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Thermal modeling of localized laser heating in multi-level interconnects
Microelectronics Reliability 43 (2003) 297–305 www.elsevier.com/locate/microrel
Thermal modeling of localized laser heating in multi-level interconnects Paiboon Tangyunyong
*
Microelectronics Failure Analysis Department, Sandia National Laboratories, Albuquerque, NM 87185, USA Received 25 February 2002; received in revised form 15 October 2002
Abstract Thermal modeling was used to simulate thermal profiles from localized laser heating on two multi-level interconnect structures with metallization complexity comparable to those used in advanced interconnect systems. The modeling focused on addressing issues with regard to the effectiveness of laser-based techniques in defect localization in state-ofthe-art metallization schemes. Modeling results indicate that indirect heating from the laser does not propagate effectively through adjacent metal layers from both the front side and the back side. Poor heat conduction and its associated thermal spreading during laser heating make defect detection difficult beyond three levels of metal. Thermal distribution and spreading were found to be more affected by interconnect geometries than by variations in laser spot size. Smaller temperature rises during laser heating were observed in the newer interconnect structures consisting of copper and low-k dielectric materials than in those with conventional aluminum, tungsten, and silicon dioxide. The smaller temperature rise leads to weaker signal strength at the defect sites and makes it more difficult to detect defects in the newer-material structures. Metallization density also affects heat conduction in advanced interconnect systems but the temperature rise during laser heating varies slowly as a function of metallization density. Ó 2003 Elsevier Science Ltd. All rights reserved.
1. Introduction Localized laser heating is the basis of several new failure analysis techniques such as thermally induced voltage alteration (TIVA) [1], Seebeck effect imaging (SEI) [1], optical beam induced resistance change (OBIRCH) [2], and resistive interconnect localization (RIL) [3]. Heating of defects changes some electrical properties of integrated circuits (ICs) that can be monitored. All these techniques use an infrared (1320-nm wavelength) focused laser beam to heat defects directly or indirectly. Since silicon is relatively transparent at infrared wavelengths, these techniques can probe ICs from the front side of the die through the passivation layer or from the back side of the die through the silicon substrate. These techniques are performed using a laser scanning microscope (LSM). The LSM scans the laser in
*
Tel.: +1-505-844-3460; fax: +1-505-844-2991. E-mail address: [email protected] (P. Tangyunyong).
the region of interest on ICs in a raster fashion, and changes in electrical properties are then monitored and displayed. Since most defects are extremely small and localized, the presence of a defect does not significantly alter the thermal conduction, and hence thermal profiles at or near the defect sites during laser heating. The temperature profiles at a defect site in the failed interconnect system are ‘‘identical’’ to an equivalent non-defect site in its functional counterpart. The defect area, however, produces a significantly different electrical response from a non-defect area even if the same laser heating is delivered to both areas. For example in RIL, a resistive interconnect in the failed system generates a strong electrical signal while a non-resistive interconnect produces no signal. This difference in the signal response is the basis of detecting defects with laser-based techniques. It has been shown experimentally that the signal response from the defect sites is non-linear with respect to laser power and local temperature rise [4]. The most
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effective way of improving the sensitivity of any laserbased techniques is to heat up the defect areas as much as possible to increase the detectable signals. This can be accomplished by using a higher-power laser, increasing the throughput through scanning laser microscope system, or coating the samples with anti-reflective coating to minimize the reflection loss and improve the transmission throughput to the defect. Direct heating by focusing the laser on defects is preferable as it maximizes the local temperature rise (the difference between local temperature and base die temperature of 25 °C) at the heated area and increases the signal strength from the defects. In many state-of-the-art ICs with multi-level interconnects, the defect sites are, however, obscured by lower- or upper-level interconnects and are not easily accessible by direct heating. Indirect heating is the only means of reaching the defects in many instances. Indirect heating is not efficient as heat from the laser has to propagate through several levels of interconnects before reaching the defects, resulting in smaller temperature rises than direct heating. The nearest focal point of the laser may be so far away from the defect sites that essentially no heat reaches the defect areas. In this case, there is no temperature rise at the defect site, and the defect will not be detected. Thermal spreading is also a concern in indirect heating because it degrades the spatial resolution of these failure analysis techniques, making it more difficult to pinpoint defect locations. Besides defect locations, local geometric structures and material differences can affect the thermal profiles during laser absorption. State-of-the-art and next-generation ICs use interconnection schemes with dense metallization. Dual-damascene copper [5] and low-k dielectrics [6] are materials of choice in these new interconnect structures. A variety of low-k materials such as SiLK, CORAL, and Black Diamond are currently used for dielectric isolation between metal interconnects. These low-k materials have significantly different physical and thermal properties than silicon dioxide which has been the traditional dielectric used for isolation. The thermal conductivity of low-k materials is at least a factor of five smaller than that of silicon dioxide. The thermal conductivity of copper, on the other hand, is approximately a factor of two larger than that of aluminum or tungsten. The thermal profiles from localized laser heating in the new interconnect structures should be significantly different from those in conventional structures using aluminum, tungsten, and silicon dioxide. Thermal modeling and simulation were done for the first time to study both the front-side and back-side localized laser heating on two interconnect structures. Several issues with regard to the effectiveness of laserbased techniques were addressed by the modeling. These include (1) whether laser-based techniques can be used in
localizing defects in higher-level metal lines such as M5, M6, and M7 from the back side or localizing defects in the lower-level metal lines such as M1, M2, and M3 from the front side, (2) the effect of interconnect geometries, interconnect density, and laser spot size on the thermal profiles, and (3) the effect of using copper and low-k dielectrics on the sensitivity of laser-based techniques.
2. Thermal modeling and simulation Thermal profiles of multi-level interconnect structures resulting from small-area laser heating were simulated with a commercial finite difference solver [7]. The three-dimensional steady-state heat transfer equation was solved subject to the specified boundary conditions. The solver worked in an interactive visual environment to generate a mesh geometry. This mesh geometry, coupled with specified material conductivity properties, heat inputs, and boundary conditions, gave a detailed description of temperatures within the interconnect structures. A model was constructed with brick elements describing the material shapes of the interconnect structures. The brick elements with orthogonal edges had their heat transfer described by twelve internode thermal resistance, Rij . Rij can be written as Rij ¼
Dxij ; kAij
where Dxij is the spacing between nodes i and j; k is the thermal conductivity; and Aij is the cross-sectional area of the brick element. When the brick elements had angles other than 90° or when anisotropic material properties were used, additional diagonal resistances between the nodes were added. Heat inputs and fixed temperature boundary conditions were then assigned to specific nodes. Temperature was solved iteratively at each unconstrained node with the finite difference solving routine. A steady-state solution was determined using P j Tj =Rij þ Qi P Tui ¼ Ti ð1 bÞ þ b ; j 1=Rij where Tui is the updated temperature for the ith node and is related to the previous temperature, Ti . b (typically 1.5–1.9) is a parameter selected to optimize convergence of the solution. Qi is the heat input to the node. Tui is iterated until the solution converges to generate a maximum DT below some convergence criteria, typically 104 °C. A thermal conductivity value of 1.56 W/cm °C was used for aluminum [8], and a value of 0.011 W/cm °C was used for silicon dioxide films [9]. Thermal conductivity values of 1.49, 1.73, and 4.01 W/cm °C were used for silicon, tungsten, and copper respectively [10].
