Measurement of Thermal Stress by X-ray Nano-Diffraction in (111)-Oriented Nanotwinned Cu Bumps for Cu/SiO2 Hybrid Joints

X-ray nanodiffraction was used to measure the thermal stress of 10 µm nanotwinned Cu bumps in Cu/SiO2 hybrid structures at −55 °C, 27 °C, 100 °C, 150 °C, and 200 °C. Bonding can be achieved without externally applied compression. The X-ray beam size is about 100 nm in diameter. The Cu bump is dominated by (111) oriented nano-twins. Before the hybrid bonding, the thermal stress in Cu bumps is compressive and remains compressive after bonding. The average stress in the bonded Cu joint at 200 °C is as large as −169.1 MPa. In addition, using the strain data measured at various temperatures, one can calculate the effective thermal expansion coefficient (CTE) for the 10 µm Cu bumps confined by the SiO2 dielectrics. This study reports a useful approach on measuring the strain and stress in oriented metal bumps confined by SiO2 dielectrics. The results also provide a deeper understanding on the mechanism of hybrid bonding without externally applied compression.

Nanotwinned Cu (NT-Cu) has high strength and low resistivity compared with nanocrystalline Cu and coarse-grained Cu [25].The common methods of fabrication of NT-Cu are sputter and pulse electroplating, but the cost of sputter and the time duration of pulse electroplating is not suitable for the micro-electrical industry [25][26][27][28][29][30][31].In 2012, Chen's group introduced NT-Cu fabricated by direct-current electroplating [32].In particular, the highly (111)-oriented NT-Cu has the highest surface diffusivity and a low oxidation rate [33][34][35], so it is highly suitable for Cu direct bonding.Also, the NT-Cu is thermal stable up to 300 • C and has high resistance against electromigration and high strength [36][37][38][39].The NT-Cu has abnormal grain growth, which can enhance the bonding strength [40], so (111)-oriented NT-Cu would be a promising candidate of Cu hybrid bonding.
The kinetic mechanism for forming the Cu/SiO 2 joints is surface creep, illustrated in Figure 1 [16,19].Those Cu bumps with a slight recess in SiO 2 vias are aligned and pressurized at near room temperature, and the SiO 2 -SiO 2 dielectric first bonded to each other.After the pressurization process, the Si wafer pair was heated to a high temperature of 150-300 • C [41,42].Because the thermal expansion coefficient (CTE) of Cu is larger than that of SiO 2 , the two Cu bumps expand to touch each other and provide the compressive stress gradient needed for creep to occur, as depicted in Figure 1a,b.It is worth noting that it does not need any external compression during the heating process.The value of the generated stress due to the CTE mismatch was simulated by finite element analysis [43][44][45].However, there is no experimental measurement of the strain/stress value in the Cu joints near the bonding temperature so far. of pulse electroplating is not suitable for the micro-electrical industry [25][26][27][28][29][30][31].In 2012, Chen's group introduced NT-Cu fabricated by direct-current electroplating [32].In particular, the highly (111)-oriented NT-Cu has the highest surface diffusivity and a low oxidation rate [33][34][35], so it is highly suitable for Cu direct bonding.Also, the NT-Cu is thermal stable up to 300 °C and has high resistance against electromigration and high strength [36][37][38][39].The NT-Cu has abnormal grain growth, which can enhance the bonding strength [40], so (111)-oriented NT-Cu would be a promising candidate of Cu hybrid bonding.
The kinetic mechanism for forming the Cu/SiO2 joints is surface creep, illustrated in Figure 1 [16,19].Those Cu bumps with a slight recess in SiO2 vias are aligned and pressurized at near room temperature, and the SiO2-SiO2 dielectric first bonded to each other.After the pressurization process, the Si wafer pair was heated to a high temperature of 150-300 °C [41,42].Because the thermal expansion coefficient (CTE) of Cu is larger than that of SiO2, the two Cu bumps expand to touch each other and provide the compressive stress gradient needed for creep to occur, as depicted in Figure 1a,b.It is worth noting that it does not need any external compression during the heating process.The value of the generated stress due to the CTE mismatch was simulated by finite element analysis [43][44][45].However, there is no experimental measurement of the strain/stress value in the Cu joints near the bonding temperature so far.In this study, the strain in the 8 µm Cu pad, 10 µm Cu pad, and 8 µm Cu joint was in situ measured by synchrotron X-ray at −55, 27, 100, 150, and 200 °C using nanobeam diffraction.The resolution of the beam size is 100 nm.Therefore, we can obtain the strain and stress distribution in the Cu joints at different temperatures, which can provide a deeper In this study, the strain in the 8 µm Cu pad, 10 µm Cu pad, and 8 µm Cu joint was in situ measured by synchrotron X-ray at −55, 27, 100, 150, and 200 • C using nanobeam diffraction.The resolution of the beam size is 100 nm.Therefore, we can obtain the strain and stress distribution in the Cu joints at different temperatures, which can provide a deeper understanding than the previous studies on the fabrication and reliability of Cu-Cu hybrid joints.

