Numerical Analysis of the Welding Behaviors in Micro-Copper Bumps

: In this study, three-dimensional simulations of the ultrasonic vibration bonding process of micro-copper blocks were conducted using the ﬁnite element method. We analyzed the effects of ultrasonic vibration frequency on the stress ﬁeld, strain ﬁeld, and temperature ﬁeld at the copper bump joint surface. The results showed that the bonding process is successfully simulated at room temperature. The stress curve of the bonding process could be divided into three stages: stress rising stage, stress falling stage, and stress stabilization stage. Moreover, it was found that the end of the curve exhibited characteristics of a solid solution phase at higher frequencies. It is hypothesized that the high-density dislocations formed at this stage may result in conveyance channels that facilitate the atomic diffusion at the contact surface. The simulation results indicated that copper micro-bump bonding occurs at an ultrasonic frequency of 50 kHz or higher.


Introduction
Modern science and technology are booming, and the development of semiconductors has progressed from two-dimensional integrated circuits (2D IC) to three-dimensional integrated circuits (3D IC). Manufacturers worldwide are hoping to build more modules on a single chip to achieve even higher integration density. The high integration density translates into a reduction of the total semiconductor and shortening of the internal circuit transmission path, which can accelerate the transmission of information. The increased efficiency and reduction in energy consumption is anticipated to further postpone the claim that the Moore's law has reached its limit [1,2].
To achieve the above-mentioned goals, semiconductor manufacturers have proposed some key technologies in recent years, which can be divided into two categories: through silicon via (TSV) and micro-bump bonding technologies. It is noted, however, that despite the recent progresses driven by the increasing demands of converting from 2D to 3D IC, there are still plenty of challenges and opportunities requiring tremendous research and development in improving the reliability of vertical connections. In addition to intermetallic compound (IMC) formation, issues such as joule heating, harsh temperature gradients and associated thermo-migration, electro-migration, as well as stress-migration still must be addressed [3,4]. The key feature of the TSV technology is the formation of a vertical channel inside the silicon substrate, which is filled with a selected metal [5]. On the other hand, the bonding technology establishes junctions between wafers by using metal bonding bumps. Both technologies have been demonstrated to be capable of realizing 3D IC by forming a stack of wafers with built-in transistors and devices. Direct copper-copper bonding shorter bonding time (100 s) compared to those of the conventional method (CM) [19]. This is a promising process because it can be performed at ambient temperature without requiring special environmental conditions. It is essential, and of interest, to improve our understanding of the fundamental mechanisms involved in this bonding process. In the present study, the finite element method is adopted to establish a simulation model of copper micro-bump bonding by studying the bonding process that occurs at the interface of two micron-sized copper blocks. In particular, the effects of the ultrasonic vibration frequency applied on the stress field, the strain field, and the temperature field at the interface between the two copper blocks are addressed in detail.

Methodology
As mentioned previously, the present research was aimed at understanding the underlying mechanisms of the ultrasonic vibration-induced dislocation of the activated solidsolution formation relevant to the couples bonding process. The introduction of ultrasonic vibrations produces a friction effect, which then generates a substantial amount of heat that increases the interface temperature and facilitates the atomic diffusion at the interfaces to allow bonding between the micron-sized copper blocks. The methodology used in the present study was the finite element method, which is briefly summarized below.

Simulation Assumptions
In general, it is difficult to simulate real situations of bonding behavior in great detail. Consequently, although we tried to explore as many relevant parameters as possible in the simulation, we had to leave out some relatively less important factors to save simulation time by establishing some basic, but reasonable, assumptions. The assumptions we made are briefly listed below: 1.
The silicon wafer was assumed to be linear, elastic, and isotropic.

2.
Except for the silicon wafers, the other properties of the materials had bilinear isotropic characteristics.

4.
With the exception of copper blocks, the material parameters at high temperatures were assumed to be the same as those at room temperature.

5.
The boundary conditions at the bottom of the Si wafer layer had zero degrees of freedom in the x, y, and z directions.