P. Tangyunyong / Microelectronics Reliability 43 (2003) 297–305
A value of 0.0012 W/cm °C was used as a representative value for low-k materials [11]. All thermal conductivity values were assumed to be constant with temperature. Convection and radiation were not included in the simulations, and thermal profiles were calculated based only on thermal conduction. Selecting interconnect structures for modeling has presented a challenge. There are a large variety of interconnect systems used in advanced ICs. Differences exist among different IC manufacturers and among different technologies. The two structures used for the modeling in this paper were chosen for their simplicity. Although their interconnect geometries are arbitrary, the complexity in these structures is comparable to those used in advanced interconnect systems. The modeling results obtained from these structures should, therefore, be applicable to the interconnect systems used in advanced ICs. The first interconnect structure used in the modeling is shown in Fig. 1(a). In this structure, the silicon die thickness is 10 lm. There are six levels of interconnects in this die. Metal-1 (M1), M2, M3, M4, M5, and M6 lines are made of either aluminum or copper. The metal lines in M1, M3, and M5 run in parallel in the x-direction, while the metal lines in M2, M4, and M6 are along the y-direction. All the metal lines are 0.5 lm wide, 0.5 lm thick, 12 lm long, and spaced horizontally in a 2.0 lm pitch. M1 lines are connected to the silicon substrate by tungsten or copper contacts that are 0.5 lm wide, 0.5 lm long, and 1 lm thick. The metal lines in all levels are connected to one another by either tungsten or copper vias that are 0.5 lm wide, 0.5 lm long, and 1 lm thick. The interlevel metal lines are separated by a 1-lm thick SiO2 or a 1-lm thick low-k dielectric layer. No laser absorption was assumed to occur in both the silicon substrate and the dielectric layers. A laser power of 40 mW was input on one of the metal lines with a spot size of either 0.5 or 1 lm square area. Since both aluminum and copper are highly reflective at 1320 nm, about 97% of the laser power [12] was assumed to reflect from the aluminum or copper with about 3% of the laser power or 1.2 mW being absorbed by the metal. The silicon/air interface was assumed to be at room temperature (25 °C) with no temperature rise during laser heating. Temperatures were then calculated with 1.2 mW of power input on one of the metal lines at different metal levels. The second interconnect structure used is shown in Fig. 1(b). The silicon die thickness is also 10 lm. There are 10 levels of interconnects in this die. All the metal lines are made of either aluminum or copper. The metal lines in M1, M3, M5, M7, and M9 run in parallel in the x-direction while the metal lines in M2, M4, M6, M8, and M10 are along the y-direction. All the metal lines are 0.2 lm wide, 0.2 lm thick, 9.6 lm long, and spaced horizontally in a 0.8 lm pitch. M1 lines are connected to
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Fig. 1. The lattice structure used to simulate the heating effect of a focused infrared laser beam on (a) a six-level metal interconnect structure and (b) a 10-level metal interconnect structure.
the silicon substrate by tungsten or copper contacts that are 0.2 lm wide, 0.2 lm long, and 0.4 lm thick. The metal lines in all levels are connected to one another by either tungsten or copper vias that are 0.2 lm wide, 0.2 lm long, and 0.4 lm thick. The interlevel metal lines are separated by a 0.4-lm thick silicon dioxide or a 0.4-lm thick low-k dielectric layer. No absorption was assumed to occur in both the silicon substrate and the dielectric
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layers. A laser power of 40 mW was also input on one of the metal lines with a spot size of 0.5 or 1 lm square area. Similar to the first structure in Fig. 1(a), 3% of the laser power or 1.2 mW was assumed to be absorbed by the metal line. The same boundary conditions were assumed in this structure as in the first structure with no temperature rise occurring at the silicon/air interface. Temperatures were then calculated with 1.2 mW of power input on one of the metal lines in M1, M2, M3, M8, M9, or M10. The laser spot sizes (0.5 or 1.0 lm square) used in the modeling are several times smaller than those obtainable from traditional optics. Laser spot sizes, however, have little effect on the thermal profiles except for the peak temperature rises, as will be shown in the next section. The modeling results from the smaller spot sizes are, therefore, applicable to the understanding of issues with regard to the effectiveness of laser-based techniques in advanced interconnect systems. In addition, several commercial companies are actively developing solidstate-immersion lenses [13] that can drastically reduce the laser spot size. These future lenses can potentially achieve laser spot sizes that are comparable or smaller that those used in this paper.
3. Results and discussion Thermal modeling was first performed on the sixlevel metal (Fig. 1(a)) interconnect structure consisting of aluminum, tungsten, and silicon dioxide. The laser power was input on one of the metal lines in M1 with a spot size of 0.5 lm square area to simulate the back-side heating through the substrate. Figs. 2 and 3 show the vertical and horizontal profiles, respectively, for the heated surface area on M1 in the six-level interconnect structure. Fig. 2(c) shows the corresponding vertical line temperature profile through the center of the heated area on M1. The peak temperature was found to be 37.9 °C at the heated surface on M1 relative to the base die temperature of 25 °C. Even though the laser beam cannot penetrate M1, heat generated by the laser heating conducts through M1 to the higher-level metal lines. There is, however, a sharp drop in temperatures beyond M1. Peak temperature values are 29.7, 27.3, 26.6, 26.3, and 26.3 °C at M2, M3, M4, M5, and M6 respectively. As heat conducts through M1, it also diverges, resulting in thermal spreading. Thermal spreading is quite significant even on the M2 and M3 aluminum lines as shown in Fig. 3(c) and (d). Horizontal spreading also occurs in the M1 plane and primarily along the metal line as shown in Fig. 3(a). Thermal modeling was also done on the 10-level interconnect structure using a laser spot size of 0.5 lm square. The interconnect structure was also assumed to consist of conventional materials with aluminum lines,
Fig. 2. (a) Side view of the lattice structure used in the simulation of temperature profiles from back-side laser heating on M1. The simulation is for the six-level metal interconnect structure made of Al, W, and SiO2 . The dashed arrow indicates the back-side laser illumination on a M1 aluminum line. (b) Calculated temperature profiles over the area shown in (a) for the absorbed power of 1.2 mW in a 0.5 lm square area on a M1 aluminum line. (c) A vertical line temperature profile that passes through the center of the heated area on M1 shown in (b).
