and a s are te biaxial modulus = 1 n s Š and termal expansion coe cient, respectively, of te Si substrate. Equation (8) is used for curvature evolution of te uniform passivation layer, wic is a continuous SiO layer in tis work..1. Unpassivated lines 8 Te total strains during termal excursions are te same along te Cu and SiO lines, and tey are related to te e ective termal expansion coe cient along te lines as a x DT ˆ s li E l a l DT ˆ s oi E o a o DT 9 were s l i and s o i are te volume-averaged stresses in te Cu and SiO lines, respectively. A force balance equation for tis geometry, Fig. 1(a), gives f l s l i f o s o iˆ0: 10 From equations (9) and (10), te e ective termal expansion coe cient along te line direction is a x ˆ fle l a l f o E o a o f l E l f o E o : 11 Te e ective elastic modulus along te line direction is written, using te composite teory, as E x ˆ f l E l f o E o : 1 Substituting E x and a x from equations (11) and (1) for te corresponding properties in equation (6), te curvature cange along te lines, k x, is found to be k x ˆ 6 E x a x a s DT: s 13 Across te lines, consideration of termal expansion in te line and of te Poisson e ect gives Substituting s l i and s o i from equations (9) and (10) into equation (14), te e ective termal expansion coe cient across te line direction is calculated as a y ˆ f l a l f o a o f lf o n l E o n o E l a l a o f l E l f o E o : 15 Te e ective elastic modulus across te line direction is written, wit standard composite teory, as E l E o E y ˆ : 16 f l E o f o E l Substituting E y and a y from equations (15) and (16) into equation (6), te curvature cange across te lines, k y, becomes k y ˆ 6 s E y a y a s DT: 17 WikstroÈ m et al. [9] derived expressions for te normal components of volume-averaged stresses in interconnect lines for two limiting cases: very low and ig line aspect ratios, /w. At a very low line aspect ratio, =w 4 0, te interconnect structure can be considered as comprising individual Cu and SiO lms. Terefore, te curvature canges in bot directions, i.e. along and across te lines, are te same and are obtained by adding te appropriate contribution from eac lm k low x ˆ k low y ˆ 6 s 1 n s f l s l i low f o s o i low Š 18 were s l i low and s o i low are te volume-averaged biaxial stresses in te lines and te oxide, respectively, for te case of te low line aspect ratio. Similarly, k low l and k low o are te curvatures in te Cu and SiO lms, respectively. As integration of te devices increases wit decreasing line widt, te aspect ratio of interconnect lines currently used in te semiconductor industry is also increased. At ig line aspect ratios, =wr1, te curvature canges in eac direction are obtained as follows: " # k ig x k ig y ˆ 6 s " 1 1 ns n s 1 f l s l xx iig f o s o xx iig f l s l yy iig f o s o yy iig # 19 were te superscript ``ig'' denotes te ig line

4 317 PARK and SURESH: CURVATURE EVOLUTION IN INTERCONNECT LINES Cu interconnect lines can also be assessed using te above simple model by invoking te concept of superposition. Figure sows a scematic of passivated Cu lines, wic can be regarded as superimposition of te composite layer and te passivation layer. For a given passivation material, te curvature cange resulting from te passivation layer, k p, is obtained in terms of te biaxial modulus of te passivation layer, E p ˆ E p = 1 n p Š), its termal expansion coe cient, a p, and its tickness, p, using equation (8) as k p ˆ 6 p E p a p a s DT: s 0 Fig.. Scematic of passivated Cu interconnect lines on a Si substrate following passivation: (a) actual interconnect structure; (b) superimposition of te composite layer and passivation layer. aspect ratio for te components of volume-averaged stresses and curvatures in te Cu and SiO lines in tis regime. At f l ˆ f o ˆ 0:5, equations (13) and (17) give approximate values wit less tan 5% error compared wit te values from equation (19). Terefore, te present model sows a reasonably good matc in te range of practical line geometry, =wr1, in spite of its simplifying assumption tat te curvatures along and across te line direction do not in uence one anoter. By adding k p from equation (0) to k x and k y from equations (13) and (17), respectively, curvature canges of passivated lines, kx 0 and k y 0, are obtained: k 0 x ˆ k x k p ˆ 6 s a s DT E x a x a s DT 6 p s E p a p 1.. Passivated lines Te evolution of curvatures in passivated elastic Fig. 3. A representative unit cell (top portion) and nite element discretization for Cu lines in te Damascene process. Fig. 4. Curvature canges of unpassivated Cu lines in te Damascene process at xed line geometry ˆ 1 mm, s ˆ 55 mm, =w ˆ 1, p=w ˆ ). Te Cu layer is deposited at 008C: (a) along lines; (b) across lines.

