Beamline components and layout

Figure 6.1 shows the schematic layout of the X-ray microdiffraction beamline. The X-ray beam from a bending magnet source (1.9 GeV, 400 mA, 250 μm FWHM × 40 μm FWHM, up to 3 × 0.2 mrad divergence in the horizontal and vertical, respectively) is 1 : 1 refocused at the entrance of the hutch by a 700 mm long platinum-coated silicon toroidal mirror operating at a grazing angle of 5.4 mrad (Tamura et al., 2003; Valek et al., 2003). Among few suitable methods for focusing high brightness white-beam X-rays, Kirkpatrick-Baez (KB) mirror pairs has been chosen for producing our X-ray focused beam in the Beamline 7.3.3 (now Beamline 12.3.2) as it is the only focusing solution to combine both achromaticity and high efficiency (Tamura et al., 2003). The principle of these KB mirrors has been described in detail elsewhere (MacDowell et al., 2001). These KB mirrors focus the X-ray synchrotron beam into a submicrometer spot size (0.5 μm × 0.5 μm FWHM). Acting as an adjustable size source for the KB demagnifying optics inside the hutch are the water-cooled tungsten slits at the entrance of the hutch. In this way spot size can be traded for flux. As white-beam has been mostly used in the studies described in the rest of this chapter, the 4-crystal monochromator in Fig. 6.1 is not utilized.

As shown in Fig. 6.1, after the X-ray white-beam is focused by the KB mirrors, there remain two main components: the sample stage, and the large area charge-coupled device (CCD) X-ray detector, both of which are mounted on a goniometer as shown in Fig. 6.2. The sample under consideration would sit on a fine XY piezoelectric stage (range of +/− 50 μm), which is mounted on a coarse XYZ Huber stage (range of +/− 5 mm in XY and +/− 10 mm in Z) as shown in Fig. 6.3. The sample can also be mounted on a heating stage for experiments requiring temperatures up to 600 °C.

The diffraction patterns are collected with a MAR133 X-ray CCD (active area of 133 mm × 133 mm). The sample is usually mounted in a 45° reflective geometry as illustrated in Fig. 6.3, with the CCD detector on a vertical slide at a distance of approximately 50 mm from the sample area illuminated by the beam. This sample–CCD distance is optimized to give the maximum total number of reflections at a reasonable angular resolution. When illuminated with a white beam of 5–20 keV energy range, a (111) oriented Al grain, for example, gives a total of ~18 reflections, at an angular resolution of 0.01° (MacDowell et al., 2001).

Compared with electron microscopy techniques, X-rays offer the advantages of characterization of buried grains under overlying cap layers and multilayered films without the need of any sample preparation/destruction. In situ measurement under a variety of different conditions (in air, liquid, gas, vacuum, at different temperatures and pressures) thus becomes a possibility and opens opportunities for many experimental applications. The lack of sample preparation is especially important since the sample stress state can be greatly affected by any preparation processes.

White-beam μSXRD as local plasticity probe

The unique capability of the technique as a local plasticity probe stems from the polychromatic (white-beam) characteristics of the synchrotron radiation. This is what makes it sensitive with respect to local lattice curvature or rotation in the crystals under consideration. Because plasticity, especially in its special configurations in the forms of geometrically-necessary dislocations (GNDs) (Gao and Huang, 2003), is directly related to the local lattice curvature (Budiman, 2008), this technique has been most suitable for probing and studying the evolution of microstructure of materials especially in terms of its plasticity. This sensitivity to local lattice curvature is related to the continuous range of wavelengths in a white X-ray beam, allowing Bragg’s Law (Bragg, 1913) to be satisfied even when the lattice is locally rotated or bent, resulting in the observation of streaked Laue spots.

White-beam Laue diffraction is a standard crystallographic method used to determine crystal orientation without rotation of the sample. Laue diffraction is usually rarely used to measure strain because the precision of most Laue instruments is low compared with modern diffractometers, and because the unit cell volume cannot be determined with a standard Laue measurement. Nevertheless, with suitable instrumentation, such as that used in the experimental setting described above, precise determination of crystal orientation and distortional strain is possible. Laue diffraction might even be further extended by measuring the energy of one or more reflections to determine the full strain tensor in polycrystalline samples.

A single white-beam Laue diffraction pattern as shown in Fig. 6.4 contains a wealth of information about crystallographic orientation (Fig. 6.4a), deviatoric stresses/strains (Fig. 6.4b), and dislocation structure/density (Fig. 6.4c) as well as crystal rotation (Fig. 6.4d) in each individual crystal of the typically polycrystalline samples. Figure 6.4 shows features in a Laue diffraction pattern and the associated structural and mechanical information that they contain about the materials/sample. The shape of the Laue peak provides information about plastic deformation in the crystal (Fig. 6.4c), especially the one involving GNDs. The change in the absolute position of the Laue peak gives us the rotational deformation of the crystal body (Fig. 6.4d).

A typical X-ray microdiffraction scanning of a sample usually yields hundreds to a few thousands of these Laue diffraction patterns. Without a set of software tools that can rapidly analyze the multiple Laue patterns contained in each of the CCD images produced by our experiments, the abundant raw data could not translate to meaningful information about the materials. A computer automated technique developed for crystallographic indexing, orientation, and strain determinations of grains in thin film samples (Chung and Ice, 1999; Ice and Larson, 2000; Tamura et al., 1999; 2002) was used, and a custom-made software was developed, namely X-ray microdiffraction analysis software (XMAS) (Tamura et al., 2002). It is based on an algorithm first described by Chung and Ice (1999).

