**4.1. Slim plates**

As mentioned earlier, the rated clamping force of the single IGBT submodule is obtained through the displacement on a proper designed force spreader. The calculated clamping force of the submodule is used to compare with different conditions, and it is the real clamping force existing in the submodule after the submodule is clamped by the desired displacement. Furthermore, the selection or the design of the disc spring is also quite important in the applications. The most important parameter for disc spring is the equivalent elastic coefficient. The higher this value, the disc spring is harder to deform which means higher force is needed to obtain the same deformation. And the lower this value, the disc spring can compensate more displacement with the same clamping force. Therefore, the selection of the equivalent elastic coefficient is a tradeoff problem. The rated clamping force of the submodule is designed to 1 kN and the displacement is 1 mm. Therefore, the rated equivalent elastic coefficient is 1e6 N/m. The submodule under the heating phase with different coefficients, range from 1e6 to

where "without" means no disc spring is applied in the simulation and the value with a unit of N/m is the equivalent elastic coefficient of the disc spring applied in the simulation. The results show that there is no difference in the calculated clamping force of the single submodule whether a disc spring is applied or not during the clamping phase. And the calculated value is almost equal to the rated clamping force of 1 kN. That is to say, the disc spring has no influence on the clamping phase after the submodule is clamped. The disc spring is used to slow down the change rate of the clamping force during the clamping process but it will not affect the final value after the submodule is clamped. Just like the inductance in the circuit, it

However, the clamping force will increase sharply due to the thermal stress generated by the high temperature when the silicon chip is heated up. And the value is almost 14 times of the rated clamping force. This high clamping force may mechanically damage the silicon chip. The reason is that the submodule is constricted by the clamping fixture. Thus, a disc spring is needed to compensate the displacement or deformation due to the thermal stress, and the calculated clamping force can be controlled to some extent. The increment of the clamping force is also influenced by the equivalent elastic coefficient. The calculated clamping force will be higher with a higher value of equivalent elastic coefficient. And the increment rate of 2.14, 10.65, and 21.06% is also proportional to the value of equivalent elastic coefficient. The reason is that the allowed displacement of the disc spring is 1, 0.2, and 0.1 mm with the same clamped conditions. Actually, the increment of the clamping force cannot be eliminated if the submodule is clamped even if adequate disc spring is applied. And this will not only increase the cost but also will be very difficult to obtain the desired clamping force. Therefore, the design of the disc spring should consider the requirements from application and it is a tradeoff problem.

**Without 1e6 (N/m) Without 1e6 (N/m) 5e6 (N/m) 1e7 (N/m)**

**Clamping phase (N) Heating phase (N)**

**Table 2.** Calculated clamping force of the submodule comparison.

Calculated 997.57 997.59 13,948 1021.4 1106.5 1210.6

1e7, is also analyzed and the results are shown in **Table 2**.

is used to restrict the change rate of current.

82 Design, Simulation and Construction of Field Effect Transistors

Until now, there are two main packaging styles for PP IGBTs: press pack and StakPak. The StakPak packaging style contains a spring to distribute the clamping force which is patent protected by ABB and the research is very limited. The press pack is widely used by Poseico, Fuji, Westcode, and Toshiba [20, 24]. All the researches are based on the press pack, and there are also some variations between different manufacturers. As shown in **Figure 3** and stated before, a slim plate of silver is proposed to mechanically support the single chip submodule and compensate few deformations because of its good softness.

The contribution of slim plate to the clamping force distribution within PP IGBTs is revealed with three different conditions. As it is known, it is difficult to ensure the same high of all submodules due to the machining accuracy of each component within PP IGBTs or some errors during the assembling process. Condition I is that all the submodules in PP IGBTs have the same height and condition II is that one of those submodules is 0.5 μm lower than others. Condition III is that one of those submodules is 0.5 μm higher than others. The finite element model for this simulation is also shown in **Figure 7** with nine silicon chips, and the height of chip 5 is selected to change. The clamping force distribution within the PP IGBT with different conditions is shown in **Table 3**.


**Table 3.** Clamping force distribution with different conditions.

The results show no big difference between the single submodules with applied slim plate or without. That is to say, the influence of the slim plate on the clamping force distribution can be ignored. The reason is that the deformation of the silver slim plate is very limited even it has a relative small Young's modulus.
