A new method for preventing stress cracking in repairable ceramic packages by changing the sealing ring shape

High-reliable ceramic packages are impressionable to the parallel seam welding (PSW) parameters leading to low yield and reliability. In this study, the structure of the ceramic package was modified by changing the sealing ring to improve weldability and high-temperature reliability. Three types of ceramic packages with different-shaped sealing rings, which are conventional rectangular rings, notch inward rings, and notch outward rings, were fabricated by Au-Sn soldering and a follow-up PSW process. The packages with the rectangular ring failed in the subsequent high-temperature aging test. The packages with the notch inward ring exhibited an early failure after PSW. Cracks were generated in the Au-Sn solder and propagated into the ceramic substrate. The packages with the notch outward ring exhibited remarkable weldability and reliability. Sequential thermo-structural coupling was used to simulate the temperature and stress distribution in the packages. The maximum principal stress in the aforementioned ceramic substrates rapidly increased to approximately 170.0 MPa, 168.5 MPa and 101.4 MPa in the PSW process. Stress concentration existed at the outside corner around the rectangular and notch inward-shaped sealing rings. The maximum temperature at the local position in the ceramic was raised to 250.3 °C, 238.6 °C and 157.2 °C depending on the shape of the sealing ring. The extra transmission path in the notch outward ring relieved thermal mismatch and deformation at the Au-Sn/ceramic interface during PSW. The packages with notch outward rings were recommended especially in the repairable ceramic packaging.