Modeling and Setting of Finite Element Analysis
We selected the elements 3D solid 164 and shell 163 from ANSYS LS-DYNA for this model. It created a layer of shell 163 at the top of the model and all the surface nodes applied the load by ultrasonic vibration. In addition to the above areas, all other structures used 3D Solid 164 elements. In the selection of the material, the silicon wafer has a higher hardness and a smaller amount of relative deformation during the simulation, so it was set to linear elastic isotropic. Except for the silicon wafers, all material models were set to bilinear isotropic. A large deformation occurs in the material and plastic deformation occurs in the contact, so the elastoplastic properties must be selected for the material model in the process of ultrasonic friction. This study used thermo-solid coupling, so it was necessary to consider the effect of temperature on the material by adding some thermal parameters to the Si, while the other materials were assumed to be temperature-dependent bilinear isotropic models.

Geometry and Dimensions
This study used metric units (SI), namely length in micrometers (µm), mass in kilograms (kg), time in second (s), and temperature units in Kelvin (K). The model established in this research was the actual model size using the actual micro-copper block bonding process, as shown in Figure 1. However, Ni, IMC, and Sn2.5Ag were not included in our present study. The main research focus was on copper and copper bonding, because a copper-to-copper mono-metallic interface does not form brittle IMC phases. There is no material parameter mismatch between the same materials, such as a thermal expansion coefficient. Therefore, the focus on copper was expected to eliminate mechanical problems and to maintain stable electrical properties due to the elimination of brittle IMC formations. The upper and lower parts were in a symmetrical relationship: The lower part included, from the bottom to the top, a silicon wafer layer, protection layer, aluminum pad, and micro-copper block, and the upper part was inverted. There was a 0.01 µm interval between the two copper blocks, in order to prevent the software from judging the two copper blocks as a connection body. The origin of the model's coordinates was at the center of the bottom silicon wafer layer, the Y axis was the direction of the vertical silicon wafer layer and the parallel silicon wafer layer was the XZ plane. The geometric dimensions of the model were adopted from Reference [20] and the geometric parameters are listed in Table 1. This study used mapped meshing to create the elements of the model. The element size sets were 1 µm and 2 µm, which divided the number of elements into groups of 10,336 and 1836, respectively. We followed Von-Mises stress and temperature at the center position of the contact surface on the bottom micro-copper bump. The maximum and deviation values are listed in Table 2 from the condition of a 50 kHz frequency. The deviation values of the maximum Von-Mises stress and maximum temperature were only 0.98% and 0.78% between element numbers 10,336 and 1836, respectively. Thus, we used element numbers 1836 as the model setting in this study. For the conversion of frictional heat generation to temperature, we use the mechanical equivalent of heat equal to 10 to speed up the analysis time. At the same temperature, the simulation time to produce the same temperature was 8.63% of the actual time. The mechanical and thermal parameters of materials at room temperature are listed in Table 3. In addition, the mechanical and thermal parameters of copper at high-temperature are listed in Tables 4 and 5, respectively. We considered the material parameters before the copper melting point to follow the material properties of 973 K to observe the phenomenon when it was close to the melting point.

Boundary Conditions, Load, and Contact Settings
At the beginning of the simulation, the upper copper block was punched towards the lower copper block and moved downward in a parallel Y-axis direction without rotation. The next ultrasonic vibration was parallel XZ plane movement and the amplitude of vibration was 0.9 µm. In the model's lower part, the surface was bound to the X direction and the Z direction, assuming that it extended indefinitely, except for the copper block. At the bottom of the lower silicon wafer layer, the degrees of freedom of its nodes were set to fixed. The boundary conditions of the model are plotted in Figure 2.

