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Modelling and validation of a ceramic/metal joining technique for power electronic applications

   
A TWI Exploratory Report by Ruth Sanderson, Abbas Mohimi and Alec Gunner

Introduction

Thermal management is a fundamental problem with current and next generation electronic systems. Devices are running hotter due to increased functionality requirements and processing speeds. Therefore, there is a demand to manage the excess heat that is generated.

The sensors used in the oil and gas, aerospace, and power industry are increasingly being used at higher temperatures eg  200°C to 400°C, and as a result bonds at the interfaces between materials are getting more difficult to make. The current commonly used attachment techniques of adhesive bonding and soldering are not appropriate and also the polymer based substrates can not easily work at these temperatures.

Alternative materials and joining methods will need to be developed. This project aimed to develop a joining method for operation at temperatures of up to 400°C, through use of a validated thermo-mechanical model to aid the design of ceramic to metal joining techniques.

This work was performed in collaboration, between the Specialist Materials and Joining team and the    Numerical Modelling and Optimisation section. 

Modelling

Finite element modelling was used to assess a range of alumina to aluminium joints. ABAQUS version 6.9-1 was used to generate, solve and post process the models.

Three different geometries were considered: square, circular and strips, as shown in Figure 1. First the conventional square design was tested in detail. The model simulated eutectic bonding between alumina and aluminium using a silver foil. The alumina was 50mm by 50mm by 0.635mm thick; the silver foil was 40mm by 40mm by 0.05mm thick and the Aluminium was 40mm by 40mm. The thickness of the aluminium was varied in order to find an optimum condition. The thickness of the aluminium was also varied for the circular and strip cases in order to test the sensitivity to thickness with a view to finding a condition where the bonding procedure is successful (ie neither the aluminium nor alumina crack during or after the bonding process).

In order to increase computation speed, the finite element model used two symmetry planes so that a quarter of the geometry was simulated. Figure 2 shows the finite element mesh. The mesh was refined around the areas of expected high stress. Quadratic brick elements with reduced integration were used (ABAQUS element code C3D20R). A prescribed linear temperature history from the theoretical eutectic bonding temperature, 577°C to ambient, 20°C was imposed in order to simulate the stresses arising from cooling down after the bond has formed. All of the material properties used in the analysis were assumed to vary with temperature. The model assumed elastic-plastic properties for the aluminium and silver and elastic only properties for the alumina. Figures 3 and 4 show the plastic stress-strain curves used in the analyses for aluminium and silver respectively. Figure 5 shows the assumed Young’s modulus for all three materials. The other required material property was the thermal expansion coefficient, see Figure 6.

Boundary conditions were applied to the model to simulate the symmetry planes and to prevent rigid body motion in the vertical direction. Additionally, a 4N weight placed on top of the Aluminium was simulated since this is used experimentally to hold the three layers together during the bonding process.

Table 1 gives details of all of the models run.

Table 1 Case list of models run
Model Ref Geometry Thickness of aluminium, mm 
 gl8  Square  0.25
 gl9  Square  0.35
 gm1  Square  0.5
 gm2  Square  0.75
 gm3  Square  0.9
 gm4  Square  1
 gm5  Square  1.25
 gm6  Square  2
 gm7  Square  3
 gm8  Square  4
 gm9  Circular  0.35
 gn1  Circular  0.5
 gn2  Circular  1
 gn3  Circular  2
 gn4  Circular  3
 gn5  Circular  4
 gn7  Strips  3
 gn6  Strips  6

Results and Discussion

Figures 7 to 9 show the maximum principal stress field for three examples of different thicknesses of aluminium for the square design (0.35mm, 1mm and 3mm). It can be seen that there are two critical regions, namely, on the bottom surface and at the corners. Note that the strength of the alumina is around 300MPa therefore models showing red or grey are likely to result in tensile failure.

Figures 10 to 12 show the maximum principal stress field for the same three examples of different thicknesses of aluminium for the circular design (0.35mm, 1mm and 3mm). The circular design has the benefit of reducing the corner peak as the corner is replaced by a smooth transition (compare figures 8a and 11a). However, in most cases the failure location is on the bottom side of the alumina and in the case of the 3mm thick aluminium, the circular design actually increases the value of the stress at this location.

Figures 13 and 14 show the maximum principal stress field for the two strip designs (3mm and 6mm). It can be seen that there is a high stress on the bottom of the alumina for the 3mm thick aluminium case of a similar level to that of the square and circular design. The stress on the bottom of the alumina is much reduced for 6mm thick aluminium, as expected. However, the stress peaks at the edges are high, as for the square and circular designs. There is therefore no obvious advantage to using a strip design.