Introduction
Devices and components are usually faced with threats in harsh environments such as radiation, extremely high and low temperatures, and corrosion like moisture acid or alkali.An organic sealed package will be ultimately intruded by water vapor or gases due to the permeability of organic materials [1].Active devices in harsh environments are preferentially recommended in a metal or ceramic hermetic package [2][3][4].Sealing a package with a lid, usually the final process in packaging, allows an integrated circuit assembled inside in an isolated environment to prevent aggression of contaminants.As defined by MIL-STD-883C, a hermetic package means the leak rate of helium after pressurization is below the rate specified with reference to the package size.Improper sealing methods or parameters will cause function loss, not only hermetic failure but also electrical or physical failure [5].The method for sealing the lid with the base plays a key role in the reliability of the package.Solder sealing, glass sealing and parallel seam welding are the most commonly used methods for sealing the lid [6].For solder sealing or glass sealing, the sealing mechanisms are almost the same.It requires a temperature of approximately 300 °C for solder sealing (usually an Au-20Sn solder), and about 400 °C for glass sealing.However, these temperatures are too high for some chips [7].Moreover, the Au-20Sn solder and glass are susceptible to mechanical and thermal stress due to their brittleness.The mechanism of PSW is resistance welding, which is considered the most traditional metal welding method [8,9].The electrode of PSW is a rotating disc-shaped roller.At the beginning of the PSW process, the lid is pressed by the roller electrode with an appropriate amount of pressure.The continuous or pulse current flows through the electrodes and generates Joule heat, as shown in figure 1.The magnitude of Joule heat is determined by the welding current, welding time and the total resistance between the roller electrodes.In this case, the total resistance consists of electrode resistance, metal resistance and the contact resistance between the electrode and lid as well as that between the lid and sealing ring.Generally, the contact resistance is influenced by the resistivity of the dissimilar metals and the contact status such as the contact area, contact pressure, and temperature [10].The magnitude of the contact resistance is usually a megohm level, which is much larger than that of the electrode and metal.Most of the Joule heat is generated between the electrode and lid as well as between the lid and sealing ring, rather than the whole package.Therefore, PSW is especially suitable for temperature-sensitive chip packaging.
A sealing ring and a lid made of ASTM F-15 alloy (Kovar alloy) with Ni and Au plating are commonly employed to form the packaging structure.In the temperature range from 20 °C to 400 °C, the coefficient of thermal expansion (CTE) of Kovar (6.0 ppm C −1 ) matches well with Al 2 O 3 ceramic (7.0 ppm C −1 ) [11,12].The residual stress in the Kovar/Al 2 O 3 joint is relatively small after welding.Therefore, Kovar alloys have been widely used as the pin, lead frame, lid and sealing ring in ceramic packaging.The platings on the Kovar lid and sealing ring are melted and bonded by the Joule heat.With the movement of the roller electrode, the plating layer is repeatedly melted and solidified to form a series of overlapping solder joints to achieve bonding [13].In the PSW process, the temperature in the welding pool should be higher than the melting point of Au and lower than that of Ni.However, the control of the appropriate temperature is usually difficult in practice.If the temperature exceeds the melting point of Ni, Ni plating will remelt and change from an amorphous state to a crystalline state losing its effectiveness in protecting the Kovar alloy from corrosion [14].The standard electrode potentials of Au 3+ /Au, Ni 2+ /Ni and Fe 2+ /Fe are +1.498V, −0.257 V and −0.447 V, respectively [15].When the Kovar alloy has been exposed in the salt spray environment, rapid electrochemical corrosion occurs due to the large electrode potential difference between Au and Fe.A multi-layer of Ni/Au plating is found to be beneficial for corrosion resistance [16].In the PSW process, Joule heat is only generated at the contact region between the multi-layer plating on the lid and the sealing ring.The internal plating close to the Kovar may not be melted, which acts as a barrier to improve the corrosion resistance.Therefore, the Kovar covered with a multi-layer of Ni/Au plating is more difficult to expose in a corrosive environment.
In addition to corrosion failure, another common failure mode of substrate cracking often occurs with unsuitable welding parameters.The effect of PSW parameters on the thermal stress in the ceramic substrate has been widely investigated, a significant percentage of which is through the simulation method [17][18][19][20].A welding cycle can be divided into welding time and cooling time.The welding parameter of pulse width can be regarded as the real welding time in one cycle.It is found that the decrease of pulse width, which is to decrease the ratio of welding to cooling time, can reduce the thermal shock on the substrate [17].It has been reported that the grain size of the ceramic affects the fracture toughness [21].The ceramics with smaller grain sizes are more likely to initiate cracks under equal stress conditions [22].Therefore, using a ceramic substrate with an appropriate grain size is helpful to prevent stress cracking.The method of adding a soft metal interlayer with a low melting point between the Kovar and ceramic has been proven to be effective in relieving residual stress after brazing [23][24][25].However, the interlayer metal may be remelted when welding the lid, leading to the skewing of the sealing ring.Therefore, this method could hardly be applied to the electronic packaging.In some cases, packages may show qualified weldability but fail in the following reliability tests or the surface mounting process.A reasonable explanation can be concluded that unexpected residual stress has accumulated after the PSW process [26][27][28].Therefore, selecting a lower heat input might be advisable without endangering the welding quality, such as decreasing the welding power or increasing the welding speed.
The welding pressure of the roller electrode also plays a key role in the stress generation in the package.If the pressure is small, the welding contact resistance will significantly increase, resulting in sparking and further damage to the lid.On the contrary, a large pressure on the lid will lead to insufficient contact resistance.The Joule heat might not be enough to melt the Au plating to form an effective connection.Moreover, the overload of the pressure stress will result in an insupportable plastic deformation on the lid and even cause cracking in the ceramic substrate.Hu et al [13] ranked the factors by the individual degree of influence on the thermal stress generation in the sealing ring based on orthogonal experiments.The results show that the welding current has the strongest influence on thermal stress, followed by welding speed and pressure.The overlap width of the roller electrode has little influence on stress generation.The design of the welding parameters relies on a large number of experiments and experience, leading to high costs and procrastination.Therefore, most of the abovementioned studies are carried out through finite element simulation.However, these studies have one commonality the heat source in the simulation was assumed to be a fixed heat source on the edge of the lid.Therefore, whether the assumption of the heat source is reasonable lacks experimental verification due to the difficulty of in situ temperature and stress measurement during PSW.
Generally, the welding power and welding speed are preferentially adjusted when sealing a new product.However, some of the products as presented in figure 1 are difficult to drive reliability, yield, and performance improvement by only adjusting the welding parameters.The sealing ring and the ceramic substrate are first to be bonded by solder sealing, generally through the Au-Sn solder or Ag-Cu solder [29].Compared with Ag-Cu solder, the Au-Sn solder especially Au-20Sn eutectic has its advantage in melting temperature.It means that the structure as presented in figure 1 has the special advantage of the repairable ability.With the repeated increase and decrease in temperature caused by the following processes such as reflowing the flip chip, solidification of the underfill and PSW of the lid, cracks easily form in the Au-20Sn solder due to its brittleness [30].The Au-20Sn solder will face a higher failure risk when bearing thermal shock during the PSW process.However, the investigation on how to reduce the stress generation in this repairable ceramic package via a structural change has not been reported.
In this paper, a new and convenient method that only needs to change the shape of the sealing ring is proposed to improve the manufacturability and reliability of the ceramic packages.Three groups of repairable ceramic packages were fabricated with the rectangular sealing ring, notch inward ring and notch outward ring, respectively.The cracks in the packages after PSW and thermal aging were observed and analyzed.Thermostructural coupling analysis on the stress distribution during packaging was simulated by Ansys.Moreover, the geometry of the sealing ring was further optimized by the Optislang software.