Crystal bending, polygonization and rotation

In traditional XRD experiments, a peak at a certain angle θ means a particular (hkl) plane is detected, i.e. the particular angle θ, interplanar distance d_hkl and wavelength λ_Cu,kα (for instance) conspire such as to satisfy Bragg’s Law (Bragg, 1913):

[6.1]

Using this methodology, only elastic deformation of crystal can be determined, where strain can simply be computed from the difference of interplanar distances between atomic planes, before and after the deformation. In contrast, plastic deformation may involve curved and polygonized crystal planes, such as shown in Fig. 6.5. In such configurations, a particular crystal plane (with a fixed d_hkl interplanar distance) may have a range of values of θ angle. This lattice curvature information is lost in traditional XRD (using a single wavelength and no tilt). However, using a white-beam X-ray, which has a range of wavelengths, Bragg’s law can still be satisfied even though the θ angle varies. This means that with white-beam, a presence of lattice curvature can still be detected and even measured.

For a curved crystal plane (crystal bending), a broadened Laue diffraction peak in a certain direction is observed (Fig. 6.5) instead of a single, sharp, rounded peak typical of an undeformed crystal plane. The Laue peak broadening (also called ‘peak streaking’) is continuous, representing the continuum of θ values involved in the curved crystal. Crystal polygonization, in contrast, involves multiple, discreet peaks coming from slightly misoriented sub-crystal structures (such as shown in Fig. 6.5). Such polygonization often occurs following bending of the crystal where more and more dislocations pile up, and thus become unstable with respect to glide and eventually climb to form a low-angle boundary (Cahn, 1949; Gilman, 1955; Hibbard and Dunn, 1956; Patel, 1958).

This is the unique capability of our white-beam X-ray diffraction technique. Using this white-beam methodology, we can start to directly and quantitatively study the evolution of microstructure of crystalline materials especially in terms of its plasticity. This technique is especially sensitive towards crystal bending or polygonization in their simplest geometries, where a net density of parallel like-sign GNDs is formed.

Furthermore, in traditional XRD, when a body of crystal rotates, the angle θ changes and, without rotating the sample, equation [6.1] can no longer be satisfied. In contrast, using a white-beam X-ray, another wavelength is available to satisfy the diffraction condition, and thus give a constructive interference in the diffracted intensity (a Laue diffraction peak) instead on a slightly different position in the CCD camera, such as shown in Fig. 6.6. In other words, a crystal rotation would appear as a shift in the absolute positions of each of the Laue peaks belonging to the same crystal (it is to be noted that a change in the relative position of the Laue peaks, relative to other peaks belonging to the same crystal, in contrast, does not mean crystal rotation, but instead, shear deformation or in other words, deviatoric strains).

Experimental

The interconnect test structure used here is an electroplated Cu damascene line manufactured by Intel Corporation (Budiman et al., 2004; 2006a; 2006b). The test line has dimensions of 70 μm in length and approximately 1 μm in thickness, with two different widths of 1.6 and 0.6 μm. The lines are embedded in a SiO₂/SiOF interlayer dielectric film. The structure is then passivated with nitride and polyimide. The interconnect lines were produced by the damascene technique in which the copper is plated out into open channels and then mechanically polished to the desired thickness. Both vias at either end of the line connect to a lower metallization level, which, in turn, connects to unpassivated bond pads which are used for electrical connection. A schematic diagram of these structures with line dimensions is shown in Fig. 6.7.

The white-beam X-ray microdiffraction experiment was performed on Beamline 7.3.3 (now Beamline 12.3.2) at the Advanced Light Source, Berkeley, CA. The electromigration test was conducted first at 300 °C. Current and voltage were monitored at 10 s increments. The sample (width 1.6 μm) was scanned in 0.5 μm steps, 10 steps across the width of the line and 160 steps along the length of the line, for a total of 1600 CCD frames collected as illustrated in Fig. 6.8. A complete set of CCD frames takes about 6 to 7 h to collect. The exposure time was 4 s plus about 10 s of electronic readout time for each frame. In this manner the Laue pattern and information regarding plastic deformation for each grain in the sample was collected for each time step during the experiment. The current was ramped up to 50 mA (j = 3.1 MA cm⁻²) over the course of 96 h, and then set at that value for the rest of the test.

The second group of tests was conducted at a higher temperature, 360 °C, for reasons that are discussed later in this chapter. The narrow sample (0.6 μm) was scanned in the same manner as above, except that the current ramp up was ≤ 20 mA (j = 3.3 MA cm⁻²) over the course of 96 h, and then set at that value for the rest of the test.

A rough elemental map of the sample has first to be created using scanning X-ray fluorescence, so that the region of interest can be more precisely pinpointed. For the samples in our experiments, we typically used copper, titanium, platinum and gold fluorescence signals. Subsequently, the area of interest can be precisely located by using the piezoelectric positioning stage. A typical big-picture elemental map is shown in Fig. 6.9, from which the exact co-ordinates can be determined for a more precise X-ray microdiffraction scan, and Laue patterns can thus be collected from each discrete area in the coordinates of interest.

Initial microstructure

We first describe the microstructure of the wide (1.6 μm) damascene Cu test structures. The grain out-of-plane and in-plane orientations in these lines as determined by white-beam X-ray microdiffraction through the passivation layer are shown in Fig. 6.10a and 6.10b, respectively.

Figure 6.10a shows all grains along the interconnect line with the < 111 > direction of the individual grains varying from 0° (normal to sample surface) to 54.7° away from the normal of the sample surface. In other words, the darker the color of the grains, the closer those grains are to having < 111 > out-of-plane orientation, and the lighter the color, the further away they are from having < 111 > out-of-plane orientation. It is evident from Fig. 6.10a that Cu grains in the damascene interconnect test structures were found in a wide range of out-of-plane orientations. This is consistent with observations on industry-relevant Cu interconnect test structures (Lingk et al., 1999a; 1999b; 2000). Only a few of the grains (black-colored in Fig. 6.10a) are actually < 111 > grains, some others are quite close (dark) to being < 111 > grains, whereas many others are far off (light white to colored), even approaching < 100>-out-of-plane-oriented grains (54.7° off).