5 PARK and SURESH: CURVATURE EVOLUTION IN INTERCONNECT LINES 3173 k 0 y ˆ k y k p ˆ 6 s a s DT: E y a y a s DT 6 p s E p a p Table 1. Material properties used in te simulations E (GPa) n a (10 6 /8C) Si Cu SiO Te accuracy of tis result will be assessed in Section FINITE ELEMENT ANALYSIS Te nite element metod (FEM) was used to verify te present analytical model. For tis purpose, te general purpose nite element program ABAQUS [10] was employed. Te mes used in te present numerical simulation is sown in Fig. 3. Due to te periodicity and symmetry of te arrangement, only a unit segment ranging from a symmetric axis and te neigboring periodic boundary is needed. Here, w, and p represent te eigt, widt, and spacing of Cu lines, respectively. A generalized plane strain formulation, wic is an extension of te plane strain framework (wit te y±z plane being te plane of deformation), was used in te calculations. Tis was accomplised by superimposing a longitudinal strain, e xx, on te plane strain state. Te detailed procedure for obtaining te curvatures using suc numerical simulation can be found in earlier papers [11, 1]. Table 1 sows te material properties used in te simulations [1, 13]. Isotropic material properties were used, and residual stresses wic may result from Cu deposition and/or polising were not taken into account. Tis analysis deals wit only elasticity, wic is expected to be valid over a wide range of practical interest since te material surrounding te Cu lines, especially in te case of passivated lines, leads to elevated levels of ydrostatic stress in te lines tereby inducing constrained deformation [6]{. oxidation at 10008C, cooled down to 008C, and ten patterned into trences (at A). Te residual stress formed during oxidation is not considered in tis simulation. At 008C, a Cu layer is deposited on patterned SiO lines, and ten cooled down to room temperature A4 B). A very large curvature cange occurs during cooling in tis direction. Wen an excess Cu layer (1 mm tick) is removed by polising B 4C), te curvature drops drastically. Ten as te temperature is raised from room temperature C 4 D), te curvature canges in te opposite direction. Across te lines, Fig. 4(b), te curvature cange sows di erent slopes from tose along lines during cooling and eating. Analytical predictions (Equations (13) and (17) for unpassivated lines and equations (1) and () for te case 4. RESULTS AND DISCUSSION 4.1. Canges in curvature during te Damascene process Figure 4(a) sows curvature canges along te unpassivated Cu lines from te Damascene process for a xed line geometry =w ˆ 1, p=w ˆ ). First we assume tat te SiO layer is grown by termal { In te unpolised Cu layer (before CMP), owever, plastic deformation can occur because te yield strengt of unpassivated Cu lms can be very low at moderate temperature (well below 4008C) [14]. Unpassivated Cu lines (after CMP) wic are in te trenc wit its top face being free may also plastically deform due to ig deviatoric components unless te aspect ratio is very ig. Tese inelastic deformations sould be considered wen experimental data are compared wit te present model. Fig. 5. Curvature canges of unpassivated Cu lines ˆ 1 mm, s ˆ 55 mm during eating from room temperature to 008C as a function of: (a) aspect ratio at xed pitc ratio p=w ˆ ); (b) reciprocal of pitc ratio at xed aspect ratio =w ˆ 1).

6 3174 PARK and SURESH: CURVATURE EVOLUTION IN INTERCONNECT LINES in te layer wic consists of Cu and SiO lines. Wen a pure Cu lm is considered w=p41), te present one-dimensional model gives k x ˆ k y ˆ 6 s E l a l a s DT: 3 However, te biaxial modulus of te Cu lm and te Si substrate sould be used to obtain exact curvature canges for tis two-dimensional structure: k exact x ˆ k exact y ˆ 6 s E l a l a s DT 1 ns 6 ˆ E l a l a s DT: 1 n l s 4 Fig. 6. Curvature canges of passivated Cu lines wit SiO passivation layer ˆ 1 mm, p ˆ 1 mm, s ˆ 55 mm during eating from room temperature to 008C as a function of: (a) aspect ratio at xed pitc ratio p=w ˆ ); (b) reciprocal of pitc ratio at xed aspect ratio =w ˆ 1). wit excess Cu.) are exactly matced wit calculated values by FEM in bot directions during te above fabrication and termomecanical processes. 