Materials and Methods
This study used three types of samples to measure the thermal strain: the top die, bottom die, and bonded joint.The top die (6 × 6 mm 2 ) consists of arrays of Cu bumps with 10 µm diameter, and the bottom die (15 × 15 mm 2 ) comprises arrays of Cu bumps with 8 µm diameter on top of Cu redistribution layers (RDLs).The thickness of Cu bumps and Cu RDLs is ~1.25 µm; thus, the total thickness of the top die, bottom die, and bonded joint is ~1.25, ~2.5, and ~3.75 µm, respectively.The fabrication method of the hybrid Cu/SiO 2 joints was reported in a previous study [16].Nano-twinned Cu with highly (111) preferred orientation was fabricated by electrodeposition [32].We adopted a complete package without being cut or ground for the thermal strain measurement, so the strain/stress distribution is similar to the state during bonding.The thickness of the top Si wafer is only 100 µm, so the X-ray can penetrate the entire device and can directly detect the diffraction signals from Cu bumps.The strain distribution was performed by using the X-ray nanodiffraction (XND) beamline, BL21A station, at Taiwan Photon Source (TPS) at the National Synchrotron Radiation Research Center (NSRRC) in Hsinchu, Taiwan.The instrument accommodates an FE-SEM and X-ray fluorescence (nano-XRF) system to navigate the 100 nm focused white/mono X-rays on a specific bump region.The energy range of the focused X-ray covers from 5 to 30 keV, and for the experiment, we quickly switched to the mono X-ray beam by introducing the 4-bunch crystal monochromator (4BCM) [46].The entire system was combined in a high-vacuum chamber (10 −7 Torr) to prevent air scattering of diffracted signals, as shown in Figure 2a.
In the nano-diffraction technique, to avoid the displacement caused by the rotation of the sample, we fixed the sample at an angle and scanned the energy of the incident X-ray instead of rotating the sample.Considering Bragg's equation, scanning the incident X-ray energy allowed us to obtain the distribution of the lattice spacing of the sample at a fixed angle.This technique is called energy-dispersive nano-diffraction (ED-XND), as shown in Figure 2b.In this study, the sample was fixed at a 45 • angle, and the diffraction signal was collected using a large-area detector (Pilatus 6M, Dectris, Baden, Switzerland) at a reflection geometry 90 • above the sample stage.We chose a region of interest (2-theta ROI) on the detector and converted the incident X-ray energy into scattering wave vector, Q, or reciprocal lattice units, r.l.u.; an 1-D diffraction pattern from a nanometer scale region can be obtained for structural determination.We selected the X-ray energy from a lattice plane vector and scanned the sample for two-dimensional mapping; by analyzing the angular shift of this crystal plane on the detector, the crystal plane and strain distribution can be observed in real space.
The strain caused by the CTE mismatch is of interest at different temperatures, especially near the bonding temperatures; also, we were concerned about the reliability during thermal cycling test of hybrid bonding, so we measured the temperature at low temperature [15,16].Therefore, in this study, the sample temperature was set at −55, 27, 100, 150, and 200 • C. The thermal strain at various temperatures was calculated by Equation (1).
where ε is the lattice strain, d s is the strain lattice parameter, and d 0,T is the unstrained lattice parameter at temperature T, which would change with temperature, so the unstrained lattice parameter d 0,T was calculated by Equation (2).
where d 0,25 • C is the unstrained lattice parameter at 25 • C, and α is the coefficient of thermal expansion.At room temperature (25 • C), the unstrained lattice parameter of Cu was taken as 0.3615 nm, which is the lattice constant in powder diffraction (PDF 00-004-0836), and the coefficient of thermal expansion was 16.99 × 10 −6 / • C at 25 • C. The microstructure of the top die, the bottom die, and the bonded joint was observed with a focused ion beam (FIB).