Preparation of the package sample
The packaging sample fabricated in this study consisted of the high-temperature co-fired ceramic (HTCC) substrate, Kovar sealing ring and Kovar lid.The structure of the sample was similar to the sketch presented in figure 1.The content of Al 2 O 3 in the ceramic substrate was approximately 95.0 wt%.A tungsten layer with a thickness of 8.0 μm was fired onto the ceramic surface.To improve the adherence between the sealing ring and ceramic substrate, Ni and Au metallization were plated onto the tungsten, respectively.Kovar alloy with the chemical compositions of Fe-29wt%Ni-17wt%Co was used as the sealing ring and lid.The Ni and Au metallic layers were plated on the sealing ring.
The packaging process can be divided into two steps: solder sealing the ring and parallel seam welding the lid.In the first process, the ceramic substrates and sealing rings were exposed to nitrogen at 120 °C to remove the absorbed water vapor and then cleaned by gas plasma.Three different kinds of sealing rings were adopted to assess the influence of shape on the weldability and reliability of the packages.The shape of the sealing ring in this study was machined into the rectangular ring, notch inward ring and notch outward ring, respectively, as presented in figure 2. The cross-sectional dimensions of the rings were 1 mm in height and 1 mm in width.The substrates and rings were soldered by Au-20Sn solder at a peak temperature of 320 °C in the nitrogen atmosphere.The voids in the solder seam were detected by x-ray diffraction and screened with a porosity lower than 10 vol%.
The combination of the lid and pre-prepared base was realized by parallel seam welding.Before welding, the lid and base were dried and cleaned by the aforementioned methods.The parameters of PSW were properly controlled with a power of 2500 W. The pressure of the roller electrode was set to 1.0 N with a welding speed of 1 mm s −1 .

Reliability test and microstructure characterization
Referring to the shape of the sealing ring, the packages were classified into three groups, which were named the rectangular group, the notch inward group and the notch outward group.At least eight samples were prepared in each group.To better compare the reliability of the packages, a thermal aging process with a peak temperature of 265 °C was applied to the packages to imitate the surface mounting process.The leak rates of the packages were measured after the PSW and thermal aging process.An optical microscope was used to observe the damaged areas in the packages.
The packages were ground to the damaged area and polished for metallographic observation.The crosssectional microstructures of the packages were characterized by field-emission scanning electron microscopy.The working mode was set to the backscattered electron at 20 kV.The chemical compositions of the phases in the welding seam were detected by the energy dispersive spectrum.

