**2.1. Governing equations**

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

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:

$$-\nabla \cdot \sigma = F \tag{1}$$

$$
\sigma = E \cdot \varepsilon \tag{2}
$$

$$
\varepsilon = \nabla \cdot \boldsymbol{\mu} \tag{3}
$$

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

## **2.2. Finite element model**

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

spreader is used to transmit the clamping force to the heatsink and then transfer from the heatsink to the surface of the PP IGBTs as shown in **Figure 6**. The disc spring is also needed to compensate the displacement during the clamping phase, and this parameter will be analyzed in the next part. The force spreader is quite important in the clamping fixture for the press pack packaging style devices to transmit the uniform clamping force on the devices. Different from those devices with the whole wafer, like thyristors, IGCT, and so on, PP IGBTs contain multi-chips which are connected in parallel to improve the current rating. The uniform of the clamping force on the surface of PP IGBTs will greatly influence the clamping force within PP IGBTs and lower the reliability. Thus, the design of the force spreader is quite important to ensure

Clamping Force Distribution within Press Pack IGBTs http://dx.doi.org/10.5772/intechopen.75999 79

According to the basic principle of elastic mechanics, there are two boundary conditions to solve the elasticity problems: force load and displacement load. Force load is the most used boundary condition in the finite element simulations. Most of the studies that focus on the clamping force distribution within PP IGBTs used the force load principle. However, the PP IGBTs clamped by the clamping fixture are restricted by the prescribed displacement. Which boundary condition is suitable for the mechanical analysis of PP IGBTs is unclear. Those two boundary conditions directly applied on the surface of the PP IGBT are compared based on the finite element model mentioned earlier. Nine silicon chips are used as shown in **Figure 7**,

From the results, we can see that chip 5 located in the center of the PP IGBT has a relatively lower clamping force than other chips with the force load boundary condition, and the error is about −30.32%. As the study [19] shows, the thermal contact resistance existed in the contact interface within PP IGBTs depends on the clamping force to a large extent. Thus, the uniform clamping force distribution will influence the characteristic and reliability of PP IGBTs. However, the clamping force distribution within PP IGBT is relative even with the displacement of load condition that the maximum error is about 1.39%. In the real applications, the PP IGBTs are restricted by the prescribed displacement through clamping fixture. However, it is impossible to ensure a uniform displacement on the surface like the displacement load boundary

**Figure 6.** Simplified schematic diagrams for the clamping system: (a) structure diagram and (b) simulation diagram.

its basic functions and improve the reliability of the whole system.

and the clamping force of each silicon chip is shown in **Table 1**.

**Figure 5.** Boundary conditions of the mechanical model.

the boundary conditions are set as follows. In the application of PP IGBTs, a force spreader or a clamp stack is used to transmit the clamping force to the heatsink and then transfer from the heatsink to the surface of the PP IGBTs. A disc spring, usually changing several mm under the clamped phase, is needed to compensate the physical movements, usually several μm, during the process of clamping and thermal expansion. To approximate the working conditions, a prescribed displacement, which is equivalent to the rated clamping force, is applied to the disc spring on the surface of the heatsink of the PP IGBT collector side. A fixed support is placed on the surface of the heatsink of the PP IGBT emitter side. The simplified diagram of the boundary conditions for the mechanical model is shown in **Figure 5**. The mechanical model should also consider the frictional interconnections among the different layers. The interconnections between heatsinks and PP IGBT are set as the bonded interconnection, and the interconnections between multilayers within PP IGBT are set as a frictional contact. A friction coefficient of 0.5 is assumed for the contact layers within the PP IGBT [21, 22], because the friction coefficient has little influence on the pressure distribution [23]. All finite element models used in this chapter to analyze the clamping force distribution within PP IGBTs, with the exception of the specified models, are set as in **Figure 5**.