Most of the grains are large grains spanning across the width of the line. It is reasonable to suspect that the Cu grains here extend through the whole thickness of the line, making it a bamboo structure. This is true along the line, however, in areas close to the via regions, grains are smaller, and more likely to be three-dimensional in structure (not bamboo). This trend has been reported (Besser et al., 2001; Doan et al, 2000; Lingk et al, 1999a; 1999b; 2000), where the wider Cu damascene lines were shown to be closer to the behavior of Cu blanket films (bamboo structure), whereas the narrower lines exhibit behaviors toward three-dimensional polycrystalline structure.

Similar observations were found with the in-plane orientation. Figure 6.10b shows all grains along the interconnect line with the < 100 > direction of the individual grains, projected to the sample surface, varying from 0° (exactly lining up with the positive x direction) to 45° away from x-axis. It may appear that the in-plane orientations of the Cu grains in this line are not too widely-ranged. However, it should be noted that as it is projected < 100 > direction on the sample surface, the same color in this map does not necessarily mean a single crystal/grain, but in contrast to the out-of-plane orientation mapping (Fig. 6.10a), it is evident that the same color in this map can actually be a few grains. Thus, we suspect that the Cu grains in this wide line are as varied in in-plane orientations as they are in out-of-plane orientations.

Exact grain orientation mapping of the narrow line (0.6 μm) of these Cu damascene test structures, however, proves to be difficult and rather unreliable. The X-ray spot size (0.5 μm × 0.5 μm) currently used in ALS Beamline 7.3.3 (now Beamline 12.3.2) was relatively large for the dimensions of the narrow line (0.6 μm linewidth). That makes diffraction spot indexing often very difficult and thus mapping of grain orientations and other further quantitative analyses unreliable.

Upon electromigration loading

Electromigration tests were conducted in situ on the damascene Cu test structures. Figure 6.11 shows the evolution of the Laue diffraction spots for several grains in the wide (1.6 μm) Cu line during the in situ electromigration experiment. If we examine the individual diffraction spots after electromigration in some detail we find that in certain grains the spots broaden not in any random direction but always in the y direction across the line. The Laue diffraction spots coming from undeformed crystals are nominally rounded in shape, such as shown in Fig. 6.11 at the initial stage of the electromigration test (at j = 0, t = 0, and room temperature).

The diffraction spots have been converted to q-space (reciprocal space), with the x-axis along the length of the line, the y-axis across the line, and the z-axis normal to its surface. We find that, as the electromigration test progresses, in certain grains the spots broaden, whereas in some grains, they split into two different spots. This broadening and splitting of diffraction spots is observed not in any random direction but always along the y-axis in q-space, which is the width direction of Cu line.

Broadening of the peak is observed in a few grains that are large and span across the width of the line. Figure 6.12a–6.12c display exemplary results of such grains, Grain 2 (in the middle of the line). Here the results of digital intensity traces across the broadening direction of the Diffraction spots in the initial, mid- and end-state (after the end of the electromigration test) are shown.

Such broadening and splitting of the diffraction spots were observed in all three different wide test structure samples examined in our experiments. In each of them, a few grains (between 5 and 9) among a total of usually around 100 to 150 grains, were found to show this behavior after electromigration under similar test time, current and temperature.

The broadening of the diffraction spots represents crystal bending of the Cu grains in the line, whereas the split diffraction spots indicate the formation of low-angle boundary subgrain structures. From Fig. 6.12a–6.12c, it is thus evident that Grain 2 has evolved from initially, an undeformed crystal, to a plastically-bent crystal, and then lastly, to polygonized subgrain structures, such as illustrated in Fig. 6.12d. Each of the features here illustrates the corresponding Laue diffraction observations on the left side. From the amount of broadening we can calculate the bending of the Cu crystal, and from the amount of splitting, the angle of misorientation.

We can then use the broadening and the spot splitting observed to obtain information about the dislocation structure in the grain induced by electromigration. For instance, from the streak length of Fig. 6.12b as measured in the CCD camera and the sample to detector distance we obtain the curvature angle of the grain of 0.75°. Because the mapping of the out-of-plane orientation of the crystal along the Cu line indicates a near bamboo structure, the grain width is about the same as the width of the line (1.6 μm), from which we get the radius of curvature of the grain, R = 126 μm. The GND density to account for the curvature observed can be calculated from the Cahn–Nye relationship (Cahn, 1949; Nye, 1953), ρ = 1/Rb, where b is the Burgers vector. The GND density is then ρ = 3 × 10⁹ cm⁻². The total number of dislocations introduced is only 49.

To obtain quantitative information on polygonization walls (small angle grain boundaries) from the spot split in Fig. 6.12c we observe that the Laue spot splitting, Δ_θ = 0.73°. From this misorientation and Burgers’ model of a small angle grain boundary Δ_θ = b/L, where L = dislocation spacing, we find L = 212 Ǻ which amounts to 45 dislocations in the boundary.

Similar basic observations were made by Valek et al. (2002; 2003) in a related prior study in Al(Cu) interconnect lines in which a very early stage of plastic deformation and microstructural evolution during an electromigration test was also detected (shown in Fig. 6.13) long before any macroscopic damage became visible, by using the same technique (Budiman, 2008; Tamura et al., 2003; Valek et al., 2003). In addition, it was observed that, during in situ electromigration, a gradient of plastic deformation evolves along the line, resulting in bending and in polygonization of the largest grains between the cathode and the anode end. Smaller grains do not readily deform but do rotate as electromigration proceeds. Plastic deformation is initiated at the cathode end and gradually progresses toward the anode end until a steady state is reached. Further quantitative analyses of these Al(Cu) results were later conducted by Kai et al. (2008a; 2008b) and showed a consistent trend of plasticity in Al(Cu) as in Cu interconnect lines (Budiman et al, 2004; 2006a; 2006b).