Diffraction Intensity and Microstructure
The thermal strain/stress generated by the mismatch of CTE provides the driving force for the Cu-Cu bonding.According to the ED-XND technique, we collected a diffraction pattern in the range of 1000 eV with a step of 10 eV.From the results, we observed a strong diffraction signal on the detector that was close to 86 • two theta degrees when the incident mono X-ray energy was 8.7 keV.After calculation, this diffraction signal corresponds to Cu (222) and was oriented along the normal direction of the sample surface.Based on our previous studies, the surface (111) orientation of the nano-twin in the Cu bump on the top and bottom die is about 78% [16].Hence, to understand the variation of strain between Cu-Cu bumps, measuring the lattice changes of the Cu {111} family along the bonding direction is the optimal choice.
Due to the geometric limitations of the XND beamline and the surface orientation of the Cu bump, as shown in Figure 2c, we selected Cu (222) crystal plane, detected at 8.7 keV incident X-ray, to plot the distribution of a single Cu-Cu bump. Figure 2d shows the spatial distribution of diffraction peak intensity from the Cu (222) crystal plane.A precision stage (SmarAct) moved the sample at an interval of 200 nm for two-dimensional mapping, and the measured region is 20 µm × 20 µm, which is completely included in one Cu joint.The thickness of the top Si die was ground from 725 µm to 100 µm to enhance the diffraction signals from Cu.The secondary electron image and ion image of the top die and the bottom die are shown in Figure 3. Figure 3a is the secondary electron image of the top die.There are four Cu pads in Figure 3a.In this study, we only measured the thermal strain of one Cu pad or joint in every sample.Figure 3b-d

