**1.3. Clamping force distribution**

For PP IGBTs, the clamping force is a special and very important parameter that many other parameters are correlated with this value, including the electrical and thermal behavior, reliability, and so on. For example, the current and junction temperature distributions are affected by the clamping force distribution a lot [17] through the electrical and thermal contact resistance [18, 19]. Too much clamping force will mechanically damage the silicon chip and too little clamping force will increase the junction temperature caused by the increased thermal contact resistance. Eventually, this leads to the silicon chip thermal damage as shown in **Figure 4** [20]. Therefore, the clamping force distribution within PP IGBTs is quite important that it not only affects both the electrical and thermal behavior but also the longtime reliability of PP IGBTs.

**2. Basic theory**

**2.1. Governing equations**

**2.2. Finite element model**

example, nonlinearity, material yield problem, and so on.

Mechanics is a very useful discipline established to explain many phenomena existing in nature, for example, material mechanics, structure mechanics, elastic mechanics, elastic–plastic mechanics, and so on. Material mechanics is mainly used to explain the deformation of a single simple object. Elastic mechanics can be used to research the micro-deformation phenomenon, and elastic–plastic mechanics is mainly used to explain the macro-deformation, for

**Figure 4.** Failed silicon chips caused by nonuniform clamping force [20]: (a) too much pressure and (b) too little pressure.

Clamping Force Distribution within Press Pack IGBTs http://dx.doi.org/10.5772/intechopen.75999 77

PP IGBTs consist of many components that undergo micro-deformation as stated before, thus the elastic mechanics is suitable for its mechanical analysis. The mechanical analysis of a specific material can be explained through the physical properties of materials, deformation, and the balance of forces. Just like in the electrical engineering area, Maxwell's equations can be used to explain all electromagnetic phenomena. Coupled with specific boundary conditions, three equations, including the constitutive equations of materials, geometric equations, and equilibrium equations of force as shown in Eqs. (1)–(3), are used to solve all the elastic mechanics problems:

−∇⋅ *σ* = *F* (1)

*σ* = *E* ⋅ *ε* (2)

*ε* = ∇⋅ *u* (3)

where *σ* is stress, *F* is external force, *E* is elasticity modulus, *ε* is strain, and *u* is displacement.

Eqs. (1)–(3) can be used to explain all the elastic mechanics phenomena, and the equations without specific boundary conditions have unbounded solution. But for engineering problems, there must be a specific solution. Thus, we need to appoint the boundary condition for engineering problems to get the unique solution. In this chapter, the finite element model of PP IGBTs is proposed to predict the clamping force distribution under different conditions and

There are many factors that may influence the clamping force distribution within PP IGBTs not only during the design process but also in the applications. And the affect factors can be divided into external and internal factors. All the factors that may affect the clamping force distribution within PP IGBTs are shown subsequently and analyzed through the finite element method. For high-power IGBT modules or PP IGBTs, some Fast Recovery Diode (FRD) chips are always connected in anti-paralleled with the IGBT chips to provide the current path while the IGBT chips are turned off. Actually, the matching of the silicon chips, which means the internal layout of IGBT chips and FRD chips within PP IGBTs, will also influence on the clamping force distribution. However, the electrical and thermal behaviors, for example, the collector current and junction temperature distributions, of the PP IGBTs depend on the internal layout or matching of the silicon chips to a large extent. Therefore, the matching of the silicon chips should pay more attention to the electrical and thermal behaviors rather than the clamping force distribution.

**A.** External affect factors


**Figure 4.** Failed silicon chips caused by nonuniform clamping force [20]: (a) too much pressure and (b) too little pressure.
