*This article presents the results of digital simulations of stress-deformation states in system silicon – ceramic – metal-matrix composite, in power IGBT module with soldered interfaces as example. Influence of design materials and assembling technology on residual stresses in system was studied. The results can be used in power electronics by design and reliability evaluation of power semiconductor devices for cycle operation.*

*By A.A. Khapugin, V.A. Martynenko (Electrovipryamitel JSC) and K.N. Nischev,
M.I. Novopoltsev (Ogaryov-name Mordovian State University), Saransk, Russia *

The basic connection technology in power semiconductor modules is nowadays soldering. The main challenge is strength of soldered joints. Properties of connected materials and solders should be taken into account, as well as physical, chemical, constructive and technological factors that are responsible for soldered joints.

Solder material is of most importance in this case. It should restrict residual thermal stresses to minimum and create conditions for uniform distribution of stresses all over the interface between main design elements: semiconductor chip – DCB – base plate.

It is known from experimental investigations that most vulnerable places in soldered joints are boundaries of interfaces semiconductor chip – DCB and DCB – base plate. Analytical calculations and digital simulations show [1] that stresses in these regions depend on mechanical and thermal loadings. The lower are residual stresses after soldering, the higher is joint strength, on condition that both mechanical and thermal loadings influence the same region simultaneously. Evaluation criterion of interface optimal structure and composition is very important for prediction of solder layer strength. Maximal stretching residual stress is used often as criterion for measurement of connection strength. Other affected the destruction factors should be taken in account too. Some authors [2] propose elastic deformation energy as damage measure.

Digital simulations are most acceptable method of stress-deformation states calculation in heterogeneous systems, in the first place finite element method that is widely used in modern software for design element analysis – COSMOS/Design STAR, ANSYS, LS Dyna and other.

From mathematical point of view, the problem comes to founding of displacement vector U(x, y, z) – edge problem solution for equation system of constrained thermal elasticity. This problem can be turned into equivalent variation problem that consist in the finding of solution U(x, y, z) for minimal free energy functional. Elastic deformation energy is calculated in this method by means of elastic energy summarization for all elements of investigating area \[W_d = \Sigma s_{ij}\cdot \epsilon_{ij}\cdot V_{ij}\] where: W_{d} – elastic deformation energy, s_{ij} and ε_{ij} – characteristic values of stress and deformation for element with volume V_{ij}. It is considered that stipulated by residual thermal stresses minimal elastic energy corresponds to maximal strength of soldered joint.

The simplified 2D model of power semiconductor module with soldered interfaces was used for determination of solder joint physical and mechanical characteristics, as well as influence of solder layers thickness and properties on mechanical stresses. “Electrovipryamitel” IGBT module with AlSiC base plate was used as example for calculations (Figure 1a).

Figure 1b shows 2D model of IGBT module multilayer soldered joint having structure Al–Si–Cu–AlN–Cu–AlSiC.

The model includes following main components:

- IGBT chip 0,19 mm thick with contacts from Al and Ni 4 and 0,5μm
- thick, accordingly;
- DCB substrate including AlN ceramic 0,63 mm thick and two Cu
- layers 0,3 mm thick with electric circuit layout;
- AlSiC base plate 3 mm thick with Al and Ni plating.

These components are connected during two successive soldering processes:

- soldering of IGBT chip on DCB substrate by means of solder alloy 95,5Sn-3,8Ag-0,5Cu with melting point 217ºC:
- soldering of DCB substrate on AlSiC base plate by means of solder alloy 62,5Sn-37Pb-0,5Ag with melting point 182ºC.

These two processes determine basic residual stresses in layers of investigating structure.

Figure 2 shows two-dimensional finite element model of multilayer soldered structure in x-y plane with calculation grid created in software complex ANSYS.

Assuming that in z-direction model is not deforming, flat deformation approximation can be used in 2D-interface of solid state mechanics. Supposing that model is subjected only to thermal loads, general differential equations can be written as: \[\sigma = D\epsilon_{e1} + \sigma_0 = D(\epsilon -\epsilon_{th} -\epsilon_0) +\sigma_0\] and \[\epsilon_{th} = \begin{bmatrix} \; \\ \epsilon_x \\ \epsilon_y \\ \epsilon_z \\ \gamma_{xy} \\ \gamma_{yz} \\ \gamma_{xz} \\ \;\end{bmatrix}_{th} = \alpha_{vec}(T - T_{ref})\] where: σ – stress vector, D – elasticity matrix, ε_{x}, ε_{y}, ε_{z}, γ_{xy}, γ_{yz}, γ_{xz} – deformation components, α_{vec} – thermal expansion coefficient, T – temperature, initial temperature when mechanical stresses are equal to zero.

