Local Joule Heating and Overall Resistance Increase

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1 Journal in oid-containing of ELECTRONIC MATERIALS, Aluminum ol. 30, Interconnects No. 4, Special Issue Paper Local Joule Heating and Overall Resistance Increase in oid-containing Aluminum Interconnects Y.-L. SHEN The University of New Mexico, Department of Mechanical Engineering, Albuquerque, NM 87131; Local Joule heating and the overall resistance change due to void formation in aluminum interconnects were studied numerically. In the model the TiN/Al/TiN metallization stack is embedded within the SiO 2 dielectric. Three-dimensional finite element analyses, taking into account the current shunting into the barrier layer and the coupling between heat conduction and electrical conduction, were carried out. The temperature field and overall resistance increase were obtained for various combinations of void geometry and applied current densities. It was found that the Joule heat produced at the void site is largely conducted away by the Al line, leading to only small temperature gradients along the interconnect. The voiding-induced temperature rise is significant only under very high current densities and when the void is very large. The overall resistance increase is dominated by the void geometry, not by the Joule heat and the inherent high resistivity of the barrier layer material. Key words: Aluminum, interconnect, Joule heating, electrical resistance, numerical modeling INTRODUCTION In multilayer interconnects, thin barrier layers such as titanium nitride (TiN) directly above and below aluminum (Al) lines can act as alternative conducting paths. In cases where sufficiently large voids caused by electromigration and/or thermal stresses develop in the Al line, the electrical current can be shunted to the barrier layers. This has been regarded as a built-in reliability feature. 1 As highperformance devices are being developed, the reliability of this feature itself is subject to investigation. It has been proposed that local Joule heating due to current shunting into a barrier layer at a void in the Al or copper (Cu) metallization is primarily responsible for the detectable resistance increase of the interconnect under test conditions. 2 The stronger local heating is conceived by considering current crowding and the fact that the barrier layer normally has a much higher resistivity compared to Al and Cu. A quantitative understanding of this effect, however, remains to be explored since the void-containing metal stack is a complex three-dimensional structure which is not readily amenable to simple analytical predic- (Received October 9, 2000; accepted January 10, 2001) tions. Furthermore, it has been experimentally demonstrated that the resistance increase of Al interconnects is directly related to the void configuration. 3 6 This at least implies that the overall resistance change is associated with the existence of the voids themselves and is not necessarily influenced highly by the barrier layers and local Joule heating. In this study we seek to address the above materials/geometrical issues by recourse to three-dimensional finite element analyses. The specific objectives include: To quantitatively predict the local temperature rise due to voiding-induced current redistribution in the model TiN/Al/TiN interconnect structure, to see if it is of significant importance compared to the undamaged structure To analyze the resistance change associated with voiding damage, with and without the incorporation of barrier layers in the structure, for examining the relative contributions of pure voiding in Al and conducting path-induced local Joule heating to the overall resistance increase, and To numerically characterize the effects of void geometry on interconnect resistance in a systematic manner 367

2 368 Shen NUMERICAL MODEL AND APPROACH Figure 1a shows the interconnect geometry used in the modeling. The aluminum line, with height 0.7 µm and width 1 µm, is sandwiched between two 0.15 µmthick TiN layers, and the metal stack is laterally surrounded by the silicon dioxide (SiO 2 ) dielectric spanning 0.5 µm on four sides. The length of the model (l) is taken to be 5 µm. There is no silicon substrate included in the model. A side void exists at x = l/2 in Al. The void is assumed to have straight sidewalls through the thickness of Al. For the purposes of carrying out a systematic analysis of the effects of void configuration, the void is taken to be brickshaped. Figure 1b shows a plane view of the Al line at a fixed z. The void geometry is specified by its