Boundary Conditions, Load, and Contact Settings
At the beginning of the simulation, the upper copper block was punched towards the lower copper block and moved downward in a parallel Y-axis direction without rotation. The next ultrasonic vibration was parallel XZ plane movement and the amplitude of vibration was 0.9 μm. In the model's lower part, the surface was bound to the X direction and the Z direction, assuming that it extended indefinitely, except for the copper block. At the bottom of the lower silicon wafer layer, the degrees of freedom of its nodes were set to fixed. The boundary conditions of the model are plotted in Figure 2. The process of ultrasonic friction was performed by controlling the shell 163 element of the model's uppermost layer, because the displacement condition of the uppermost shell element drives the entire model's upper part to move. It was an impact process during the initial time 0~2 μs of the simulation. At this stage, the upper shell element was set to move down at a constant speed of 0.005 m/s, which makes the upper copper block just touch the lower copper block. During the period of 0~2 μs, a pressure of 70 MPa was also gradually applied to the shell element. When the downward displacement distance reached 0.01 μm, it stayed at this height, and when the time reached 2 μs, the displacement constraint was removed, which was set to the constraint's birth time and dead time. After 2~3 μs, the pressure effect on the upper copper block was moved down by 0.03 μm, starting the ultrasonic vibration for 3 μs and the correspondence between X and Z coordinates and time at different ultrasonic vibration frequencies. The TCB process of copper-copper direct bonding is shown in Figure 3. The process of ultrasonic friction was performed by controlling the shell 163 element of the model's uppermost layer, because the displacement condition of the uppermost shell element drives the entire model's upper part to move. It was an impact process during the initial time 0~2 µs of the simulation. At this stage, the upper shell element was set to move down at a constant speed of 0.005 m/s, which makes the upper copper block just touch the lower copper block. During the period of 0~2 µs, a pressure of 70 MPa was also gradually applied to the shell element. When the downward displacement distance reached 0.01 µm, it stayed at this height, and when the time reached 2 µs, the displacement constraint was removed, which was set to the constraint's birth time and dead time. After 2~3 µs, the pressure effect on the upper copper block was moved down by 0.03 µm, starting the ultrasonic vibration for 3 µs and the correspondence between X and Z coordinates and time at different ultrasonic vibration frequencies. The TCB process of copper-copper direct bonding is shown in Figure 3.
In terms of contact setting, the top and bottom copper blocks in this study were surface-to-surface contact. This contact type is used when the face of one object penetrates the face of another object, the face-to-face contact is symmetrical, so the contact surface is equal to the target surface. The target surface and the contact surface are defined by using the nodes set. Face-to-face contact is usually used to solve the problem of large relative sliding between two objects. Then, the coefficient of friction is 0.2 [27] between the copper contact surface.
In terms of contact setting, the top and bottom copper blocks in this study were surface-to-surface contact. This contact type is used when the face of one object penetrates the face of another object, the face-to-face contact is symmetrical, so the contact surface is equal to the target surface. The target surface and the contact surface are defined by using the nodes set. Face-to-face contact is usually used to solve the problem of large relative sliding between two objects. Then, the coefficient of friction is 0.2 [27] between the copper contact surface.

The Yield Strength Depends on the Temperature Result for Each Frequency
The temperature results of ultrasonic vibration frequency are shown in Figure 4. The simulation results produce a temperature value that changes over time for each frequency. Combining the results of the yield strength and temperature of copper, the yield strength curves of the TCB process for each frequency were obtained. The yield strength curve could be an index for Von-Mises stress in the process of reaching the material yield state, or not. There was a severe temperature shock in the end of the temperature range at frequencies of 130 kHz, 170 kHz, and 200 kHz. At the frequencies of 170 kHz and 200 kHz, not only was there severe shock, but they also stopped the simulation time early. The results are discussed in detail in later sections.

The Yield Strength Depends on the Temperature Result for Each Frequency
The temperature results of ultrasonic vibration frequency are shown in Figure 4. The simulation results produce a temperature value that changes over time for each frequency. Combining the results of the yield strength and temperature of copper, the yield strength curves of the TCB process for each frequency were obtained. The yield strength curve could be an index for Von-Mises stress in the process of reaching the material yield state, or not. There was a severe temperature shock in the end of the temperature range at frequencies of 130 kHz, 170 kHz, and 200 kHz. At the frequencies of 170 kHz and 200 kHz, not only was there severe shock, but they also stopped the simulation time early. The results are discussed in detail in later sections.

Strain Softening
According to Figure 3, the simulation process is an iterative behavior of ultrasonic vibration: even if the model results from different frequencies are shown, only the result

Strain Softening
According to Figure 3, the simulation process is an iterative behavior of ultrasonic vibration: even if the model results from different frequencies are shown, only the result value changes. It is not easy to observe the phenomenon from the model result graph as shown in Figure 5a, and the maximum value in the contour is affected by the stress concentration of the geometric effect, as shown in Figure 5b. The results of the study are continued over time, and the location of the discussion is at the center of the contact surface. Therefore, we used the curve to express the results, so that we could directly understand the difference between different frequencies. The curves of equivalent stress and plastic strain of the copper block at the frequency of 5 kHz are plotted in Figure 6. It was found that the yielding strength curve decreased slowly. In addition, the equivalent stress increased to