Thermal Strain/Stress Maps
The strains in the top die Cu pad, the bottom die Cu pad, and the bonded Cu joint were calculated by Equation (1).The average thermal strain of all specimen is listed in Table 1. Figure 4 shows the thermal strain maps of the top die measured at 27, 100, 150, and 200 • C. The positive value indicates tensile strain, and the negative value represents compressive strain.The yellow circles in Figure 4 locate the site of the bump.At 27 • C, the top die Cu pad is under compressive strain, and compressive strain rises as the temperature increases.The thermal strain maps indicate higher compressive strain at the middle of the top die bump, as shown in Figure 4. We suspect that the non-uniform planarization in the Cu bumps caused the higher strain.It is reported that dishing may occur in the Cu via chemical-mechanical polishing (CMP).The Cu near the edge of the bump is thicker than that near the center of the bump [36].Therefore, the Cu near the edge was compressed more during the bonding process, as illustrated in Figure 1a.The average thermal strain of the top die Cu pad is −0.018%, −0.07%, −0.089%, and −0.111%, at 27, 100, 150, and 200 • C, respectively.At 27 °C, the top die Cu pad is under compressive strain, and compressive stra as the temperature increases.The thermal strain maps indicate higher compressive at the middle of the top die bump, as shown in Figure 4. We suspect that the non-u planarization in the Cu bumps caused the higher strain.It is reported that dishin occur in the Cu via chemical-mechanical polishing (CMP).The Cu near the edge bump is thicker than that near the center of the bump [36].Therefore, the Cu near th was compressed more during the bonding process, as illustrated in Figure 1a.The a thermal strain of the top die Cu pad is −0.018%, −0.07%, −0.089%, and −0.111%, at 150, and 200 °C, respectively.
Figure 5 shows the thermal strain maps of the bottom die Cu pad measured 100, 150, and 200 °C.The blue (large) and green (small) circles in Figure 5 locate the Figure 5 shows the thermal strain maps of the bottom die Cu pad measured at 27, 100, 150, and 200 • C. The blue (large) and green (small) circles in Figure 5 locate the site of the bump and the RDL, respectively.The average thermal strain of the bottom die Cu pad is −0.037%, −0.074%, −0.105%, and −0.113% at 27, 100, 150, and 200 • C, respectively.Figure 6 shows the thermal strain maps of the bonded Cu joint measured at −55, 27, 100, 150, and 200 • C. In Figure 6, we used blue (large) and green (small) circles to locate the site of the bump and the RDL, respectively.The average thermal strain of the bonded Cu joint is 0.007%, −0.039%, −0.072%, −0.094%, and −0.121% at −55, 27, 100, 150, and 200 • C.However, the misalignment between bumps in the top and bottom dies could not be observed from these maps.The thermal strain maps of the bonded joint have higher strain at the edge of the bottom die RDL in Figure 6b-d.This is not observed in the thermal strain maps of the top die and the bottom die, so we suspect the higher strain was caused by the thermal-compression bonding process.The thermal-compression bonding may cause some defects at the edge of the bottom die RDL.The trend of the average thermal strain of all samples is the same.All samples obtain higher compressive strain with increasing temperatures.
the bottom die RDL in Figure 6b-d.This is not observed in the thermal strain map top die and the bottom die, so we suspect the higher strain was caused by the th compression bonding process.The thermal-compression bonding may cause some at the edge of the bottom die RDL.The trend of the average thermal strain of all s is the same.All samples obtain higher compressive strain with increasing tempera  Furthermore, the Young's modulus of Cu was taken as 140 GPa to calculate the change of thermal strain to thermal stress with Equation (3) [37].
where σ is thermal stress, E is Young's modulus, and ε is thermal strain.The thermal stress of the top die Cu pad, bottom die Cu pad, and bonded Cu joint is shown in Figures 7-9        One might expect that the stress in Cu bumps in the top and bottom dies would b small in the vertical direction because the Cu may expand in the direction of the top fre surface and release the stress imposed by the surrounding SiO2 layer.However, the stre values we measured are over 100 MPa in compression at temperatures higher than 100 °C This is explained as follows.As the temperature increases, the Cu should expand mor than the surrounding SiO2 because the CTE of Cu is much larger than that of the SiO2.A shown in Figure 3b,c, the Cu bumps would experience compressive stress from the later surrounding SiO2 layer.The Cu might relieve the stress through the expansion to the to surface.However, the Cu bumps adhere to the sidewalls of the SiO2 quite well.Thus, th vertical expansion might be limited to some extent.Therefore, the Cu bumps were unde One might expect that the stress in Cu bumps in the top and bottom dies would be small in the vertical direction because the Cu may expand in the direction of the top free surface and release the stress imposed by the surrounding SiO 2 layer.However, the stress values we measured are over 100 MPa in compression at temperatures higher than 100 • C.This is explained as follows.As the temperature increases, the Cu should expand more than the surrounding SiO 2 because the CTE of Cu is much larger than that of the SiO 2 .As shown in Figure 3b,c, the Cu bumps would experience compressive stress from the lateral surrounding SiO 2 layer.The Cu might relieve the stress through the expansion to the top surface.However, the Cu bumps adhere to the sidewalls of the SiO 2 quite well.Thus, the vertical expansion might be limited to some extent.Therefore, the Cu bumps were under high compressive stress in the vertical direction.