dimensions along the length direction l v and along the width direction w v. arious combinations of l v and w v are used to simulate a variety of void geometries. The coupled electrical-thermal analysis under steady state was performed. The flow of electrical current is described by Ohm s law: a J = 1 ρ φ (1) where J is current density vector, ρ is electrical resistivity, φ is electrical potential and represents the gradient operation. The governing equation, written in variational form, for the electrical analysis is δφ Jd = δφ( J n) ds where δ is the variational symbol, and S are volume and surface of the body, n represents the outward unit normal vector, and means inner product between two vectors. The steady-sate heat conduction is described by k( δt) ( T) d = δtρ( J J) d S + S (2) ( δ T) qds (3) where k is thermal conductivity, T is temperature, and q is heat flux flowing into the body. Coupling arises from two sources: the conductivity in the electrical problem is temperature dependent, and the Joule heat generated in the thermal problem is a function of electrical current. Equations 2 and 3 are solved simultaneously for both temperature and electrical potential at the nodal points of the finite element model. Within the region of SiO 2 only the thermal analysis is considered. The material properties used for the calculation are listed in Table I. 7-9 All interfaces between dissimilar materials were taken to be in perfect thermal contact. 10 In performing the modeling an effective current density is imposed at the end of the TiN/Al/TiN line on the plane x = 0. The electrical potential at the other end of the metal stack is set to vanish. This produces b Fig. 1. (a) Three-dimensional interconnect structure used in the present study; (b) a section view (along the xy plane) showing the geometry of the void in aluminum. Table I. Material Properties used in the Numerical Analysis* Al TiN SiO 2 k (W/m(K) at 300 K K K K ρ (Ω m) at 293 K K *A linear variation of properties with temperature between the indicated temperatures and a constant value below the lowest temperature indicated are assumed. a near-uniform current distribution at locations away from the void site, i.e., near x = 0 and x = l. A fixed temperature of 20 C is imposed at the bottom surface z = 0. The top surface is assumed to have a uniform heat flux flowing along the negative z direction. The flux value is determined by considering the same interconnect structure directly above the current one, with the metal line carrying the same overall current density but free of any void. All the other boundary surfaces are assumed to be adiabatic. Note that this preserves mirror symmetry about the four side planes of the structure. The constant temperature and uniform inward heat flux at, respectively,

3 in oid-containing Aluminum Interconnects 369 a b Fig. 2. Contours of constant temperature in the TiN/Al/TiN structure under the overall current densities of (a) 1 MA/cm 2 and (b) 5 MA/cm 2. The void geometry is taken to be l v = 0.4 w and w v = w. The SiO 2 elements are not shown in the plots. the bottom and top surfaces pertain to the overall heat conduction pattern obtained from our earlier analysis featuring general multilevel interconnect structures free of any defects. 10 The finite element program ABAQUS 11 was employed for all calculations. The discretization uses eight-noded brick elements. Depending on the size of the void in the model, a total of elements were used in the computational domain. The temperature distribution is directly obtained from the analysis. The effective resistivity of the void-containing metal stack is determined by ρ = (1/J eff )( φ/l), where J eff is the effective current density in the metal stack away from the void and φ is the electrical potential difference over the line length, a quantity obtained directly from the analysis. The fractional change of this effective resistivity is taken to be the fractional resistance change ( R/R 0 ) in the voided structure. RESULTS AND DISCUSSION In this section the Joule heating effects are presented first. Figure 2a and b shows the contours of constant temperature in the TiN/Al/TiN stack containing a through-width void under overall current densities of 1 and 5 MA/cm 2, respectively. The void geometry is described by l v = 0.4 w and w v = w. In the figure the SiO 2 elements were removed for clarity. It can be seen that the maximum temperature appears in the upper layer TiN directly above the void. A closer look at the temperature field, however, reveals that the maximum temperature is only moderately higher than those away