Strain Softening
According to Figure 3, the simulation process is an iterative behavior of ultrasonic vibration: even if the model results from different frequencies are shown, only the result value changes. It is not easy to observe the phenomenon from the model result graph as shown in Figure 5a, and the maximum value in the contour is affected by the stress concentration of the geometric effect, as shown in Figure 5b. The results of the study are continued over time, and the location of the discussion is at the center of the contact surface. Therefore, we used the curve to express the results, so that we could directly understand the difference between different frequencies. The curves of equivalent stress and plastic strain of the copper block at the frequency of 5 kHz are plotted in Figure 6. It was found that the yielding strength curve decreased slowly. In addition, the equivalent stress in-     An equivalent stress curve at 50 kHz that clearly divides the curve into three parts is plotted in Figure 8. The first part is the stress rise stage caused by the copper block being pushed down for 0~3 μs. The ultrasonic vibration was carried out at 3 μs and the equivalent stress reached about 25 MPa. Furthermore, the equivalent stress kept increasing because of the repeating friction effects on the copper blocks. Thus, it can be observed that the equivalent stress reached a maximum value of 204 MPa at the time of 56.5 μs, indicating the "simultaneous several lattice slip region" [28]. A modeling of ultrasonic hardening and softening was carried out. The analytical model was constructed by the generalization of the synthetic theory of plastic deformation. The ultrasonic defect intensity was thus introduced, so that the phenomenon of both hardening and softening could be described by the uniform system of constitutive equations [29]. At the beginning of the ultrasonic vibration, the entire contact surface was used as the medium when the energy was transmitted. The contact surface appears to be a hard material; therefore, the amount of deformation at this stage was relatively small. The stress value decreased from 204 MPa to 63 MPa within the time of 56.5-500 μs. In this stage, the reduction of the yielding strength of material was caused by the effects of the "friction effect" and "temperature effect"; that is, the softening phenomenon [30]. An equivalent stress curve at 50 kHz that clearly divides the curve into three parts is plotted in Figure 8. The first part is the stress rise stage caused by the copper block being pushed down for 0~3 µs. The ultrasonic vibration was carried out at 3 µs and the equivalent stress reached about 25 MPa. Furthermore, the equivalent stress kept increasing because of the repeating friction effects on the copper blocks. Thus, it can be observed that the equivalent stress reached a maximum value of 204 MPa at the time of 56.5 µs, indicating the "simultaneous several lattice slip region" [28]. A modeling of ultrasonic hardening and softening was carried out. The analytical model was constructed by the generalization of the synthetic theory of plastic deformation. The ultrasonic defect intensity was thus introduced, so that the phenomenon of both hardening and softening could be described by the uniform system of constitutive equations [29]. At the beginning of the ultrasonic vibration, the entire contact surface was used as the medium when the energy was transmitted. The contact surface appears to be a hard material; therefore, the amount of deformation at this stage was relatively small. The stress value decreased from 204 MPa to 63 MPa within the time of 56.5-500 µs. In this stage, the reduction of the yielding strength of material was caused by the effects of the "friction effect" and "temperature effect"; that is, the softening phenomenon [30]. As ultrasonic energy is applied to a copper bond, only the intrinsic defects are activated [31]. Therefore, the high-density dislocation of materials is generated by the repeated stress, further becoming the strain-hardening phenomenon. Therefore, this area is called the "dislocation multiplied increasing region" [31]. On the other hand, the temper- As ultrasonic energy is applied to a copper bond, only the intrinsic defects are activated [31]. Therefore, the high-density dislocation of materials is generated by the repeated stress, further becoming the strain-hardening phenomenon. Therefore, this area is called the "dislocation multiplied increasing region" [31]. On the other hand, the temperature at the interface of two copper blocks is increased significantly due to the friction effect during the ultrasonic bonding process. Thus, the temperature was clearly increased within the time of 56.5-500 µs, as shown in Figure 4. This area is called the "slip by dislocation shifting region" [32]. In addition, the high-density dislocations and the formation of atomic diffusion channels are exhibited in materials because of the repeated stress-induced stress concentration [33][34][35][36]. Therefore, the copper blocks are successfully bonded together to form a connection.
In Figure 8, the equivalent stress curve is displayed above the theoretical yield strength curve, indicating that the contact surface is in a strain-hardened state. Because the strain hardening occurred at the contact surface, the plastic strain was close to a stable value (0.06) shortly after 400 µs. It can be found that the yield strength curve of 50 kHz is significantly lower than those of 5 kHz and 10 kHz. This means the yield strength of the material was decreased at the high temperature with the aid of the bonding behavior. In addition, the temperature of the contact surface was increased to 830 K at the frequency of 50 kHz. Consequently, it was possible to make the contact surface of the two copper blocks bond at the ultrasonic vibration frequency of 50 kHz.
The equivalent stress curve at 80 kHz can also be divided into three parts and is plotted in Figure 9. The copper block was pushed down to make the equivalent stress value increase to 30 MPa within the time 0~3 µs. Then, this equivalent stress reached a maximum value of 205.43 MPa at 33 µs. Next, the equivalent stress decreased rapidly within the time of 33-300 µs and reached 33 MPa at the time of 300 µs. In addition, the plastic strain increased quickly to a value of 0.06 at 300 µs. When the frequency was higher than 50 kHz, the yield strength curve was very similar. From the temperature field of 80 kHz in Figure 4, the temperature increased and reached 827 K at 300 µs, and further increased to a stable temperature of 894 K. On the other hand, the plastic strain tended to a stable value of 0.07; the corresponding stress value was about 20.44 MPa, as displayed in Figure 9.

