Characterization of electromigration-induced short-range stress development in Al(0.25 at. % Cu) conductor line

Aluminum–copper alloy [Al(Cu)] metallurgy has maintained its technological importance in microelectronics since it was reported over 50 years ago that doping with Cu significantly mitigated electromigration degradation in Al interconnects.¹ As the alloy-based interconnect technology quickly matured in the industry, the fundamental mechanism for Cu to slow down the degradation has been a subject of great interest and extensive investigation.^1–8 It is generally agreed that Cu atoms in grain boundaries retard Al grain boundary diffusion due to preferential Cu-vacancy binding.^2,6,8 During electromigration, Al migration occurs only in the (cathode) region where Cu has depleted to below a critical concentration, resulting in the short-range stress development within the Cu depletion region.

The short-range stress gradient was proposed to rationalize the incubation time during the early stage of Al(Cu) electromigration where no mass depletion could be observed by either drift velocity⁴ or resistance⁹ measurements. While the stress development in Al(Cu) conductor lines has been modeled by assuming a critical Cu concentration above which Al diffusivity is significantly reduced,^5,6 we are aware of only two experimental studies to observe the stress development in relation to Cu depletion.^8,10 Both of these experiments employed synchrotron-based real-time x-ray microbeam diffraction and fluorescence measurements as briefly introduced in Sec. II.

Electromigration in metal interconnects has been studied by various synchrotron x-ray microbeam techniques in the past 25 years. With the strain detectability of the diffraction signals, these techniques have proven uniquely valuable in providing insight into local stress evolution during electromigration with micrometer or sub-micrometer spatial resolution.

For example, electromigration-induced stress gradient in passivated 10 μm-wide pure Al conductor lines with a thickness-to-width aspect ratio of 0.05 was directly observed by x-ray microdiffraction experimentation using white x-ray microbeam formed by a pinhole collimator.¹¹ In this study, Al(111) diffractions from properly oriented grains were collected to determine the strain change along the film normal during electromigration. Using a similar technique and employing a tapered glass capillary to form white x-ray microbeam, Kao et al.⁸ reported the simultaneous characterization of changes in both normal strain and Cu concentration in passivated 10 μm-wide Al(0.25 at. % Cu) conductor lines with a 0.05 aspect ratio. These measurements provided direct and quantitative spatially resolved strain analyses in real time during electromigration, with pronounced variations in the spatial distributions either due to counting statistics from limited diffracting grains or microstructural inhomogeneity in the conductor line.

Sub-micrometer white x-ray microbeam formed by Kirkpatrick–Baez mirror was employed to collect Laue diffractions from individual Al grains in passivated 4.1 μm-wide Al(∼0.22 at. % Cu) conductor lines with an aspect ratio of 0.183.^12,13 By tracing the Laue spots and analyzing their shapes during electromigration, it was observed that plastic deformation occurred at an early stage of electromigration before visible damage developed. The plastic deformation involves the generation and lineup of dislocations in response to the stress development, leading to grain bending, polygonization, and rotation. However, the Cu distribution in the conductor lines was not monitored during these measurements, and the relationship between the plastic deformation and Cu concentration was not addressed.

A scanning x-ray microbeam topography technique using monochromatic x-ray microbeam formed by a tapered glass capillary was also developed to characterize electromigration stress development in thin film conductor lines on substrates.^10,14 Based on the high-resolution x-ray topography method pioneered by Lang¹⁵ and the inherent divergence of the incident x-ray microbeam,¹⁶ this technique senses lattice distortions in single crystal surfaces or interfaces from enhanced diffractions with insignificant measurement uncertainties. In these experiments, Si(004) diffraction intensity from the Si(001) substrate underneath the conductor line was used to infer the stress in the conductor line.¹⁶ While the technique does not measure directly in the conductor line, its excellent sensitivity in detecting lattice distortion in the Si surface allows detailed observation of electromigration stress development in 10 μm-wide unpassivated Al lines¹⁴ and a passivated Al(Cu) conductor line,¹⁰ with an aspect ratio of 0.05 in both cases.

Simultaneous scanning x-ray microbeam topography and fluorescence experiments were first attempted to observe both the local stress change and Cu distribution in Al(Cu) conductor lines during electromigration.¹⁰ Though feasibility of the measurement was demonstrated, the results were obscured by the pre-existing local defectivity in the conductor line, as evidenced by the extended lateral extrusion away from the anode end observed after the experiment.

The relationship between copper concentration and short-range stress development in Al(Cu) was characterized, for the first time, using x-ray microbeam fluorescence and diffraction.⁸ In this extensive experimental and modeling work, several important parameters dictating Al(Cu) electromigration were determined, including a stress gradient in the cathode region where the Cu concentration is below a critical value of ∼0.15 at. %. Also, it was proposed that the preferential “electromigration of Cu is accompanied by a backflow of Al rather than vacancies,” and, therefore, “electromigration of Cu in Al(Cu) is much less affected by stress gradients than is electromigration of Al in Al(Cu) or in pure Al.” Besides this study by Kao et al.,⁸ we are not aware of other publications on the experimental characterization of this subject matter.

This paper reports the latest scanning x-ray microbeam topography and fluorescence study of Al(Cu) electromigration to provide another experimental perspective on this topic. Results of the Cu distribution and stress change measurements are interpreted and discussed in Sec. IV. Complementary numerical modeling is discussed in Sec. V, which was carried out to reproduce the observations and interpretations, as well as to extract relevant parameters related to electromigration in Al(Cu).