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surface area on M1 are shown in Figs. 4 and 5 respectively. Similar to the six-level structure, there is a significant drop in peak temperatures from M1 (36.6 °C) to M2 (28.4 °C) and M3 (26.5 °C). Thermal spreading are also significant even at M2 and M3 as shown in Fig. 5. As mentioned previously, the signal response of most ICs is non-linear with respect to the laser intensity and local temperature rise. Although thermal spreading occurs during direct heating on the M1 metal line (predominantly along the metal line), the area with peak temperature rise normally coincides with the laser spot. It is this area with the peak temperature rise that is responsible for the observed defect signals; consequently, thermal spreading in M1 does not affect the spatial
Fig. 3. (a) Top view of the lattice structure in Fig. 1(a) in M1 plane. The dashed circle indicates the back-side laser illumination on a M1 aluminum line. Calculated temperature profiles over the same area in (a) on (b) M1, (c) M2, and (d) M3 for the absorbed power of 1.2 mW in a 0.5 lm square area on a M1 aluminum line, showing thermal spreading on both M2 and M3.
tungsten contacts, tungsten vias, and silicon dioxide layers. The vertical and horizontal profiles for the heated
Fig. 4. (a) Side view of the lattice structure used in the simulation of temperature profiles for back-side laser heating on M1. The simulation is for the 10-level metal interconnect structure made of Al, W, and SiO2 . The dashed arrow indicates the backside laser illumination on a M1 aluminum line. (b) Calculated temperature profiles over the same area in (a) for the absorbed power of 1.2 mW in a 0.5 lm square area on a M1 aluminum line.
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Fig. 5. (a) Top view of the lattice structure in Fig. 1(b) in M1 plane. The dashed circle indicates the back-side laser illumination on a M1 aluminum line. Calculated temperature profiles over the same area in (a) on (b) M1, (c) M2, and (d) M3 for the absorbed power of 1.2 mW in a 0.5 lm square area on a M1 aluminum line, showing thermal spreading on both M2 and M3.
resolution of laser-based techniques. At M2 and M3, thermal spreading is severe due to indirect heating, and the defect signals are generated primarily from areas several times larger than the laser spot size. Therefore, thermal spreading at M2 and M3 makes it more difficult to pinpoint defect locations. For interconnects above M3, signal strength is much weaker and thermal spreading is progressively worse; consequently, it is unlikely that any laser-based techniques will be effective in localizing defects with back-side indirect heating in higher-level interconnects. Detection of defects at higher-level interconnects may still be possible if the defects are not obscured by lower-level interconnects and are accessible by direct heating. Back-side thermal profiles were also calculated for 1.2-mW power input on one of the M2 and M3 metal lines. Back-side simulations were not performed on the metal lines in M4, M5, and M6 since they were unlikely to be accessible from the back side. The situation is reversed for front-side heating. Front-side simulations were performed only on the three top levels of interconnects since these layers were more accessible from the front side. The results of the modeling are shown in Figs. 6 and 7 for both interconnect structures. Whether from the front side or the back side, the modeling results are quite similar to those observed in Figs. 2–5, showing significant reduction in temperatures and thermal spreading at the metal layers adjacent to the heated surface. Thermal modeling was also performed on both interconnect structures with different interconnect materials and with a 0.5 lm square laser spot size. Thermal line profiles were generated by assuming laser absorption occurring at different metal levels. Thermal profiles obtained from structures with aluminum, tungsten, and silicon dioxide were compared to those with copper and low-k dielectric (Figs. 6 and 7). The profiles between these two material combinations are quite similar except for the smaller peak temperatures in the structures with copper and a low-k dielectric. Peak temperatures due to laser absorption at different metal levels for the four different material combinations are tabulated in Tables 1 and 2. Tables 1 and 2 show significant differences in peak temperatures between structures with copper and aluminum, but not between those with silicon dioxide and low-k dielectric layers. These differences reflect the dominance of metal thermal properties in determining heat dissipation, thermal distribution and spreading in the interconnect structure. The modeling results have significant implications with regard to the effectiveness of new laser-based techniques to detect defects in state-of-the-art and next-generation ICs. Copper and low-k dielectrics are the materials of choice for interconnection schemes in these ICs. Tables 1 and 2, however, show that the temperature rises (difference between local temperature and base die tem-
P. Tangyunyong / Microelectronics Reliability 43 (2003) 297–305
Fig. 6. Vertical line temperature profiles that compare the thermal distribution of the six-level interconnect structures consisting of (a) Al, W, and SiO2 , and (b) Cu and low-k dielectric with a laser spot size of 0.5 lm square. The temperature profiles were calculated based on back-side heating on M1, M2, and M3 and front-side heating on M4, M5, and M6, and were drawn through the center of the heated areas on different metal levels.
perature of 25 °C) due to laser absorption for these materials are at least a factor of two smaller than those with the conventional materials of aluminum, tungsten, and silicon dioxide. Smaller temperature rises at the defect sites mean weaker signal strength and less sensitivity for defect detection; consequently, the new laser-
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Fig. 7. Vertical line temperature profiles that compare the thermal distribution of the 10-level interconnect structures consisting of (a) Al, W, and SiO2 , and (b) Cu and low-k dielectric with a laser spot size of 0.5 lm square. The temperature profiles were calculated based on back-side heating on M1, M2, and M3 and front-side heating on M8, M9, and M10, and were drawn through the center of the heated areas on different metal levels.
based techniques may not be as effective in localizing defects in structures with newer materials. The effects of laser spot size were also investigated. Thermal profiles simulated from a laser spot size of 0.5 lm square with heat input on M1 were compared to
Table 1 Peak temperatures in °C at the heated surfaces due to laser absorption at different metal levels for four different interconnect material combinations in the six-level metal interconnect structurea Materials (metal line, via/ contact, and dielectric layer)
M1
M2
M3
M4
M5
M6
Al, W, and SiO2 Al, W, and low-k Cu, Cu, and SiO2 Cu, Cu, and low-k
37.9 38.5 31.0 31.2
42.1 43.5 32.6 32.8
44.7 46.2 33.7 33.9
45.3 47.1 33.9 34.3
45.5 47.6 34.2 34.5
52.5 56.0 37.2 37.9
a The laser spot and the base temperature of the die were assumed to be 0.5 lm square and 25 °C respectively. The peak temperatures were calculated based on back-side heating on M1, M2, and M3 and front-side heating on M4, M5, and M6.
