Prediction of thermal behavior based on temperature measurements can improve the thermal management of the electronic devices. Finite difference and volume software programs provide the temperature distribution solving the heat conduction equation provided the boundary conditions, but in real chips the thermal information is provided directly by temperature sensors. There is no information about the heat generation to create these temperature maps. If one wants to retrieve the heat sources from the temperature distribution, one needs to solve the inverse heat conduction problem in the chip.

 

The work presented assesses inverse methodologies to solve conjugate heat transfer starting from the temperature measurements of a microchip. The evaluation is performed using a commercial solver coupled with Matlab inverse routines which based on an iterative and non-iterative procedures can estimate the source of heat inside of the microchip. The methodology is validated experimentally with a microchip with individually controlled heaters and based on infrared measurements on the top surface of the test article.

 

The effect of the number of sensors is also considered. Reducing the number of sensors reduces the information provided about the inverse problem, increasing its ill-conditioned behavior. This study aims about the minimization of the number of temperature sensors based on the allowable error in the heat prediction. In this case, instead of relaying in infrared thermography to predict the heat sources, scattered measurements taken from resistant temperature detectors embedded in the chips are used and combined with the inverse methodology. Finally, the location of the sensors is also optimized, and a detailed assessment of the uncertainty of the method is performed.