Strain Hardening
The equivalent stress curve at 100 kHz can also be divided into three parts and is shown in Figure 10. During the time of 0-3 μs, the copper block was pushed down to make the equivalent stress value rise to 27 MPa. then, the equivalent stress dropped very rapidly within the time of 33-300 μs. In contrast, the plastic strain increased quickly during this time region. The third part is the stage of stress stabilization. Despite the oscillation behavior exhibited in the curve, the equivalent stress value tended to about 17.94 MPa. In addition, the corresponding plastic strain was 0.08. At the same time, the temper-

Strain Hardening
The equivalent stress curve at 100 kHz can also be divided into three parts and is shown in Figure 10. During the time of 0-3 µs, the copper block was pushed down to make the equivalent stress value rise to 27 MPa. then, the equivalent stress dropped very rapidly within the time of 33-300 µs. In contrast, the plastic strain increased quickly during this time region. The third part is the stage of stress stabilization. Despite the oscillation behavior exhibited in the curve, the equivalent stress value tended to about 17.94 MPa. In addition, the corresponding plastic strain was 0.08. At the same time, the temperature reached to 947 K, as shown in Figure 4. Figure 9. The equivalent (Von-Mises) stress, yield strength, and effective plastic strain for a 80 kHz frequency.

Strain Hardening
The equivalent stress curve at 100 kHz can also be divided into three parts and is shown in Figure 10. During the time of 0-3 μs, the copper block was pushed down to make the equivalent stress value rise to 27 MPa. then, the equivalent stress dropped very rapidly within the time of 33-300 μs. In contrast, the plastic strain increased quickly during this time region. The third part is the stage of stress stabilization. Despite the oscillation behavior exhibited in the curve, the equivalent stress value tended to about 17.94 MPa. In addition, the corresponding plastic strain was 0.08. At the same time, the temperature reached to 947 K, as shown in Figure 4. The equivalent stress curve at 120 kHz can also be divided into three parts and is plotted in Figure 11. At the beginning, the equivalent stress increased clearly within the time of 0-3 μs. Then, the curve dropped very rapidly within the time of 38-300 μs. Finally, the equivalent stress value, the corresponding plastic strain, and the temperature tended to about 24.73 MPa, 0.09, and 1043 K, respectively. The equivalent stress curve at 120 kHz can also be divided into three parts and is plotted in Figure 11. At the beginning, the equivalent stress increased clearly within the time of 0-3 µs. Then, the curve dropped very rapidly within the time of 38-300 µs. Finally, the equivalent stress value, the corresponding plastic strain, and the temperature tended to about 24.73 MPa, 0.09, and 1043 K, respectively.

Solid Solution State
The stress curve of 130 kHz that can be divided into four parts is displayed in Figure  12. The fourth part is presented in the solid solution. The first part was the stress rising stage from time 0~3 μs. Then, the stress dropped very rapidly within the time of 33-300 μs. The plastic strain increased quickly in the initial stage and finally tended to stable after 300 μs. From the stress distribution at the curve end of 28.04 MPa, it can be found that the tendency of the vibration amplitude was no longer stable, which is the difference of the above-mentioned three stages. In addition, the plastic strain also presented a larger value.