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Table 2 Peak temperatures in °C at the heated surfaces due to laser absorption at different metal levels for four different interconnect material combinations in the 10-level metal interconnect structurea Materials (metal line, via/ contact, and dielectric layer)
M1
M2
M3
M8
M9
M10
Al, W, and SiO2 Al, W, and low-k Cu, Cu, and SiO2 Cu, Cu, and low-k
36.5 37.5 30.3 30.4
37.7 38.8 30.6 30.7
38.8 40.0 30.9 31.2
39.9 41.4 31.5 31.7
41.2 43.0 32.1 32.3
46.1 49.0 34.3 34.8
a The laser spot and the base temperature of the die were assumed to be 0.5 lm square and 25 °C respectively. The peak temperatures were calculated based on back-side heating on M1, M2, and M3 and front-side heating on M8, M9, and M10.
M1
M1 (a)
36
Temperature (C)
Temperature (C)
38
M2
34
M3 M4
32
M5
30
M6
28 26 24 0
2
4
6
8
10
12
42 40 38
(a) M2 M3
36 34 32 30
M4 M5 M6
28 26 24 0
14
2
M1
Temperature (C)
Temperature (C)
(b)
36 34 M3
32 30
M5
M7 M9
28 26
42 40 38
2
4
6
8
8
10
12
14
(b) M1
36 34 32 30
M2
10
12
14
Position ( m) Fig. 8. Vertical line temperature profiles that compare the thermal distribution of two laser spot sizes: 0.5 lm square (full circle) and 1 lm square (open triangle). The profiles were drawn through the center of the heated areas on one of M1 lines for (a) the six-level interconnect structure and (b) the 10-level interconnect structure consisting of Al, W, and SiO2 .
those from a laser spot size of 1 lm square in Fig. 8. The thermal profiles in Fig. 8 were generated from both interconnect structures with aluminum, tungsten, and silicon dioxide. The thermal line profiles for both laser spot sizes are quite similar except for the smaller peak temperatures observed in the larger-spot-size profiles
M3
M4 M5
M6
28 26 24 0
24 0
6
Position ( m)
Position ( m)
38
4
2
4
6
8
10
12
14
Position ( m) Fig. 9. Temperature line profiles showing the effects of metallization density. The profiles were drawn through the center of the heated area on one of the M1 lines for the six-level interconnect structure consisting of (a) Al, W, and SiO2 and (b) Cu and low-k dielectric with a laser spot size of 0.5 lm square. Three different metallization densities are shown: (1) the same metallization density shown in the interconnect structure of Fig. 1(a) (full square), (2) 100% increase in metallization density (full triangle), and (3) 50% decrease in metallization density (full circle) compared to that of Fig. 1(a).
(open triangle in Fig. 8). The smaller peak temperatures are due to less efficient heating by the larger laser spot and lower power density deposited on the metal lines.
P. Tangyunyong / Microelectronics Reliability 43 (2003) 297–305
The thermal profiles for the 10-level interconnect structure in Fig. 8(b) are quite similar to those in the sixlevel structure (Fig. 8(a)), except for the narrower peak width. This difference in peak width was observed even though the same laser spot size was used for both structures during the simulation. The data in Fig. 8 suggest that the thermal distribution and spreading are strongly dependent on the local interconnect geometries such as intermetal spacing, metal line width, and metal thickness and less dependent on the laser spot size. Modeling was also performed to study the effect of variations in metallization density on thermal distribution. The metallization density encompasses the density of metal lines, contact density, and via density in all metal levels. Two additional metallization densities were used in the modeling besides the one shown in Fig. 1(a). The metallization density is increased by 100% in one case (full triangles in Fig. 9) and decreased by 50% in the other (full circles in Fig. 9). Thermal profiles with these two metallization densities were then compared to those with original density shown in Fig. 1(a). The results of the modeling are shown in Fig. 9. The profiles in Fig. 9 were calculated from the heat input on one of the M1 lines for the six-level interconnect structure consisting of either conventional materials (aluminum, tungsten, and silicon dioxide), Fig. 9(a), or newer materials (copper and low-k dielectric), Fig. 9(b), with a laser spot size of 0.5 lm square. Since heat is conducted more efficiently though metal than in dielectric layers, denser metallization schemes result in a smaller temperature rise. The temperature rise, however, varies slowly as a function of metallizaton density. A fourfold increase in metallization density only results in the 50–60% changes in temperature as shown in Fig. 9.
4. Conclusions Thermal modeling results show that indirect laser heating is not efficient and does not propagate effectively beyond three levels of metal from both the front side and the back side. Defect detection beyond three immediate levels of metal from the heated area is difficult due not only to poor heat conduction but also to thermal spreading. Thermal distribution and spreading were found to be more affected by interconnect geometries than by variations in laser spot size. It is also easier to detect defects in conventional interconnect systems with aluminum, tungsten, and silicon dioxide than in systems with copper and low-k dielectric materials because of larger temperature rises during laser heating in conventional systems. Metallization density also affects heat conduction in advanced interconnect systems but the
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temperature rise during laser heating varies weakly as a function of metallization density.
Acknowledgements The authors would like to thank Rich Anderson, Ed Cole, and Craig Nakakura for reviewing this manuscript. This work was performed at Sandia National Laboratories. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL8500.