We report the scanning x-ray microbeam topography and fluorescence characterization of a polycrystalline Al(0.25 at. % Cu) conductor line with 0.5 μm in thickness, 10 μm in width, and 200 μm in length. The line was sputter deposited on an oxidized Si(001) substrate at room temperature and annealed at 400 °C after reactive ion etching (RIE) patterning. As shown schematically in Figs. 1(a) and 1(b) for the top view and cross-sectional view, respectively, the conductor line has a 100 Å titanium (Ti)/600 Å titanium nitride (TiN) liner underneath and resides on a thermally oxidized Si(001) substrate, passivated with 1.5 μm-thick silicon dioxide (SiO₂) deposited at 350 °C by plasma enhanced chemical vapor deposition. The conductor line is connected to wire-bonding pads via tungsten (W) bars as blocking boundaries for electromigration flux divergence, with about a 1 μm overlap between the conductor line and W bars. The SiO₂ passivation above the wire-bonding pads was removed by RIE for electrical connection to an external current source. Note that the specimen is nominally identical to the one characterized in earlier reports.^8,10

The in situ synchrotron-based scanning x-ray microbeam topography and fluorescence measurements were conducted at beamline X20C at the National Synchrotron Light Source of Brookhaven National Laboratory before it was decommissioned, with the instrumentation and technique described previously.^14,16 Briefly, stress in thin film features generates local lattice distortion within the x-ray irradiated volume in the single crystal Si substrate surface, enhancing the diffraction intensity from the substrate.^15,17 Changes in local stress in the film can, therefore, be indicated by the change in the Si diffraction intensity collected around the location of interest. While this technique can be used to detect change in the film stress with high sensitivity,¹⁴ it does not easily distinguish between tension and compression in the thin film features since both generate lattice distortion in the Si surface and induce such intensity enhancement.¹⁸ 

Monochromatic x rays of 9.0 keV were condensed by a tapered glass capillary, producing an incident microbeam with a projected size of approximately 10 × 15 μm² on the sample surface. As shown schematically in Fig. 2, the Si(004) diffraction from the Si surface was collected using a scintillation detector in a symmetric reflection configuration at 2θ ≈ 61° to observe the local stress change in the conductor line; the Cu Kα fluorescence was measured with a Si(Li) solid-state detector to monitor the distribution of Cu concentration.

The Si(004) diffraction was first optimized by tilting the sample stage about the two in-plane axes to find the maximum intensity on bare Si. The distributions of the Si(004) and Cu Kα intensities were then obtained simultaneously by translating the sample stage laterally along the x- and y-directions to bring different locations of the sample into the x-ray microbeam, as illustrated in Fig. 2. Specifically, sets of 11 evenly spaced line-scans across the conductor line were conducted repetitively between 15 and 185 μm from the cathode end of the line before and during electromigration. The closest distance of 15 μm from the end of the conductor line was chosen to avoid influence from the intrinsic stress in the W bars. To normalize for the drift in the incident beam intensity, the measurement time at each step of the line-scan was determined by the upstream ion chamber monitor before the x-ray beam entered the glass capillary. Each line-scan distance (in the y-direction) is 160 μm which took about 3.3 min, and each set of 11 line-scans took approximately 0.6 h to complete.

As examples, Fig. 3(a) shows four line-scans of Cu Kα collected at 15, 32, 49, and 66 μm from the cathode end before electromigration (dashed lines) and after ∼9 h of electromigration (solid lines), where the depletion of Cu in the region of the conductor line can be observed. Figure 3(b) shows the corresponding line-scans of Si(004) intensity, where significant variation induced by electromigration can be seen clearly. To quantify the line-scan results, the intensity peaks across the conductor line were fitted with the Gaussian function. With the Cu Kα line-scans, the local Cu concentrations were determined by the fitted peak areas, calibrated by setting 0.25 at. % to the averaged peak area over the 11 locations collected before electromigration. The detection limit was about 0.08 at. % below which the Cu concentrations were assigned to 0 at. %. For the Si(004) line-scans, the fitted peak area divided by the fitted background was defined as the Si(004) intensity contrast. With the complimentary numerical modeling discussed in Sec. V, the evolutions of the Si(004) intensity contrast provide evidence of the short-range stress development in the Al(Cu) conductor line under electromigration.

Electromigration experiment was conducted under a constant DC current of 20 mA (0.4 MA/cm², 4× higher than the previous study¹⁰) at 303 °C specimen temperature determined by its temperature coefficient of resistance measurement. The resistance of the conductor line was monitored with four-point measurement during the 24 h of electromigration experimentation. As shown in Fig. 4, the resistance changed very little during the first 5.3 h of incubation time before consistent mass depletion took place in the conductor line, where the incubation time is defined as the time for the electron-wind driven Al flux to exceed the stress-induced backflow, leading to mass depletion from the cathode and resistance increase.

