Measuring residual stresses in individual on-chip interconnects using synchrotron nanodiffraction

The miniaturization of electronic devices is one of the most important driving forces for advances in the semiconductor industry. This trend has led on-chip interconnect to evolve from μm scale to nm scale in both width and height. As the interconnect dimensions are reduced, these narrow metal interconnects are also subjected to higher current densities.¹ The effects of electromigration (EM) have become more pronounced, making EM design a critical focus in the semiconductor field.^2–5 

Over the years, several multi-physics electromigration models have been developed to understand the failure mechanisms and predict the failure time.^6–13 However, there are errors in these models, and some have not yet been experimentally verified. Recognizing this gap, a new 3D general coupling model was proposed.¹⁴ To support the theoretical framework and ensure its validity, experimental verification is essential. Moreover, a critical part of this verification process involves understanding the stress distribution within interconnects since stress migration affects EM differently under different conditions.¹⁵ 

X-ray nanodiffraction is a nondestructive method that offers high resolution for stress measurements in micro-sized structures, providing information about the lattice expansion along the entire interconnect. Several studies have characterized the stress distribution in interconnect structures. Lee et al. applied synchrotron x-ray techniques to study Sn electromigration and whisker growth in Blech structures. Their study not only indicated the Sn depletion at the cathode and whisker formation at the anode but also linked the observed Sn whiskering to internal stress resulting from atomic accumulation.¹⁶ 

In addition to Sn, copper (Cu), the main material in on-chip interconnects, has also been studied. Hsu et al. employed x-ray nanodiffraction to analyze thermal strain in nano-twinned Cu and regular Cu redistribution lines.¹⁷ Lin et al. measured the strain at different points along a pure Cu line during electromigration and found non-uniform lattice expansion caused by electron flow and described the mechanism that leads to electromigration-induced failure, especially when the electron-induced strain exceeds the yield point.¹⁸ However, the structure used in this paper is the dog-bone shape (mainly used to study the Joule heating effect during electromigration), with a metal line connected to sizable pads, which influenced the results through mechanical constraints.

In our research, we employed x-ray nanodiffraction to analyze pure copper with the Blech structure. This structure can be used not only to determine the critical length but also to measure the drifty velocity.¹⁹ Notably, no existing studies have reported on the use of Blech structures in copper to examine potential residual stresses. The purpose of our study is to demonstrate that the residual stress in micro-sized Cu lines can be reliably measured using synchrotron nanodiffraction and that this method can measure the stress state under different EM test conditions. It can be considered as a proof-of-principle study, and we discuss the implications of the current ex situ results on possible strategies for future in situ measurements.

The sample fabrication process starts with the growth of 300 nm thick silicon dioxide (SiO₂) by thermal oxidation on the silicon (100) substrate. Then, we deposited a 300 nm TiN film via sputtering, patterned it using lithography and etching, and conducted plasma etching to prevent oxide layer formation. Cu films with a thickness of 200 or 500 nm thick were sputtered onto the TiN layer at room temperature. The Blech structure is patterned by photolithography and wet etching, as shown in Fig. 1(a). The detailed process can be found elsewhere in our previous study.²⁰ As depicted in Fig. 1(b), the x-ray analysis focused on regions where the Cu stripes were 60 μm long and 4 μm wide, with each sample containing five sets of these stripes connected in series.

The electromigration tests were conducted using an in-house setup, with the equipment specifics available in a previous work.²⁰ Samples were tested in a $3.75 × 10 − 6$ Torr vacuum to avoid oxidation and under different current stresses and temperatures. The testing details for each sample are provided in Table I. After the test, the microstructures of each sample under different conditions were examined using scanning electron microscopy (SEM, Hitachi Regulus 8230).

The nanodiffraction measurements were performed using the nanodiffraction endstation²¹ at the NanoMAX beamline²² at MAX IV Laboratory in Lund, Sweden. At this beamline, a spatial resolution down to 50 nm can be reached, allowing studies of very small samples. It accommodates two optical microscopes used to navigate to the measurement position and align the sample to the x-ray focal position. Throughout the measurement process, a monochromatic x-ray beam with an energy of 14 keV and a spot size of 62 nm in the focal plane of the Kirkpatrick–Baez (KB) mirror focusing optics was employed.²³ The diced samples were vertically mounted on aluminum flat holders, as shown in Fig. 1(c), and the diffracted signal was collected in reflection geometry by a downstream Pilatus 1M area detector at a sample-to-detector distance of 148.1 mm (a LaB6 standard calibrated the position).

The Cu lines of interest were located within 50 μm from the downstream edge of the Si wafer. Coarse positioning was performed by tilting the samples up to 30° around the ω axis, which allowed visual access for the online optical microscope. Once the line was correctly positioned, the sample was tilted back to give an incidence angle α = 2°, in order to prevent obstruction of the convergent beam by upstream structures on the chip and to minimize the shadowing of the detector by the downstream part of the substrate. The geometry allowed us to capture half of the Debye–Scherrer rings corresponding to (111) and (200) peaks of Cu.

For the as-fabricated 500 nm sample, the resulting average value of the residual stress in the entire Cu line is $σ = 175 ± 18$ MPa (only a single line was measured, and the error is the standard error of the linear fit). The 200 nm sample had lower stress, $σ = 130 ± 14$ MPa (average and standard deviation of three lines, see Table I for the values and errors of individual lines).