References [1] Cole Jr EI, Tangyunyong P, Barton DL. Backside localization of open and shorted IC interconnections. In: Proc. 36th International Reliability Physics Symposium, IRPS 98, Reno, NV, March/April 1998. p. 129–36. [2] Nikawa K, Saiki T, Inoue S, Ohtsu M. High spatial resolution OBIRCHand OBIC effects realized by near-field optical probe in the analysis of high resistance 200 nm wide TiSi line. In: Proc. 24th International Symposium for Testing and Failure Analysis, ISTFA 98, Dallas, TX, November 1998. p. 25–9. [3] Cole Jr EI, Tangyunyong P, Hawkins CF, Bruce MR, Bruce VJ, Ring RM, et al. Resistive interconnection localization. In: Proc. 27th International Symposium for Testing and Failure Analysis, ISTFA 2001, San Jose, CA, November 2001. p. 43–50. [4] Tangyunyong P, Benson D, Cole Jr EI. Thermal modeling of a polysilicon–metal test structure used for thermally induced voltage alteration characterization. J Vac Sci Technol B 2000;18(6):2820–5. [5] DeJule R. Dual-Damascene: Overcoming process issues. Semicond Int 2000;23(6):94. [6] Peters L. Low-k dielectrics: Will spin-on or CVD prevail? Semicond Int 2000;23(6):108. [7] Thermal Analysis System, TAS, Harvard Thermal Inc., Harvard, MA 01451. [8] Sergent J, Krum A. Thermal management handbook for electronic assemblies. New York: McGraw-Hill; 1998. [9] Kleiner MB, Kuhn SA, Weber W. Thermal conductivity measurements of thin silicon dioxide films in integrated circuits. IEEE Trans Electron Devices 1996;43:1602–9. [10] Weast RC. CRC handbook of chemistry and physics. 59th ed Boca Raton, FL: CRC Press; 1979. p. E12–6. [11] Internet website: www.dupont.com/kapton/general/spphythe.html. [12] Bass M, Van Stryland EW, Williams DR, Wolfe WL. In: Handbook of optics, vol. II, 2nd ed. New York: McGrawHill; 1995 [Chapter 25]. [13] Ippolito SB, Goldberg BB, Unlu MS. High spatial resolution subsurface microscopy. Appl Phys Lett 2001;78(26): 4071–3.
Thermal modeling of localized laser heating in multi-level interconnects Paiboon Tangyunyong
*
Microelectronics Failure Analysis Department, Sandia National Laboratories, Albuquerque, NM 87185, USA Received 25 February 2002; received in revised form 15 October 2002
Abstract Thermal modeling was used to simulate thermal profiles from localized laser heating on two multi-level interconnect structures with metallization complexity comparable to those used in advanced interconnect systems. The modeling focused on addressing issues with regard to the effectiveness of laser-based techniques in defect localization in state-ofthe-art metallization schemes. Modeling results indicate that indirect heating from the laser does not propagate effectively through adjacent metal layers from both the front side and the back side. Poor heat conduction and its associated thermal spreading during laser heating make defect detection difficult beyond three levels of metal. Thermal distribution and spreading were found to be more affected by interconnect geometries than by variations in laser spot size. Smaller temperature rises during laser heating were observed in the newer interconnect structures consisting of copper and low-k dielectric materials than in those with conventional aluminum, tungsten, and silicon dioxide. The smaller temperature rise leads to weaker signal strength at the defect sites and makes it more difficult to detect defects in the newer-material structures. Metallization density also affects heat conduction in advanced interconnect systems but the temperature rise during laser heating varies slowly as a function of metallization density. Ó 2003 Elsevier Science Ltd. All rights reserved.
1. Introduction Localized laser heating is the basis of several new failure analysis techniques such as thermally induced voltage alteration (TIVA) [1], Seebeck effect imaging (SEI) [1], optical beam induced resistance change (OBIRCH) [2], and resistive interconnect localization (RIL) [3]. Heating of defects changes some electrical properties of integrated circuits (ICs) that can be monitored. All these techniques use an infrared (1320-nm wavelength) focused laser beam to heat defects directly or indirectly. Since silicon is relatively transparent at infrared wavelengths, these techniques can probe ICs from the front side of the die through the passivation layer or from the back side of the die through the silicon substrate. These techniques are performed using a laser scanning microscope (LSM). The LSM scans the laser in
*
Tel.: +1-505-844-3460; fax: +1-505-844-2991. E-mail address: [email protected] (P. Tangyunyong).
the region of interest on ICs in a raster fashion, and changes in electrical properties are then monitored and displayed. Since most defects are extremely small and localized, the presence of a defect does not significantly alter the thermal conduction, and hence thermal profiles at or near the defect sites during laser heating. The temperature profiles at a defect site in the failed interconnect system are ‘‘identical’’ to an equivalent non-defect site in its functional counterpart. The defect area, however, produces a significantly different electrical response from a non-defect area even if the same laser heating is delivered to both areas. For example in RIL, a resistive interconnect in the failed system generates a strong electrical signal while a non-resistive interconnect produces no signal. This difference in the signal response is the basis of detecting defects with laser-based techniques. It has been shown experimentally that the signal response from the defect sites is non-linear with respect to laser power and local temperature rise [4]. The most
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effective way of improving the sensitivity of any laserbased techniques is to heat up the defect areas as much as possible to increase the detectable signals. This can be accomplished by using a higher-power laser, increasing the throughput through scanning laser microscope system, or coating the samples with anti-reflective coating to minimize the reflection loss and improve the transmission throughput to the defect. Direct heating by focusing the laser on defects is preferable as it maximizes the local temperature rise (the difference between local temperature and base die temperature of 25 °C) at the heated area and increases the signal strength from the defects. In many state-of-the-art ICs with multi-level interconnects, the defect sites are, however, obscured by lower- or upper-level interconnects and are not easily accessible by direct heating. Indirect heating is the only means of reaching the defects in many instances. Indirect heating is not efficient as heat from the laser has to propagate through several levels of interconnects before reaching the defects, resulting in smaller temperature rises than direct heating. The nearest focal point of the laser may be so far away from the defect sites that essentially no heat reaches the defect areas. In this case, there is no temperature rise at the defect site, and the defect will not be detected. Thermal spreading is also a concern in indirect heating because it degrades the spatial resolution of these failure analysis techniques, making it more difficult to pinpoint defect locations. Besides defect locations, local geometric structures and material differences can affect the thermal profiles during laser absorption. State-of-the-art and next-generation ICs use interconnection schemes with dense metallization. Dual-damascene copper [5] and low-k dielectrics [6] are materials of choice in these new interconnect structures. A variety of low-k materials such as SiLK, CORAL, and Black Diamond are currently used for dielectric isolation between metal interconnects. These low-k materials have significantly different physical and thermal properties than silicon dioxide which has been the traditional dielectric used for isolation. The thermal conductivity of low-k materials is at least a factor of five smaller than that of silicon dioxide. The thermal conductivity of copper, on the other hand, is approximately a factor of two larger than that of aluminum or tungsten. The thermal profiles from localized laser heating in the new interconnect structures should be significantly different from those in conventional structures using aluminum, tungsten, and silicon dioxide. Thermal modeling and simulation were done for the first time to study both the front-side and back-side localized laser heating on two interconnect structures. Several issues with regard to the effectiveness of laserbased techniques were addressed by the modeling. These include (1) whether laser-based techniques can be used in
localizing defects in higher-level metal lines such as M5, M6, and M7 from the back side or localizing defects in the lower-level metal lines such as M1, M2, and M3 from the front side, (2) the effect of interconnect geometries, interconnect density, and laser spot size on the thermal profiles, and (3) the effect of using copper and low-k dielectrics on the sensitivity of laser-based techniques.