The next assumptions were taken during elastic energy calculation by means of finite element method:

- external influence is absent,
- design elements operate in elasticity limits on ε(σ) diagram,
- elasticity properties change with temperature is not considered.

Four mechanical and thermal parameters of design materials are sufficient to calculation of stresses and deformations in soldered joints according to described above model. Table 1 summarized physical properties of materials used in calculation.

Software complex ANSYS allows choice of different material properties including their temperature dependencies of AlSiC produced by CPS Company.

Calculation of multilayer soldered structure is very complicated because of contact layer soldering in different processes by means of solder alloys with different melting points, taken for reference temperatures T_{ref}. Calculation model can be simplyfied by means of exclusion of layers that weackly influence system stress-deformation state (SDS), and dividing of calculation into some stages in each of them only one process is modelled.

Three stage calculation algorythm of contact joint stress-deformation state for model figure 2 is descriebed below.

- Stage 1. DCB substrate heating from Tref = 20ºC up to first soldering temperature and SDS transmission into second model.
- Stage 2. Soldering of IGBT chip and DCB substrate by means of solder alloy 95,5Sn-3,8Ag-0,5Cu ond cooling from Tref = 217ºC up to second soldering temperature and SBS transmission into third model.
- Stage 3. Soldering of DCB substrate and AlSiC base plate by means of solder alloy 62,5Sn-37Pb-0,5Ag and cooling from Tref = 182ºC up to T = 20ºC.

SBS calculations in accordance with this algorythm were made for IGBT module with AlSiC base plate and IGBT module with copper base plate.

Figure 3 shows SDS distribution on deformed AlN DCB substrate heated up to first soldering temperature.

Stresses are concentrated on the copper edges where copper layer contacts with ceramic.

Figure 4 shows SDS calculation results for DCB substrate with IGBT chip by room temperature after first soldering (a) and during second soldering (b).

a) Room Temperature

b) Second soldering temperature

It can be seen from fig.5 that maximal stresses after first soldering arise in the solder joint area of IGBT chip with DCB substrate. These stresses decrease after heating up to second soldering temperature.

Figure 6 shows for comparison calculated bottom surface profiles of Al2O3 and AlN DCB substrates by room temperature after first soldering.

It can be seen from figures that substrate deformation and stressdeformation state in system Al-Si-Cu-AlN-Cu are suffuciently lower that in system Al-Si-Cu-Al2O3-Cu. It can be explained by lower CTE difference between Si and AlN ceramic in comparison with that between Si and Al2O3 ceramic.

Next calculations of stress-deformation states were made for systems chip–substrate–base plate in IGBT modules. Two systems were chosen for calculations: Si–AlN–AlSiC and Si–Al2O3–Cu.

Figure 7 shows SDS calculation results for IGBT module model by room temperature after DCB substrate soldering on AlSiC base plate (a) and on Cu base plate (b).

It can be seen from fig.7 that maximal mechanical stresses after second soldering lay in contact area chip-solder. It is also seen that system with Al2O3 DCB substrate and Cu base plate has sufficient stresses between ceramic and copper layer of DCB substrate (Fig. 7b). System AlN–AlSiC (Fig. 7a) has no similar stresses.

Figure 8 shows bottom surface profiles of Cu base plate and AlSiC base plate after second soldering.

### Conclusion

Simulations of stress-deformation states in power IGBT modules were carried out in several stages in accordance with manufacturing process. Calculation results of bottom surface shape are in good agreement with measurement results. Calculations confirm well known advantages of AlSiC as material for base plate. Proposed calculation method can be useful for IGBT module designers for material choice and geometry parameter determination of substrates, solder layers and base plates providing minimal stress-deformation states, hence minimal thermal resistance and high power cycling capability.

**References:**

1. V.A. Demchuk, N.S. Kostyukov, B.B. Kalinichenko (Institut for Geology and Nature Resources, Blagoveschensk), 2008.

2. Park J.-W., Mendez P.F., Eagar T.W. Strain energy distribution in ceramic to metal joints // Acta Materialia. – 2002. – V. 50. – P.883- 889.

3. Mussin R,A., Konyushkov G.V. Connection of metalls with ceramics. – Moscow, 1991