4.. E ects of line and passivation geometry Figure 5(a) sows curvature canges during eating from room temperature to 008C as a function of aspect ratio at a xed pitc ratio p=w ˆ ). Wen te pitc ratio is xed, te fraction of Cu in tis composite layer is uncanged. Terefore, equations (13) and (17) give constant curvature values, wic reasonably t te results of numerical simulation over a wide range. Figure 5(b) sows curvature canges during eating from room temperature to 008C as a function of te reciprocal of pitc ratio (w/p ), wic corresponds to te volume fraction of Cu, at xed aspect ratio =w ˆ 1). As te spacing between te Cu lines increases, te fraction of Cu in tis layer decreases. Considering te volume fraction in equations (13) and (17), analytical values agree closely wit FEM results over all Cu volume fraction Terefore, te factor of 1 n s = 1 n l can be regarded as an error of te present model in tis limiting case, and it gives only 3% error for te pure Cu lm. In te same way, te corresponding factor for a pure SiO lm, w=p40), can be expressed as 1 n s = 1 n o, wic sows a 17% error. But since tis SiO ric region sows very small curvature canges compared wit tat wit ig Cu volume fraction, tis error is not large in an absolute value. Terefore, it sows a very good agreement wit numerical simulation in a fairly wide range, were practical interconnect line geometries lie. Analytical predictions and FEM results for passivated lines wit SiO passivation layer are sown in Fig. 6. Tey represent almost te same trends as unpassivated lines wit smaller absolute values because te termal expansion coe cient of oxide is lower tan Si substrate. Due to te ig di usivity of Cu troug SiO and Si, a di usion barrier suc as TaN is commonly employed [7]. Altoug it makes more complicated interconnect structures, te e ect of tis additional layer can be easily incorporated in te present model by superimposition for linear elasticity condition and may be negligible if tis layer is very tin, i.e. of te order of a few undred A Ê ngstroè ms. 5. CONCLUSIONS In tis paper, a simple analytical model based on a composite analogy as been used to predict curvature in unpassivated and passivated Cu lines in te Damascene process. A layer consisting of copper and oxide lines is modeled as a omogenized composite layer consisting of Cu and SiO lines. Te e ective termoelastic properties of te composite layer are computed in terms of volume fractions and termoelastic properties of eac line using standard composite teory, wic enables us to calculate curvature canges during te Damascene process employing termal cycling and polising. Finite element analyses ave been used to assess te accuracy of te simple analytical model. Tese

7 PARK and SURESH: CURVATURE EVOLUTION IN INTERCONNECT LINES 3175 values are exactly matced wit eac oter during Cu deposition, polising, passivation, and termal cycling under te assumption of isotropic material properties and linear elasticity conditions. Altoug residual stresses are not incorporated into te analyses, tey can be appropriately superimposed to modify te predicted curvatures if te magnitudes of residual stresses are known. Te e ects of line geometry suc as aspect ratio, /w, and pitc ratio, p/w, can also be rationalized wit te present model. In addition, te model can also be easily extended to include passivated copper lines, for any passivation material, by superimposing te curvature cange resulting from an additional layer. AcknowledgementsÐTis work was supported by te O ce of Naval Researc under Grant N to MIT. Te autors acknowledge elpful discussions wit A. WikstroÈ m and Y.-L. Sen. REFERENCES 1. Koronen, M. A., Bùrgesen, P., Tu, K. N. and Li, C.-Y., J. appl. Pys., 1993, 73, Clement, J. J. and Tompson, C. V., J. appl. Pys., 1995, 78, Gleixner, R. J., Clemens, B. M. and Nix, W. D., J. Mater. Res., 1997, 1, Greenbaum, B., Sauter, A. I., Flinn, P. A. and Nix, W. D., Appl. Pys. Lett., 1991, 58, Bùrgesen, P., Lee, J. K., Gleixner, R. and Li, C.-Y., Appl. Pys. Lett., 199, 60, Moske, M. A., Ho, P. S., Mikalsen, D. J., Cuomo, J. J. and Rosenberg, R., J. appl. Pys., 1993, 74, Hu, C.-K., Luter, B., Kaufman, F. B., Hummel, J., Uzo, C. and Pearson, D. J., Tin Solid Films, 1995, 6, Timosenko, S., in Strengt of Materials, 3rd edn. Krieger, Huntington, NY, 1976, p WikstroÈ m, A., Gudmundson, P. and Sures, S., J. appl. Pys., 1999, 86, ABAQUS Version 5. 8, general purpose nite element program, Hibbit, Karlson and Sorensen Inc., Pawtucket, RI, Sen, Y.-L., Sures, S. and Blec, I. A., J. appl. Pys., 1996, 80, Gouldstone, A., Sen, Y.-L., Sures, S. and Tompson, C. V., J. Mater. Res., 1998, 13, WikstroÈ m, A., Gudmundson, P. and Sures, S., J. Mec. Pys. Solids, 1999, 47, Sen, Y.-L., Sures, S., He, M. Y., Bagci, A., Kienzle, O., RuÈ le, M. and Evans, A. G., J. Mater. Res., 1998, 13, 198.