Linewidth effects

We now describe in situ electromigration studies on another damascene Cu test structure with a different linewidth (0.6 μm). The higher test temperature of this group of experiments was designed to give more pronounced streaking of the Laue peaks as the grains undergo electromigration. A previous similar electromigration study has shown an extensive broadening of peaks in the Al(Cu) system (Valek et al., 2002; 2003). By increasing the test temperature of this group of experiments, we aim to have a similar homologous temperature (T/T_M) to that of the previous study on Al(Cu), which was ~ 0.51. The homologous test temperature (T/T_M) for the present study of narrow Cu lines was ~ 0.48, which is higher than the homologous temperature for the wide line experiments discussed above (~ 0.4).

However, our observation of the peaks of the grains in the narrow Cu line (width = 0.6 μm) did not show any broadening of the peaks during electromigration. This is true despite the higher temperature used in this group of experiments. Instead, grain rotations, similar to that of Grain 3 in Fig. 6.11, are observed throughout the length of the line. The rotation of grains manifests itself as a shifting in the position of the Laue spot; from the direction and magnitude of the shift, we can calculate the axis and amount of the crystal rotation.

The narrow Cu line thus appears to behave less plastically in response to similar electromigration current density stressing than the wide (1.6 μm) line. Narrower Cu lines thus seem to have higher electromigration resistance (than the wider Cu line). The resistance to plastic flow and the reasons why only grain rotation occurs in the narrow Cu line are not well understood at present. However, a higher resistance to plastic deformation in smaller structures, especially for Cu line structures, has also been reported by Spolenak et al. (2000; 2002).

In these studies (Spolenak et al., 2000; 2002), thermal cycling of the wide Cu damascene line (5 μm) was shown to exhibit plastic deformation with yield stresses in the range 50–100 MPa in compression (Fig. 6.14). In contrast, the narrower line (0.8 μm) in that study indicated no such yield behavior and deformed only elastically over the entire temperature cycling range. These observations are consistent with our electromigration results. Streaking of X-ray Laue spots indicating plastic bending of grains is observed for the wider 1.6 μm line, but is absent for the narrower line (0.6 μm).

Effects of in-plane orientations

The consistent direction in which the electromigration-induced plasticity has been observed both in Al (Valek et al., 2002; 2003) as well as Cu interconnect lines (Budiman et al., 2004; 2006a; 2006b) was discussed earlier. Here, we further investigate the specific direction of the plastic deformation in term of electromigration current direction. We use the Laue peak streaking simulation to study the possible mechanisms of plasticity. By matching the simulation with the actual streaking pattern, we can make some conjectures as to which particular slip system, among the 12 possible slip systems known for FCC metals, might be responsible for the streaking pattern.

Coming back to the wide lines, Fig. 6.15 shows the movement of Laue spots of Grain 2 during the electromigration test, and a comparison with simulation result. Working within the Cahn–Nye crystal bending model (Cahn, 1949; Nye, 1953), and knowing the initial and end states of each of the diffraction spots, we can simulate the dislocation processes in the crystal necessary to cause the transformation of diffraction spots from their initial state to their final streaked/split/shifted state. We discovered that indeed the movement of the diffraction spots in Fig. 6.15a can be simulated by certain dislocation slip processes belonging to a slip system known to operate in FCC crystals (Fig. 6.15b). Figure 6.16a then describes the particular slip plane, slip direction and line direction in Grain 2 with respect to the interconnect line co-ordinates that are involved in the respective movement of diffraction spots.

Grain 2 is a large grain spanning across the cross-section of the line, and thus can be modeled as shown in Fig. 6.16b. The simulation shows one possible scenario of evolution of the grain as electromigration progresses. Point defect transport on the interfaces of the Cu line initiates the production of dislocations within the crystal of Grain 2 and activates their movement. Dislocations glide on a {111} plane that is tilted 41° from the surface of the sample. As dislocations accumulate on the glide planes, they become unstable with respect to climb and begin to coalesce into tilt dislocation walls as illustrated in Fig. 6.16c. This series of events would manifest itself in the form of split Laue peaks following a certain direction as experimentally observed during electromigration to Grain 2 as shown in Fig. 6.15a.

We also observe that the < 112 > type direction for the tilt axis of the crystal is very close (within a few degrees) to the direction of the electron flow, or in other words, to the direction along the length of the line. The example in Fig. 6.16b shows a 6° deviation between the axis of tilt, which is a < 112 >, and the direction of electron flow. More specifically, upon further inspection, this particular < 112 > was also found to be the closest < 112 > in Grain 2 to the direction of electron flow.

Further, more complete, studies confirmed that this observation holds true for all the Cu grains in the current experiment exhibiting plastic bending and/or polygonization (formation of subgrain structures). This is shown in Fig. 6.17a. Nine large Cu grains with the observed plastic bending/polygonization are represented by the nine bullets within 10° of the closest < 112 > direction of their respective crystal to the direction of the electron flow. The bullets represent the direction of the in-plane crystallographic orientation of each of the respective grains in the direction of the electron flow in the line. To put it simply, all grains with a < 112 > direction pointing in the direction of the length of the line were observed with plastic bending/polygonization. More specifically, it has also been consistently observed that the particular < 112 > direction then becomes the tilt axis of the plastic deformation in the respective grain. This suggests a correlation of the proximity of certain < 112 > line directions to the direction of electron flow with the occurrence of plastic behavior.