2. Thermal modeling and simulation Thermal profiles of multi-level interconnect structures resulting from small-area laser heating were simulated with a commercial finite difference solver [7]. The three-dimensional steady-state heat transfer equation was solved subject to the specified boundary conditions. The solver worked in an interactive visual environment to generate a mesh geometry. This mesh geometry, coupled with specified material conductivity properties, heat inputs, and boundary conditions, gave a detailed description of temperatures within the interconnect structures. A model was constructed with brick elements describing the material shapes of the interconnect structures. The brick elements with orthogonal edges had their heat transfer described by twelve internode thermal resistance, Rij . Rij can be written as Rij ¼
Dxij ; kAij
where Dxij is the spacing between nodes i and j; k is the thermal conductivity; and Aij is the cross-sectional area of the brick element. When the brick elements had angles other than 90° or when anisotropic material properties were used, additional diagonal resistances between the nodes were added. Heat inputs and fixed temperature boundary conditions were then assigned to specific nodes. Temperature was solved iteratively at each unconstrained node with the finite difference solving routine. A steady-state solution was determined using P j Tj =Rij þ Qi P Tui ¼ Ti ð1 bÞ þ b ; j 1=Rij where Tui is the updated temperature for the ith node and is related to the previous temperature, Ti . b (typically 1.5–1.9) is a parameter selected to optimize convergence of the solution. Qi is the heat input to the node. Tui is iterated until the solution converges to generate a maximum DT below some convergence criteria, typically 104 °C. A thermal conductivity value of 1.56 W/cm °C was used for aluminum [8], and a value of 0.011 W/cm °C was used for silicon dioxide films [9]. Thermal conductivity values of 1.49, 1.73, and 4.01 W/cm °C were used for silicon, tungsten, and copper respectively [10].
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A value of 0.0012 W/cm °C was used as a representative value for low-k materials [11]. All thermal conductivity values were assumed to be constant with temperature. Convection and radiation were not included in the simulations, and thermal profiles were calculated based only on thermal conduction. Selecting interconnect structures for modeling has presented a challenge. There are a large variety of interconnect systems used in advanced ICs. Differences exist among different IC manufacturers and among different technologies. The two structures used for the modeling in this paper were chosen for their simplicity. Although their interconnect geometries are arbitrary, the complexity in these structures is comparable to those used in advanced interconnect systems. The modeling results obtained from these structures should, therefore, be applicable to the interconnect systems used in advanced ICs. The first interconnect structure used in the modeling is shown in Fig. 1(a). In this structure, the silicon die thickness is 10 lm. There are six levels of interconnects in this die. Metal-1 (M1), M2, M3, M4, M5, and M6 lines are made of either aluminum or copper. The metal lines in M1, M3, and M5 run in parallel in the x-direction, while the metal lines in M2, M4, and M6 are along the y-direction. All the metal lines are 0.5 lm wide, 0.5 lm thick, 12 lm long, and spaced horizontally in a 2.0 lm pitch. M1 lines are connected to the silicon substrate by tungsten or copper contacts that are 0.5 lm wide, 0.5 lm long, and 1 lm thick. The metal lines in all levels are connected to one another by either tungsten or copper vias that are 0.5 lm wide, 0.5 lm long, and 1 lm thick. The interlevel metal lines are separated by a 1-lm thick SiO2 or a 1-lm thick low-k dielectric layer. No laser absorption was assumed to occur in both the silicon substrate and the dielectric layers. A laser power of 40 mW was input on one of the metal lines with a spot size of either 0.5 or 1 lm square area. Since both aluminum and copper are highly reflective at 1320 nm, about 97% of the laser power [12] was assumed to reflect from the aluminum or copper with about 3% of the laser power or 1.2 mW being absorbed by the metal. The silicon/air interface was assumed to be at room temperature (25 °C) with no temperature rise during laser heating. Temperatures were then calculated with 1.2 mW of power input on one of the metal lines at different metal levels. The second interconnect structure used is shown in Fig. 1(b). The silicon die thickness is also 10 lm. There are 10 levels of interconnects in this die. All the metal lines are made of either aluminum or copper. The metal lines in M1, M3, M5, M7, and M9 run in parallel in the x-direction while the metal lines in M2, M4, M6, M8, and M10 are along the y-direction. All the metal lines are 0.2 lm wide, 0.2 lm thick, 9.6 lm long, and spaced horizontally in a 0.8 lm pitch. M1 lines are connected to
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Fig. 1. The lattice structure used to simulate the heating effect of a focused infrared laser beam on (a) a six-level metal interconnect structure and (b) a 10-level metal interconnect structure.
the silicon substrate by tungsten or copper contacts that are 0.2 lm wide, 0.2 lm long, and 0.4 lm thick. The metal lines in all levels are connected to one another by either tungsten or copper vias that are 0.2 lm wide, 0.2 lm long, and 0.4 lm thick. The interlevel metal lines are separated by a 0.4-lm thick silicon dioxide or a 0.4-lm thick low-k dielectric layer. No absorption was assumed to occur in both the silicon substrate and the dielectric
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layers. A laser power of 40 mW was also input on one of the metal lines with a spot size of 0.5 or 1 lm square area. Similar to the first structure in Fig. 1(a), 3% of the laser power or 1.2 mW was assumed to be absorbed by the metal line. The same boundary conditions were assumed in this structure as in the first structure with no temperature rise occurring at the silicon/air interface. Temperatures were then calculated with 1.2 mW of power input on one of the metal lines in M1, M2, M3, M8, M9, or M10. The laser spot sizes (0.5 or 1.0 lm square) used in the modeling are several times smaller than those obtainable from traditional optics. Laser spot sizes, however, have little effect on the thermal profiles except for the peak temperature rises, as will be shown in the next section. The modeling results from the smaller spot sizes are, therefore, applicable to the understanding of issues with regard to the effectiveness of laser-based techniques in advanced interconnect systems. In addition, several commercial companies are actively developing solidstate-immersion lenses [13] that can drastically reduce the laser spot size. These future lenses can potentially achieve laser spot sizes that are comparable or smaller that those used in this paper.