Figure 15 shows the trend of peak maximum principal stress against aluminium thickness for all three designs. It can be seen that for aluminium thicknesses of around 1mm, the stresses are at their highest. This peak tends to occur on the bottom surface of the alumina, as can be seen in Figures 8b and 11b. However, there is a second potential failure location predicted at the sharp edges between the aluminium and the alumina. This is observed to increase as the aluminium thickness increases. There is a trade-off between the two failure modes. As the aluminium becomes thicker, the whole structure becomes stiffer and therefore less able to deform, reducing the stress in the alumina. This is particularly noticeable in the strip geometry, see Figure 14. The stress on the bottom of the alumina is relatively low but there are stress peaks on the front face where the strips are joined. 

Validation

Based on the modelling work it was decided to initially investigate the square and circular heat sinks. Three aluminium sheets of different thicknesses were produced for square and circular shapes, as shown in table below:

 Thickness, mm  Square  Circular
 0.5  x  x
 1.0  x  x
 4.0  x  x


Table 2 The square aluminium sheets were 40 x 40 mm and the circular sheets had a diameter of 40 mm.
 
Eutectic bonding run

The samples (alumina substrates, Aluminium heat sinks and the silver foils) were cleaned with acetone in an ultrasonic bath and handled only with tweezers. Powder free gloves were worn at all times when preparing the samples.

The samples were then assembled in the correct order, as shown in Figure 16, and placed in the vacuum brazing furnace. A load of 4N was placed on the assembly to ensure that intimate contact was made at the interfacial regions.

All the samples were placed in a single run to ensure that the bonding conditions were consistent for all the joints.

The following temperature profile was used for the eutectic bonding run:

  • Heat to 570°C at 10°C/minute

  • Dwell for ten minutes

  • Heat to 600°C at 10°C/minute

  • Dwell for ten minutes

  • Cool to room temperature at 10°C/minute

Results

It was evident for all the samples that the silver interlayer had melted and formed a bond between the aluminium and the alumina substrate. However, only two of the samples, as shown in table below, had formed a bond without the alumina substrate breaking at the edges, as shown in Figure 17.  

Thickness, mmSquareCircular
 0.5  x  
 1.0  x  
 4.0    

Table 3 The 1 mm thick square sample did fail at the edges following the furnace run.

ConcluDiscussion
The potential for applying an FEA approach to analysis of ceramic/metal joints has been demonstrated. Specifically:

  • The stress peaks observed at the interface between the aluminium and the alumina were reduced by changing the geometry from square to circular. However, these changes were small and did not significantly change the thickness of aluminium possible and the stress on the bottom of the alumina was not reduced

  • A successful bond was made for an aluminium thickness of 0.5 mm. This was correctly predicted by the model to be the least likely to fail

  • It has been demonstrated that modelling can be effectively used to design eutectic bond layouts and predict failure The approach should now be validated for real component geometries

  • Further work is required to evaluate the effect of ramp-down rate in relieving stress through plastic strain.