Simulation model establishment and simplification
The thermal and force coupled simulations aiming at the physical process involved in packaging processes were conducted based on Ansys Workbench software.To clarify the heat transfer among the parts of the ceramic packages, the variations and distribution of temperature in the packages in the soldering and PSW processes were simulated by the transient thermal module.The time-dependent temperature field was imported into the static structure module as the boundary condition for calculating the stress distribution in the ceramic.In the simulation for the solder sealing process, a temperature load of 280 °C was simultaneously applied on the ceramic substrate, Au-20Sn solder and Kovar ring.The package was cooled to room temperature through convection.
For resistance welding, the Joule heat is generated by the current flowing through the contact resistance.In the PSW process, the contact resistance exists at the interface between the roller electrode and lid as well as between the lid and base.The contact resistance between the dissimilar metals can be expressed as below [31]: where R c is the contact resistance, r 1 and r 2 are the resistivity of the dissimilar metals, s y is the yield strength of the softer metal, P is the contact pressure, and h is the roughness of the contact surface which is defined as a function related to s / P .
y The change of the ring shape could affect the heat dissipation, further impacting the resistivity and yield strength.In this study, the Joule heat generation was equivalent to a moving heat source with a constant temperature of 850 °C.The power of the roller electrode was set to 2500 W in the experiment.The rigorous high power could melt the Ni plating and Kovar alloy.The electrical resistivity of the melting metal hardly changed with the variation of temperature.The yield strength of the melting metal can be ignored.Thus, the generation of Joule heat at the edge of the lid in the three types of packages is almost the same.In this study, the Joule heat generation was simplified to a moving heat source with a constant temperature of 850 °C.Therefore, the effect of the ring shape on the contact resistance was ignored in this study.The model of the moving heat source and the reason for temperature determination are stated in the supplementary section S1.The mesh density at the location of the heat source was refined as shown in figure 2. The high-temperature mechanical properties of the materials for simulation were calculated by JMatPro software.The simulation takes into account the nonlinear variation of material properties with temperature.To facilitate the convergence in simulation, the extremely thin Ni-P and Au metallic layers were ignored as well as the tungsten layer.Heat conduction and convection were considered according to the actual condition.In this study, the soldering of the sealing ring process was conducted by a reflow oven.At the cooling stage, flowing nitrogen at room temperature was injected into the chamber of the oven.Therefore, the coefficient of thermal convection was set as 25 W/(m 2 •K).The radiative heat transfer follows the Stefan-Boltzmann law, which can be expressed as [32] where e 1 is the emissivity of the package, A 1 is the radiant heat transfer area of the package, T 1 is the temperature of the packaging, and T 2 is the temperature of the inside wall of the oven.In this study, the flowing nitrogen was used to cool the package, which means the temperature difference between the package and the oven inside wall is small.Therefore, the heat flux generated by radiation can be ignored.