3. Results and discussion Thermal modeling was first performed on the sixlevel metal (Fig. 1(a)) interconnect structure consisting of aluminum, tungsten, and silicon dioxide. The laser power was input on one of the metal lines in M1 with a spot size of 0.5 lm square area to simulate the back-side heating through the substrate. Figs. 2 and 3 show the vertical and horizontal profiles, respectively, for the heated surface area on M1 in the six-level interconnect structure. Fig. 2(c) shows the corresponding vertical line temperature profile through the center of the heated area on M1. The peak temperature was found to be 37.9 °C at the heated surface on M1 relative to the base die temperature of 25 °C. Even though the laser beam cannot penetrate M1, heat generated by the laser heating conducts through M1 to the higher-level metal lines. There is, however, a sharp drop in temperatures beyond M1. Peak temperature values are 29.7, 27.3, 26.6, 26.3, and 26.3 °C at M2, M3, M4, M5, and M6 respectively. As heat conducts through M1, it also diverges, resulting in thermal spreading. Thermal spreading is quite significant even on the M2 and M3 aluminum lines as shown in Fig. 3(c) and (d). Horizontal spreading also occurs in the M1 plane and primarily along the metal line as shown in Fig. 3(a). Thermal modeling was also done on the 10-level interconnect structure using a laser spot size of 0.5 lm square. The interconnect structure was also assumed to consist of conventional materials with aluminum lines,
Fig. 2. (a) Side view of the lattice structure used in the simulation of temperature profiles from back-side laser heating on M1. The simulation is for the six-level metal interconnect structure made of Al, W, and SiO2 . The dashed arrow indicates the back-side laser illumination on a M1 aluminum line. (b) Calculated temperature profiles over the area shown in (a) for the absorbed power of 1.2 mW in a 0.5 lm square area on a M1 aluminum line. (c) A vertical line temperature profile that passes through the center of the heated area on M1 shown in (b).
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surface area on M1 are shown in Figs. 4 and 5 respectively. Similar to the six-level structure, there is a significant drop in peak temperatures from M1 (36.6 °C) to M2 (28.4 °C) and M3 (26.5 °C). Thermal spreading are also significant even at M2 and M3 as shown in Fig. 5. As mentioned previously, the signal response of most ICs is non-linear with respect to the laser intensity and local temperature rise. Although thermal spreading occurs during direct heating on the M1 metal line (predominantly along the metal line), the area with peak temperature rise normally coincides with the laser spot. It is this area with the peak temperature rise that is responsible for the observed defect signals; consequently, thermal spreading in M1 does not affect the spatial
Fig. 3. (a) Top view of the lattice structure in Fig. 1(a) in M1 plane. The dashed circle indicates the back-side laser illumination on a M1 aluminum line. Calculated temperature profiles over the same area in (a) on (b) M1, (c) M2, and (d) M3 for the absorbed power of 1.2 mW in a 0.5 lm square area on a M1 aluminum line, showing thermal spreading on both M2 and M3.
tungsten contacts, tungsten vias, and silicon dioxide layers. The vertical and horizontal profiles for the heated
Fig. 4. (a) Side view of the lattice structure used in the simulation of temperature profiles for back-side laser heating on M1. The simulation is for the 10-level metal interconnect structure made of Al, W, and SiO2 . The dashed arrow indicates the backside laser illumination on a M1 aluminum line. (b) Calculated temperature profiles over the same area in (a) for the absorbed power of 1.2 mW in a 0.5 lm square area on a M1 aluminum line.
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Fig. 5. (a) Top view of the lattice structure in Fig. 1(b) in M1 plane. The dashed circle indicates the back-side laser illumination on a M1 aluminum line. Calculated temperature profiles over the same area in (a) on (b) M1, (c) M2, and (d) M3 for the absorbed power of 1.2 mW in a 0.5 lm square area on a M1 aluminum line, showing thermal spreading on both M2 and M3.
resolution of laser-based techniques. At M2 and M3, thermal spreading is severe due to indirect heating, and the defect signals are generated primarily from areas several times larger than the laser spot size. Therefore, thermal spreading at M2 and M3 makes it more difficult to pinpoint defect locations. For interconnects above M3, signal strength is much weaker and thermal spreading is progressively worse; consequently, it is unlikely that any laser-based techniques will be effective in localizing defects with back-side indirect heating in higher-level interconnects. Detection of defects at higher-level interconnects may still be possible if the defects are not obscured by lower-level interconnects and are accessible by direct heating. Back-side thermal profiles were also calculated for 1.2-mW power input on one of the M2 and M3 metal lines. Back-side simulations were not performed on the metal lines in M4, M5, and M6 since they were unlikely to be accessible from the back side. The situation is reversed for front-side heating. Front-side simulations were performed only on the three top levels of interconnects since these layers were more accessible from the front side. The results of the modeling are shown in Figs. 6 and 7 for both interconnect structures. Whether from the front side or the back side, the modeling results are quite similar to those observed in Figs. 2–5, showing significant reduction in temperatures and thermal spreading at the metal layers adjacent to the heated surface. Thermal modeling was also performed on both interconnect structures with different interconnect materials and with a 0.5 lm square laser spot size. Thermal line profiles were generated by assuming laser absorption occurring at different metal levels. Thermal profiles obtained from structures with aluminum, tungsten, and silicon dioxide were compared to those with copper and low-k dielectric (Figs. 6 and 7). The profiles between these two material combinations are quite similar except for the smaller peak temperatures in the structures with copper and a low-k dielectric. Peak temperatures due to laser absorption at different metal levels for the four different material combinations are tabulated in Tables 1 and 2. Tables 1 and 2 show significant differences in peak temperatures between structures with copper and aluminum, but not between those with silicon dioxide and low-k dielectric layers. These differences reflect the dominance of metal thermal properties in determining heat dissipation, thermal distribution and spreading in the interconnect structure. The modeling results have significant implications with regard to the effectiveness of new laser-based techniques to detect defects in state-of-the-art and next-generation ICs. Copper and low-k dielectrics are the materials of choice for interconnection schemes in these ICs. Tables 1 and 2, however, show that the temperature rises (difference between local temperature and base die tem-
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Fig. 6. Vertical line temperature profiles that compare the thermal distribution of the six-level interconnect structures consisting of (a) Al, W, and SiO2 , and (b) Cu and low-k dielectric with a laser spot size of 0.5 lm square. The temperature profiles were calculated based on back-side heating on M1, M2, and M3 and front-side heating on M4, M5, and M6, and were drawn through the center of the heated areas on different metal levels.