The subsequent resistance increase implies the onset of Al depletion from the cathode end. It took about 1.5 h for Al to deplete off the W bar, as signaled by the abrupt resistance jump at 6.8 h when Ti/TiN liner started to shunt the current, which was most likely due to the change in contact resistance and local Joule heating in the liner. For the remainder of the experiment, the resistance generally increased steadily, except for during the 6.8–12.7 and 14.8–16.8 h periods, suggesting steady Al depletion off the cathode end of the conductor line. The irregularities in the resistance shift were also observed previously¹⁹—the reason is not clear but may be related to change in the Ti/TiN liner under high shunting current density and excessive local heating.

Figure 5 includes the overall and zoomed-in postmortem optical micrographs of the Al(Cu) conductor line after 24 h at the electromigration stress conditions and subsequently ∼37 h of high temperature storage at 303 °C with no electrical stressing. An approximately 16 μm-long Al depleted region at the cathode end of the line was caused by electromigration, corresponding to a depletion rate of ∼0.86 μm/h after the incubation period. Also, fracture in the SiO₂ passivation at the anode end of the line is observed, which is presumably a result of the stress from electromigration-induced Al₂Cu precipitation and Al pileup and is discussed along with the x-ray measurements in Secs. IV B and IV C.

To further inspect the damage at the anode end, the sample was inspected by electron beam techniques after most of the SiO₂ passivation was removed by hydrofluoric acid (HF) wet etch. Figure 6(a) shows the scanning electron microscopy (SEM) image in the anode region, revealing details of the ∼40 μm long fracture in the remaining passivation with no apparent Al extrusion. Figure 6(b) shows the corresponding energy dispersive spectrometry (EDS) mapping, identifying the presence of the ∼2 × 6 μm² electromigration-induced Al₂Cu precipitation at the anode end that remained after the subsequent 37 h of high temperature storage.

In this section, the local Cu concentrations and the Si(004) intensity contrasts extracted from the in situ line-scans before and during the electromigration experiment are summarized; spatial distributions are analyzed along the conductor line at different stages and discussed in Secs. IV A and IV B, and their time evolutions at various locations along the conductor line are also explored and discussed in Sec. IV C. The measured Cu concentration and the Si(004) intensity contrast were plotted together for direct observation of their relationship, and these results were reproduced by the numerical modeling discussed in Sec. V to provide a quantitative interpretation of the relationship between Cu and Al electromigration.

Figure 7 shows several snapshots of the spatial distribution of Cu concentration at various times during the initial ∼15 h of electromigration. Each data set includes 11 individual line-scan measurements at different locations (starting from the anode end). With each line-scan taking about 3.3 min, each data set took a total of ∼0.6 h to complete. For convenience, the times listed in the legend refer to the average times over each set of measurements and should be treated as approximate. Note that the measurements were limited to between 15 and 185 μm from the cathode end to avoid the influence from the W bar at the line ends. Therefore, the 11 line-scans in each data set were conducted at varying times, with ∼0.3 h earlier at 185 μm and ∼0.3 h later at 15 μm than the time listed in the legend. For example, for the 0.98 h data set shown in Fig. 7, the Cu concentration and Si(004) intensity contrast were measured between ∼0.68 h (at 185 μm) and ∼1.28 h (at 15 μm). This representation allows the observations of overall spatial distributions with acceptable uncertainty, considering the relatively slow electromigration process under the experimental condition.

Prior to electromigration, Cu was evenly distributed over the entire length as expected, with the error bars representing ± one standard deviation from three measurements at each location prior to electromigration. Upon electromigration, the general trend of Cu redistribution is observable, with consistent depletion from the cathode and accumulation into the anode. For example, after ∼3.7 h, the Cu concentration was reduced below the detection limit of about 0.08 at. % within the first 32 μm, and it started to decrease at 49 μm. After ∼8.1 h, Cu depletion extended to ∼83 μm with a noteworthy reduction in the Cu concentration. For subsequent discussions, the distance of the region with apparent Cu depletion or reduction is termed “effective Cu depletion length L_eff” which increased with time over the 15 h of electromigration. It can then be roughly determined from Fig. 7 that L_eff was approximately 49 and 83 μm after 3.7 and 8.1 h of electromigration, respectively. At the end of this 15 h period, Cu has been fully depleted over up to ∼134 μm from the cathode end. Presumably, the Cu migrated into the anode region, as evidenced by the excessive Cu Kα intensity at 185 μm that suggests Al₂Cu precipitation in the x-ray irradiated area.

Other notable observations can be made from Fig. 7. At about 1 h of electromigration, the Cu concentration at 66 μm was higher than its solubility limit of 0.4 at. % in Al at 303 °C,¹⁹ indicating temporary Cu supersaturation or segregation.²⁰ Since Cu electromigration occurs primarily along grain boundaries in polycrystalline Al(Cu) conductor lines, this could be attributed to Cu flux divergence from sudden change in grain structure.² At 185 μm (or 15 μm from the anode end), Cu concentration approached the solubility limit within an hour of stress and subsequently stayed relatively unchanged until it abruptly increased beyond the solubility limit as a result of supersaturation or formation of Al₂Cu precipitate in the x-ray irradiated area.

The spatial distributions of Si(004) intensity contrast are also shown in Fig. 7, which is related to the magnitude of local stress in the conductor line as described previously. To discuss these results, it is important to mention that the overall conductor line was originally under slight equibiaxial tensile stress at the experimental temperature of 303 °C prior to electromigration. This is because of the thermal history in the fabrication process with 400 °C post-Al-deposition annealing and 350 °C SiO₂ passivation. It can be observed that the initial thermal stress was fairly uniform along the conductor line before electromigration, with the error bars determined from three sets of identical measurements.