Microstructure of the packages
The leak rate of the package with the rectangular ring is 8.5 × 10 −10 atm cm 3 s −1 after the PSW process, lower than the reject limit of 5.0 × 10 −8 atm cm 3 s −1 (Helium).However, a crack has formed in the Au-Sn solder around the corner of the sealing ring, as shown in figure 3 It can be concluded that macro cracks formed in the packages with rectangular rings and propagated in the subsequent aging test.The packages with notch inward rings immediately cracked and failed after PSW.The packages with notch outward rings showed remarkable weldability and reliability.
It is worth noting that all of the cracks were found at the corners of the packages.Therefore, the samples for metallographic observation were cut along the diagonal that passes through the corner where the crack is located.The cross-sectional microstructures of the packages are shown in figure 4. The macrostructure of the three different sealing rings are shown in figures 4(a1), (b1) and (c1) respectively.It can be seen that the Ni-P and Au chemical coatings have melted and aggregated at the edge of the lid due to the excess Joule heat.The melting points of Ni-P and Au are about 850 °C and 1064 °C, respectively.It indicates that the temperature on the Kovar lid is higher than 1064 °C during PSW.The high temperature yield strength of the Kovar was calculated by Jmatpro software, as illustrated in the supplementary section S2.The yield strength of Kovar is only 40 MPa when the temperature rises to 1000 °C.At the beginning of PSW, the roller electrodes were pressed on the Kovar lid to provide welding pressure.In this study, the welding pressure of the electrodes was set as 1.0 N. The stress distribution in the lid under the welding pressure was simulated by ANSYS, as illustrated in the supplementary section S2.The equivalent stress is higher than the yield strength of 40 MPa (Kovar at 1000 °C) within a certain area.Therefore, plastic deformation has formed at the edge of the lid, as shown in the white circles.Among the three sealing rings, the notch outward ring exhibits the largest plastic deformation due to the lowest structural stiffness, as shown in figure 4(c1).The magnified microstructure and the element mapping of the lid are shown in figure 5.According to the distribution of the Fe element, it is believed that the surface of the Kovar lid has been melted the same as the plating.During PSW, the liquid Au and Ni aggress into the grain boundary of the Kovar alloy, leading to the inconsecutive microstructure.The excessive melting of the plating is detrimental to the corrosion resistance and mechanical properties.
In figure 4(a1), a partial crack can be seen between the rectangular ring and the Au-Sn solder.The magnified microstructure of the crack is presented in figure 4(a2).The width of the crack on the left is larger than the right side, indicating the crack develops from the outside and propagates to the inside.The crack grows along the Ni

Simulation results of the temperature and stress field
The coefficient of thermal expansion (CTE) of Kovar ring, Au-Sn solder and Al 2 O 3 ceramic are 6 ppm C −1 , 16.0 ppm C −1 and 7.0 ppm C −1 , respectively [37,38].The mismatch of the CTE leads to stress generation in the ceramic substrate during the sealing ring soldering process.Generally, stress concentration occurs at the irregular geometry area, such as the corner of the sealing ring.Moreover, high temperature and heat conduction will aggravate the stress concentration in the substrate.The process and characteristics of heat transfer by the sealing rings have been simulated in this study.The maximum temperature and principal stress generated in the ceramic substrate during soldering, PSW and aging are plotted in figure 6.
The initial temperature on the ceramic substrate is 280 °C, in accordance with the melting temperature of Au-20Sn solder, as shown in figure 6(a).The principal stress in the substrate has not formed at the initial stage due to the liquid solder, as presented in figure 6(b).The temperature on the substrate simultaneously decreases with the decrease of the soldering temperature.The geometry difference on the sealing rings barely influences the cooling process.Although the sealing rings have different geometrical shapes, the bonding areas are identical.Therefore, the thermal stress formed at the Au-Sn/ceramic interface is only affected by the CTE mismatch.The distribution of the principal stress in the ceramic is shown in figure 7. It can be seen that the stress in the ceramic with three different rings is almost the same after the soldering process.The principal stress exhibits compressive stress at the outside corner and tensile stress at the inside corner, as illustrated by the white arrows in figure 7(a1).The stress in the substrate with the notch inward and outward rings is slightly lower than that with the rectangular ring.
In the PSW process, the temperature on the substrate increases with the movement of the heat source, as shown in figure 6(a).The maximum temperature on the substrate with the rectangular ring and notch inward ring is close to the melting point of Au-20Sn, which is much higher than that with the notch outward ring.The heat generated at the edge of the lid can directly conduct to the substrate along the rectangular ring and notch inward ring, as illustrated by the red arrows in figure 4(a1) and figure 4(b1).However, it needs an extra path to conduct the temperature to the bottom for the notch outward ring, as illustrated in figure 4(c1).In addition to the low structure stiffness, the yield strength of Kovar decreases at high temperatures.Therefore, the notch outward ring exhibits larger plastic deformation than the other two rings.For the characteristics of the local heat source, the substrate rapidly cools to room temperature after PSW.The stress generation in the substrate presents a difference during PSW.For the rectangular ring, the stress in the substrate rapidly increases to approximately 170.0 MPa first and then decreases to 91.4 MPa.As for the notch inward ring, the stress remains almost unchanged after reaching the peak value.The stress for the notch outward ring is about 101.4 MPa at the initial stage of PSW and then slightly increases to 106.1 MPa.The distribution of the stress after PSW is presented in figures 7(a2), (b2) and (c2).For the rectangular ring, the tensile stress is distributed at two sides near the outside corner, while the stress concentration only occurs at the corner for the notch inward ring.Although the content of Al 2 O 3 in the ceramic substrate is up to 95.0 wt%, a large quantity of micro holes exists in the ceramic, as shown in the supplementary section S2.The ceramic may fracture, even though the tensile stress is lower than the fracture strength of Al 2 O 3 [39,40].
In the aging process, the packages with three different sealing rings are kept at 265 °C to imitate the surface mounting process.The maximum principal stress in the ceramic with different types of rings shows differences as plotted in figure 6(b).The stress increases to 268.5 MPa in the ceramic with the notch inward ring.The stress distribution in the substrate of the thermal aging stage is presented in figures 7(a3), (b3) and (c3).The stress concentrate is intensified at the aging process in the notch inward package although the sample has failed after PSW.An increase in stress can be seen in both the ceramics with the rectangular and notch outward rings.It indicates that the crack has formed in the package with the rectangular ring due to the high stress during the PSW process.With the increase of the stress during aging, the crack propagated in the package.
The stress distribution with the wireframe of the sealing rings at the aging stage is magnified in figure 8.In figure 8(a), it can be seen that the tensile stress concentrates at the outside corner during aging.Moreover, the inside corner exhibits a high stress level with compressive stress.The existence of a large stress gradient may lead to crack growth along the interface.For the package with the inward ring, the ceramic substrate exhibits compressive stress, as presented in figure 8(b).Therefore, the crack prefers to propagate into the ceramic.In the package with the outward ring shown in figure 8(c), the maximum stress has not been distributed at the edge of the sealing ring.Cracks are hard to form due to the low porosity in the Au-Sn solder.The simulation results are in accord with the microstructure observation.Therefore, compared with the frequently used rectangular ring, the package with the notch inward ring shows an initial failure and the ring with the notch outward exhibits excellent weldability and reliability.