The effects of EM were explored by measuring a range of samples exposed to varying combinations of current, temperature, and loading time. The quality of the diffraction patterns (statistics) became worse after EM testing, and a slightly coarser caking scheme (14 cakes, corresponding to a cake angle of 12.9°) was used to improve the statistics in each individual cake. Summed detector images, caked data, and final d₂₀₀ vs $sin 2 Ψ$ fits are shown for all samples in the supplementary material (Figs. S2–S7). For each sample, three separate lines were selected for measurement.

Figure 3 shows the results for all investigated conditions. After 5 h at 250 °C with $J EM$ = 1.7 MA cm⁻², the stress increased to 362 ± 25 MPa, but after 10 h, it dropped to 288 ± 48 MPa. It should be noted, however, that the difference is only statistically significant at a confidence level of 8%, as estimated from a two-sample t-test, suggesting further research is needed for confirmation. SEM images in Fig. 4(a) show EM tested at $J EM$ = 1.7 MA cm⁻² and 250 °C. At the cathode side, small defects can be observed on the surface after 5 h of EM testing. With the testing time extended to 10 h, the void size increases. The increased formation of hillocks can be seen at the anode with increasing testing time.

To further investigate the impact of EM conditions on residual stress, we performed comparative measurements, including different current densities and temperatures. EM analysis, as depicted in Fig. 4(b), shows after 10 h with temperature reduced to 200 °C that hillock formation was significantly less. Additionally, there were no voids or surface defects on the cathode side. This situation is similar to that observed when the current density is reduced to 1.6 MA cm⁻². The measured residual stresses, however, did not change significantly as a result of lowering the current density or reducing the testing temperature. The stresses after 10 h at both 1.7 MA cm⁻² and 200 °C (295 ± 45 MPa), and 1.6 MA cm⁻² at 250 °C 257 ± 26 MPa, were within the standard deviation span of the value after 10 h at 1.7 MA cm⁻² and 250 °C reported above (288 ± 48 MPa).

We also tested samples at higher currents and with extended EM duration. When the current density reached $J EM$ = 1.8 MA cm⁻² after 5 h at 250 °C, void size increased, and large hillocks were formed at the anode side, as shown in Fig. 4(c). It also led to changes in the microstructure, such as grain enlargement, which prevented reliable stress measurements. Similarly, as the testing time extended to 20 h, the voids and hillock regions grew larger, resulting in an undesirably large grain size under the current density of 1.7 MA cm⁻² at 250 °C.

In examining the 500 nm samples tested at 1.7 MA cm⁻² at 250 °C, an unexpected decreasing trend in residual stress between 5 and 10 h EM testing emerges. Initially, there is an increase in stress after 5 h compared to the as-deposited state, attributable to stress relaxation during the test. It is known that thin Cu films relax at temperatures exceeding roughly 200 °C,^29,30 and thus, the compressive stress developed during heating to 250 °C [−275 MPa for a room temperature stress of 175 MPa, according to Eq. (2)] should continuously relax toward zero during the test duration. Cooling will introduce thermal stresses in the tensile direction, and as the compressive stress has relaxed, the addition of the thermal stress will result in a higher tensile stress compared to the untested state. However, for un-capped Cu films, the relaxation process is generally not completed within 10 h in the temperature range of the present study.^31,32 Consequently, the sample tested at 10 h is expected to have even lower compressive stresses (more progressed relaxation) and exhibits even higher tensile stresses after cooling (here we note that the residual stress development during cooling is not linear with temperature due to relaxation processes,^29,30 but we assume that the behavior during cooling is similar after 5 and 10 h of testing). For the tensile stress to be lower after 10 h, the starting compressive stress during the cooling phase must be greater than that after 5 h, which contradicts the expected trend of advanced relaxation. This observed behavior strongly suggests that the current-induced stresses during the EM process (arising from volumetric strains due to the local changes in vacancy concentration produced by current-driven diffusion¹⁴) play a significant role. Development of an in-plane compressive stress component during EM has indeed been predicted from the general coupling model.¹⁴ The coupled effects of elastic, thermal, and EM strain introduces a complex dynamic, where the fast relaxation dominates at shorter times, whereas the compressive stresses developed due to EM govern the behavior at longer times. We note that there may be further coupled effects in the presence of current stressing, such as generation of dislocations, the increased strain energy of which can accelerate recrystallization.

Furthermore, previous experimental studies and simulations^15,18 indicate that EM induces a stress gradient along the line, which can also be influenced by mechanical constraints.¹⁸ We attempted spatially resolved analysis of the data from the 500 nm sample by dividing it into shorter segments and analyzing the parts individually, but as illustrated in the supplementary material (Fig. S8), this approach did not yield reliable results. To allow spatially resolved measurements, increased statistics are required, which could potentially be achieved by rocking the sample during measurements. Furthermore, using microbeams (in combination with sample rocking) will increase the time resolution and allow full-line (or even multi-line) mapping, thus supporting in situ measurements. The proposed approaches, however, remain to be explored.

In conclusion, our study revealed that it is possible to differentiate residual stress states in Cu lines in Blech structures obtained after EM testing under different conditions using x-ray nanodiffraction. The results suggest that the measured residual stresses in the early stages of EM are related to relaxation of stresses caused by CTE mismatch, while the stress reduction observed after extended test duration results from interactions between the thermal mismatch stress and a developing current-induced compressive stress. In situ measurements are essential to verify this hypothesis and also permit investigations of current-induced, or current-enhanced, changes such as plastic deformation and recrystallization through peak width evolution and changes in the spottiness of the diffraction rings.