Upon electromigration, significant changes in Si(004) intensity contrast were observed particularly in the Cu-depleted region. These results clearly indicate significant short-range stress development within the Cu-depleted region, starting at the very early stages of electromigration at the cathode end and extending with the growing Cu-depleted region. For the convenience of discussing this 15 h of electromigration, the conductor line is classified into three ranges, including range I from the cathode end to ∼66 μm, range II between ∼66 and 134 μm, and range III from ∼134 μm to the anode end.

In the upstream region of range I, the Si(004) intensity contrast at 15 μm sharply increased within 1 h of electromigration and stayed elevated afterward. Since the conductor line was under slight tension prior to electromigration, this implies that the tensile stress quickly increased as Al started to migrate from the cathode end after Cu was depleted, further enhancing the Si(004) intensity contrast in the region. On the other hand, the Si(004) intensity contrast shows a different trend in the downstream region between ∼50 and 66 μm. For example, it decreased from the initial value at 50 μm after ∼3.7 h, suggesting a reduction in the initial tensile stress. Similarly, at 66 μm, or the downstream end of range I, it reached a minimum before starting to increase at ∼5.1 h, implying relief of the initial tensile stress followed by the development of compressive stress.

While more detailed time evolutions of the Si(004) intensity contrast are provided in Fig. 8 and discussed in Sec. IV C, these observations can be understood by correlating with the effective Cu depletion length L_eff, recognizing that Cu solutes effectively mitigate Al electromigration.⁵ As Al migration was blocked by the presence of Cu solute at the end of the effective Cu depletion length L_eff, Al accumulation deposited at the grain boundaries first reduced the initial thermal tensile stress and subsequently induced compressive stress, causing the Si(004) intensity contrast to reduce to a minimum before increasing. A similar trend was observed beyond range I throughout most of the conductor line.

As previously shown in Fig. 4, the incubation time of the Al(Cu) conductor line is ∼5.3 h before resistance increase due to mass transport from the cathode end. Hu et al. attributed the incubation period to the initial development of a short-range stress gradient bounded by the two Al flux divergence sites: the W bar at the upstream (cathode) end and presence of Al₂Cu precipitates retarding Al migration at the downstream end.⁴ The stress gradient induces Al backflow that counteracts the electron-wind driven Al flux.²¹ Assuming steady-state stress gradient, a critical length L_c can be determined from the current density j through the threshold product $(j× L c)=Δ σ emΩ/ Z Al ∗eρ$⁠, where Δσ_em is the difference in electromigration-induced stress between cathode and anode ends of the conductor line, Ω is the Al atomic volume, e is the absolute of the electronic charge, and $Z Al ∗$ and ρ are the Al effective valence and resistivity, respectively. The threshold product (j × L_c) defines the electromigration immortality condition below which the stress gradient induced backflow exactly balances the electron-wind driven flux.²¹ Note that the immortality condition only applies when the electromigration length is fixed, such as in the case of pure Al line with terminating W bars at both ends.¹¹ For the Al(Cu) conductor line in this study, the critical length can be regarded as the previously defined effective Cu depletion length L_eff that continuously extends over time due to preferential Cu electromigration. Therefore, the ∼5.3 h incubation period corresponds to the time for the effective Cu depletion length L_eff to reach the critical length L_c.

Referring to Fig. 7, the L_eff value can be estimated from the Si(004) intensity contrast at ∼5.1 h which is the measurement closest to the incubation time. The electromigration-induced stress gradient appears to span over range I, with tension at the cathode end and compression at ∼66 μm. The effective Cu depletion length L_eff at the end of the incubation period can, thus, be estimated to be approximately 66 μm. For an otherwise nominally identical pure Al conductor line, the threshold (j × L_c) product was determined to be 3200 A/cm by a previous x-ray microdiffraction experiment.¹¹ This translates to a critical length L_c of 80 μm under a current density of 0.4 MA/cm² used in the present study. Considering the experimental uncertainties associated with the 17 μm step size between measured locations, the 10 μm projected x-ray beam size on the specimen, and the range over which the stress in the conductor line influences the Si lattice,¹⁷ the critical length estimated from this experiment for the Al(Cu) line is in good agreement with the value for a pure Al line. This consistency confirms the effectiveness of Cu solute in blocking Al grain boundary diffusion, and that the incubation time commonly observed in Al(Cu) interconnects is dictated by the time for Cu to migrate off a distance equivalent to the Al critical length L_c.^4,22 Also, it can be concluded that range I contained the initial short-range stress gradient that developed and extended with Cu depletion (with electromigration-induced tensile stress at the cathode end and compressive stress at the downstream end), counteracting the electron wind to prevent Al electromigration during the incubation period. The stress gradient fully developed after about 5.3 h when the compressive stress at the downstream end of range I (∼66 μm from the cathode end) reached the elastic limit.²³ 

As the effective Cu depletion length L_eff extended beyond the critical length L_c after the incubation period, the Al backflow from the stress gradient could no longer balance the electromigration flux. Mass transport was then initiated, as evidenced by the resistance increase shown in Fig. 4. Since the compressive stress at 66 μm presumably reached its limit at about 5.3 h, the subsequent increase in the Si(004) intensity contrast (e.g., at ∼8.1 h shown in Fig. 7) can be attributed to localized plastic flow in the conductor line. For example, lattice bending, rotation, and polygonization have been observed as the mechanism for plastic deformation during electromigration in Al conductor lines.^12,13 Also, plastic deformation through line thickening is expected in conductor lines with small thickness-to-width aspect ratio, lifting the SiO₂ passivation above and stressing the interface between the surrounding passivation and Si substrate. These mechanisms can affect the Si surface below the conductor line or the nearby SiO₂ passivation layer, further enhancing the Si(004) intensity at the downstream end of L_eff.