With the strain values at various temperatures, one can calculate the effective CTE of the Cu bumps embedded in the SiO 2 layer.Figure 10 plots the average thermal strain of the top die, bottom die, and the bonded joint against temperature.Since the strains we calculated were using Equations ( 1) and ( 2), the slopes of the fitting lines in Figure 10 represent the mismatch of the CTE between the confined Cu bumps and free-standing Cu.The slope of the top die Cu pad, bottom die Cu pad, and bonded Cu joint is −5.3, −4.6, and −4.9 ppm/ • C, respectively.Then, one can obtain the effective CTE of the Cu pad by adding the above value to the CTE of free-standing Cu, which is 16.99 ppm/ • C. Therefore, the effective CTE of the top die Cu pad, bottom die Cu pad, and the bonded Cu joint is calculated to be 11.7, 12.4, and 12.1 ppm/ • C, respectively.In our previous study, we found the effective CTE of the Cu line is about 21 ppm/ • C, which is greater than the CTE of the free-standing Cu [46].Because the Cu line is not embedded in the SiO 2 , the effective CTE is higher.Moreover, we can use the effective CTE to calculate the expansive height due to thermal expansion at the bonding temperature with Equation (4).
where ∆L is the difference in height, α eff is the effective CTE, L 0 is the thickness of Cu pad, and ∆T is the temperature difference.We substituted α eff as 11.7 and 12.4 ppm/ • C for the top die Cu pad and the bottom die Cu pad, L 0 as 1250 nm, and ∆T as 173 • C.Then, we obtained the expansive height of the top die Cu pad and the bottom die Cu pad as 2.5 and 2.7 nm, respectively.These values represent the maximum recess of the top die and the bottom die Cu pad, which cannot be over 2.5 and 2.7 nm for good bonding quality.
In addition, as the pitch and the thickness of the Cu pad shrink, the maximum recess should decrease as well.As the size of Cu pad decreases to 500 nm, the calculated thermal expansion should be less than 4 nm [47].However, the constraint of the surrounding SiO 2 would be aggravated in smaller bumps.Thus, the effective CTE and the behavior of thermal expansion in fine pitch needs more investigation in the future.
Nanomaterials 2023, 13, x FOR PEER REVIEW 13 of 17 the top die, bottom die, and the bonded joint against temperature.Since the strains we calculated were using Equations ( 1) and ( 2), the slopes of the fitting lines in Figure 10 represent the mismatch of the CTE between the confined Cu bumps and free-standing Cu.
where ΔL is the difference in height, αeff is the effective CTE, L0 is the thickness of Cu pad, and ∆T is the temperature difference.We substituted αeff as 11.7 and 12.4 ppm/°C for the top die Cu pad and the bottom die Cu pad, L0 as 1250 nm, and ∆T as 173 °C.Then, we obtained the expansive height of the top die Cu pad and the bottom die Cu pad as 2.5 and 2.7 nm, respectively.These values represent the maximum recess of the top die and the bottom die Cu pad, which cannot be over 2.5 and 2.7 nm for good bonding quality.In addition, as the pitch and the thickness of the Cu pad shrink, the maximum recess should decrease as well.As the size of Cu pad decreases to 500 nm, the calculated thermal expansion should be less than 4 nm [47].However, the constraint of the surrounding SiO2 would be aggravated in smaller bumps.Thus, the effective CTE and the behavior of thermal expansion in fine pitch needs more investigation in the future.The thermal stress results provide a fundamental understanding of the mechanism of the Cu-Cu bonding.For previous study on the Cu-Cu bonding using blanket films, an external pressure ranging from 1 MPa to tens of MPa was applied to the Cu films at elevated temperatures, which is called "thermal compression bonding", and bonding was achieved after approximately 1 h of the creep process.However, for real applications in microelectronic devices, the Cu bumps are embedded in dielectric films, as illustrated in Figure 1, so a hybrid bonding is needed.Although there is no external pressure applied to the top and the bottom wafer at the bonding temperature at 200 • C in this study, the local stress in the Cu bumps is as high as −169.1 MPa, which is generated by the mismatch of CTE in the heterogeneous integrated structure.The high thermal stress provides the pressure needed for the Cu-Cu diffusion bonding.On the other hand, the local high pressure may cause failure on the fragile, porous, low-K dielectric materials underneath the Cu joints.Therefore, managing the pressure during Cu-Cu bonding is an essential task for the microelectronic industry.