Origin of the stress in the ceramic substrate
It is worth noting that most of the fracture area in the package is only observed in one corner.No cracks can be observed in the other three corners.The movement of the roller electrode and the risky region in the ceramic substrate during PSW are illustrated in figure 9.In the soldering process, the CTE mismatch mainly formed between the Au-20Sn and Al 2 O 3 leads to the generation of thermal stress.The residual stress is generated in the ceramic around the corner after cooling.In the PSW process, the roller electrode is energized and rolled along the relative lid to form a continuous weld.The Joule heat transfers along the sealing ring and leads to the temperature increment in the soldering area.The distribution and variation of the temperature in the ceramic of the three packages during the PSW process are shown in figure 10.In the package fabricated by the rectangle ring, the maximum temperature in the ceramic is 217.1 °C when PSW ends on one edge.In the next step, the package will be rotate 90°to weld the adjacent edge, as illustrated in figure 9.The maximum temperature reaches the peak value of 250.3 °C in the total PSW process.The temperature near the soldering area is approximately 75.3 °C.The mismatch of the temperature aggravates the stress concentration at the outside corner.Similar distribution and variation of temperature can be found in the package with the notch inward ring during the PSW process.The peak temperature in the package fabricated by the notch outward ring is about 157.2 °C and the surrounding temperature is approximately 55.4 °C.The mismatch of the temperature in the package with the notch outward ring is the lowest among the three packages.Therefore, most of the fracture areas are observed in one corner.The package fabricated by the notch outward ring exhibits an outstanding weldability.
The principle stress in the ceramic substrate changes with the soldering of the ring and PSW of the lid, as shown in figure 6(b).After soldering the rectangle sealing ring, the maximum principle stress in the ceramic is about 48.2 MPa.However, the stress is maintained at approximately 91.4 MPa after welding the lid.Generally, high residual stress in the packages is harmful to reliability.Therefore, understanding the reason for the rise of the residual stress is beneficial for preventing welding failure and improving reliability.
During PSW, the local high temperature at the welded area in the lid will gradually decrease with the movement of the roller electrode.The shrinkage of the lid may tensile the ceramic substrate through the sealing ring, leading to an increase in the residual stress.For a better understanding of the effect of the lid on the residual stress evolution in the ceramic, a simulation of ceramic deformation of the packages with and without a lid has been conducted under the same temperature field condition, as shown in figure 11.After soldering the sealing ring, the maximum deformation of the substrate is approximately 7.5 μm, as shown in figures 11(a1) and (b1).In figure 11(a2), the package with a lid shows a smiling face shape and the warpage of the substrate increases during PSW.After cooling to room temperature, the warpage sequentially increases to 37.1 μm, as presented in figure 11(a3).The package without a lid shows a difference in warpage during PSW.Although the package lacks a lid, the temperature fields on the ring, Au-Sn and substrate are in accord with the normal package.In figure 11(b2), it can be seen that the warpage of the substrate slightly increases during PSW.The local area that receives high temperatures shows a raised morphology.After cooling to room temperature, hardly any warpage exists in the substrate, as shown in figure 11(b3).By comparing figures 11(a3) and (b3), it is believed that the existence of the lid has a noteworthy influence on the deformation of the substrate.The shrinkage of the lid will tensile the ceramic substrate through the sealing ring, leading to an increase in the residual stress.
The above discussion indicates that the stress in the ceramic is affected by the generation of the residual stress after soldering, temperature mismatch during PSW and shrinkage of the lid after PSW.The experimental and simulated results indicate that the notch outward ring owns the best weldability.The residual stress in the ceramic with three different rings is almost the same after soldering, as mentioned in figure 7. Due to the different ring shapes, the heat dissipation and shrinkage of the lid also differ.The transient temperature  distributions and the deformation of the rings in the Z direction are shown in figure 12.The temperature distributions in the rings are compared after welding for 0.1 s.There is a difference in temperature at the bottom of the three rings.In the notch inward ring, the bottom temperature is approximately 70.1 °C, as illustrated by the white arrow in figure 12(c).The temperature at a similar location in the rectangular ring is about 66.6 °C, as shown in figure 12(a).The temperature has not risen at the bottom in the notch outward ring due to the long heat transfer path, as shown in figure 12(e).The ceramic in the package with the notch outward ring exhibits the least temperature increment during the PSW process.After the PSW process, the shrinkage of the lid leads to the deformation of the sealing rings, as shown in figures 12(b), (d) and (f).The deformation of the rings in the Z direction can more easily lead to the fracture of the Au-Sn or ceramic.After cooling to room temperature, among the three rings, the notch outward ring owns the maximum displacement at its top position as shown in figure 12(f).However, the displacement at the bottom of the notch outward ring is the least among the three rings.The decrease of the stiffness by the notch outward keeps the stabilization at the soldering area during cooling.Therefore, the packages with the notch outward ring show outstanding weldability and reliability.