Based on this interpretation, the evolution of the Si(004) intensity contrast within range II can also be understood by the stress change in the conductor line. As shown in Fig. 7, the Si(004) intensity contrast remained relatively unchanged in range II before the incubation period, since Al migration and associated stress development was hindered by the presence of Cu solute in the region. As Cu depletion and the associated Al pileup extended into range II after the incubation period, the local stress and, thus, the Si(004) intensity contrast underwent several stages of evolution in the region, including (1) little change in Si(004) intensity contrast before Al migrated to the location, (2) initial reduction in thermal tension that decreased Si(004) intensity contrast, (3) complete elimination of thermal tension that caused the Si(004) intensity contrast to reach a minimum, (4) development of compression that increased Si(004) intensity contrast, and (5) plastic flow once the compression limit was exceeded, further inducing Si lattice distortion and enhancing Si(004) intensity contrast. Therefore, range II envelops the portion of the conductor line where localized plastic flow took place during the 15 h of electromigration.²³ 

It is also important to observe from Fig. 7 that the Si(004) intensity contrasts (thus, the stress levels) at ∼1 h of electromigration remained relatively unchanged in range II, while the Cu concentrations had changed significantly in this region. The apparent independence of the local stress on Cu concentration outside the Cu depletion region suggests that the preferential electromigration of Cu is accompanied by a compensating backflow of Al from anode to cathode. The absence of significant stress change from Cu electromigration was also observed by Kao et al. and was attributed to Cu-vacancy binding.⁸ The mechanism was originally proposed by Rosenberg² to rationalize the effect of Cu on slowing Al electromigration, where “binding between solute and boundary defects,” such as vacancies, reduces the Al mobility. Upon Cu electromigration, the accompanying downstream vacancy flux from the Cu-vacancy binding causes a flux of Al against the electron wind toward the cathode end. The reversal of Al flux in Al(Cu) has also been illustrated by molecular dynamics simulations, particularly when the electromigration driving force for Cu is at least twice as large as for Al.²⁴ 

Range III encompasses the rest of the conductor line where Cu had not been depleted during the 15 h of electromigration, as seen Fig. 7. The Si(004) intensity contrast remained relatively unchanged at around 150 μm in the upstream region of range III, again indicating no Al electromigration and, thus, no stress change before Cu depletion reached this region. While Al₂Cu precipitation is expected at the anode end of the conductor line early in the electromigration process, it is beyond the closest measurement location at 185 μm and could not be observed directly. The Cu concentration at 185 μm remained relatively stable between the initial 0.25 and the 0.4 at. % solubility limit until it sharply increased after ∼10 h (the detailed time evolutions are shown in Fig. 8 and discussed in Sec. IV C). On the other hand, the Si(004) intensity contrast at 185 μm consistently increased over the same time frame before abruptly dropping at ∼11 h, which is unexpected since Al migration was blocked by the presence of Cu. The correlation between the changes in Cu concentration and the Si(004) intensity contrast is not clear at this time, although it is hypothesized that the intrinsic stress of the Al₂Cu precipitate nearby or further downstream affected the Si surface at 185 μm and enhanced the Si(004) intensity.

To examine how the Cu concentration and Si(004) intensity contrast changed during electromigration in more detail, Fig. 8 shows their time evolutions at eight of the 11 line-scan measurement locations along the conductor line where each simultaneous measurement took ∼3.3 min. At 15 μm near the upstream cathode end of range I, Cu depleted in the first ∼2 h while the Si(004) intensity contrast quickly rose in an hour and approximately plateaued through the rest of the time. The rise in the Si(004) intensity contrast suggests an immediate increase in tensile stress upon electromigration as Al migrated away from the upstream region of range I.

At 66 μm, or the end of the critical length L_c, the Si(004) intensity contrast stayed roughly unchanged during the first ∼3 h due to no Al migration or stress change. The Si(004) intensity contrast started to decrease right before the Cu started to migrate away, indicating that Al migration started to accumulate near this location and release the initial thermal tension. At ∼4.5 h, the Cu concentration dropped below 0.2 at. % and the Si(004) intensity contrast reached the minimum, implying that the Al migrated into this location completely released the initial thermal tension. Subsequent increase in the Si(004) intensity contrast is observed at ∼5.3 h, hinting at a development of compression. Referring to the 5.1 h of incubation period and mass depletion afterward, as observed electrically in Fig. 4, the remarkable increase in the Si(004) intensity contrast can be attributed to the plastic flow. Similar electromigration stress evolution can also be observed in other locations within range II between 66 and 134 μm, with the five stress evolution stages described previously in Sec. IV B closely correlated with the Cu concentration evolution.