We now recap our main observations up to this point. Almost immediately upon the application of high-density current flow, Cu grains behave plastically (crystal bending, polygonization, or simply rotation). We confirm that when large single grains spanning across the cross-section of the Cu lines are exhibiting crystal bending (and/or crystal polygonization), the rotation axis of this plastic deformation, which is always one of the < 112 > of the 12 possible slip systems in FCC crystals, was found to be very close (within 10°) to the direction of the electron flow, as illustrated in Fig. 6.17a. This particular < 112 > is also always the closest < 112 > to the direction of electron flow. This finding thus suggests that the proximity of a < 112 > direction in the grain to the direction of the length of the line is correlated to the occurrence of plastic behavior in a given grain.

This particular finding might have an important practical implication. If all the grains exhibiting crystal bending/polygonization are those with a < 112 > direction that falls closely within the direction of the electron flow, then we could propose that if a grain is oriented such that none of its < 112 > direction falls within 10° of the electron flow direction, then this grain would be less susceptible to plastic deformation induced by electromigration. Such grains have their crystallographic orientations in the direction of the electron flow if the lines fall within the shaded regions as shown in Fig. 6.17b. Therefore, it could be proposed that these are the particular in-plane textures of Cu interconnect lines that might give the wires lower susceptibility towards electromigration-induced plastic deformation, or in other words, higher resistance to electromigration later damage.

Experimental

The interconnect test structure used here (shown in Fig. 6.18) is a variation of a back-end-of-line (BEoL) process for a 65 nm CMOS technology manufactured by AMD, Inc. (Budiman et al., 2007a; 2007b; 2009). In this technology, the dual-damascene Cu fill process includes a standard Ta-based barrier and Cu seed, electroplated Cu fill, post-plating anneal, chemical-mechanical polish and a dielectric cap layer. Two different inter-layer dielectrics (ILD) were integrated with copper: Cu/low-k ILD (low-k = chemical vapor deposition (CVD) carbon-doped oxide) and Cu/hybrid ILD (hybrid = Cu/low-k at the line level and Cu/fluorine-doped tetraethyl orthosilicate (FTEOS) at the via layer). Both ILD materials were studied in order to provide a comparison of the extent of plasticity. The metal two (M2) lines were studied after partial removal of the top dielectric to expose the capped Cu lines (Fig. 6.18a). In these electromigration tests, the current was forced from the wide, upper metal layer (M3) into narrow M2 (called a V2M2 test) or from a wide lower metal layer (M1) into a narrow M2 (referred to as a V1M2 test). Both structures are designed to force failure in M2 at its critical dimension.

The first set of test structures consists of 200 μm-long lines, approximately 0.2 μm thick, and 0.5 μm wide. Owing to limited beam time, typical of synchrotron experiments, only segments of 50 μm length at both cathode and anode ends of the line were studied (Fig. 6.18a). The dielectric is carbon-based CVD oxide (‘low-k’ in Fig. 6.18c). The second set of interconnect test structures was prepared with dimensions similar to those of the first one, but with the hybrid ILD material (SiO₂-based). The line length is 200 μm, the thickness is approximately 0.25 μm and the width is 0.7 μm. Similarly, only segments of 50 μm length at both cathode and anode ends of the line were studied.

The experiment was performed on the Beamline 7.3.3 (now Beamline 12.3.2) at the Advanced Light Source, Berkeley, CA. The electromigration test was conducted at 300 °C on a via-terminated test structure (Figure 6.18(b)). The current was ramped up to 2 mA (j = 2 MA cm⁻²) and then set at that value for the rest of the test (up to 36 h). The ambient temperature in the synchrotron end-station (hutch) where the tests were performed is 20 °C.

Electromigration-induced plasticity in copper interconnects

The in situ electromigration observations are described first. Figure 6.19 shows the typical evolution of the Laue diffraction spots during the in situ electromigration test. Figure 6.19 is early in the electromigration test (after 36 h of testing). The observed broadening of the Laue diffraction spots (streaking) represents plastic deformation of the Cu grains induced by electromigration (Budiman et al., 2004; 2006a; 2006b; Valek et al., 2002; 2003).

As the electromigration test progresses, plasticity is observed in the Cu grains throughout the line, such as demonstrated in Fig. 6.20a. Plasticity here may manifest itself either in the form of diffraction spot broadening (streaking) or in the form of diffraction spot splitting (into two or even more different spots). The broadening of the diffraction spots represents crystal bending of the Cu grains in the line, whereas the split diffraction spots indicate the formation of low-angle boundaries or sub-grain structures (Budiman et al., 2004; 2006a; 2006b; Valek et al, 2002; 2003).

Not only was plasticity observed, but also the direction of the plastic deformation is generally consistent across grains throughout the segments of the line under observation, as shown in Fig. 6.20a. This is consistent with our observation on the previous set of Cu lines (Budiman et al., 2004; 2006a; 2006b). Cu grains plastically deform in a direction transverse to the electron flow direction in the line. Such directionality can simply be accommodated by a distribution of same-sign edge dislocations with cores as illustrated in Fig. 6.20b, i.e. with the < 112 > line direction of the dislocations all lining up along the direction of electron flow in the line.

Exact grain orientation mapping of these Cu lines unfortunately could not be obtained in the present study. The X-ray spot size (0.5 μm × 0.5 μm) used in the Beamline 7.3.3 (now Beamline 12.3.2) was relatively large for the dimensions of these state-of-the-art interconnect lines. That makes diffraction spot indexing very difficult and thus mapping of grain orientations and other further quantitative analyses unreliable. The few Cu grains that we show in Fig. 6.20 were among the limited number of grains in the two Cu lines for which indexing of the diffraction spots happens to be sufficiently clear and unambiguous for this analysis. In general, the larger the Cu grains and the more bamboo-like they are, the more they diffract sharply and give numerous diffraction spots, thus giving higher confidence on the reliability of these results. That being said, it is fortunate that the evolution of Cu diffraction spots before and after some period of electromigration testing can still be compared qualitatively, as demonstrated in Fig. 6.19.