Figures 1-17

Figure 1 Three proposed designs for parametric study using finite element analysis - Variation of thickness of aluminium, square design (side elevation)
Figure 1 Three proposed designs for parametric study using finite element analysis:
a) Variation of thickness of aluminium, square design (side elevation)
b) Consideration of circular shape of aluminium (plan view)
c) Consideration of using strips of aluminium (side elevation)
Figure 2 Typical finite element mesh (model ref. gl9)
Figure 2 Typical finite element mesh (model ref. gl9)
Figure 3 Plastic stress strain curves at different temperatures for Aluminium 1050 used in analysis
Figure 3 Plastic stress strain curves at different temperatures for Aluminium 1050 used in analysis
Figure 4 Plastic stress strain curves at different temperatures for silver used in analysis
Figure 4 Plastic stress strain curves at different temperatures for silver used in analysis
Figure 5 Young’s Modulus versus temperature for all three materials involved in the analysis
Figure 5 Young's Modulus versus temperature for all three materials involved in the analysis
Figure 6 Coefficient of thermal expansion versus temperature used in analysis
Figure 6 Coefficient of thermal expansion versus temperature used in analysis
Figure 7 Predicted maximum principal stress field in model of square arrangement for 0.35mm thick aluminium - Top face showing relatively low stress levels
Figure 7a
Figure 7 Predicted maximum principal stress field in model of square arrangement for 0.35mm thick aluminium - Bottom face showing stress peaks in alumina
Figure 7b
Figure 7 Predicted maximum principal stress field in model of square arrangement for 0.35mm thick aluminium:
a) Top face showing relatively low stress levels
b) Bottom face showing stress peaks in alumina
Figure 8 Predicted maximum principal stress field in model of square arrangement for 1mm thick aluminium - Top face showing stress peaks around corners
Figure 8a
Figure 8 Predicted maximum principal stress field in model of square arrangement for 1mm thick aluminium - Bottom face showing extremely high stress levels well above yield (300MPa)
Figure 8b
Figure 8 Predicted maximum principal stress field in model of square arrangement for 1mm thick aluminium:
a) Top face showing stress peaks around corners
b) Bottom face showing extremely high stress levels well above yield (300MPa)
Figure 9 Predicted maximum principal stress field in model of square arrangement for 3mm thick aluminium - Top face showing stress peaks around corners
Figure 9a
Figure 9 Predicted maximum principal stress field in model of square arrangement for 3mm thick aluminium - Bottom face showing high stress in alumina
Figure 9b
Figure 9 Predicted maximum principal stress field in model of square arrangement for 3mm thick aluminium:
a) Top face showing stress peaks around corners
b) Bottom face showing high stress in alumina
Figure 10 Predicted maximum principal stress field in model of circular arrangement for 0.35mm thick aluminium - Top face showing low stress levels
Figure 10a
Figure 10 Predicted maximum principal stress field in model of circular arrangement for 0.35mm thick aluminium - Bottom face showing general stress level is below yield (300MPa)
Figure 10b
Figure 10 Predicted maximum principal stress field in model of circular arrangement for 0.35mm thick aluminium:
a) Top face showing low stress levels
b) Bottom face showing general stress level is below yield (300MPa)
Figure 11 Predicted maximum principal stress field in model of circular arrangement for 1mm thick aluminium - Top face showing some raised stress around edges
Figure 11a
Figure 11 Predicted maximum principal stress field in model of circular arrangement for 1mm thick aluminium - Bottom face showing extremely high stress levels well above yield (300MPa)
Figure 11b
Figure 11 Predicted maximum principal stress field in model of circular arrangement for 1mm thick aluminium:
a) Top face showing some raised stress around edges
b) Bottom face showing extremely high stress levels well above yield (300MPa)
Figure 12 Predicted maximum principal stress field in model of circular arrangement for 3mm thick aluminium - Top face showing low stress levels
Figure 12a
Figure 12 Predicted maximum principal stress field in model of circular arrangement for 3mm thick aluminium - Bottom face showing extremely high stress levels well above yield (300MPa)
Figure 12b
Figure 12 Predicted maximum principal stress field in model of circular arrangement for 3mm thick aluminium:
a) Top face showing low stress levels
b) Bottom face showing extremely high stress levels well above yield (300MPa)
Figure 13 Predicted maximum principal stress field in model of strips arrangement for 3mm thick aluminium - Top face showing relatively low stress levels
Figure 13a
Figure 13 Predicted maximum principal stress field in model of strips arrangement for 3mm thick aluminium - Bottom face showing high stress in alumina
Figure 13b
Figure 13 Predicted maximum principal stress field in model of strips arrangement for 3mm thick aluminium:
a) Top face showing relatively low stress levels
b) Bottom face showing high stress in alumina
Figure 14 Predicted maximum principal stress field in model of strips arrangement for 6mm thick aluminium - Top face showing high stress peaks around edges of joint
Figure 14a
Figure 14 Predicted maximum principal stress field in model of strips arrangement for 6mm thick aluminium - Bottom face showing relatively low stress levels in alumina
Figure 14b
Figure 14 Predicted maximum principal stress field in model of strips arrangement for 6mm thick aluminium:
a) Top face showing high stress peaks around edges of joint
b) Bottom face showing relatively low stress levels in alumina
Figure 15 Peak maximum principal stress predicted versus thickness of aluminium for all three designs
Figure 15 Peak maximum principal stress predicted versus thickness of aluminium for all three designs
Figure 16 A schematic of how the parts were assembled
Figure 16 A schematic of how the parts were assembled
Figure 17 Aluminium heat-sink attached to the alumina substrate via eutectic bonding
Figure 17 Aluminium heat-sink attached to the alumina substrate via eutectic bonding

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