The location at 168 μm is within range III and was beyond the effective Cu depletion length L_eff throughout the 15 h of electromigration. Therefore, Al migration is not expected and, thus, the local stress stayed in the first stage of stress evolution, in agreement with the relatively unchanged Si(004) intensity contrast shown in Fig. 8. It appears that the Si(004) intensity contrast started to shift after ∼9 h without first reaching the minimum. The reason for this evolution is not clear, though it is suspected that the intrinsic stress of the Al₂Cu precipitate forming in the anode region had a longer-range influence on the Si lattice distortion at this location. Also, the passivation fracture observed in the anode region shown in Figs. 5 and 6(a) may have been initiated and altered the stress field.

At 185 μm, or the measured location closest to the anode end, the Cu concentration quickly increased to the 0.4 at. % solubility limit and maintained at this level up to ∼10 h, and the Si(004) intensity contrast consistently increased during the time frame after the initial fluctuation. Since Al₂Cu precipitate at the anode end is expected to form after the solubility limit is exceeded, it can be speculated that the growing Al₂Cu precipitate had a longer-range influence on the Si surface and enhanced the Si(004) intensity contrast in the neighboring region. At ∼11 h, the Cu concentration appeared to increase beyond the solubility limit, implying that the Al₂Cu precipitate had grown into the x-ray irradiated area and contributed to the Cu Kα intensity measured at 185 μm. On the other hand, the Si(004) intensity contrast precipitously dropped, corresponding to a sudden change in the Si lattice distortion. These observations can again be rationalized by the growth of Al₂Cu precipitate of which the intrinsic stress had a longer-range effect on the neighboring Si surface and thus on the Si(004) intensity contrast. It is also possible that the growing precipitate ruptured the above passivation layer and thereby altered the Si lattice distortion at the nearby Si/SiO₂ interface [see the fracture observed in Figs. 5 and 6(a) after a total of 24 h of electromigration]. These results demonstrate the sensitivity of the topographic technique in detecting stress changes in thin film features on Si substrates.

To summarize the experimental observations from all the line-scan measurements, Fig. 9 shows the Cu concentration as a function of position along the conductor line and time during a total of 21.5 h of electromigration. The Cu concentration distribution is represented by the false color map and the contour lines, noting that the initial Cu concentration was 0.25 at. % and the Cu solubility limit in Al is about 0.4 at. % at the experimental temperature. Each data point in constructing the map was determined by the corresponding line-scan measurement at the specific location and time. Note that each line-scan measurement took ∼3.3 min which gives rise to uncertainty in the time axis. However, this time uncertainty is insignificant compared with the timescale of the electromigration process under the experimental condition. Also, the map is cropped at 0.5 at. % (area shown in gray) to reveal more details at lower concentrations.

In general, Cu was depleted from the cathode end at a rate of about 10 μm/h under the stress condition during the first 15 h, as the electron-wind driven Cu flux dominated the process while the back-diffusion of Cu from concentration gradient was insignificant in slowing down the Cu depletion. Also, Al₂Cu precipitation appears to occur at the anode end that contributed to the Cu Kα measurement after ∼10 h, causing the measured Cu concentration to exceed the 0.4 at. % solubility limit.

Figure 10 shows the Si(004) intensity contrast in false color as a function of position and time, overlapped with the Cu concentration contour lines from Fig. 9 to highlight the correlation. As can be observed, most of the changes in the Si(004) intensity contrast, hence the electromigration-induced stress, occurred in the region where the Cu concentration was reduced below detectability. A clear boundary at ∼60 μm along the time axis can be seen between ranges I and II, starting after the 5.3 h incubation period and persisting throughout the rest of the electromigration experiment. As previously described in reference to Fig. 7, once the electromigration-induced stress gradient in range I was fully established after the incubation period, stress change started in range II and extended to follow Cu depletion. As seen in Fig. 10, the extension of range II that followed the 0.1 at. % Cu concentration contour line conforms to this notion.

Since the extension of range II was accompanied by the resistance increase and mass depletion, the enhancement in the Si(004) intensity contrast in range II is attributed to electromigration-induced compression and the subsequent plastic deformation at the downstream end of the growing Cu depletion region. After ∼18 h, the enhanced Si(004) intensity contrast in range II coalesced with that in range III from the Al₂Cu precipitation and the associated passivation fracture at the anode. Therefore, the extensive fracture observed postmortem and shown in Figs. 5 and 6 was mostly likely initiated by the precipitation of Al₂Cu at the anode end and subsequently propagated upstream as the stress gradient approached and eventually bridged the stress field from the precipitate.

A raster scan was conducted to map the Cu Kα and Si(004) intensities over the area encompassing the conductor line after 21.5 h of line-scan measurements. To avoid relaxation, electromigration stress was continued during the raster scan that took an additional 2 h to complete. Figure 11(a) shows the false color contour map of Cu Kα intensity with evidence of Al₂Cu precipitation at the anode end that was also observed by the EDS analysis shown in Fig. 6(b). Figure 11(b) shows the distribution of Si(004) diffraction intensity which is related to the lattice distortion in the Si surface from the stress in the thin film features above. Note that the conductor line spans between 0 and 200 μm, beyond which are the W bars connecting the conductor line ends to the probe pads.