The extent of the electromigration-induced plasticity observed in the present samples is now determined. Figures 6.21a and 6.21b show still different additional diffraction spots observed during this experiment (after EM testing of 36 h, at 300 °C and 2 MA cm⁻² current loading) from Cu lines with the low-k and the hybrid dielectrics, respectively. The diffraction spots have been converted to χ-θ angular space, with χ running along the direction of the length of the line, and θ across the direction of the width of the line. The χ-θ angles refer to the plane normals responsible for the Laue streaks.

The observed broadening and spot splitting can be used to obtain information about the dislocation structure induced into the grain by electromigration. For instance, from the streak length of Fig. 6.21a, as measured in the digital camera image, and knowing the sample-to-detector distance, we determine the curvature angle of the grain to be 9.8°. Assuming a near bamboo structure, the grain width is the same as the width of the line (0.5 μm), from which we determine the radius of curvature of the grain, R = 2.34 μm. The GND density needed to account for the observed curvature can be calculated from the Cahn-Nye relationship (Cahn, 1949; Nye, 1953), ρ = 1/Rb, where b is the Burgers vector. The GND density is then ρ = 1.68 × 10¹⁵ m⁻². The total number of dislocations in the area of the cross-section of the Cu line/grain is approximately 142.

To obtain quantitative information on polygonization walls (subgrain boundaries) from the spot split in Fig. 6.21b, we observe that the Laue spot splitting, Δ_θ = 9.1°. From this misorientation and Burgers’ model of a small-angle grain boundary, Δ_θ = b/L, where L = dislocation spacing, we find that L = 16 Ǻ which amounts to a total of 110 dislocations in the subgrain boundaries in the cross-section of the Cu line/grain. This translates to a GND density of ρ = 1.12 × 10¹⁵ m⁻².

The extent of the plasticity as described here (ρ ~ 10¹⁵ m⁻²) is observed across all grains throughout the segments of both lines with different dielectric schemes. The significance of the difference in our analysis above, in terms of the extent of the plasticity, as well as, its manifestation (grain bending versus polygonization) between the two Cu lines with different dielectric schemes requires added confirmation. Nevertheless, they provide a general indication of the extent of plasticity in these Cu lines.

Effects of texture

Compared with the typical observation of the extent of the electromigration- induced plasticity in the previous set of Cu interconnect lines (Budiman et al., 2004; 2006a; 2006b), this set of samples exhibits at least a two-order of magnitude difference, in terms of GND density (Fig. 6.22). The samples studied in the previous section (referred to as ‘Samples A’) exhibited ρ ~ 10¹²–10¹³ m⁻² (Budiman et al., 2004; 2006a; 2006b), and the samples in this section (referred to as ‘Samples B’) exhibited ρ ~ 10¹⁵ m⁻² (Budiman et al., 2007a; 2007b; 2009). Samples A and B differ fairly significantly in dimensions, as well as the dielectric materials used, as shown in Fig. 6.22 (the dimensions are to scale).

Figure 6.22 shows the typical evolution of the Laue reflections from the Cu lines from the initial state (room temperature, j = 0, t = time = 0) to the electromigration state (after some electromigration, T = 300 °C, j ~ 2.0–3.1 MA cm⁻², t ~ 36–96 h). Care was taken in order for the observed intensity contours in the χ-2θ co-ordinate in Fig. 6.22 to be similar (the windows all cover areas of squares of a range of 7° to 10° in angle space, and the threshold of the lower-bound intensity display was set to be similar). Thus, it is obvious from the relative apparent difference in the extent of streaking/splitting of the Laue diffraction spots that the level of plastic deformation that developed during the course of electromigration in Samples B is distinctly larger than that of Samples A.

As the two sets of samples (Samples A and B) under investigation are provided by different integrated circuit manufacturers, it is not possible to completely quantify the process differences (dielectric type, materials processing and thermal history) in their technologies in this section. It is known that the two sets of samples differ in terms of dimension and dielectric materials used; however, it is assumed that the main difference, as far as electromigration-induced plasticity is concerned, is the crystallographic texture of the Cu lines. From the texture analysis conducted in our previous study (Budiman et al., 2004), we know that Samples A have a rather weak (111) texture. As mentioned earlier, the exact grain mapping for the present study (Samples B) could not be obtained; however, Samples B came from the same manufacturer of the inlaid Cu lines studied by Besser et al. (2001). It is therefore reasonable to assert that Samples B would have the typical strong (111) texture as observed by Besser et al. (2001).

Although other process differences between these two sets of samples, including dimensions and dielectric materials, are acknowledged, we believe that these differences cannot satisfactorily explain the differences in the extent of plastic deformation. For example, the Cu in Samples A is surrounded completely by dielectric material, which is a fluorinated SiO₂-based dielectric and, thus, generally believed to constrain the Cu lines better, and this should result in less plastic deformation. This is consistent with our observation of Samples A compared with Samples B, but the different dielectric schemes in Samples B, do not appear to affect the level of plasticity in the Cu lines. Another example involves the size effect. Wider lines seem to exhibit more plastic deformation in our previous study (Budiman et al., 2004; 2006a; 2006b), such as also shown in the previous section. However, Samples B are much narrower, and also much smaller in all cross-sectional dimensions, than Samples A, but Samples B exhibits two orders of magnitude more electromigration-induced plasticity.