Solid Solution State
The stress curve of 130 kHz that can be divided into four parts is displayed in Figure 12. The fourth part is presented in the solid solution. The first part was the stress rising stage from time 0~3 µs. Then, the stress dropped very rapidly within the time of 33-300 µs.
The plastic strain increased quickly in the initial stage and finally tended to stable after 300 µs. From the stress distribution at the curve end of 28.04 MPa, it can be found that the tendency of the vibration amplitude was no longer stable, which is the difference of the above-mentioned three stages. In addition, the plastic strain also presented a larger value.
12. The fourth part is presented in the solid solution. The first part was the stress rising stage from time 0~3 μs. Then, the stress dropped very rapidly within the time of 33-300 μs. The plastic strain increased quickly in the initial stage and finally tended to stable after 300 μs. From the stress distribution at the curve end of 28.04 MPa, it can be found that the tendency of the vibration amplitude was no longer stable, which is the difference of the above-mentioned three stages. In addition, the plastic strain also presented a larger value.
In Figure 4, it is interesting to note that the oscillation behavior (so-called a solid solution phenomenon) is observed at the temperature of 1131 K for the frequency of 130 kHz. Moreover, the smaller stress value corresponds the larger strain value at the same time and can be found in Figure 12. Therefore, the material temperature was increased in the solid solution via the friction and temperature effects, resulting in a softer material and larger plastic strain (0.11).  In Figure 4, it is interesting to note that the oscillation behavior (so-called a solid solution phenomenon) is observed at the temperature of 1131 K for the frequency of 130 kHz. Moreover, the smaller stress value corresponds the larger strain value at the same time and can be found in Figure 12. Therefore, the material temperature was increased in the solid solution via the friction and temperature effects, resulting in a softer material and larger plastic strain (0.11).

Solid Solution Time Point Advances with Frequency
The stress curves of 170 kHz and 200 kHz are divided into four parts, as shown in Figures 13 and 14, respectively. For 170 kHz, the equivalent stress value, the corresponding plastic strain, and the temperature tended to about 81.94 MPa, 0.37, and 1307 K, respectively. For 200 kHz, the equivalent stress value, the corresponding plastic strain, and the temperature tended to about 100.65 MPa, 0.34, and 1384 K, respectively. As the mentioned above, the equivalent stress, plastic strain, and temperature increased with increasing ultrasonic vibration frequency. The solid solution occurred earlier as the frequency increased, and the solid solution in 170 kHz appeared at 650 µs and the in 200 kHz occurred at 450 µs. All the values of stress, strain, and temperature for different frequencies are listed in Table 6. spectively. For 200 kHz, the equivalent stress value, the corresponding plastic strain, and the temperature tended to about 100.65 MPa, 0.34, and 1384 K, respectively. As the mentioned above, the equivalent stress, plastic strain, and temperature increased with increasing ultrasonic vibration frequency. The solid solution occurred earlier as the frequency increased, and the solid solution in 170 kHz appeared at 650 μs and the in 200 kHz occurred at 450 μs. All the values of stress, strain, and temperature for different frequencies are listed in Table 6.   spectively. For 200 kHz, the equivalent stress value, the corresponding plastic strain, and the temperature tended to about 100.65 MPa, 0.34, and 1384 K, respectively. As the mentioned above, the equivalent stress, plastic strain, and temperature increased with increasing ultrasonic vibration frequency. The solid solution occurred earlier as the frequency increased, and the solid solution in 170 kHz appeared at 650 μs and the in 200 kHz occurred at 450 μs. All the values of stress, strain, and temperature for different frequencies are listed in Table 6.

Conclusions
The three-dimensional simulation model of the ultrasonic vibration bonding process of micro-copper blocks was investigated by using the finite element method. The effects of ultrasonic vibration frequency on the stress field, strain field, and temperature field at the copper bump joint surface were discussed. The main findings are summarized as follows: 1.
By using other frequencies to compare with the simulation results of 50 kHz, it can be found that the bonding phenomenon will not occur in the simulation time of 1500 µs if the frequency is lower than 50 kHz.

2.
The low temperature copper-to-copper bonding technology requires lower temperature (573 K) and a shorter bonding time (100 s), establishing the effectiveness of this better bonding method by improving the reduction of temperature and time with the TCB by 100 times. This research will have a major impact on the industry.

3.
From the high frequency simulation, it was found that the end of the curve was in the solid solution phase. Near the end of the simulation, it can be found that the trend of the amplitude of the vibration (similarly to the temperature curve) becomes larger from the stress distribution. That is, the materials structure at this stage is not very stable. For this phenomenon, it is called a solid solution.