Based on the qualitative analyses discussed previously, the variation in the Si(004) intensity along the x-direction can be explained by the following. Beyond the cathode end of the conductor line (x < 0), the enhanced Si(004) intensity was mainly caused by the stress in the W bar and the Ti/TiN liner underneath. A recess in the Si(004) intensity profile at the beginning of the conductor line (approximately between 0 and 20 μm) was presumably due to the Al depletion shown in Fig. 5. The profile between 20 and 160 μm indicates an electromigration-induced stress gradient, with tension in the upstream region transitioning into compression and plastic deformation in the downstream region. At the anode end (x = 200 μm), significant enhancement in the Si(004) intensity around the Al₂Cu precipitate can be seen in Fig. 11(b), extending up to ∼30 μm beyond the precipitate into the conductor line. This observation supports the interpretation of the measurements at 185 μm (see Figs. 7 and 8) that the precipitate exerted a longer-range influence in the neighboring Si surface.

Preliminary Cu simulation results are shown by the dashed line in Figs. 7 and 8. Adopting $D Cu eff=1.0× 10 − 9 c m 2/ s$ and ρ = 5.9 × 10⁻⁶ Ω cm at 303 °C,¹⁹ agreement with the experimental results for j = 4 × 10⁵ A/cm² was achieved by $Z Cu ∗=−5.6$⁠. The apparent discrepancy at low Cu concentrations between the model calculations and the experimental data is mainly due to the Cu detectability limit (∼0.08 at. %) below which the concentration was set to 0 at. %. Also, the experimental data at 185 μm deviated significantly from the calculation after ∼10 h of electromigration, which was a result of Al₂Cu precipitation at the anode end contributing to the Cu Kα measurement. As mentioned previously in Sec. IV A, the localized high Cu concentration at ∼66 μm at 0.98 h observed in Fig. 7 was most likely due to Cu flux divergence from an abrupt change in the grain structure. The $| Z Cu ∗|=5.6$ from this preliminary study is lower than the previously reported range between 6.6 and 16.8 as summarized by Kao et al.¹⁹ Since $Z Cu ∗$ cannot be extracted from the experimental data independently of $D Cu eff$⁠, a more accurate estimate is being attempted by analyzing the relaxation data collected after the electromigration current was turned off.²³ Nevertheless, the simulation and the parameters used provide a satisfactory description of Cu electromigration in the Al(Cu) conductor line, as well as support the interpretation of the Si(004) intensity contrast evolution in terms of short-range stress development.

Preliminary Al simulations were conducted by adjusting relevant material parameters in Eq. (8) to reflect the short-range stress development discussed in Sec. IV, including a maximum stress gradient fully developed over the critical length L_c of 66 μm from the cathode end within the 5.3 h incubation time. Figure 13 shows the simulated profiles along the conductor line at various times during the electromigration process, with natural Al atomic density n_Al,0 = 6.04 × 10²² cm⁻³, j = 4 × 10⁵ A/cm², ρ = 5.9 × 10⁻⁶ Ω cm, Ω = 1.7 × 10⁻²³ cm³, and B = 50 GPa.²⁶ Also, based on the maximum stress gradient Δσ_EM/Δx = 3.3 MPa/μm over 120 μm reported by Kao et al.,⁸ the upper and lower limits of the atomic density n_Al were estimated through Eq. (7) to be (1 + 4.50 × 10⁻³)n_Al,0 and (1−3.38 × 10⁻³)n_Al,0, respectively. Adopting $D Al eff=2.8× 10 − 10 c m 2/ s$ for 303 °C based on the reported value 8.2 × 10⁻¹¹ cm²/s at 260 °C¹¹ and an activation energy 0.76 eV,¹⁹ consistency between the simulated short-range stress gradient and the interpretation of the experimental results seen in Fig. 7 was achieved by using the following values in the simulation: effective valence $Z Al ∗=−1.9$⁠, critical Cu concentration C_Cu,crit = 0.164 at. %, and an initial Al effective atomic density of (1−1.00 × 10⁻⁵)n_Al,0 which corresponds to an initial equibiaxial stress of 0.5 MPa in tension.

Though the uncertainties of these model parameters are under further analysis, they are in good agreement with the prior studies. The $Z Al ∗$ value is between the previously reported values of −1.6 (for similar, pure Al conductor lines at T = 260 °C)¹¹ and −3.3 [for nominally identical Al(Cu) conductor lines at T = 300 °C].⁸ The C_Cu,crit value is higher than 0.1 at. % assumed by Korhonen et al. for their model calculations,⁵ and it is within the range of 0.15–0.23 at. % experimentally determined by Kao et al.⁸ The initial small tensile stress is consistent with the process-induced thermal stress described previously. Further, by simulating the incubation time for different current densities with these model parameters, the current exponent n in Black's equation of electromigration lifetime²⁸ was estimated to be 2.0. This is in agreement with the reported observation for Al(Cu) interconnects.²² An optimization algorithm is currently under development to assess the correlation and uncertainties of these model parameters.