Figure 6.23 is a summary of the known information about the Cu lines in Samples A compared with Samples B. First, Samples A shows a weak (111) texture, and we found the extent of electromigration-induced plasticity of the order of ρ ~ 10¹²–10¹³ m⁻². Subsequently, Samples B was found with ρ ~ 10¹⁵ m⁻² after similar electromigration conditions, a significantly larger amount of electromigration-induced plasticity. Besser et al. (2001) suggested that Samples B have the typical strong (111) texture. This observation of significantly larger electromigration-induced plasticity in Samples B than in Samples A, is consistent with our earlier observation, as described in the previous section, that the occurrence of plastic deformation in a given grain can be strongly correlated with the availability of a < 112 > direction of the crystal in the proximity of the direction of the electron flow in the line (within an angle of 10°). In < 111 > out-of-plane oriented grains in a damascene interconnect scheme, the crystal plane facing the sidewall tends to be a {110} plane, so as to minimize the interfacial energy (Paik et al., 2004; Besser et al., 2001; Sanchez and Besser, 1998). Therefore, it is deterministic rather than probabilistic that the (111) grains have a < 112 > direction nearly parallel to the direction of electron flow or the direction of the length of the line. This is illustrated in Fig. 6.23b.

In Samples B, most grains are < 111 > in out-of-plane orientation (such as shown in the focused ion beam mapping in Fig. 6.23b), and thus prefer energetically to have the < 110 > directions normal to the sidewalls, thus causing a < 112 > direction to be very close to the direction of the electron flow. When this condition is met, our proposed correlation discussed in the previous section (Budiman et al., 2004; 2006a; 2006b) suggests that plasticity occurs in these Cu grains upon electromigration, and not only did it occur in this study, the extent of the plasticity here was rather extreme. Samples A, in the meantime, have only a few grains that are < 111 > in out-of-plane orientation, which leads to the occurrence of plasticity only in these few grains in the Cu lines after electromigration. In most other grains (i.e. non < 111>-oriented grains), a < 112 > direction of the Cu crystal is not likely to be the direction of the electron flow of the lines. Thus, plasticity was not observed in many grains in the Cu lines of Samples A.

Materials degradation mechanisms

We have, earlier in the manuscript, established that dislocations with cores running along the electron flow direction and densities in the order of 10¹⁵ m⁻² are present in the Cu lines undergoing electromigration (accelerated test conditions) for 36 h. Figure 6.27 is a comparison of calculated diffusivities as a function of temperature between the interface diffusion path and those of dislocation cores of various densities in Cu interconnect lines (10¹² m⁻², 10¹⁵ m⁻², and 10¹⁷ m⁻²) when each diffusion mechanism is assumed to act alone. The diffusivities are calculated based on diffusion coefficient values in the literature (Frost and Ashby, 1982; Gan et al., 2006) for Cu interconnect lines (Table 6.3), and for the interconnect dimensions as described earlier in this section.

The dislocation density observed in the present study (ρ_GND = ρ_core = 10¹⁵ m⁻²) is illustrated as the solid line in Fig. 6.27, illustrating that dislocation core diffusion is on the same order of magnitude as that of interface diffusion (the dotted line) at the test conditions (T = 300 °C or 1000/T = 1.75/K). Thus, a core dislocation density of 10¹⁵ m⁻² is the dislocation density threshold necessary for dislocation core diffusion to be on a par with interface diffusion. In other words, at this dislocation density the contribution of dislocation cores to the overall/effective diffusivity in the Cu line during accelerated electromigration is expected to be at least the same order of magnitude as interface diffusion and thus cannot be neglected.

It is to be noted, however, that at temperatures at or below 100 °C, the required dislocation density for cores to have a significant contribution to the diffusion would be on the order of 10¹⁷ m⁻² (the dashed line in Fig. 6.27). These lower temperatures correlate with the typical use or operational conditions of the interconnects. The typical initial (as fabricated) dislocation density in Cu/metallic lines was taken to be 10¹² m⁻² (following Baker et al., 2000), and the corresponding diffusivity is shown by the dashed-dotted line in Fig. 6.27.

It is therefore reasonable to propose that the contribution from the dislocation core diffusion (the second term in equation [6.2]) can no longer be neglected in the Cu lines now that we have evidence of the existence of such high density of dislocation cores in the real Cu interconnect structure. It is certainly true in the Cu lines investigated in the present study especially during electromigration at accelerated test conditions. The contribution from dislocation cores would enhance the electromigration diffusion, or in other words, the total electromigration flux (J_EM), since the total or overall diffusion includes the existing, usually-dominant interface diffusion, plus the observed dislocation core or ‘pipe’ diffusion. The increase in this core diffusion to the point of significance in the overall electromigration diffusion is related to the kind and the extent of plasticity induced by the electromigration process itself (i.e. through the increase in the core dislocation density from the pre-electromigration density ρ_core = 10¹² m⁻² to the observed density ρ_core = 10¹⁵ m⁻²).

The result of this study gave a key piece of experimental evidence that opens up the possibility that such a high dislocation density may generally be present in the Cu test structures undergoing electromigration. The circumstances and the important implications of this special configuration of dislocation cores for the electromigration degradation processes warrant discussion, as do the electromigration reliability assessment methodologies. With ρ_GND ~ 10¹⁵ m⁻² observed in this study, and D_core^eff that is not much reduced by grain boundary diffusion (as derived above and in Budiman et al., 2009), the second term in equation [6.2] (i.e. the contribution of the dislocation core diffusion) can indeed no longer be neglected. This means it will have important implications to the fundamental understanding of the electromigration degradation processes, as well as to the electromigration reliability assessment methodologies.