Optimization of the notch outward ring
The geometry of the notch outward ring has been further optimized by Optislang software in this study.The design parameters of the sealing ring include location, depth and half-width of the notch, as shown in figure 13(a).At least two hundred design points have been calculated by Monte Carlo method.The coefficient of the prognosis matrix of the parameters is shown in figure 13(b).It can be seen that the location and depth of the notch in a sealing ring primarily affect the principle stress in the ceramic substrate, especially for the PSW and thermal aging process.The half-width of the notch has less influence on the stress generated during packaging.The notch near the lid will significantly hinder the heat transmission along the perpendicular direction.Moreover, the depth of the notch can lengthen the heat transfer path.Therefore, the key parameters of the notch in a sealing ring are location and depth.
The response surfaces of the location and depth on the principle stress during PSW and thermal aging are shown in figure 14.The location and depth are nonlinearly related to the stress generated in the ceramic.The low stress generation will increase the yield of the packages during welding and reliability for further application.The stress evolution with the location and depth are similar during PSW and thermal aging, as shown in figures 14(a) and (b).It is found that with the increase of location and depth, the principle stress decreases.However, in consideration of the pressure on the lid generated by the electrode rollers, the notch outward ring should have sufficient stiffness.The optimized geometry can be concluded that the notch should have a large depth and be close to the lid under the condition of satisfying the stiffness.

