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**The nonlinear compact thermal model of power MOS transistors**

Krzysztof Górecki and Janusz Zarębski Department of Marine Electronics Gdynia Maritime University, POLAND

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**Outline Introduction The thermal model form**

Estimation of the model parameters Verification of the model accuracy Conclusions

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Introduction Three phenomena responsible for abstraction of the heat dissipated in semiconductor devices: conduction, convection and radiation The efficiency of these mechanisms depend on the device inner temperature Tj, the case temperature TC and the ambient temperature Ta. In modeling of the device cooling the compact thermal model is used. The compact thermal models describe the difference Tj - Ta as a function of the thermal power pth dissipated in the device. In this model the transient thermal impedance Z(t) or the thermal resistance Rth of the device exists. The network representations of the device thermal model:

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Introduction (cont.) Both the network are fully equivalent from the point of view of the terminal Tj, but the Foster network has no direct physical interpretation, the Cauer network results directly from dyscretization of the one-dimensional heat transfer equation. The compact thermal models presented in the literature are linear models - influence of the device inner temperature on the efficiency of the heat abstraction is not included in these models. From measurements Z(t) = f(pth) and Rth = f(pth) The nonlinear thermal model is needed.

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**The model form The network form of the nonlinear compact thermal model**

In order to obtain the nonlinear compact thermal model, five following stages have to be performed: the device Z(t) in the wide range of pth should be measured. the values of the elements Ri,Ci (Cauer network) are estimated with the use of the algorithm ESTYM at various values of the power. the dependence Ri(pth) and Ci(pth) are drafted. Then, on the basis of these dependences, the proper approximation function is fitted. the values of the parameters existing in the dependences Ci(pth) and Ri(pth) are estimated. the proper model of the network form is formulated and implemented to SPICE.

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**Estimation of the model parameters**

The described algorithm is illustrated on the example of the uncapsulated transistor MTD20N06V operating without any heat-sink at Ta = 20oC. The courses of Z(t) at pth in the range from 0.05 W to 1.2 W are measured. The measured Tj has values from 28oC to 150oC. The dependences Ri(pth) and Ci(pth) are obtained with the use of the algorithm ESTYM.

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**Estimation of the model parameters**

the following description of the dependence Ci(pth) and Ri(pth) is proposed where Ci0, ai1, ai2, bi1, bi2, di1, di2, ei1, ei2, Ri0, pi1, pi2, pi3, pi4 are the model parameters of the values

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**Verification of the model accuracy**

P0 = Pm = 0.5 W f = 0.01 Hz Nonlinear thermal model Linear thermal model for high power Linear thermal model for small power

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**Verification of the model accuracy (cont.)**

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Conclusions In the paper the compact nonlinear thermal model of a semiconductor device is proposed. The accuracy of this model is verified on the example of the power MOS transistor MTD20N06V. A good agreement between the measurements and the calculations in the wide range of changes of the device dissipated power and for various cooling conditions is achieved. The examples show a strong influence of the power dissipated in the device on the values of its thermal parameters – the thermal resistance and the transient thermal impedance. For the device operating without a heat-sink, the changes of thermal resistance corresponding to the considered changes of the power equal to even 50% are observed. So, omitting nonlinearities in the device thermal model can leads to serious errors in the calculations of the device inner temperature. The proposed nonlinear thermal model can be used in the construction of the electrothermal model of the power MOS transistors, dedicated to the analyze and design electronic circuits.

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**Thank you for your attention**

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