Joule heating effect versus electromigration-induced plasticity

A recent study comparing two sets of samples in which the main difference was the initial microstructures of Cu interconnects (Budiman et al., 2010) aims to provide insights into this question. The first set has been described above (Fig. 6.29) and is expected to have typical initial microstructures of annealed Cu grains. The second set is expected to have plastically deformed microstructures based on our earlier plasticity observations on similar Cu interconnect samples (Budiman et al., 2007a; 2007b; 2009). The experiment has been described in great detail by Budiman et al. (2010).

Electromigration test results for the two sets of samples: nominal versus ‘pre-damaged’ are compared in Fig. 6.30a. The electromigration test results of the nominal samples have been discussed above (Fig. 6.29). The median times to failure (MTFs) here are again represented by the solid features (circles for nominal samples and squares for the ‘pre-damaged’ ones), and the error bars represent the ranges of the failure times coming from the 20 samples from each group at each of the test conditions. All failure times are again normalized with respect to the minimum MTF observed in the present study. The current densities are also normalized with respect to the minimum value, which is 0.5 MA cm⁻². It is clear from these data sets that there is a significant difference in time to failure between samples from the two different groups especially in the low j range (ln j/j_min < 1.95 or j < 3.5 MA cm⁻²).

In Fig. 6.30b, we consider just the MTFs of two sets of samples (the solid data points; without the error bars for clarity). The significant difference in the MTFs between the two sets of samples in the low j range suggests that Joule heating alone cannot be responsible for the deviation of MTF from the n = 1 line at the high j range such as shown in Fig. 6.29b. However, because the ‘pre-damaging’ phase was done at accelerated conditions of high temperature and high current density (at T = 350 °C and j = 3.5 MA cm⁻²) even though for a very brief period of time (50 h), it could perhaps cause very aggressive void growth such that the failure times for the second set of samples become somewhat lower than those of the nominal samples. In order to account for this equivalent lifetime used by the ‘pre-damaging’ phase, we now add the ‘hypothetical’ data points (i.e. the ‘plus’ and ‘minus’ signs) to indicate the shortened lifetime of the ‘pre-damaged’ samples if the ‘pre-damaging’ phase degrades the MTF more than its nominal 50 h owing to the very aggressive void growth.

The ‘equivalent’ lifetimes used by the ‘pre-damaging’ phase (the ‘plus’ and ‘minus’ signs) here were calculated using the proportionality assumption (i.e. MTF(j)ⁿ = constant; MTF′ = (j/j′)ⁿMTF; for the ‘plus’ signs, as the ‘pre-damaging’ phase was actually done at j = 3.5 MA cm⁻² for 50 h, the ‘equivalent’ lifetime used at j = 0.5 MA cm⁻² is 350 h, that is 7 times, 3.5 MA cm⁻² divided by 0.5 MA cm⁻² with n = 1, the nominal 50 h). Even if we assume an extremely aggressive void growth during the ‘pre-damaging’ phase and thus introduce an n = 1.7 such as actually determined from the data shown in Fig. 6.29a for the conditions in the ‘pre-damaging’ phase to the above proportionality calculation, the hypothetically degraded MTF would then be shown as the ‘minus’ signs in Fig. 6.30b. Evidently, there remains a significant gap with the MTFs of the second set of samples.

These data sets thus strongly indicate that Joule heating cannot act alone here in these Cu interconnect samples. In the range of ln j/j_min < 1.95, the MTFs of the ‘pre-damaged’ samples (the square data points) are still significantly reduced from those of the nominal samples even after considering the shortened lifetime owing to the ‘pre-damaging’ phase (the ‘plus’ and ‘minus’ signs). Such a significant difference can be explained by electromigration-induced plasticity which introduces some permanent effects, perhaps in addition to the Joule heating effect. The significant difference here strongly suggests that the second set of samples have also suffered substantially higher electromigration fluxes than those of the first set of samples even though both were tested at the same low j, which further indicates there might be effects of a structural permanent difference between the two sets of samples. We believe that the high j ‘pre-damaging’ phase for 50 h had created dislocation configurations at such high densities that they had accordingly aggravated the electromigration fluxes in the second set of samples beyond the nominal 50 h or even beyond the hypothetically degraded lifetimes owing to the aggressive/extremely aggressive void growth scenarios during the ‘pre-damaging’ phase.

Even though Joule heating is widely cited as the source of the deviation from n = 1 at high j, recent studies (Chang et al., 2003; Hau-Riege, 2006; Labun and Jagjitkumar, 2008; Wang et al., 2004; Wu et al., 2001) both experimentally as well computationally have shown that its effects on the global transport of atoms along the metal interconnect lines are somewhat modest. In the absence of extreme local instabilities (such as hot spots or local meltdown owing to current crowding effects, for instance), the effect of Joule heating is predicted to be merely a rise of between 5 and 10% at high j compared with at low j in the global temperature of the interconnect lines (Chang et al., 2003; Gurrum et al., 2008; Hau-Riege, 2006; Labun and Jagjitkumar, 2008; Wang et al., 2004; Wu et al., 2001). This is insufficient to cause a large drop in MTF at high j that would be required to cause the n to deviate from n = 1 line significantly. This is especially true for the case of the Cu–SiO₂ interconnect scheme, such as used in the present study, owing to the high thermal conductivity of SiO₂ (Wu et al., 2001). For the Cu–SiO₂ interconnect scheme, Wu et al. (2001) for instance using a combination of an analytical thermal model with a two-dimensional (2D) numerical simulation using the finite element method, has reported a less than 7% rise in global interconnect temperature at j = 4.5 MA cm⁻² compared with at j = 0.5 MA cm⁻² and, consequently, a factor of less than 2 in the MTF reduction owing to the temperature rise. The corresponding test conditions in the control data sets (i.e. the nominal samples) in the present study show at least a factor of 20 in the MTF reduction.