Conclusions
In this paper, ceramic packages with three different shapes of rings were fabricated by Au-Sn soldering and PSW.The weldability and reliability of the packages were comparatively investigated.The geometry of the sealing ring was further explored by the response surface optimization.The following conclusions are drawn: (1) There are partial interfacial cracks in the Au-Sn solder in the packages with rectangular rings.The cracks propagate into the ceramic substrate in packages with the notch inward ring after PSW.The packages with the notch outward ring exhibit remarkable weldability and reliability.
(2) The maximum principal stress in ceramic packages fabricated by the rectangular ring, notch inward ring and notch outward ring are approximately 170.0 MPa, 168.5 MPa and 101.4 MPa in the PSW process.Stress concentration exists at two sides near the outside corner for the rectangular ring and the corner for the notch inward-shaped sealing ring.
(3) The failure position in the packages is usually found in only one corner which is continuously heated by the roller electrode.The stress in the ceramic substrate is affected by the residual stress after soldering, temperature mismatch during PSW and shrinkage of the lid after PSW.ring mitigates the thermal mismatch and deformation in the ceramic substrate during PSW.The stress in the ceramic can be further reduced with the increase of the notch depth and location.

Figure 1 .
Figure 1.Sketch diagram of the repairable ceramic package sealed by PSW.

Figure 2 .
Figure 2. Cross-sectional geometry and elements mesh of the sealing rings: (a) rectangular ring, (b) notch inward ring, (c) notch outward ring.
(a).It indicates that the crack has not propagated into the inside of the package.The macroscopic crack is observed at a similar area in the package with the notch inward ring, as shown in figure3(b).The leak rate is measured to be 3.7 × 10 −5 atm cm 3 s −1 , indicating the airtightness has been lost.The package with the notch outward ring shows the best sealing property with a leak rate of 4.3 × 10 −10 atm cm 3 s −1 .No cracks are found around the sealing ring, as presented in figure3(c).After thermal aging, the leak rates of the packages were remeasured.The leak rate of the package with a rectangular ring increases from 8.5 × 10 −10 atm cm 3 s −1 to 6.3 × 10 −8 atm cm 3 s −1 .It is considered that the crack has further enlarged during the aging process.No cracks have been observed in the packages with the notch outward ring.

Figure 4 .
Figure 4. Microstructure of the cracks in the packages with different rings: (a) rectangular ring, (b) notch inward ring, (c) notch outward ring.

Figure 5 .
Figure 5. Element mapping at the edge of the lid after PSW.

Figure 6 .
Figure 6.(a) Peak temperature and (b) maximum principal stress in the ceramic substrate.

Figure 7 .
Figure 7. Stress evolution in the ceramic substrates during packaging.

Figure 8 .
Figure 8. Stress distribution in the ceramics during aging.

Figure 9 .
Figure 9. Movement of the roller electrode and the risky region during PSW.

Figure 10 .
Figure 10.Distribution and variation of the temperature in the ceramic during PSW.

Figure 11 .
Figure 11.Warpage of the packages with and without a lid during PSW.

( 4 )
For samples of three types of rings, the maximum temperature at the local position in the ceramic has increased to 250.3 °C, 238.6 °C and 157.2 °C, respectively.The extra dissipation path in the notch outward

Figure 13 .
Figure 13.(a) Sketch diagram of the design parameters and (b) the effects of the parameters on the principle stress in the ceramic substrate.

Figure 14 .
Figure 14.Response surfaces of the principle stress during: (a) PSW process and (b) thermal aging.