from the void site. In Fig. 2a when the current density is 1 MA/cm 2, the temperature for the entire structure is within 10 C above the controlled temperature (20 C) at the bottom of SiO 2. If the very high current density of 5 MA/cm 2 is imposed (Fig. 2b), high temperatures (around 200 C) appear throughout the metal structure and the local maximum temperature is not particularly high compared to the rest of the structure. The calculated temperature field is no doubt affected by the specific geometry and boundary conditions chosen. Nevertheless, the present analysis suggests that the temperature distribution is quite uniform throughout the structure even if a large void exists. Figure 3a c shows the maximum temperature rise ( T) as a function of normalized void width (w v /w) for the void lengths l v of 0.1w, 0.4w, and 0.8w, respectively. (The contour plots in Fig. 2 correspond to the case of l v = 0.4w and w v /w = 1.) Several current density values are considered in Fig. 3 as indicated therein. In general, the maximum temperature rise increases with the width (for a fixed length) and length (for a fixed width) of the void. When the current density is below about 1 MA/cm 2, the temperature rise is insignificant unless the void is very large. With a current density as high as 5 MA/cm 2, the maximum temperature rise is approximately 20 C for the intact metal line and can become well over 100 C for the voidedthrough line. Considering the fact (from Fig. 2b) that the high temperature field is rather uniform, i.e., away from the void the temperature increase drastically exceeds 20 C (the typical value in the void-free circumstance), it can be concluded that the aluminum

4 370 Shen density specified, because essentially a constant fractional resistance change was obtained from the modeling when the imposed current density is less than about 5 MA/cm 2. Therefore the results in Fig. 4 are considered valid for the entire range of current densities treated in the above Joule heating analyses. Note that the resistance changes shown in Fig. 4 appear to be very large compared to most experimentally measured values, due to the fact that the void dimension relative to the total metal size is taken to be very large in our computational model. Nevertheless, the overall trend of the modeling results is consistent with recent experimental measurements on correlating the resistance change and void volume in Al interconnects. 6 It is seen in Fig. 4 that the fractional resistance change increases with the void width (for a fixed length) and length (for a fixed void width). One important observation is that the fractional resistance change does not scale with the void volume. For instance, the case of l v = 0.4w and w v = 0.8w and the case of l v = 0.8w and w v = 0.4w have the same void volume, but the former shows more than three times more resistance ina b c Fig. 3. Maximum temperature rise as a function of normalized void width (w v /w) for the void lengths of (a) l v = 0.1w, (b) l v = 0.4w, and (c) l v = 0.8w, under various applied current density values. Fig. 4. Fractional resistance change as a function of normalized void width (w v /w) for the void lengths of l v = 0.1w, 0.4w, and 0.8w. line itself serves as an efficient path to partially conduct the local Joule heat away from the void site. oiding induces local concentration of current density and energy dissipation, but it is essentially the entire structure that suffers heating. This effect, however, is significant only when the applied current density is very high and when the void is very large. Although in our modeling the ambient was taken to be 20 C, it is expected that the qualitative result shown here will also be valid under testing conditions involving high ambient temperatures. This is simply because aluminum is still capable of conducting most of the Joule heat away from the void site, so very high temperatures, if existent, will not only be specific to the void vicinity but well into the interior of the lines. This argument, however, is limited to the presumption that local melting and other relevant damage mechanisms are inoperative. Attention is now turned to the change in resistance in the voided interconnect line. Figure 4 shows the fractional resistance change ( R/R 0 ) as a function of normalized void width (w v /w) for various void lengths (l v ) of 0.1, 0.4, and 0.8 w. There is no imposed current Fig. 5. Fractional resistance change as a function of normalized void width (w v /w) for the void lengths of l v = 0.1w, 0.4w, and 0.8w. In this case the two TiN layers were not included in the model.