perature of 25 °C) due to laser absorption for these materials are at least a factor of two smaller than those with the conventional materials of aluminum, tungsten, and silicon dioxide. Smaller temperature rises at the defect sites mean weaker signal strength and less sensitivity for defect detection; consequently, the new laser-
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Fig. 7. Vertical line temperature profiles that compare the thermal distribution of the 10-level interconnect structures consisting of (a) Al, W, and SiO2 , and (b) Cu and low-k dielectric with a laser spot size of 0.5 lm square. The temperature profiles were calculated based on back-side heating on M1, M2, and M3 and front-side heating on M8, M9, and M10, and were drawn through the center of the heated areas on different metal levels.
based techniques may not be as effective in localizing defects in structures with newer materials. The effects of laser spot size were also investigated. Thermal profiles simulated from a laser spot size of 0.5 lm square with heat input on M1 were compared to
Table 1 Peak temperatures in °C at the heated surfaces due to laser absorption at different metal levels for four different interconnect material combinations in the six-level metal interconnect structurea Materials (metal line, via/ contact, and dielectric layer)
M1
M2
M3
M4
M5
M6
Al, W, and SiO2 Al, W, and low-k Cu, Cu, and SiO2 Cu, Cu, and low-k
37.9 38.5 31.0 31.2
42.1 43.5 32.6 32.8
44.7 46.2 33.7 33.9
45.3 47.1 33.9 34.3
45.5 47.6 34.2 34.5
52.5 56.0 37.2 37.9
a The laser spot and the base temperature of the die were assumed to be 0.5 lm square and 25 °C respectively. The peak temperatures were calculated based on back-side heating on M1, M2, and M3 and front-side heating on M4, M5, and M6.
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Table 2 Peak temperatures in °C at the heated surfaces due to laser absorption at different metal levels for four different interconnect material combinations in the 10-level metal interconnect structurea Materials (metal line, via/ contact, and dielectric layer)
M1
M2
M3
M8
M9
M10
Al, W, and SiO2 Al, W, and low-k Cu, Cu, and SiO2 Cu, Cu, and low-k
36.5 37.5 30.3 30.4
37.7 38.8 30.6 30.7
38.8 40.0 30.9 31.2
39.9 41.4 31.5 31.7
41.2 43.0 32.1 32.3
46.1 49.0 34.3 34.8
a The laser spot and the base temperature of the die were assumed to be 0.5 lm square and 25 °C respectively. The peak temperatures were calculated based on back-side heating on M1, M2, and M3 and front-side heating on M8, M9, and M10.
M1
M1 (a)
36
Temperature (C)
Temperature (C)
38
M2
34
M3 M4
32
M5
30
M6
28 26 24 0
2
4
6
8
10
12
42 40 38
(a) M2 M3
36 34 32 30
M4 M5 M6
28 26 24 0
14
2
M1
Temperature (C)
Temperature (C)
(b)
36 34 M3
32 30
M5
M7 M9
28 26
42 40 38
2
4
6
8
8
10
12
14
(b) M1
36 34 32 30
M2
10
12
14
Position ( m) Fig. 8. Vertical line temperature profiles that compare the thermal distribution of two laser spot sizes: 0.5 lm square (full circle) and 1 lm square (open triangle). The profiles were drawn through the center of the heated areas on one of M1 lines for (a) the six-level interconnect structure and (b) the 10-level interconnect structure consisting of Al, W, and SiO2 .
those from a laser spot size of 1 lm square in Fig. 8. The thermal profiles in Fig. 8 were generated from both interconnect structures with aluminum, tungsten, and silicon dioxide. The thermal line profiles for both laser spot sizes are quite similar except for the smaller peak temperatures observed in the larger-spot-size profiles
M3
M4 M5
M6
28 26 24 0
24 0
6
Position ( m)
Position ( m)
38
4
2
4
6
8
10
12
14
Position ( m) Fig. 9. Temperature line profiles showing the effects of metallization density. The profiles were drawn through the center of the heated area on one of the M1 lines for the six-level interconnect structure consisting of (a) Al, W, and SiO2 and (b) Cu and low-k dielectric with a laser spot size of 0.5 lm square. Three different metallization densities are shown: (1) the same metallization density shown in the interconnect structure of Fig. 1(a) (full square), (2) 100% increase in metallization density (full triangle), and (3) 50% decrease in metallization density (full circle) compared to that of Fig. 1(a).
(open triangle in Fig. 8). The smaller peak temperatures are due to less efficient heating by the larger laser spot and lower power density deposited on the metal lines.
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The thermal profiles for the 10-level interconnect structure in Fig. 8(b) are quite similar to those in the sixlevel structure (Fig. 8(a)), except for the narrower peak width. This difference in peak width was observed even though the same laser spot size was used for both structures during the simulation. The data in Fig. 8 suggest that the thermal distribution and spreading are strongly dependent on the local interconnect geometries such as intermetal spacing, metal line width, and metal thickness and less dependent on the laser spot size. Modeling was also performed to study the effect of variations in metallization density on thermal distribution. The metallization density encompasses the density of metal lines, contact density, and via density in all metal levels. Two additional metallization densities were used in the modeling besides the one shown in Fig. 1(a). The metallization density is increased by 100% in one case (full triangles in Fig. 9) and decreased by 50% in the other (full circles in Fig. 9). Thermal profiles with these two metallization densities were then compared to those with original density shown in Fig. 1(a). The results of the modeling are shown in Fig. 9. The profiles in Fig. 9 were calculated from the heat input on one of the M1 lines for the six-level interconnect structure consisting of either conventional materials (aluminum, tungsten, and silicon dioxide), Fig. 9(a), or newer materials (copper and low-k dielectric), Fig. 9(b), with a laser spot size of 0.5 lm square. Since heat is conducted more efficiently though metal than in dielectric layers, denser metallization schemes result in a smaller temperature rise. The temperature rise, however, varies slowly as a function of metallizaton density. A fourfold increase in metallization density only results in the 50–60% changes in temperature as shown in Fig. 9.
4. Conclusions Thermal modeling results show that indirect laser heating is not efficient and does not propagate effectively beyond three levels of metal from both the front side and the back side. Defect detection beyond three immediate levels of metal from the heated area is difficult due not only to poor heat conduction but also to thermal spreading. Thermal distribution and spreading were found to be more affected by interconnect geometries than by variations in laser spot size. It is also easier to detect defects in conventional interconnect systems with aluminum, tungsten, and silicon dioxide than in systems with copper and low-k dielectric materials because of larger temperature rises during laser heating in conventional systems. Metallization density also affects heat conduction in advanced interconnect systems but the
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temperature rise during laser heating varies weakly as a function of metallization density.
Acknowledgements The authors would like to thank Rich Anderson, Ed Cole, and Craig Nakakura for reviewing this manuscript. This work was performed at Sandia National Laboratories. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL8500.
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