Conclusions
We used X-ray nano-diffraction to measure the thermal stress in a (111)-oriented NT-Cu bump of the hybrid Cu/SiO 2 joint at various temperatures.At room temperature, the average thermal strain is compressive, and as the temperature increases, the thermal compressive strain increases.The average thermal stress of the top die Cu

Figure 1 .
Figure 1.Structure of Cu/SiO2 hybrid joints.(a) Schematic drawing after the SiO2-SiO2 bonding near room temperature.(b) Schematic structure showing the Cu expanding die to CTE mismatch at elevated temperature.

Figure 1 .
Figure 1.Structure of Cu/SiO 2 hybrid joints.(a) Schematic drawing after the SiO 2 -SiO 2 bonding near room temperature.(b) Schematic structure showing the Cu expanding die to CTE mismatch at elevated temperature.

Figure 2 .
Figure 2. (a) Schematic diagram of measurement at BL21A.(b) The measured method of ED-XND.(c) The schematic diagram of the (111)-oriented Cu in SiO2 via and beamline limitation.(d) The spatial distribution of diffraction peak intensity from the Cu (222) crystal plane.

Figure 2 .
Figure 2. (a) Schematic diagram of measurement at BL21A.(b) The measured method of ED-XND.(c) The schematic diagram of the (111)-oriented Cu in SiO 2 via and beamline limitation.(d) The spatial distribution of diffraction peak intensity from the Cu (222) crystal plane.
show the cross-sectional FIB image of the top die Cu pad, the bottom die Cu pad, and the bonded Cu joint.As can be seen, the microstructure of all samples has a nano-twin structure.The thickness of the Cu bump and RDL is 1.25 µm in each Cu layer.Therefore, the diffractions were from all of the three Cu layers.Nanomaterials 2023, 13, x FOR PEER REVIEW 6 of 1 diffraction signals from Cu.The secondary electron image and ion image of the top die and the bottom die are shown in Figure 3. Figure 3a is the secondary electron image of th top die.There are four Cu pads in Figure 3a.In this study, we only measured the therma strain of one Cu pad or joint in every sample.Figure 3b-d show the cross-sectional FIB image of the top die Cu pad, the bottom die Cu pad, and the bonded Cu joint.As can b seen, the microstructure of all samples has a nano-twin structure.The thickness of the Cu bump and RDL is 1.25 µm in each Cu layer.Therefore, the diffractions were from all o the three Cu layers.

Figure 3 .
Figure 3. Microstructure of NT-Cu pad.(a) Plan-view SEM secondary electron image of top die NT Cu pads.(b) Cross-sectional ion image of the top die NT-Cu pad.(c) Cross-sectional ion image o the bottom die NT-Cu pad.(d) Cross-sectional ion image of the bonded NT-Cu joint.

Figure 3 .
Figure 3. Microstructure of NT-Cu pad.(a) Plan-view SEM secondary electron image of top die NT-Cu pads.(b) Cross-sectional ion image of the top die NT-Cu pad.(c) Cross-sectional ion image of the bottom die NT-Cu pad.(d) Cross-sectional ion image of the bonded NT-Cu joint.

Figure 4 .
Figure 4. Thermal strain maps of the top die measured at (a) 27, (b) 100, (c) 150, and (d) 200 The yellow circles represent the site of the bump.

Figure 4 .
Figure 4. Thermal strain maps of the top die measured at (a) 27, (b) 100, (c) 150, and (d) 200 • C. The yellow circles represent the site of the bump.

Figure 5 .
Figure 5. Thermal strain maps of the bottom die measured at (a) 27, (b) 100, (c) 150, and (d) The blue and green circles locate the site of the bump and the RDL, respectively.

Figure 5 .
Figure 5. Thermal strain maps of the bottom die measured at (a) 27, (b) 100, (c) 150, and (d) 200 • C. The blue and green circles locate the site of the bump and the RDL, respectively.
. The average thermal stress of the top die Cu pad, bottom die Cu pad, and the bonded Cu joint is listed in Table 2.The average thermal stress of the top die Cu pad is −25.2, −98.0, −124.6, and −155.4MPa measured at 27, 100, 150, and 200 • C, respectively.The average thermal stress of the bottom die Cu pad is −51.8, −103.6,−147.0, and −158.2MPa measured at 27, 100, 150, and 200 • C, respectively.Additionally, the average thermal stress of the bonded Cu joint is 9.8, −54.6, −100.8,−131.6, and −169.1 MPa measured at −55, 27, 100, 150, and 200• C, respectively.In the Cu/SiO 2 structure, the Cu pads were confined by the surrounding SiO 2 , so the thermal expansion behavior of the Cu pads would be inhibited.It is noteworthy to state that the stress values we measured were in the vertical direction of the Cu bumps because we adopted the diffraction spots from the (222) planes, as shown in Figure2.