5 in oid-containing Aluminum Interconnects 371 crease than the latter. Our numerical results are consistent with the experimental analysis in Ref. 6 but disagree with that in Refs. 3 and 4, where a proportionality of resistance change with void volume was concluded. The possible errors in Refs. 3 and 4 were discussed in Ref. 6. One of the present objectives is to examine the effects of local Joule heating on resistance change. This can be achieved by comparing Figs. 3 and 4. If one focuses on a low current density value (for instance, less than 1 MA/cm 2 ), then Fig. 3a c shows that the temperature rises are very small (negligible in most cases). However, very large values of fractional resistance change are still seen in Fig. 4. This leads to the conclusion that local Joule heating contributes very little to the overall resistance increase. Although for very large current densities the temperature increase can be high, the primary cause of resistance increase is due to the void formation, not the Joule heat. When a high ambient temperature is imposed as in industrial test conditions, the above conclusion is still expected to be valid if local melting of Al is not of concern. One important question remains: is the barrier layer itself responsible for the resistance change after voiding, due to its inherently larger resistivity compared to Al? To explore this we carried out simulations assuming no TiN layers in the interconnect structure. The results are shown in Fig. 5, where the fractional resistance change as a function of void width is plotted for the same void lengths used in Fig. 4. It is seen that, with the TiN layers excluded, the overall resistance changes are only affected slightly. The general features stay unchanged. Therefore, it is realized that the resistance change is dominated by the void itself, not by the partial diversion of current into the TiN layers. The current is forced to flow around the void with a reduced cross section for conduction. A greater void width is much more detrimental than a greater void length. The void geometry plays a decisive role in the increase of resistance over the line segment. CONCLUSIONS We have constructed a three-dimensional interconnect model and performed finite element analyses to study local Joule heating and overall resistance change in an aluminum line containing voiding damage. Particular attention is devoted to the effects of current shunting into the barrier layers and void geometry. The important findings are listed in the following: 1. With the existence of a large void, the maximum temperature appears in the TiN layer at the void site. The temperature gradient, however, is not large throughout the metal structure for all void sizes. 2. The Al line is efficient in conducting the local Joule heat away from the void site, so it is the entire metal line that experiences additional heating. The temperature rise is insignificant if the imposed current density is smaller than about 1 MA/cm Although the fractional resistance change increases with void width and void length, it is not proportional to the void volume. The shape of the void plays an important role. 4. Both the current shunting-induced Joule heating and the high-resistivity nature of TiN contribute very little to the overall resistance increase. The dominant factor is the geometry of the void in Al. ACKNOWLEDGEMENT This work was supported by the National Science Foundation under Grant CMS The author thanks W. Li for his assistance. REFERENCES 1. G.K. Rao, Multilevel Interconnect Technology (New York: McGraw-Hill, 1993). 2. P.R. Besser, D. Brown, C.R. Reilly, and J.E. Sanchez, Abstract in Materials Research Society 1999 Spring Meeting: Materials Reliability in Microelectronics IX. 3. M. Genut, Z. Li, C.L. Bauer, S. Mahajan, P.F. Tang, and A.G. Milnes, Appl. Phys. Lett. 58, 2354 (1991). 4. Z. Li, C.L. Bauer, S. Mahajan, and A.G. Milnes, J. Appl. Phys. 72, 1821 (1992). 5. B. Miner, T.S. Sriram, A. Pelillo, and S.A. Bill, MRS Symp. Proc. 473, 351 (1997). 6. J.C. Doan, J.C. Bravman, P.A. Flinn, and T.N. Marieb, 37th Annual IEEE Int. Reliability Physics Symp. Proc. (Piscataway, NJ: IEEE, 1999), p F.P. Incropera and D.P. Dewitt, Introduction to Heat Transfer, 3rd ed. (New York: Wiley, 1996). 8. D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics, 5 th ed. (New York: Wiley, 1997). 9. S. Wolf, Silicon Processing for the LSI Era, ol. 2: Process Integration (Sunset Beach, CA: Lattice Press, 1990). 10. Y.-L. Shen, J. ac. Sci. Technol. B 17, 2115 (1999). 11. ABAQUS, ersion 5.8 (Pawtucket, RI: Hibbit, Karlson and Sorensen, Inc., 1998).