The present experiments demonstrate the capability of scanning x-ray microbeam topography in detecting real-time composition and stress changes in Al(Cu) conductor lines induced by electromigration. Unlike the direct strain measurements from Al diffraction reported previously,^8,11 the topography technique senses the lattice distortion in the Si surface resulted from the stress in the conductor line. Complemented by the numerical modeling, material parameters and stress levels were estimated to confirm the short-range stress development in Al(Cu) lines observed by Kao et al.⁸ Also, the independence of local stress on the Cu concentration outside the Cu depletion region supports the Cu-vacancy binding model where a concurrent equal backflow of Al minimizes the stress change.⁸ 

Due to the nature and sensitivity of the topography measurement, other phenomena that influence the Si surface can also be observed. For example, it was observed that significant change in Si lattice distortion occurred during electromigration at the anode end. Similar observation was also made in the previous topography measurements of Al(Cu) conductor line by Wang et al.¹⁰ which was attributed to the compressive stress from the electromigration-induced mass pileup in the conductor line. However, based on the present results, the change in the Si lattice distortion at the anode end in the early stage appears to be associated with the intrinsic stress of the Al₂Cu precipitate. The extensive passivation fracture observed postmortem in the anode region was presumably initiated by the precipitation, and the fracture propagated upstream as the stress gradient extended near the anode region in the later stage of the electromigration experiment.

The short-range stress gradient described here was further confirmed qualitatively by the post-electromigration relaxation experiments after the electrical current was turned off while the sample was kept at 303 °C. It was observed that the Si(004) intensities measured in the cathode region (at 15 and 32 μm from the cathode end) show ∼30% decrease within the first 5 h, indicating the relaxation of tensile stress previously generated by electromigration. On the other hand, no significant or consistent trend can be observed in the Si(004) intensity contrasts in the region where irreversible plastic deformation was expected. Further analyses are in progress to estimate Cu and Al diffusion parameters from the relaxation data, and physical failure inspection will be conducted to obtain further evidence of plastic deformation in the conductor line.

Since the present experiment did not measure the stress in the conductor line directly, the maximum stress gradient of Δσ_EM/Δx = 3.3 MPa/μm over 120 μm obtained by Kao et al.⁸ was used for the model calculations. Note, however, that these values were used merely to estimate the upper and lower stress limits for the conductor line from which the boundary conditions in the Al atomic density were set for the numerical modeling. The (j × L_c) product and other important material parameters, including the initial thermal stress in the conductor line, the effective valences $Z Cu ∗$ and $Z Al ∗$ for Cu and Al electromigration, and the critical Cu concentration C_Cu,crit above which Al migration was assumed to be blocked, were all obtained by matching the model calculations with the present experimental observations and are in good agreement with previous studies.^8,11,21

Scanning x-ray microbeam topography and fluorescence was employed to study the detailed relationship between the Cu concentration and the stress change during electromigration in a passivated polycrystalline Al(0.25 at. % Cu) conductor line. Though this technique does not measure stress directly from the conductor line, it detects the changes in stress in thin film features and their interfaces on a single crystal substrate with high sensitivity. Quantitative analyses can be accomplished through proper calibration and complimentary modeling. The method can also be valuable in the study of other material systems with thin film features on the single crystal substrate, such as Cu alloy metallization or various epitaxial films.

Observations in this study include the preferential electromigration of Cu solute and the subsequent development of the short-range stress gradient in the Cu-depleted region. Al₂Cu precipitations occurred at the anode end in the early stage and its intrinsic stress appears to initiate the passivation fracture. Meanwhile, once Cu depletion exceeded the critical length, plastic deformation occurred at the downstream end of the extending stress gradient. The stress gradient eventually approached the anode end which presumably propagated the fracture upstream.

The measurements also evidence the development of the short-range stress gradient from Al migration in the cathode region where the Cu concentration is below ∼0.16 at. %, providing another experimental observation to support the previous x-ray microdiffraction measurements by a different group. The preferential electromigration of Cu solute outside the Cu depletion region did not induce observable stress change in the conductor line, except for the intrinsic stress from Al₂Cu precipitation at the anode end. This supports the hypothesis that Cu electromigration takes place with concurrent backflow of Al through Cu-vacancy binding. Preliminary numerical modeling was conducted to reproduce the experimental results using model parameters (e.g., effective diffusion coefficient and effective valence of Cu and Al, tensile and compressive stress limits of the Al conductor line, etc.) that are consistent with previously reported values. The simulated current exponent n is also in agreement with the observed value of 2 for Al(Cu) interconnects, further validating the interpretation of the scanning x-ray microbeam topography measurement results.

The authors are indebted to I. C. Noyan of Columbia University for pioneering the scanning x-ray microbeam topography technique in characterizing thin film stresses. We thank IBM Research Division for the generous resources to sponsor the experiment, including sample preparation by C.-K. Hu and x-ray microbeam measurement support by J. Jordan-Sweet and S. K. Kaldor. Insightful discussions with G. S. Cargill III are gratefully acknowledged. We also thank the Research, Scholarship, and Creative Activities (RSCA) office of the State University of New York at New Paltz for funding the summer research opportunities. The experiment was conducted at the National Synchrotron Light Source, Brookhaven National Laboratory while one of the authors (P.-C.W.) was at IBM Microelectronics Division, supported by DOE Contract No. DE-AC02-76CH00016.

The authors have no conflicts to disclose.

P.-C. Wang: Conceptualization (lead); Formal analysis (lead); Investigation (lead); Writing – original draft (lead). K. T. Cavanagh: Data curation (equal); Methodology (equal); Writing – review & editing (supporting). J. S. Gordineer: Data curation (equal); Methodology (equal); Writing – review & editing (supporting). N. M. Caprotti: Software (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.