Figure 6 .
Figure 6.Thermal strain maps of the bonded joint measured at (a) −55, (b) 27, (c) 100, (d) 150, a (e) 200 °C.The blue and green circles represent the locations of the bump and the RDL, respective

Figure 6 .
Figure 6.Thermal strain maps of the bonded joint measured at (a) −55, (b) 27, (c) 100, (d) 150, and (e) 200 • C. The blue and green circles represent the locations of the bump and the RDL, respectively.

Figure 7 .
Figure 7. Thermal stress maps of the top die measured at (a) 27, (b) 100, (c) 150, and (d) 200 °C.The yellow circles represent the site of the bump.

Figure 7 . 17 Figure 8 .
Figure 7. Thermal stress maps of the top die measured at (a) 27, (b) 100, (c) 150, and (d) 200 • C. The yellow circles represent the site of the bump.Nanomaterials 2023, 13, x FOR PEER REVIEW 11 of 17

Figure 8 .
Figure 8. Thermal stress maps of the bottom die measured at (a) 27, (b) 100, (c) 150, and (d) 200 • C. The blue and green circles represent the sites of the bump and the RDL, respectively.

Figure 9 .
Figure 9. Thermal stress maps of the bonded joint measured at (a) −55, (b) 27, (c) 100, (d) 150, an (e) 200 °C.The blue and green circles represent the sites of the bump and the RDL, respectively.

Figure 9 .
Figure 9. Thermal stress maps of the bonded joint measured at (a) −55, (b) 27, (c) 100, (d) 150, and (e) 200 • C. The blue and green circles represent the sites of the bump and the RDL, respectively.

Figure 10 .
Figure 10.The average thermal strain of the top die, bottom die, and bonded joint.

Figure 10 .
Figure 10.The average thermal strain of the top die, bottom die, and bonded joint.
pad measured at 27, 100, 150, and 200 • C was −51.8, −103.6,−147.0, and −158.2MPa, respectively.The average thermal stress of the bottom die Cu pad measured at 27, 100, 150, and 200 • C was −25.2, −98.0, −124.6, and −155.4MPa, respectively.The average thermal stress of the bonded Cu joint measured at −55, 27, 100, 150, and 200 • C was 9.6, −54.1, −101.3,−131.3, and −169.1 MPa, respectively.In addition, from the slope of the average thermal strain of Cu pad against temperature, one can obtain the effective CTE of Cu bumps confined in the SiO 2 .The measured effective CTE of the top die Cu pad, bottom die Cu pad, and bonded Cu joint was 11.7, 12.4, and 12.1 ppm/ • C, respectively, which is much lower than the literature value of 16.99 ppm/ • C for the free-standing Cu.The high thermal stress at 200 • C provides the driving force for the Cu-Cu diffusion bonding.These results provided a new insight of the effect of thermal stress on Cu/SiO 2 hybrid bonding.

Table 1 .
Summary for the average thermal strain of Cu via in the top die, bottom die, and bonded joint at various temperatures.

Table 2 .
Summary for the average thermal stress in Cu via in the top die, bottom die, and bonded joint at various temperature.

Table 2 .
Summary for the average thermal stress in Cu via in the top die, bottom die, and bonded joint at various temperature.
[46]slope of the top die Cu pad, bottom die Cu pad, and bonded Cu joint is −5.3, −4.6, and −4.9 ppm/°C, respectively.Then, one can obtain the effective CTE of the Cu pad by adding the above value to the CTE of free-standing Cu, which is 16.99 ppm/°C.Therefore, the effective CTE of the top die Cu pad, bottom die Cu pad, and the bonded Cu joint is calculated to be 11.7, 12.4, and 12.1 ppm/°C, respectively.In our previous study, we found the effective CTE of the Cu line is about 21 ppm/°C, which is greater than the CTE of the freestanding Cu[46].Because the Cu line is not embedded in the SiO2, the effective CTE is higher.Moreover, we can use the effective CTE to calculate the expansive height due to thermal expansion at the bonding temperature with Equation (4).